A method and device for analyzing regional flood vulnerability of a bridge network under water resistance

Abstract

The application discloses a regional bridge network vulnerability analysis method and equipment facing water resistance and toughness, comprising the following steps: obtaining a standardized data set and a flood scenario set, and calculating the weight of each flood scenario; constructing a regional bridge network and an OD pair set, and determining the weight of the OD pair; constructing a bridge site flood intensity parameter of the bridge under the flood scenario; fitting to obtain a single bridge vulnerability function, and outputting the bridge failure probability of each bridge under the flood scenario; fitting to obtain a bridge network vulnerability function, and outputting the bridge network failure probability of all flood scenarios; calculating the comprehensive vulnerability importance index of the bridge under the flood scenario, and obtaining the key vulnerable bridge ranking result; calculating the multi-scenario comprehensive vulnerability importance index of the bridge, and obtaining the comprehensive ranking result of the key vulnerable bridge under the multi-flood scenario; and calculating the water resistance and toughness evaluation result of the regional bridge network under the flood scenario. The application significantly improves the integrity and reliability of the bridge system vulnerability evaluation.

Description

Technical Field

[0001] This invention belongs to the field of bridge loss analysis technology, and in particular relates to a method and equipment for analyzing the vulnerability of bridge groups under regional floods, focusing on water resistance and resilience. Background Technology

[0002] With the intensification of global climate change and the increase in extreme rainfall events, the frequency and intensity of flood disasters in river basins are on the rise, and the safety and functional maintenance capacity of regional bridge groups under flood and other hydrological disaster scenarios are receiving increasing attention. As a critical node in the regional infrastructure network, damage or failure of bridges under flood conditions not only weakens the overall operational capacity of the regional infrastructure system but may also induce severe socio-economic losses and secondary disasters. Therefore, it is urgent to conduct systematic vulnerability and water resistance toughness analyses of regional bridge groups based on actual flood scenarios.

[0003] Existing research on bridge flood safety assessments often focuses on individual bridges or local components, emphasizing load-bearing capacity verification under static or quasi-static conditions. These studies typically employ simplified hydrological boundaries and structural models, failing to reflect the spatiotemporal evolution characteristics and corresponding hydrodynamic effects of actual flood events. Research on the interaction between floods and bridges often uses one-dimensional or simplified hydraulic calculation methods, neglecting complex phenomena such as flood expansion, backwater, and diversion on a planar scale. Furthermore, it fails to adequately consider the hydraulic dependencies between multiple bridges along a river corridor, resulting in an insufficiently refined characterization of the bridge system response under flood conditions.

[0004] On the other hand, existing bridge risk assessment and network analysis methods mostly start from the safety of individual bridges or the reliability of traditional transportation networks, focusing mainly on the failure risk of individual key nodes or routes, and do not adequately consider the coupling relationship between "single bridge vulnerability - bridge group network structure - regional overall function". Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to provide a method and equipment for analyzing the vulnerability of bridge groups under regional floods, which is oriented towards water resistance and toughness. It can simultaneously reflect the combined effect of structural vulnerability and network correlation characteristics on emergency passage and the overall performance of regional infrastructure, significantly improving the completeness and reliability of the vulnerability assessment of bridge groups.

[0006] Technical Solution: To achieve the above objectives, the present invention provides a vulnerability analysis method for bridge network groups under regional floods, focusing on water resistance and resilience, comprising the following steps: S1. Obtain basic bridge data, bridge flood failure judgment criteria, climate and hydrological data, topographic data, road network data, OD traffic demand matrix, key service node data, and experimental data for the bridge group to form a standardized dataset; classify flood scenarios and form a flood scenario set, and then calculate the weight of each flood scenario; construct the regional bridge group network and OD pair set, and determine the OD pair weights; S2. Based on the standardized dataset and flood scenario set, determine the two-dimensional hydrodynamic computational domain, set boundary conditions and initial conditions, solve the two-dimensional depth-averaged shallow water equation, calculate the representative flood intensity parameters of a single bridge, and construct the flood intensity parameters at the bridge site. S3. Based on the flood intensity parameter at the bridge site, first calculate the bridge under the flood scenario. The engineering requirements parameters are then used to calculate the bridge's performance under flood conditions. The failure probability of a single bridge under various flood scenarios is calculated. For a set of flood scenarios, samples of bridge failure probabilities under each scenario are obtained. A single-bridge vulnerability function is then fitted, and the final output of the bridge's failure probability under each flood scenario is determined. The probability of bridge failure under these conditions; S4. Based on the regional bridge group network and bridge failure probability, construct the bridge group degradation network and calculate the OD pair disconnection probability and bridge group failure probability under a certain flood scenario; for the flood scenario set, obtain network failure probability samples under each flood scenario, fit the bridge group network vulnerability function, and finally output the bridge group network failure probability for all flood scenarios. S5. Based on the regional bridge group network, bridge failure probability, and bridge group network failure probability, construct a comparison network under single-bridge failure conditions, and calculate the single bridge failure scenario in a flood situation. The comprehensive vulnerability importance index under various flood scenarios is used to obtain the ranking results of key vulnerable bridges; the comprehensive vulnerability importance index of a single bridge under multiple flood scenarios is calculated based on the flood scenario weights to obtain the comprehensive ranking results of key vulnerable bridges under multiple flood scenarios. S6. Calculate flood scenarios Evaluation results of the water resistance toughness of the bridge network in the lower region.

[0007] Optionally, the bridge foundation data in step S1 includes the bridge location coordinates within the study area, bridge structural form, bridge deck elevation, beam bottom elevation, effective foundation depth, pier width, bridge calculated span, pier height, bridge material elastic modulus, moment of inertia of the control section, abutment water-blocking length, and bridge material parameters. The bridge flood resistance failure criteria data include the bridge pier shape correction coefficient, water flow angle of attack correction coefficient, riverbed condition correction coefficient, abutment form correction coefficient, abutment-water flow angle correction coefficient, resistance coefficient, water-facing projected area, lateral resistance, overturning moment bearing capacity, bending moment bearing capacity, shear bearing capacity, displacement limit value, and historical damage repair records of bridges in the study area. The climate and hydrological data include historical flood data records, rainfall time series, upstream flow process lines, downstream water level process lines, initial steady-state water depth field, initial steady-state flow velocity field, river water level time series, and river flow time series; The topographic data includes digital elevation models, riverbed elevation data, Manning roughness distribution, and long-term riverbed scouring and deposition variations. The road network data includes a set of network nodes, a set of connecting edges, and a mapping relationship between bridges and their connecting edges or bridge nodes. Key service node data includes sets of emergency service facility nodes, residential area nodes, hospital nodes, and school nodes; The experimental data includes model test data, prototype observation data, and existing publicly available experimental data related to bridge scour, hydrodynamic effects, bridge deck submersion, and structural response, used to calibrate the probability distribution of the scour correction coefficient for bridge material parameters.

[0008] Optionally, in step S1, a set of flood scenarios is calculated. Weights of various flood scenarios Specifically, the steps include the following: Based on historical flood data records, rainfall time series, upstream flow process lines, downstream water level process lines, river water level time series, and river flow time series, the historical annual maximum flow, annual maximum water level, or annual maximum rainfall series are determined, and flood intensity variables are established. probability distribution function The expression is: , in, Represents probability; This represents a sequence of historical annual maximum flow, annual maximum water level, or annual maximum rainfall. Classify flood intensity ranges into flood scenarios Corresponding to several non-overlapping flood intensity ranges The expression is: , Flood scenario probability of occurrence The expression is: , And satisfy: , Flood scenarios according to recurrence interval The events are set as once-in-5-years, once-in-10-years, once-in-20-years, once-in-50-years, once-in-100-years, once-in-200-years, and once-in-500-years, based on their recurrence intervals. Determine the corresponding flood intensity threshold. The expression is: , Flood scenario weights are calculated by using flood intensity values ​​corresponding to different return periods as scenario boundary points, and then calculating the probability of occurrence of adjacent flood intensity intervals, i.e., the weights of each flood scenario. The expression is: .

[0009] Optionally, in step S1, a regional bridge network is constructed based on road network data and bridge location coordinates. The expression is: , in, For regional bridge network, For a set of network nodes, For connecting edge sets; bridges Through bridge-network mapping relationship Associated with its connecting edge, Bridges The connecting edge; Based on the sets of emergency service facility nodes, residential area nodes, hospital nodes, and school nodes in the key service node data, an OD pair set is constructed, expressed as: , in, This represents the total number of OD pairs. Any OD pair Represented as: , As the starting node, The endpoint node; Based on OD traffic demand matrix For each OD pair Determine the weights of OD The expression is: .

[0010] Optionally, step S2 specifically includes the following steps: S2.1, Based on standardized datasets And flood scenario set For any flood scenario Obtain flood scenario Rainfall time series Upstream flow process line Downstream water level process line Digital Elevation Model Riverbed elevation data Manning roughness distribution ; S2.2, Based on Digital Elevation Model Riverbed elevation data Road network data and bridge location coordinates Determine the two-dimensional hydrodynamic computational domain of the study area. The expression is: , in, A two-dimensional hydrodynamic computational domain covering the main channel of the river, beaches, dikes, roads, and bridge sites; Two-dimensional hydrodynamic computational domain Divided into several hydrodynamic computational grid cells, the expression is: , in, For the first One hydrodynamic computational grid cell; Based on digital elevation model Riverbed elevation data , for the first Each hydrodynamic computational grid cell assigns the grid bed elevation. The expression is: , And based on Manning roughness distribution For the first Each hydrodynamic computational grid cell is assigned a grid roughness parameter. The expression is: , in, For the first Hydrodynamic computational grid cell The representative coordinates; S2.3 Set the boundary conditions and initial conditions within the computational domain. The boundary conditions include the surface rainfall inflow term, upstream boundary conditions, and downstream boundary conditions. The initial conditions include the initial water depth field and the initial velocity field. Specifically, based on flood scenarios Rainfall time series Constructing surface rainfall inflow terms within a two-dimensional hydrodynamic computational domain The expression is: , Based on flood scenario Upstream flow process line Set upstream boundary conditions within the computational domain The expression is: , Based on flood scenario Downstream water level process line Set downstream boundary conditions within the computational domain The expression is: , Based on flood scenario The initial steady-state water depth field and initial steady-state velocity field are defined, and the initial conditions within the computational domain are set. The initial conditions include the initial water depth field and the initial velocity field, and their expressions are as follows: , , , in, Flood scenario The initial water depth below, Flood scenario Below Initial velocity component in direction, Flood scenario Below Initial velocity component in the direction; Flood scenario The initial steady-state water depth field at position The water depth, Flood scenario The initial steady-state flow field in Initial velocity component in direction, Flood scenario The initial steady-state flow field in Initial velocity component in the direction; S2.4, Based on two-dimensional hydrodynamic computational domain Grid subgrade elevation and mesh roughness parameters Hydrodynamic computational grid cells As a basic computational unit, under the set boundary and initial conditions, the two-dimensional depth-averaged shallow water equation is solved, which includes the continuity equation and the momentum equation. The expression for the continuity equation is: , in, Flood scenario Lower bridge location coordinates At any moment The water depth, for directional depth-average flow velocity for directional depth-average flow velocity For surface rainfall inflow, This includes infiltration or other water loss items; The expression for the momentum equation is: , , in, It is the acceleration due to gravity. For riverbed elevation, for Directional friction gradient term, for Directional friction gradient term, for directional external force term, for Directional external force term; Calculate according to Manning's formula. Directional friction gradient term and The directional friction gradient term is expressed as follows: , , Two-dimensional depth-averaged shallow water equations in hydrodynamic computation grid cells Numerical discretization and iterative solutions are performed to obtain the flood scenario. Water depth field at each time point Normal velocity component field tangential velocity component field and flow field The expression is: , And calculate the velocity field The expression is: , S2.5, Based on bridges Bridge location coordinates The obtained water depth field Flow velocity field and flow field Mapped to bridge The bridge site location was determined, and the water depth sequence at the bridge site was obtained. Bridge site flow velocity sequence and bridge site flow sequence The expressions are as follows: , , , in, For the first The bridge in the flood scene Next moment The sequence of water depths at the bridge site, For the first The bridge in the flood scene Next moment Bridge site flow velocity sequence, No. The bridge in the flood scene Next moment The sequence represents the water flow direction at the bridge site; S2.6, Define the bridge In flood scenarios The following is the effective flooding time set The expression is: , in, To preset the effective flood depth threshold; Based on bridge site water depth sequence Bridge site flow velocity sequence and bridge site water flow direction sequence Calculate bridge The representative flood intensity parameters are expressed as follows: , , , , , in, The bridge site represents the water depth. The bridge site represents the flow velocity. To guide the direction of water flow For the effective duration of flooding, The unit flow rate or overcurrent intensity at the bridge site; This refers to selecting the set of effective flooding times. The maximum value in the following data. This refers to the dominant water flow direction corresponding to the water depth and flow velocity represented by the bridge site. It refers to length; Therefore, building bridges In flood scenarios Flood intensity parameters at the bridge site The expression is: , in, Used to characterize the impact of floods on bridges The intensity of local action.

[0011] Optionally, step S3 specifically includes the following steps: S3.1, Based on the representative water depth at the bridge site Bridge site represents flow velocity Calculate the Froude number of the bridge site The expression is: , in, It is the acceleration due to gravity; Based on the water depth represented by the bridge site Riverbed elevation at bridge site Calculate bridge In flood scenarios Maximum water surface elevation at the bridge site The expression is: , Based on the water depth represented by the bridge site Bridge site represents flow velocity and the bridge site Froude number Calculate the local scour depth of the bridge pier The expression is: , in, This represents the local scour depth of the bridge pier. The width of the bridge pier. This is the correction factor for the shape of the bridge pier. Indicates based on the dominant water flow direction Corrected angle of attack correction factor; This is a correction factor for riverbed conditions; Based on the water depth represented by the bridge site Length of water obstruction of bridge abutment and the Froude number of bridge sites Calculate the local scour depth of the bridge abutment The expression is: , in, This represents the local scour depth of the bridge abutment. Indicates based on the dominant water flow direction Corrected angle correction factor between bridge abutment and water flow. This is a correction factor for the abutment type; Based on the water depth represented by the bridge site and bridge site unit flow Calculate the shrinkage scour depth The expression is: , in, To reduce the scouring depth, For reference overcurrent intensity, This is a correction factor for shrinkage erosion. Calculate the total scour depth The expression is: , in, This represents the long-term changes in riverbed scouring and deposition. This represents the local scour depth of the bridge pier. This refers to the local scour depth of the bridge abutment; To reduce the scouring depth; Calculate the scouring failure demand ratio The expression is: , in, Used to indicate the percentage of total scour depth relative to the effective burial depth of the foundation; Based on the effective burial depth; S3.2, Based on the representative flow velocity of the bridge site Dominant water flow direction drag coefficient and water-facing projected area Calculate the horizontal hydrodynamics of floods The expression is: , in, For water density, To be determined by the direction of the dominant water flow Determined correction factor for the direction of water flow; Calculate the horizontal hydrodynamics of flood Overturning moment generated by the action The expression is: , in, The lever arm is the distance from the point of action of the horizontal hydrodynamic force of the flood to the anti-overturning reference point; Calculate the flood level hydrodynamic instability demand ratio The expression is: , in, Used to represent lateral resistance, Used to represent the overturning moment bearing capacity; S3.3, Based on the maximum water surface elevation at the bridge site Beam bottom elevation and bridge deck elevation Calculate the bridge inundation demand ratio The expression is: , in, Used to indicate the degree to which the floodwater level exceeds the bottom of the beam and approaches or exceeds the bridge deck; when This indicates that there is no risk of flooding at the bottom of the beam; S3.4, Based on flood horizontal hydrodynamics Bridge structural form and bridge material parameters, calculate bridge Maximum bending moment Maximum shear force and maximum displacement The expressions are as follows: , , , in, , and This is the structural response calculation function determined by the bridge's structural form and material parameters. Calculate the span of the bridge. This refers to the height of the bridge piers; The elastic modulus of bridge materials; To control the moment of inertia of the cross section; Calculate the structural response demand ratio The expression is: , in, Used to represent bending moment bearing capacity, Used to represent shear bearing capacity, Used to indicate displacement limits; S3.5, Based on the effective flooding duration and bridge site unit flow Calculate the demand ratio for the sustained effect of floods The expression is: , in, For reference to the duration of flooding, For reference overcurrent intensity, and These are the weighting coefficients for the duration of flooding and the intensity of the current, respectively. S3.6, Building a bridge In flood scenarios Engineering requirements parameters The expression is: , in, To flush out failure requirements, The ratio of flood level hydrodynamic instability demand, For the bridge flooding demand ratio, The ratio of structural response to demand, The demand ratio for the sustained effect of floods; S3.7, Based on engineering requirements parameters Define the overall demand ratio The expression is: , Define the limit state function of a single bridge The expression is: , Among them, when At that time, the bridge was determined In flood scenarios The state of failure is reached; when At that time, the bridge was determined It is in a valid state; S3.8, Bridge material parameters and effective foundation depth drag coefficient Shrinkage scour correction factor Using the scour correction coefficient as an uncertain parameter, a vector of random variables is constructed. The expression is: , Bridge material parameters include lateral resistance Overturning moment bearing capacity Bending moment bearing capacity Shear bearing capacity and displacement limit The scour correction factor includes the pier shape correction factor. Water flow angle of attack correction factor Riverbed condition correction coefficient Bridge abutment type correction factor , This is a correction factor for the angle between the bridge abutment and the water flow; Based on historical damage repair records The distribution of uncertain parameters was calibrated using experimental data; then, in a flood scenario... Below, for the vector of random variables Perform sampling and calculate the first The single-bridge limit state function corresponding to each sample The expression is: , For the first The overall demand ratio corresponding to each sample; Definition of the first Failure indication function corresponding to each sample The expression is: , according to The results of the random sampling were used to calculate the bridge. In flood scenarios Single-bridge failure probability The expression is: , S3.9, Set of Flood Scenarios Different combinations of flood intensities were used to obtain bridges The failure probability sample under multiple flood scenarios is expressed as follows: , The single-bridge vulnerability function is obtained by fitting failure probability samples: , in, For bridges The single-bridge vulnerability curve or vulnerability surface is used to represent the correspondence between flood intensity parameters and bridge failure probability; For bridges Flood intensity parameters at bridge sites under all flood scenarios; This is a fitting operation for the single-bridge vulnerability function; The final output shows each bridge in a flood scenario. Bridge failure probability The expression is: , in, For the first The bridge in the flood scene The failure probability of participating in network degradation simulation.

[0012] Optionally, step S4 specifically includes the following steps: S4.1 Flood Scenario conduct The network random failure simulation, in the... In this simulation, the bridge To generate random numbers, use the following expression: , in, To obey Uniformly distributed random numbers within an interval; Based on bridge failure probability Determine the bridge's failure status: , in, Bridge In the It failed in the simulation. This indicates that the product is not invalid. This forms the first The failure state vector of all bridges under this simulation is expressed as follows: , in, This represents the total number of bridges in the regional bridge group. S4.2, Based on bridge-network mapping relationship The failure status is The connecting edges of the bridges are from the regional bridge network. Remove it from the list, or set its access status to unavailable, to get the first... Degenerate networks under subsimulation: , in, For the first The set of network nodes that are still usable after the simulation. The set of connecting edges that are still available; When the bridge Map to connecting edges At that time, if ,but: , S4.3, Based on OD pair sets, in degenerate networks In the process, determine any OD pair The starting point and the finish line Is there a valid connected path between them? Define an OD pair connectivity indicator function, with the expression: , in, Indicates the first OD pair under the next simulation The connected state; Define the OD disconnection indicator function as follows: , in, Indicates OD pair In the The connection was interrupted in the next simulation; S4.4, based on The results of the sub-network random simulation are used to calculate the flood scenario. The probability of disconnection of OD The expression is: , S4.5, Weights based on OD and OD disconnection indication function Calculate the first Weighted OD disconnection ratio under the second simulation The expression is: , in, This represents the total number of OD pairs. Set network function failure threshold When the weighted OD disconnection ratio Exceeding the network function failure threshold When the bridge group network function is deemed to be in failure, the bridge group network function failure indication function is used. The expression is: , in, For the first Bridge group network functional failure indication function under simulation; based on The results of the sub-network random simulation are used to calculate the flood scenario. Failure probability of the underpass group The expression is: , in, Flood scenario The probability of functional failure of the underbridge group; S4.6, Set of Flood Scenarios Different combinations of flood intensities were used to obtain samples of bridge group failure probabilities under various flood scenarios: , in, Flood scenario The corresponding regional flood intensity characterization quantity can be obtained from the flood intensity parameters of each bridge. Aggregation yields; Based on the bridge group failure probability samples, the vulnerability function of the bridge group network is obtained by fitting, and the expression is: , in, This refers to the vulnerability curve or vulnerability surface of the bridge network, used to characterize the relationship between flood intensity and the failure probability of the bridge network. This is a fitting operation for the vulnerability function of the bridge group network. For the bridge site flood intensity parameter of the bridge network under all flood scenarios; The final output is a set of flood scenarios. The probability of bridge network failure for each flood scenario. The expression is: , in, For the bridge group in flood scenario The probability of bridge group network failure.

[0013] Optionally, step S5 specifically includes the following steps: S5.1, Regarding bridges Based on regional bridge network and bridge-network mapping relationship Constructing bridges Comparison network under failure conditions : , in This refers to regional bridge network Remove bridge Connecting edge Calculation operations; In flood scenarios Under the premise of keeping the failure probabilities of other bridges constant, the network random failure simulation method based on step S4 is used to compare the network... The probability of OD pair disconnection and the probability of bridge group network failure are recalculated to obtain the bridge Bridge group network failure probability under failure conditions and bridges OD probability of disconnection under failure conditions ; S5.2 Based on the flood scenario in step S4 Downbridge network failure probability and bridges Bridge group network failure probability under failure conditions Calculate bridge Marginal impact of bridge network vulnerability The expression is: , in, For bridges The marginal impact on the failure probability of the bridge group network; S5.3, Based on the OD in step S4, the probability of disconnection. and bridges OD pair disconnection probability under failure conditions Calculate bridge The impact of failure on the disconnection of OD pairs The expression is: , in, Bridge The marginal impact of failure on OD on the probability of disconnection; Based on OD weights Calculate bridge The overall contribution of all ODs to the risk of disconnection The expression is: , S5.4, Based on Regional Bridge Group Network and OD pair set Calculate bridge OD weighted betweenness centrality The expression is: , in, For OD In regional bridge network The number of valid paths in For the bridges that pass through it The number of valid paths corresponding to the connecting edge or bridge node; S5.5, Probability of Single-Bridge Failure Marginal impact Overall contribution and OD weighted betweenness centrality After normalization, the expression is: , , , , in, It is a normalization function used to convert indices with different dimensions to a unified dimension range; Calculate bridge In flood scenarios The following is a comprehensive vulnerability importance index: , in, For bridges The comprehensive vulnerability importance index; , , and For non-negative weighting coefficients, satisfying: , Used to characterize the inherent vulnerability of a single bridge. Used to characterize the impact of bridges on the overall network failure probability. Used to characterize the degree of impact of bridges on the risk of OD disconnection. Used to characterize the traffic support function of bridges in network topology; S5.6, Based on the comprehensive vulnerability importance index Regarding flood scenarios The bridges in the lower area bridge group are sorted in descending order to obtain the ranking of key vulnerable bridges: , in, Flood scenario The following are the key vulnerable bridge ranking results; Indicates a sorting operation; Indicates descending order; When considering multiple flood scenarios, based on flood scenario weights Calculate bridge The multi-scenario comprehensive vulnerability importance index is expressed as follows: , And based on multi-scenario comprehensive vulnerability importance index The bridges were ranked to obtain a comprehensive ranking of the key vulnerable bridges under multiple flood scenarios.

[0014] Optionally, step S6 specifically includes the following steps: S6.1, Based on flood scenarios Bridge failure probability for each bridge Calculate the average vulnerability index of a single bridge level in a bridge group. : , in, This is the average vulnerability index for a single bridge level. This represents the total number of bridges in the regional bridge group. Furthermore, based on the comprehensive vulnerability importance index Calculate the importance-weighted single-bridge vulnerability index: , in, Used to characterize the impact of the failure probability of key vulnerable bridges on the overall vulnerability of regional bridge groups; S6.2, Failure Probability of Bridge Group Network As a vulnerability indicator at the network level: , in, Indicating flood scenario The probability of functional failure in the downstream bridge network; S6.3, Weights based on OD and OD to disconnection probability Calculate the weighted OD connectivity vulnerability index: , in, Indicating flood scenario The weighted average probability of disconnection for the next important OD pair; S6.4 Based on the ranking results of critically vulnerable bridges Select before sorting Key bridge collection: , in, Flood scenario The next key bridge collection; Comprehensive vulnerability importance index based on key bridge sets Calculate the concentrated vulnerability index of key bridges: , in, Used to characterize whether the vulnerability of a regional bridge network is concentrated in a few key bridges; S6.5. Based on the dispersion of each vulnerability index and the decision preference coefficient under multiple flood scenarios, determine the weights and define four vulnerability evaluation indicators: , , , , in, Importance-weighted single-bridge vulnerability index , Indicators of network-level vulnerability , This indicates the weighted OD index for connectivity vulnerability. , Indicators of concentrated vulnerability of key bridges ; For the One vulnerability evaluation index, Calculate its application in the flood scenario set. Mean of: , Calculate its application in the flood scenario set. Discreteness in: , in, Indicates the first The ability of each vulnerability evaluation index to distinguish the differences in system vulnerability under different flood scenarios; Set the decision preference coefficient: , in, This indicates the level of concern regarding the vulnerability of single-bridge bridges. This indicates the level of concern regarding the overall risk of network failure. This indicates the level of concern regarding the risk of connectivity failure caused by OD (Original Design Environment). This indicates the level of concern regarding the concentrated risks on key bridges; Calculate the first The weighting coefficients of each vulnerability evaluation index are expressed as follows: , , in, , To prevent extremely small positive numbers with zero dispersion; This represents the sum of decision biases. And satisfy: , S6.6 Calculate the flood scenario based on four vulnerability evaluation indicators and their corresponding weighting coefficients. The following is a comprehensive index of regional vulnerability. : , in, Indicating flood scenario The overall vulnerability level of the regional bridge network is determined by a combination of single bridge failure, network failure, OD pair disconnection, and concentrated risks of critical bridges. S6.7, Comprehensive regional vulnerability index Converted to regional water resistance index : , in, Flood scenario The regional water resistance toughness index is below; S6.8 Flood scenario weights based on the output of step S1 Regional water resilience index under various flood scenarios Weighted summaries were performed to obtain the regional comprehensive water resistance resilience index under multiple flood scenarios. The expression is: , in, This is a comprehensive regional water resistance resilience index under multiple flood scenarios. Flood scenario The probability of occurrence or scenario weight, and satisfying: , S6.9, Final Output Flood Scenario Average vulnerability index of a single bridge level in the bridge group Importance-weighted single-bridge vulnerability index Network-level vulnerability indicators OD as a connectivity vulnerability index Key bridge concentrated vulnerability indicators Regional vulnerability index Regional water resistance index and the regional comprehensive water resistance resilience index under multiple flood scenarios .

[0015] The electronic device of the present invention includes a processor and a storage medium; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the method described above for vulnerability analysis of bridge network under regional floods with water resistance and resilience.

[0016] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: (1) This invention comprehensively utilizes the structural parameters, climate and hydrological data and topographic information of the regional bridge group to construct a two-dimensional hydrodynamic model, which can finely depict the spatiotemporal action of flood on the bridge group under different flood scenarios in multiple dimensions such as flow velocity, flow rate, water depth and inundation range, providing a more reliable, detailed and physically consistent data basis for subsequent vulnerability analysis, thereby significantly improving the accuracy and robustness of the vulnerability assessment of the bridge group under flood scenarios; (2) This invention proposes a vulnerability analysis method for single bridges. Based on the two-dimensional hydrological simulation results, it introduces structural information such as bridge design parameters, material strength, and foundation type, as well as environmental effects such as flood velocity and water level, to construct the limit state function and vulnerability surface of a single bridge, thereby realizing the probabilistic and functional description of the bridge failure probability. This invention can not only quantitatively reflect the bridge damage risk level under different flood scenarios, but also reflect the influence of key parameters on the vulnerability of the bridge, providing targeted quantitative basis for improving the water resistance toughness and strengthening design of single bridges. (3) Based on the vulnerability analysis of a single bridge, this invention introduces the failure probability of each bridge into the analysis of the bridge group network topology. It uses graph theory and complex network indices to construct a vulnerability analysis method for the bridge group network. It uses Monte Carlo simulation and other methods to characterize the impact of bridge failure on the overall functional level of the bridge group and identifies key bridges that have a significant impact on the system function. Compared with the analysis method that only starts from a single bridge or traditional static network structure, this invention can simultaneously reflect the combined effect of structural vulnerability and network correlation characteristics on emergency passage and the overall performance of regional infrastructure, which significantly improves the completeness and reliability of the vulnerability assessment of the bridge group system. (4) Under the framework of resilience analysis theory, this invention integrates the failure probability of a single bridge, the failure probability of a bridge group network, the probability of OD pair disconnection, and the concentrated risk of key bridges into the evaluation process of the water resistance resilience of a regional bridge group network. By constructing the average vulnerability index at the single bridge level, the importance-weighted single bridge vulnerability index, the network-level vulnerability index, the OD pair connectivity vulnerability index, and the concentrated vulnerability index of key bridges, the regional vulnerability comprehensive index and the regional water resistance resilience index are further calculated, and the regional comprehensive water resistance resilience index under multiple flood scenarios is obtained based on the flood scenario weights. Compared with existing technical solutions that only qualitatively describe or are limited to local structural safety, this invention achieves quantitative coupling between "single bridge failure probability - network functional degradation - regional water resistance resilience", enabling horizontal comparison and optimization of the regional water resistance resilience effects of different bridge reinforcement schemes, flood control measures, and resource allocation schemes, providing systematic and quantifiable technical support for regional bridge group flood control planning and resilience improvement decisions. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the framework of the present invention; Figure 2 This is a schematic diagram of the traffic network topology and OD pairs within the study area of ​​this invention; Figure 3 This is a schematic diagram of the vulnerability analysis function of a single bridge under regional flooding, taking bridges 1, 4 and 7 as examples in this invention; Figure 4 This is a schematic diagram illustrating the vulnerability of bridge groups under regional floods and the probability of disconnection due to OD (damped area) in this invention. Figure 5This is a schematic diagram illustrating the comprehensive vulnerability importance index of bridges under regional floods and the water resistance toughness index of regional bridge groups under flood scenarios with different return periods in this invention. Detailed Implementation

[0018] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0019] like Figure 1 As shown, taking a typical highway network in a certain region as the research object, 10 representative bridges are selected to form a research sample. The vulnerability analysis method of bridge group network under regional floods, which focuses on water resistance and toughness, in this invention includes the following steps: S1. Obtain basic bridge data, bridge flood failure assessment criteria, climate and hydrological data, topographic data, road network data, OD traffic demand matrix, key service node data, and experimental data for the bridge group in the study area, and form a standardized dataset. ; Flood scenarios are defined based on climate and hydrological data, forming a comprehensive system. A flood scenario Flood scenario collection And calculate the flood scenario set. The probability of occurrence of each flood scenario, i.e., the flood scenario weight. ; Based on road network data and bridge locations, a regional bridge network is constructed; based on key service node data and the OD traffic demand matrix, an OD pair set is constructed. And for each OD pair Determine the weights of OD .

[0020] S1.1 Bridge basic data includes the bridge location coordinates within the study area, bridge structural form, bridge deck elevation, beam bottom elevation, effective foundation depth, pier width, bridge calculated span, pier height, bridge material elastic modulus, moment of inertia of control sections, abutment water-blocking length, and bridge material parameters.

[0021] The data for judging bridge flood resistance failure include the following: pier shape correction coefficient, water flow angle of attack correction coefficient, riverbed condition correction coefficient, abutment form correction coefficient, abutment-water flow angle correction coefficient, resistance coefficient, water-facing projected area, lateral resistance, overturning moment bearing capacity, bending moment bearing capacity, shear bearing capacity, displacement limit, and historical damage repair records of bridges within the study area. Climate and hydrological data include historical flood data records, rainfall time series, upstream flow process lines, downstream water level process lines, initial steady-state water depth field, initial steady-state flow velocity field, river water level time series, and river flow time series; Topographic data includes digital elevation models, riverbed elevation data, Manning roughness distribution, and long-term riverbed erosion and deposition variations; Road network data includes a set of network nodes, a set of connecting edges, and a mapping relationship between bridges and their connecting edges or bridge nodes. Key service node data includes sets of emergency service facility nodes, residential area nodes, hospital nodes, and school nodes; The experimental data includes model test data, prototype observation data, and existing publicly available experimental data related to bridge scour, hydrodynamic effects, bridge deck submersion, and structural response, used to calibrate the probability distribution of the scour correction coefficients for bridge material parameters.

[0022] S1.2 Calculate the flood scenario set The probability of occurrence of each flood scenario, i.e., the flood scenario weight. Specifically, the steps include the following: Based on historical flood data records, rainfall time series, upstream flow process lines, downstream water level process lines, river water level time series, and river flow time series, the historical annual maximum flow, annual maximum water level, or annual maximum rainfall series are determined, and flood intensity variables are established. probability distribution function The expression is: , in, This is a sequence of annual maximum flow, annual maximum water level, or annual maximum rainfall. Represents probability; Classify flood intensity ranges into flood scenarios Corresponding to several non-overlapping flood intensity ranges The expression is: , Flood scenario probability of occurrence The expression is: , And satisfy: , Flood scenarios according to recurrence interval The events are set as once-in-5-years, once-in-10-years, once-in-20-years, once-in-50-years, once-in-100-years, once-in-200-years, and once-in-500-years, based on their recurrence intervals. Determine the corresponding flood intensity threshold. The expression is: , Flood scenario weighting uses flood intensity values ​​corresponding to different return periods as scenario boundary points to calculate the probability of occurrence of adjacent flood intensity intervals. The expression is: .

[0023] S1.3. Based on road network data and bridge location coordinates, construct a regional bridge group network, expressed as: , in, For regional bridge network, For a set of network nodes, For connecting edge sets; bridges Through bridge-network mapping relationship Associated with its corresponding edge or bridge node. Bridges The connecting edge.

[0024] like Figure 2 As shown in the diagram, gray lines represent the set of connecting edges, white dots represent the set of network nodes, and orange squares represent bridges. Bridges are connected to their respective connecting edges or bridge nodes through bridge-network mapping relationships. Red, green, purple, and brown markers represent the sets of emergency service facility nodes, residential area nodes, hospital nodes, and school nodes, respectively. The purple dashed line represents the set of OD pairs consisting of key service nodes.

[0025] Based on the sets of emergency service facility nodes, residential area nodes, hospital nodes, and school nodes in the key service node data, an OD pair set is constructed, expressed as: , in, This represents the total number of OD pairs. Any OD pair Represented as: , As the starting node, The endpoint node; Based on OD traffic demand data, OD traffic demand matrix For each OD pair Determine the weights of OD The expression is: .

[0026] S2, Based on the standardized dataset from step S1 And flood scenario set The two-dimensional hydrodynamic computational domain of the study area was defined and divided into several hydrodynamic computational grid cells. Boundary conditions and initial conditions were set within the computational domain. Using the hydrodynamic computational grid cells as the basic computational units, the two-dimensional depth-averaged shallow water equations were solved to obtain the flood scenario. The water depth field, velocity field, and direction field at each time point are shown below; these fields are then mapped onto the bridge. Based on the bridge site location, the water depth sequence, current velocity sequence, and current direction sequence at the bridge site are obtained; then the bridge is calculated. Representative flood intensity parameters are used to construct bridges. In flood scenarios Flood intensity parameters at the bridge site .

[0027] Step S2 specifically includes the following steps: S2.1, Based on standardized datasets And flood scenario set For any flood scenario Obtain flood scenario Rainfall time series Upstream flow process line Downstream water level process line Digital Elevation Model Riverbed elevation data Manning roughness distribution .

[0028] S2.2, Based on Digital Elevation Model Riverbed elevation data Road network data and bridge location coordinates The two-dimensional hydrodynamic computational domain of the study area is defined as follows: , in, A two-dimensional hydrodynamic computational domain covering the main channel of the river, beaches, dikes, roads, and bridge sites; Two-dimensional hydrodynamic computational domain Divided into several hydrodynamic computational grid cells, the expression is: , in, For the first One hydrodynamic computational grid cell; Based on digital elevation model Riverbed elevation data , for the first Each hydrodynamic computational grid cell assigns the grid bed elevation. The expression is: , And based on Manning roughness distribution For the first Each hydrodynamic computational grid cell is assigned a grid roughness parameter. The expression is: , in, For the first Hydrodynamic computational grid cell The representative coordinates.

[0029] S2.3 Set the boundary conditions and initial conditions within the computational domain. The boundary conditions include the surface rainfall inflow term, upstream boundary conditions, and downstream boundary conditions. The initial conditions include the initial water depth field and the initial velocity field. Specifically, based on flood scenarios Rainfall time series Constructing surface rainfall inflow terms within a two-dimensional hydrodynamic computational domain The expression is: , Based on flood scenario Upstream flow process line Set upstream boundary conditions within the computational domain The expression is: , Based on flood scenario Downstream water level process line Set downstream boundary conditions within the computational domain The expression is: , Based on flood scenario The initial steady-state water depth field and initial steady-state velocity field are set, and the initial conditions in the computational domain are defined. The initial conditions in the computational domain include the initial water depth field and the initial velocity field, and their expressions are as follows: , , , in, Flood scenario The initial water depth below, Flood scenario Below Initial velocity component in direction, Flood scenario Below Initial velocity component in the direction; Flood scenario The initial steady-state water depth field at position The water depth, Flood scenario The initial steady-state flow field in Initial velocity component in direction, Flood scenario The initial steady-state flow field in Initial velocity component in the direction.

[0030] S2.4, Based on two-dimensional hydrodynamic computational domain Grid subgrade elevation and mesh roughness parameters Hydrodynamic computational grid cells As a basic computational unit, under the set boundary and initial conditions, the two-dimensional depth-averaged shallow water equation is solved on the HEC-RAS two-dimensional hydrodynamic software platform. The two-dimensional depth-averaged shallow water equation includes the continuity equation and the momentum equation. The expression for the continuity equation is: , in, Flood scenario Lower bridge location coordinates At any moment The water depth, for directional depth-average flow velocity for directional depth-average flow velocity For surface rainfall inflow, This includes infiltration or other water loss items; The expression for the momentum equation is: , , in, It is the acceleration due to gravity. For riverbed elevation, for Directional friction gradient term, for Directional friction gradient term, for directional external force term, for Directional external force term; Calculate according to Manning's formula. Directional friction gradient term and The directional friction gradient term is expressed as follows: , , Two-dimensional depth-averaged shallow water equations in hydrodynamic computation grid cells Numerical discretization and iterative solutions are performed to obtain the flood scenario. Water depth field at each time point Normal velocity component field tangential velocity component field and flow field The expression is: , And calculate the velocity field The expression is: .

[0031] S2.5, Based on bridges Bridge location coordinates The obtained water depth field Flow velocity field and flow field Mapped to bridge The bridge site location was determined, and the water depth sequence at the bridge site was obtained. Bridge site flow velocity sequence and bridge site flow sequence The expressions are as follows: , , , in, For the first The bridge in the flood scene Next moment The sequence of water depths at the bridge site, For the first The bridge in the flood scene Next moment Bridge site flow velocity sequence, No. The bridge in the flood scene Next moment The sequence represents the direction of water flow at the bridge site.

[0032] S2.6, Define the bridge In flood scenarios The following is the effective flooding time set The expression is: , in, To preset the effective flood depth threshold; Based on bridge site water depth sequence Bridge site flow velocity sequence and bridge site water flow direction sequence Calculate bridge The representative flood intensity parameter is expressed as follows: , , , , , in, The bridge site represents the water depth. The bridge site represents the flow velocity. To guide the direction of water flow For the effective duration of flooding, The unit flow rate or overcurrent intensity at the bridge site; This refers to selecting the set of effective flooding times. The maximum value in the following data. This refers to the dominant water flow direction corresponding to the water depth and flow velocity represented by the bridge site. It refers to length; Therefore, building bridges In flood scenarios Flood intensity parameters at the bridge site The expression is: , in, Used to characterize the impact of floods on bridges The intensity of local action.

[0033] S3. Bridge site flood intensity parameters based on the output of step S2 Calculate the scour failure demand ratio separately. Flood level hydrodynamic instability demand ratio Bridge inundation demand ratio Structural response demand ratio Compared to the demand for sustained flood action and build bridges In flood scenarios Engineering requirements parameters Based on engineering requirements parameters Define the limit state function of a single bridge Calculate bridge In flood scenarios Single-bridge failure probability ; Targeting flood scenario set Different combinations of flood intensities were used to obtain bridges Failure probability samples under multiple flood scenarios The single-bridge vulnerability function is obtained by fitting the failure probability samples. To obtain the flood scenario for each bridge Bridge failure probability .

[0034] Step S3 specifically includes the following steps: S3.1, Based on the representative water depth at the bridge site Bridge site represents flow velocity Calculate the Froude number of the bridge site The expression is: , in, It is the acceleration due to gravity; Based on the water depth represented by the bridge site Riverbed elevation at bridge site Calculate bridge In flood scenarios Maximum water surface elevation at the bridge site The expression is: , Based on the water depth represented by the bridge site Bridge site represents flow velocity and the Froude number of bridge sites Calculate the local scour depth of the bridge pier The expression is: , in, This represents the local scour depth of the bridge pier. The width of the bridge pier. This is the correction factor for the shape of the bridge pier. Indicates based on the dominant water flow direction Corrected angle of attack correction factor; This is a correction factor for riverbed conditions; Based on the water depth represented by the bridge site Length of water obstruction of bridge abutment and the Froude number of bridge sites Calculate the local scour depth of the bridge abutment The expression is: , in, This represents the local scour depth of the bridge abutment. Indicates based on the dominant water flow direction Corrected angle correction factor between bridge abutment and water flow. This is a correction factor for the abutment type; Based on the water depth represented by the bridge site and bridge site unit flow Calculate the shrinkage scour depth The expression is: , in, To reduce the scouring depth, For bridges The corresponding reference overcurrent intensity, This is a correction factor for shrinkage erosion. Calculate the total scour depth The expression is: , in, This represents the long-term changes in riverbed scouring and deposition. This represents the local scour depth of the bridge pier. This refers to the local scour depth of the bridge abutment; To reduce the scouring depth; Calculate the scouring failure demand ratio The expression is: , in, Used to indicate the percentage of total scour depth relative to the effective burial depth of the foundation; Based on the effective burial depth.

[0035] S3.2, Based on the representative flow velocity of the bridge site Dominant water flow direction drag coefficient and water-facing projected area Calculate the horizontal hydrodynamics of floods The expression is: , in, For water density, To be determined by the direction of the dominant water flow Determined correction factor for the direction of water flow; Calculate the horizontal hydrodynamics of flood Overturning moment generated by the action The expression is: , in, The lever arm is the distance from the point of action of the horizontal hydrodynamic force of the flood to the anti-overturning reference point; Calculate the flood level hydrodynamic instability demand ratio The expression is: , in, Used to indicate the degree of hydrodynamic impact of flood levels relative to the bridge's lateral resistance and overturning resistance requirements. Used to represent lateral resistance, It is used to represent the overturning moment bearing capacity.

[0036] S3.3, Based on the maximum water surface elevation at the bridge site Beam bottom elevation and bridge deck elevation Calculate the bridge inundation demand ratio The expression is: , in, Used to indicate the degree to which the floodwater level exceeds the bottom of the beam and approaches or exceeds the bridge deck; when This indicates that there is no risk of the bottom of the beam being flooded.

[0037] S3.4, Based on flood horizontal hydrodynamics Bridge structural form and bridge material parameters, calculate bridge The expressions for the maximum bending moment, maximum shear force, and maximum displacement are as follows: , , , in, The maximum bending moment under the action of flood. The maximum shear force under flood action. This represents the maximum displacement under the influence of floodwater. , and This is the structural response calculation function determined by the bridge's structural form and material parameters. Calculate the span of the bridge. This refers to the height of the bridge piers; The elastic modulus of bridge materials; To control the moment of inertia of the cross section; Calculate the structural response demand ratio The expression is: , in, This indicates the degree to which the structural response caused by flooding is required relative to the bridge's load-bearing capacity and deformation limits. Used to represent bending moment bearing capacity, Used to represent shear bearing capacity, Used to indicate displacement limits.

[0038] S3.5, Based on the effective flooding duration and bridge site unit flow Calculate the demand ratio for the sustained effect of floods The expression is: , in, For the sustained effect of flood demand ratio, For reference to the duration of flooding, For reference overcurrent intensity, and These are the weighting coefficients for the duration of flooding and the intensity of the current, respectively.

[0039] S3.6, Building a bridge In flood scenarios Engineering requirements parameters The expression is: , in, To flush out failure requirements, The ratio of flood level hydrodynamic instability demand, For the bridge flooding demand ratio, The ratio of structural response to demand, The demand ratio for the continued effect of floods.

[0040] S3.7, Based on engineering requirements parameters Define the overall demand ratio The expression is: , Define the limit state function of a single bridge The expression is: , Among them, when At that time, the bridge was determined In flood scenarios The state of failure is reached; when At that time, the bridge was determined It is in an active, undamaged state.

[0041] S3.8, Bridge material parameters and effective foundation depth drag coefficient Shrinkage scour correction factor Using the scour correction coefficient as an uncertain parameter, a vector of random variables is constructed. The expression is: , Bridge material parameters include lateral resistance Overturning moment bearing capacity Bending moment bearing capacity Shear bearing capacity and displacement limit The scour correction factor includes the pier shape correction factor. Water flow angle of attack correction factor Riverbed condition correction coefficient Bridge abutment type correction factor , This is a correction factor for the angle between the bridge abutment and the water flow; Based on historical damage repair records The distribution of uncertain parameters was calibrated using experimental data; then, in a flood scenario... Below, for the vector of random variables Perform sampling and calculate the first The single-bridge limit state function corresponding to each sample The expression is: , For the first The overall demand ratio corresponding to each sample; Definition of the first Failure indication function corresponding to each sample The expression is: , according to The results of the random sampling were used to calculate the bridge. In flood scenarios Single-bridge failure probability The expression is: .

[0042] S3.9, Set of Flood Scenarios Different combinations of flood intensities were used to obtain bridges The failure probability sample under multiple flood scenarios is expressed as follows: , The single-bridge vulnerability function is obtained by fitting failure probability samples: , in, For bridges The single-bridge vulnerability curve or vulnerability surface is used to represent the correspondence between flood intensity parameters and bridge failure probability; For bridges Flood intensity parameters at bridge sites under all flood scenarios; This is a fitting operation for the single-bridge vulnerability function; The final output shows each bridge in a flood scenario. Bridge failure probability The expression is: , in, For the first The bridge in the flood scene The failure probability of participating in network degradation simulation.

[0043] like Figure 3 As shown, Figure 3 The horizontal axis represents the flood intensity parameter at the bridge site, and the vertical axis represents the bridge failure probability. The scatter points in the figure represent failure probability samples obtained under different flood scenarios, and the curves represent the single-bridge vulnerability function obtained by fitting the failure probability samples.

[0044] S4, based on regional bridge group network and bridge failure probability Construct a bridge degradation network and calculate flood scenarios. The probability of disconnection of OD and flood scenarios Probability of bridge failure; for a set of flood scenarios By obtaining network failure probability samples under various flood scenarios, the vulnerability function of the bridge group network is fitted, and finally the failure probability of the bridge group network under all flood scenarios is output. .

[0045] Step S4 specifically includes the following steps: S4.1 Flood Scenario conduct The network random failure simulation, in the... In this simulation, the bridge To generate random numbers, use the following expression: , in, To obey Uniformly distributed random numbers within an interval; Based on bridge failure probability Determine the bridge's failure status: , in, Bridge In the It failed in the simulation. This indicates that the product is not invalid. This forms the first The failure state vector of all bridges under this simulation is expressed as follows: , in, This represents the total number of bridges in the regional bridge group.

[0046] S4.2, Based on bridge-network mapping relationship The failure status is The connecting edges of the bridges are from the regional bridge network. Remove it from the list, or set its access status to unavailable, to get the first... Degenerate networks under subsimulation: , in, For the first The set of network nodes that are still usable after the simulation. The set of connecting edges that are still available; When the bridge Map to connecting edges At that time, if ,but: .

[0047] S4.3, Based on OD pair sets, in degenerate networks In the process, determine any OD pair The starting point and the finish line Is there a valid connected path between them? Define an OD pair connectivity indicator function, with the expression: , in, Indicates the first OD pair under the next simulation The connected state; Define the OD disconnection indicator function as follows: , in, Indicates OD pair In the The connection was interrupted in the next simulation.

[0048] S4.4, based on The results of the sub-network random simulation are used to calculate the flood scenario. The probability of disconnection of OD is expressed as: , in, Flood scenario Lower OD pair The probability of connectivity failure.

[0049] S4.5, Weights based on OD and OD disconnection indication function Calculate the first Weighted OD disconnection ratio under the second simulation The expression is: , in, For the first Weighted OD disconnection ratio under the next simulation; This represents the total number of OD pairs. Set network function failure threshold When the weighted OD disconnection ratio Exceeding the network function failure threshold When the bridge group network function is deemed to be in failure, the bridge group network function failure indication function is used. The expression is: , in, For the first Bridge group network functional failure indication function under simulation; based on The results of the sub-network random simulation are used to calculate the flood scenario. Failure probability of the underpass group The expression is: , in, Flood scenario The probability of functional failure of the underbridge group.

[0050] S4.6, Set of Flood Scenarios Different combinations of flood intensities were used to obtain network failure probability samples for each flood scenario: , in, Flood scenario The corresponding regional flood intensity characterization quantity can be obtained from the flood intensity parameters of each bridge. Aggregation yields; Based on network failure probability samples, the vulnerability function of the bridge group network is obtained by fitting, and its expression is: , in, This refers to the vulnerability curve or vulnerability surface of the bridge network, used to characterize the relationship between flood intensity and the failure probability of the bridge network. This is a fitting operation for the vulnerability function of the bridge group network. For the bridge site flood intensity parameter of the bridge network under all flood scenarios; The final output is a set of flood scenarios. The probability of bridge network failure for each flood scenario. The expression is: , in, For the bridge group in flood scenario The probability of bridge group network failure.

[0051] like Figure 4 As shown, Figure 4 This diagram illustrates the output results of the bridge group network vulnerability function and OD pair disconnection probability in step S4. In the left-hand graph, scatter points represent network failure probability samples obtained under different flood scenarios, and the curve represents the fitted bridge group network vulnerability function, used to characterize the correspondence between regional flood intensity and bridge group network failure probability. The right-hand graph shows the disconnection probability of different OD pairs under flood scenarios. Different OD pairs have different disconnection probabilities due to differences in their starting point, ending point, and travel path. This graph demonstrates that the present invention can simultaneously output the overall bridge group failure probability and the connectivity failure risk of important OD pairs.

[0052] S5, based on regional bridge group network Bridge failure probability Bridge group network failure probability Constructing bridges Comparison network under failure conditions, and calculation of bridge In flood scenarios Comprehensive vulnerability importance index The bridges were sorted in descending order to obtain the ranking results of the key vulnerable bridges. Based on flood scenario weights Calculate bridge Multi-scenario comprehensive vulnerability importance index The comprehensive ranking results of key vulnerable bridges under multiple flood scenarios were obtained.

[0053] Step S5 specifically includes the following steps: S5.1, Regarding bridges Based on bridge-network mapping relationship Constructing bridges Comparison network under failure conditions: , in, Indicates that the bridge The corresponding comparison network is obtained after removing the connecting edges; where This refers to regional bridge network Remove bridge Connecting edge Calculation operations; In flood scenarios Under the premise of keeping the failure probabilities of other bridges constant, the network random failure simulation method based on step S4 is used to compare the network... The probability of OD pair disconnection and the probability of bridge group network failure are recalculated to obtain the bridge Bridge group network failure probability under failure conditions and bridges OD probability of disconnection under failure conditions .

[0054] S5.2 Based on the flood scenario in step S4 Downbridge network failure probability and bridges Bridge group network failure probability under failure conditions Calculate bridge Marginal impact of bridge network vulnerability The expression is: , in, For bridges The marginal impact on the failure probability of the bridge group network; the larger the value, the more significantly the failure of this bridge will increase the overall failure probability of the bridge group network.

[0055] S5.3, Based on the OD in step (4) for the probability of disconnection and bridges OD pair disconnection probability under failure conditions Calculate bridge Failure to OD The impact of disconnection The expression is: , in, Bridge The marginal impact of failure on OD on the probability of disconnection; Based on OD weights Calculate bridge The overall contribution of all ODs to the risk of disconnection The expression is: .

[0056] S5.4, Based on Regional Bridge Group Network and OD pair set Calculate bridge OD weighted betweenness centrality The expression is: , in, For OD In regional bridge network The number of valid paths in For the bridges that pass through it The number of valid paths corresponding to the connecting edges or bridge nodes. The larger the value, the more important the bridge's path is to the network's origin-destination (OD) pairs, and the stronger its support for network connectivity.

[0057] S5.5, Probability of Single-Bridge Failure Marginal impact Overall contribution and OD weighted betweenness centrality After normalization, the expression is: , , , , in, It is a normalization function used to convert indices with different dimensions to a unified dimension range; Calculate bridge In flood scenarios The following is a comprehensive vulnerability importance index: , in, For bridges The comprehensive vulnerability importance index; , , and For non-negative weighting coefficients, satisfying: , Used to characterize the inherent vulnerability of a single bridge. Used to characterize the impact of bridges on the overall network failure probability. Used to characterize the degree of impact of bridges on the risk of OD disconnection. Used to characterize the role of bridges in supporting passage in network topology.

[0058] S5.6, Based on the comprehensive vulnerability importance index Regarding flood scenarios The bridges in the lower area bridge group are sorted in descending order to obtain the ranking of key vulnerable bridges: , in, Flood scenario The following are the key vulnerable bridge ranking results; Indicates a sorting operation; Indicates descending order; When considering multiple flood scenarios, based on flood scenario weights Calculate bridge The multi-scenario comprehensive vulnerability importance index is expressed as follows: , And based on multi-scenario comprehensive vulnerability importance index The bridges were ranked to obtain a comprehensive ranking of the key vulnerable bridges under multiple flood scenarios.

[0059] like Figure 5 As shown, Figure 5 This diagram illustrates the ranking of critical vulnerable bridges and the evaluation results of regional water resistance toughness. The left-hand figure shows the comprehensive vulnerability importance index for different bridges. The higher the index, the greater the combined impact of the bridge on the failure probability of the bridge network, the risk of disconnection due to OD (distant origin), and the network's traffic support function. The ranking of critical vulnerable bridges can be derived from this. The right-hand figure shows the regional water resistance toughness index under different flood scenarios and provides the regional comprehensive water resistance toughness index obtained by weighting flood scenarios with different return periods.

[0060] S6. Weights based on OD Flood scenario weights Bridge failure probability OD probability of disconnection Comprehensive vulnerability importance index Ranking results of key vulnerable bridges Calculate flood scenarios Evaluation results of the water resistance toughness of the bridge network in the lower region.

[0061] Step S6 specifically includes the following steps: S6.1, Based on flood scenarios Bridge failure probability of each bridge Calculate the average vulnerability index of a single bridge level in a bridge group. : , in, This is the average vulnerability index for a single bridge level. This represents the total number of bridges in the regional bridge group. Furthermore, based on the comprehensive vulnerability importance index Calculate the importance-weighted single-bridge vulnerability index: , in, This is used to characterize the impact of the failure probability of key vulnerable bridges on the overall vulnerability of a regional bridge group.

[0062] S6.2, Failure Probability of Bridge Group Network As a vulnerability indicator at the network level: , in, Indicating flood scenario The probability of functional failure in the downstream bridge network.

[0063] S6.3, Weights based on OD and OD to disconnection probability Calculate the weighted OD connectivity vulnerability index: , in, Indicating flood scenario The weighted average probability of disconnection for the next important OD pair.

[0064] S6.4 Based on the ranking results of critically vulnerable bridges Select before sorting Key bridge collection: , in, Flood scenario The next key bridge collection; Comprehensive vulnerability importance index based on key bridge sets Calculate the concentrated vulnerability index of key bridges: , in, It is used to characterize whether the vulnerability of a regional bridge network is concentrated in a few critical bridges; the larger the value, the more sensitive the system is to the failure of a few critical bridges.

[0065] S6.5 To avoid setting weights arbitrarily, the weights are determined based on the dispersion of each vulnerability index and the decision preference coefficient under multiple flood scenarios. Define four fragility evaluation indicators: , , , , in, Importance-weighted single-bridge vulnerability index , Indicators of network-level vulnerability , This indicates the weighted OD index for connectivity vulnerability. , Indicators of concentrated vulnerability of key bridges ; For the One vulnerability evaluation index, Calculate its application in the flood scenario set. Mean of: , Calculate its application in the flood scenario set. Discreteness in: , in, Indicates the first The ability of each vulnerability evaluation index to distinguish the differences in system vulnerability under different flood scenarios; Set the decision preference coefficient: , in, This indicates the level of concern regarding the vulnerability of single-bridge bridges. This indicates the level of concern regarding the overall risk of network failure. This indicates the level of concern regarding the risk of connectivity failure caused by OD (Original Design Environment). This indicates the level of concern regarding the concentrated risks on key bridges; Calculate the first The weighting coefficients of each vulnerability evaluation index are expressed as follows: , , in, , To prevent extremely small positive numbers with zero dispersion; This represents the sum of decision biases. And satisfy: .

[0066] S6.6 Calculate the flood scenario based on four vulnerability evaluation indicators and their corresponding weighting coefficients. The following is a comprehensive index of regional vulnerability. : , in, Indicating flood scenario The overall vulnerability level of the regional bridge network is determined by a combination of single bridge failure, network failure, OD pair disconnection, and concentrated risks of critical bridges.

[0067] S6.7, Comprehensive regional vulnerability index Converted to regional water resistance index : , in, Flood scenario The regional water resistance resilience index is used to measure the water resistance resilience of the regional bridge network under the flood scenario. The higher the value, the higher the water resistance resilience of the regional bridge network under the flood scenario.

[0068] S6.8 Flood scenario weights based on the output of step S1 Regional water resilience index under various flood scenarios Weighted summaries were performed to obtain the regional comprehensive water resistance resilience index under multiple flood scenarios. The expression is: , in, This is a comprehensive regional water resistance resilience index under multiple flood scenarios. Flood scenario The probability of occurrence or scenario weight, and satisfying: .

[0069] S6.9, Final Output Flood Scenario Average vulnerability index of a single bridge level in the bridge group Importance-weighted single-bridge vulnerability index Network-level vulnerability indicators OD as a connectivity vulnerability index Key bridge concentrated vulnerability indicators Regional vulnerability index Regional water resistance index and the regional comprehensive water resistance resilience index under multiple flood scenarios .

[0070] The vulnerability analysis results of the regional bridge network are used to identify bridges with high failure probability under flood scenarios, bridges with high OD disconnection contribution, bridges with high network marginal impact, and regional water resistance toughness index under multiple flood scenarios. They are also used to support bridge scour prevention and reinforcement, bridge flood resistance enhancement, key passage protection, and priority allocation of regional flood control resources.

[0071] Example 2: This invention discloses an electronic device, including a processor and a storage medium; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the method described above for vulnerability analysis of bridge network under regional floods with water resistance and resilience.

Claims

1. A vulnerability analysis method for bridge network groups under regional floods, oriented towards water resistance and resilience, characterized in that, The steps include the following: S1. Obtain basic bridge data, bridge flood failure judgment criteria, climate and hydrological data, topographic data, road network data, OD traffic demand matrix, key service node data, and experimental data for the bridge group to form a standardized dataset; classify flood scenarios and form a flood scenario set, and then calculate the weight of each flood scenario; construct the regional bridge group network and OD pair set, and determine the OD pair weights; S2. Based on the standardized dataset and flood scenario set, determine the two-dimensional hydrodynamic computational domain, set boundary conditions and initial conditions, solve the two-dimensional depth-averaged shallow water equation, calculate the representative flood intensity parameters of a single bridge, and construct the flood intensity parameters at the bridge site. S3. Based on the flood intensity parameter at the bridge site, first calculate the bridge under the flood scenario. The engineering requirements parameters are then used to calculate the bridge's performance under flood conditions. The failure probability of a single bridge under various flood scenarios is calculated. For a set of flood scenarios, samples of bridge failure probabilities under each scenario are obtained. A single-bridge vulnerability function is then fitted, and the final output of the bridge's failure probability under each flood scenario is determined. The probability of bridge failure under these conditions; S4. Based on the regional bridge group network and bridge failure probability, construct a bridge group degradation network, and calculate the OD pair disconnection probability and bridge group failure probability under a certain flood scenario; for the flood scenario set, obtain network failure probability samples under each flood scenario, fit the bridge group network vulnerability function, and finally output the bridge group network failure probability for all flood scenarios; step S4 specifically includes the following steps: S4.1 Flood Scenario conduct The network random failure simulation, in the... In this simulation, the bridge To generate random numbers, use the following expression: ， in, To obey Uniformly distributed random numbers within an interval; Based on bridge failure probability Determine the bridge's failure status: ， in, Bridge In the It failed in the simulation. This indicates that the product is not invalid. This forms the first The failure state vector of all bridges under this simulation is expressed as follows: ， in, This represents the total number of bridges in the regional bridge group. S4.2, Based on bridge-network mapping relationship The failure status is The connecting edges of the bridges are from the regional bridge network. Remove it from the list, or set its access status to unavailable, to get the first... Degenerate networks under subsimulation: ， in, For the first The set of network nodes that are still usable after the simulation. The set of connecting edges that are still available; When the bridge Map to connecting edges At that time, if ,but: ， S4.3, Based on OD pair sets, in degenerate networks In the process, determine any OD pair The starting point and the finish line Is there a valid connected path between them? Define an OD pair connectivity indicator function, with the expression: ， in, Indicates the first OD pair under the next simulation The connected state; Define the OD disconnection indicator function as follows: ， in, Indicates OD pair In the The connection was interrupted in the next simulation; S4.4, based on The results of the sub-network random simulation are used to calculate the flood scenario. The probability of disconnection of OD The expression is: ， S4.5, Weights based on OD and OD disconnection indication function Calculate the first Weighted OD disconnection ratio under the second simulation The expression is: ， in, This represents the total number of OD pairs. Set network function failure threshold When the weighted OD disconnection ratio Exceeding the network function failure threshold When the bridge group network function is deemed to be in failure, the bridge group network function failure indication function is used. The expression is: ， in, For the first Bridge group network functional failure indication function under simulation; based on The results of the sub-network random simulation are used to calculate the flood scenario. Failure probability of the underpass group The expression is: ， S5. Based on the regional bridge group network, bridge failure probability, and bridge group network failure probability, construct a comparison network under single-bridge failure conditions, and calculate the single bridge failure scenario in a flood situation. The comprehensive vulnerability importance index under various flood scenarios is used to obtain the ranking results of key vulnerable bridges; the comprehensive vulnerability importance index of a single bridge under multiple flood scenarios is calculated based on the flood scenario weights to obtain the comprehensive ranking results of key vulnerable bridges under multiple flood scenarios. S6. Calculate flood scenarios Evaluation results of the water resistance toughness of the bridge network in the lower region.

2. The vulnerability analysis method for bridge network under regional floods based on water resistance and resilience, as described in claim 1, is characterized in that... The bridge basic data in step S1 includes the bridge location coordinates within the study area, bridge structural form, bridge deck elevation, beam bottom elevation, effective foundation depth, pier width, bridge calculated span, pier height, bridge material elastic modulus, moment of inertia of the control section, abutment water-blocking length, and bridge material parameters. The bridge flood resistance failure criteria data include the bridge pier shape correction coefficient, water flow angle of attack correction coefficient, riverbed condition correction coefficient, abutment form correction coefficient, abutment-water flow angle correction coefficient, resistance coefficient, water-facing projected area, lateral resistance, overturning moment bearing capacity, bending moment bearing capacity, shear bearing capacity, displacement limit value, and historical damage repair records of bridges in the study area. The climate and hydrological data include historical flood data records, rainfall time series, upstream flow process lines, downstream water level process lines, initial steady-state water depth field, initial steady-state flow velocity field, river water level time series, and river flow time series; The topographic data includes digital elevation models, riverbed elevation data, Manning roughness distribution, and long-term riverbed scouring and deposition variations. The road network data includes a set of network nodes, a set of connecting edges, and a mapping relationship between bridges and their connecting edges or bridge nodes. Key service node data includes sets of emergency service facility nodes, residential area nodes, hospital nodes, and school nodes; The experimental data includes model test data, prototype observation data, and existing publicly available experimental data related to bridge scour, hydrodynamic effects, bridge deck submersion, and structural response, used to calibrate the probability distribution of the scour correction coefficient for bridge material parameters.

3. The vulnerability analysis method for bridge network under regional floods based on water resistance and resilience, as described in claim 1, is characterized in that... In step S1, the flood scenario set is calculated. Weights of various flood scenarios Specifically, the steps include the following: Based on historical flood data records, rainfall time series, upstream flow process lines, downstream water level process lines, river water level time series, and river flow time series, the historical annual maximum flow, annual maximum water level, or annual maximum rainfall series are determined, and flood intensity variables are established. probability distribution function The expression is: ， in, Represents probability; This represents a sequence of historical annual maximum flow, annual maximum water level, or annual maximum rainfall. Classify flood intensity ranges into flood scenarios Corresponding to several non-overlapping flood intensity ranges The expression is: ， Flood scenario probability of occurrence The expression is: ， And satisfy: ， Flood scenarios according to recurrence interval The events are set as once-in-5-years, once-in-10-years, once-in-20-years, once-in-50-years, once-in-100-years, once-in-200-years, and once-in-500-years, based on their recurrence intervals. Determine the corresponding flood intensity threshold. The expression is: ， Flood scenario weights are calculated by using flood intensity values ​​corresponding to different return periods as scenario boundary points, and then calculating the probability of occurrence of adjacent flood intensity intervals, i.e., the weights of each flood scenario. The expression is: 。 4. The vulnerability analysis method for bridge network under regional floods based on water resistance and resilience, as described in claim 1, is characterized in that... In step S1, a regional bridge network is constructed based on road network data and bridge location coordinates. The expression is: ， in, For regional bridge network, For a set of network nodes, For connecting edge sets; bridges Through bridge-network mapping relationship Associated with its connecting edge, Bridges The connecting edge; Based on the sets of emergency service facility nodes, residential area nodes, hospital nodes, and school nodes in the key service node data, an OD pair set is constructed, expressed as: ， in, This represents the total number of OD pairs. Any OD pair Represented as: ， As the starting node, The endpoint node; Based on OD traffic demand matrix For each OD pair Determine the weights of OD The expression is: 。 5. The vulnerability analysis method for bridge network under regional floods based on water resistance and resilience, as described in claim 1, is characterized in that... Step S2 specifically includes the following steps: S2.1, Based on standardized datasets And flood scenario set For any flood scenario Obtain flood scenario Rainfall time series Upstream flow process line Downstream water level process line Digital Elevation Model Riverbed elevation data Manning roughness distribution ; S2.2, Based on Digital Elevation Model Riverbed elevation data Road network data and bridge location coordinates Determine the two-dimensional hydrodynamic computational domain of the study area. The expression is: ， in, A two-dimensional hydrodynamic computational domain covering the main channel of the river, beaches, dikes, roads, and bridge sites; Two-dimensional hydrodynamic computational domain Divided into several hydrodynamic computational grid cells, the expression is: ， in, For the first One hydrodynamic computational grid cell; Based on digital elevation model Riverbed elevation data , for the first Each hydrodynamic computational grid cell assigns the grid bed elevation. The expression is: ， And based on Manning roughness distribution For the first Each hydrodynamic computational grid cell is assigned a grid roughness parameter. The expression is: ， in, For the first Hydrodynamic computational grid cell The representative coordinates; S2.3 Set the boundary conditions and initial conditions within the computational domain. The boundary conditions include the surface rainfall inflow term, upstream boundary conditions, and downstream boundary conditions. The initial conditions include the initial water depth field and the initial velocity field. Specifically, based on flood scenarios Rainfall time series Constructing surface rainfall inflow terms within a two-dimensional hydrodynamic computational domain The expression is: ， Based on flood scenario Upstream flow process line Set upstream boundary conditions within the computational domain The expression is: ， Based on flood scenario Downstream water level process line Set downstream boundary conditions within the computational domain The expression is: ， Based on flood scenario The initial steady-state water depth field and initial steady-state velocity field are defined, and the initial conditions within the computational domain are set. The initial conditions include the initial water depth field and the initial velocity field, and their expressions are as follows: ， ， ， in, Flood scenario The initial water depth below, Flood scenario Below Initial velocity component in direction, Flood scenario Below Initial velocity component in the direction; Flood scenario The initial steady-state water depth field at position The water depth, Flood scenario The initial steady-state flow field in Initial velocity component in direction, Flood scenario The initial steady-state flow field in Initial velocity component in the direction; S2.4, Based on two-dimensional hydrodynamic computational domain Grid subgrade elevation and mesh roughness parameters Hydrodynamic computational grid cells As a basic computational unit, under the set boundary and initial conditions, the two-dimensional depth-averaged shallow water equation is solved, which includes the continuity equation and the momentum equation. The expression for the continuity equation is: ， in, Flood scenario Lower bridge location coordinates At any moment The water depth, for directional depth-average flow velocity for directional depth-average flow velocity For surface rainfall inflow, This includes infiltration or other water loss items; The expression for the momentum equation is: ， ， in, It is the acceleration due to gravity. For riverbed elevation, for Directional friction gradient term, for Directional friction gradient term, for directional external force term, for Directional external force term; Calculate according to Manning's formula. Directional friction gradient term and The directional friction gradient term is expressed as follows: ， ， Two-dimensional depth-averaged shallow water equations in hydrodynamic computation grid cells Numerical discretization and iterative solutions are performed to obtain the flood scenario. Water depth field at each time point Normal velocity component field tangential velocity component field and flow field The expression is: ， And calculate the velocity field The expression is: ， S2.5, Based on bridges Bridge location coordinates The obtained water depth field Flow velocity field and flow field Mapped to bridge The bridge site location was determined, and the water depth sequence at the bridge site was obtained. Bridge site flow velocity sequence and bridge site flow sequence The expressions are as follows: ， ， ， in, For the first The bridge in the flood scene Next moment The sequence of water depths at the bridge site, For the first The bridge in the flood scene Next moment Bridge site flow velocity sequence, No. The bridge in the flood scene Next moment The sequence represents the water flow direction at the bridge site; S2.6, Define the bridge In flood scenarios The following is the effective flooding time set The expression is: ， in, To preset the effective flood depth threshold; Based on bridge site water depth sequence Bridge site flow velocity sequence and bridge site water flow direction sequence Calculate bridge The representative flood intensity parameters are expressed as follows: ， ， ， ， ， in, The bridge site represents the water depth. The bridge site represents the flow velocity. To guide the direction of water flow For the effective duration of flooding, The unit flow rate or overcurrent intensity at the bridge site; This refers to selecting the set of effective flooding times. The maximum value in the following data. This refers to the dominant water flow direction corresponding to the water depth and flow velocity represented by the bridge site. It refers to length; Therefore, building bridges In flood scenarios Flood intensity parameters at the bridge site The expression is: ， in, Used to characterize the impact of floods on bridges The intensity of local action.

6. The vulnerability analysis method for bridge network under regional floods based on water resistance and resilience, as described in claim 1, is characterized in that... Step S3 specifically includes the following steps: S3.1, Based on the representative water depth at the bridge site Bridge site represents flow velocity Calculate the Froude number of the bridge site The expression is: ， in, It is the acceleration due to gravity; Based on the water depth represented by the bridge site Riverbed elevation at bridge site Calculate bridge In flood scenarios Maximum water surface elevation at the bridge site The expression is: ， Based on the water depth represented by the bridge site Bridge site represents flow velocity and the Froude number of bridge sites Calculate the local scour depth of the bridge pier The expression is: ， in, This represents the local scour depth of the bridge pier. The width of the bridge pier. This is the correction factor for the shape of the bridge pier. Indicates based on the dominant water flow direction Corrected angle of attack correction factor; This is a correction factor for riverbed conditions; Based on the water depth represented by the bridge site Length of water obstruction of bridge abutment and the Froude number of bridge sites Calculate the local scour depth of the bridge abutment The expression is: ， in, This represents the local scour depth of the bridge abutment. Indicates based on the dominant water flow direction Corrected angle correction factor between bridge abutment and water flow. This is a correction factor for the abutment type; Based on the water depth represented by the bridge site and bridge site unit flow Calculate the shrinkage scour depth The expression is: ， in, To reduce the scouring depth, For reference overcurrent intensity, This is a correction factor for shrinkage erosion. Calculate the total scour depth The expression is: ， in, This represents the long-term changes in riverbed scouring and deposition. This represents the local scour depth of the bridge pier. This refers to the local scour depth of the bridge abutment; To reduce the scouring depth; Calculate the scouring failure demand ratio The expression is: ， in, Used to indicate the percentage of total scour depth relative to the effective burial depth of the foundation; Based on the effective burial depth; S3.2, Based on the representative flow velocity of the bridge site Dominant water flow direction drag coefficient and water-facing projected area Calculate the horizontal hydrodynamics of floods The expression is: ， in, For water density, To be determined by the direction of the dominant water flow Determined correction factor for the direction of water flow; Calculate the horizontal hydrodynamics of flood Overturning moment generated by the action The expression is: ， in, The lever arm is the distance from the point of action of the horizontal hydrodynamic force of the flood to the anti-overturning reference point; Calculate the flood level hydrodynamic instability demand ratio The expression is: ， in, Used to represent lateral resistance, Used to represent the overturning moment bearing capacity; S3.3, Based on the maximum water surface elevation at the bridge site Beam bottom elevation and bridge deck elevation Calculate the bridge inundation demand ratio The expression is: ， in, Used to indicate the degree to which the floodwater level exceeds the bottom of the beam and approaches or exceeds the bridge deck; when This indicates that there is no risk of flooding at the bottom of the beam; S3.4, Based on flood horizontal hydrodynamics Bridge structural form and bridge material parameters, calculate bridge Maximum bending moment Maximum shear force and maximum displacement The expressions are as follows: ， ， ， in, , and This is the structural response calculation function determined by the bridge's structural form and material parameters. Calculate the span of the bridge. This refers to the height of the bridge piers; The elastic modulus of bridge materials; To control the moment of inertia of the cross section; Calculate the structural response demand ratio The expression is: ， in, Used to represent bending moment bearing capacity, Used to represent shear bearing capacity, Used to indicate displacement limits; S3.5, Based on the effective flooding duration and bridge site unit flow Calculate the demand ratio for the sustained effect of floods The expression is: ， in, For reference to the duration of flooding, For reference overcurrent intensity, and These are the weighting coefficients for the duration of flooding and the intensity of the current, respectively. S3.6, Building a bridge In flood scenarios Engineering requirements parameters The expression is: ， in, To flush out failure requirements, The ratio of flood level hydrodynamic instability demand, For the bridge flooding demand ratio, The ratio of structural response to demand, The demand ratio for the sustained effect of floods; S3.7, Based on engineering requirements parameters Define the overall demand ratio The expression is: ， Define the limit state function of a single bridge The expression is: ， Among them, when At that time, the bridge was determined In flood scenarios The state of failure is reached; when At that time, the bridge was determined It is in a valid state; S3.8, Bridge material parameters and effective foundation depth drag coefficient Shrinkage scour correction factor Using the scour correction coefficient as an uncertain parameter, a vector of random variables is constructed. The expression is: ， Bridge material parameters include lateral resistance Overturning moment bearing capacity Bending moment bearing capacity Shear bearing capacity and displacement limit The scour correction factor includes the pier shape correction factor. Water flow angle of attack correction factor Riverbed condition correction coefficient Bridge abutment type correction factor , This is a correction factor for the angle between the bridge abutment and the water flow; Based on historical damage repair records The distribution of uncertain parameters was calibrated using experimental data; then, in a flood scenario... Below, for the vector of random variables Perform sampling and calculate the first The single-bridge limit state function corresponding to each sample The expression is: ， For the first The overall demand ratio corresponding to each sample; Definition of the first Failure indication function corresponding to each sample The expression is: ， according to The results of the random sampling were used to calculate the bridge. In flood scenarios Single-bridge failure probability The expression is: ， S3.9, Set of Flood Scenarios Different combinations of flood intensities were used to obtain bridges The failure probability sample under multiple flood scenarios is expressed as follows: ， The single-bridge vulnerability function is obtained by fitting failure probability samples: ， in, For bridges The single-bridge vulnerability curve or vulnerability surface is used to represent the correspondence between flood intensity parameters and bridge failure probability; For bridges Flood intensity parameters at bridge sites under all flood scenarios; This is a fitting operation for the single-bridge vulnerability function; The final output shows each bridge in a flood scenario. Bridge failure probability The expression is: ， in, For the first The bridge in the flood scene The failure probability of participating in network degradation simulation.

7. The vulnerability analysis method for bridge network groups under regional floods with water resistance and toughness as described in claim 1, characterized in that, Step S4 further includes the following steps: S4.6, Set of Flood Scenarios Different combinations of flood intensities were used to obtain samples of bridge group failure probabilities under various flood scenarios: ， in, Flood scenario The corresponding regional flood intensity characterization quantity can be obtained from the flood intensity parameters of each bridge. Aggregation yields; Based on the bridge group failure probability samples, the vulnerability function of the bridge group network is obtained by fitting, and the expression is: ， in, This refers to the vulnerability curve or vulnerability surface of the bridge network, used to characterize the relationship between flood intensity and the failure probability of the bridge network. This is a fitting operation for the vulnerability function of the bridge group network. For the bridge site flood intensity parameter of the bridge network under all flood scenarios; The final output is a set of flood scenarios. The probability of bridge network failure for each flood scenario. The expression is: ， in, For the bridge group in flood scenario The probability of bridge group network failure.

8. The vulnerability analysis method for bridge network under regional floods based on water resistance and resilience, as described in claim 1, is characterized in that... Step S5 specifically includes the following steps: S5.1, Regarding bridges Based on regional bridge network and bridge-network mapping relationship Constructing bridges Comparison network under failure conditions : ， in This refers to regional bridge network Remove bridge Connecting edge Calculation operations; In flood scenarios Under the premise of keeping the failure probabilities of other bridges constant, the network random failure simulation method based on step S4 is used to compare the network... The probability of OD pair disconnection and the probability of bridge group network failure are recalculated to obtain the bridge Bridge group network failure probability under failure conditions and bridges OD probability of disconnection under failure conditions ; S5.2 Based on the flood scenario in step S4 Downbridge network failure probability and bridges Bridge group network failure probability under failure conditions Calculate bridge Marginal impact of bridge network vulnerability The expression is: ， in, For bridges The marginal impact on the failure probability of the bridge group network; S5.3, Based on the OD in step S4, the probability of disconnection. and bridges OD pair disconnection probability under failure conditions Calculate bridge The impact of failure on the disconnection of OD pairs The expression is: ， in, Bridge The marginal impact of failure on OD on the probability of disconnection; Based on OD weights Calculate bridge The overall contribution of all ODs to the risk of disconnection The expression is: ， S5.4, Based on Regional Bridge Group Network and OD pair set Calculate bridge OD weighted betweenness centrality The expression is: ， in, For OD In regional bridge network The number of valid paths in For the bridges that pass through it The number of valid paths corresponding to the connecting edge or bridge node; S5.5, Probability of Single-Bridge Failure Marginal impact Overall contribution and OD weighted betweenness centrality After normalization, the expression is: ， ， ， ， in, It is a normalization function used to convert indices with different dimensions to a unified dimension range; Calculate bridge In flood scenarios The following is a comprehensive vulnerability importance index: ， in, For bridges The comprehensive vulnerability importance index; , , and For non-negative weighting coefficients, satisfying: ， Used to characterize the inherent vulnerability of a single bridge. Used to characterize the impact of bridges on the overall network failure probability. Used to characterize the degree of impact of bridges on the risk of OD disconnection. Used to characterize the traffic support function of bridges in network topology; S5.6, Based on the comprehensive vulnerability importance index Regarding flood scenarios The bridges in the lower area bridge group are sorted in descending order to obtain the ranking of key vulnerable bridges: ， in, Flood scenario The following are the key vulnerable bridge ranking results; Indicates a sorting operation; Indicates descending order; When considering multiple flood scenarios, based on flood scenario weights Calculate bridge The multi-scenario comprehensive vulnerability importance index is expressed as follows: ， And based on multi-scenario comprehensive vulnerability importance indicators The bridges were ranked to obtain a comprehensive ranking of the key vulnerable bridges under multiple flood scenarios.

9. The vulnerability analysis method for bridge network under regional floods based on water resistance and resilience, as described in claim 1, is characterized in that... Step S6 specifically includes the following steps: S6.1, Based on flood scenarios Bridge failure probability for each bridge Calculate the average vulnerability index of a single bridge level in a bridge group. : ， in, This is the average vulnerability index for a single bridge level. This represents the total number of bridges in the regional bridge group. Furthermore, based on the comprehensive vulnerability importance index Calculate the importance-weighted single-bridge vulnerability index: ， in, Used to characterize the impact of the failure probability of key vulnerable bridges on the overall vulnerability of regional bridge groups; S6.2, Failure Probability of Bridge Group Network As a vulnerability indicator at the network level: ， in, Indicating flood scenario The probability of functional failure in the downstream bridge network; S6.3, Weights based on OD and OD to disconnection probability Calculate the weighted OD connectivity vulnerability index: ， in, Indicating flood scenario The weighted average probability of disconnection for the next important OD pair; S6.4 Based on the ranking results of critically vulnerable bridges Select before sorting Key bridge collection: ， in, Flood scenario The next key bridge collection; Comprehensive vulnerability importance index based on key bridge sets Calculate the concentrated vulnerability index of key bridges: ， in, Used to characterize whether the vulnerability of a regional bridge network is concentrated in a few key bridges; S6.

5. Based on the dispersion of each vulnerability index and the decision preference coefficient under multiple flood scenarios, determine the weights and define four vulnerability evaluation indicators: ， ， ， ， in, Importance-weighted single-bridge vulnerability index , Indicators of network-level vulnerability , This indicates the weighted OD index for connectivity vulnerability. , Indicators of concentrated vulnerability of key bridges ; For the One vulnerability evaluation index, Calculate its application in the flood scenario set. Mean of: ， Calculate its application in the flood scenario set. Discreteness in: ， in, Indicates the first The ability of each vulnerability evaluation index to distinguish the differences in system vulnerability under different flood scenarios; Set the decision preference coefficient: ， in, This indicates the level of concern regarding the vulnerability of single-bridge bridges. This indicates the level of concern regarding the overall risk of network failure. This indicates the level of concern regarding the risk of connectivity failure caused by OD (Original Design Environment). This indicates the level of concern regarding the concentrated risks on key bridges; Calculate the first The weighting coefficients of each vulnerability evaluation index are expressed as follows: ， ， in, , To prevent extremely small positive numbers with zero dispersion; This represents the sum of decision biases. And satisfy: ， S6.6 Calculate the flood scenario based on four vulnerability evaluation indicators and their corresponding weighting coefficients. The following is a comprehensive index of regional vulnerability. : ， in, Indicating flood scenario The overall vulnerability level of the regional bridge network is determined by a combination of single bridge failure, network failure, OD pair disconnection, and concentrated risks of critical bridges. S6.7, Comprehensive regional vulnerability index Converted to regional water resistance index : ， in, Flood scenario The regional water resistance toughness index is below; S6.8 Flood scenario weights based on the output of step S1 Regional water resilience index under various flood scenarios Weighted summaries were performed to obtain the regional comprehensive water resistance resilience index under multiple flood scenarios. The expression is: ， in, This is a comprehensive regional water resistance resilience index under multiple flood scenarios. Flood scenario The probability of occurrence or scenario weight, and satisfying: ， S6.9, Final Output Flood Scenario Average vulnerability index of a single bridge level in the bridge group Importance-weighted single-bridge vulnerability index Network-level vulnerability indicators OD as a connectivity vulnerability index Key bridge concentrated vulnerability indicators Regional vulnerability index Regional water resistance index and the regional comprehensive water resistance resilience index under multiple flood scenarios .

10. An electronic device, characterized in that, Including processor and storage media; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the vulnerability analysis method for regional flood-resistant bridge network under water toughness according to any one of claims 1-9.

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