Bridge toughness evaluation method under scouring-earthquake multi-disaster effect

Abstract

The invention discloses a bridge toughness evaluation method under the action of multiple disasters such as scouring and earthquake, and belongs to a bridge structure health monitoring technology. The method comprises the following steps: firstly, calculating the scouring occurrence flow velocity according to the sediment starting flow velocity, evaluating the relationship between the flow velocity and the flow through a hydraulic model, and determining the occurrence probability and intensity distribution of a flood event capable of causing scouring; then establishing a bridge time-varying scouring depth calculation model based on a Markov scouring accumulation process of discrete time and discrete state; then a bridge refinement model considering the scouring effect is established based on OpenSees, a vulnerability function modeling method fusing seismic cumulative damage is proposed through nonlinear dynamic time history analysis, and seismic vulnerability analysis is performed on bridges in different service periods; and finally, representing the recovery process of the bridge after the disaster according to a typical function recovery model, and further calculating the anti-disaster toughness of the bridge.

Description

Technical Field

[0001] This invention belongs to the field of bridge structural health monitoring technology and involves the field of artificial intelligence analysis. Specifically, it relates to a method for assessing the toughness of bridges under multiple disasters such as scour and earthquake. Background Technology

[0002] Bridges are vulnerable to disasters such as earthquakes, floods, scour, corrosion, and impacts during their service life, with foundation scour and earthquakes being key factors leading to bridge damage. Between 2000 and 2014, over 30% of 106 bridge failures in China were caused by scour; between 1900 and 2015, China experienced over 890 earthquakes of magnitude 6 or higher, with 6,140 bridges damaged in the 2008 Wenchuan earthquake. When scour and earthquakes are coupled, scour can lead to the loss of lateral support in the bridge foundation, thus affecting its seismic performance. Therefore, conducting resilience assessments of bridges under multiple disasters involving scour and earthquakes is crucial.

[0003] With the increasing frequency of extreme weather events, bridge structures often face complex risks from the combined effects of scour and earthquakes. The development and optimization of assessment methods have always been a key focus for scholars at home and abroad. On the one hand, long-term scour can lead to a reduction in the depth of bridge foundations and a decrease in bearing capacity, altering the dynamic characteristics of the structure. On the other hand, earthquakes can further exacerbate the damage to the foundations, causing overall structural instability. The combination of these two factors will significantly increase the risk of bridge collapse.

[0004] However, current bridge resilience assessment research largely focuses on single disaster scenarios. Currently, for different types of disasters, multi-hazard design theory for bridge structures mainly follows the single-hazard superposition correction paradigm, which linearly combines the effects of independent disasters by introducing partial factors. While this method can ensure the safety of bridge structures under multiple disasters to a certain extent, it cannot consider the coupling effects between disasters, and a specialized assessment system for the coupling effects of scour and earthquakes is still incomplete.

[0005] Furthermore, existing research primarily focuses on scour depth at design flood frequencies, lacking systematic exploration of the impact of time-varying scour effects. Current multi-hazard assessment methods cannot accurately quantify the impact mechanism of scour on bridge seismic response, nor can they establish dynamic assessment models for bridge toughness under coupled loads. Traditional scour assessment methods cannot incorporate seismic dynamic parameters, while conventional seismic toughness assessments neglect the weakening effect of early-stage scour on structural performance. Simultaneously, assessing bridge toughness under coupled loads faces challenges such as complex parameter coupling mechanisms and difficult experimental simulations. Existing standards and technical methods have not yet formed a unified assessment standard, making it difficult to scientifically quantify and provide risk warnings for bridge toughness under coupled hazards in practical engineering.

[0006] In summary, bridge assessment methods under single disaster scenarios are no longer sufficient to meet the safety requirements under the coupled effects of scour and earthquake. Existing multi-hazard assessment studies suffer from problems such as insufficient mechanism analysis, incomplete methodological system, and low practicality. There is an urgent need to construct a targeted bridge resilience assessment framework. Summary of the Invention

[0007] To address the shortcomings of the existing technologies, this invention provides a method for assessing the toughness of bridges under multiple disasters, including scour and earthquakes, offering theoretical support and technical guidance for the structural safety protection of bridges in complex disaster environments.

[0008] To achieve the above-mentioned objectives, the present invention provides the following technical solution: A method for assessing the toughness of bridges under scour-earthquake multi-hazard loading includes the following steps: (1) Based on the sediment initiation velocity, combined with the hydraulic characteristics and bridge geometry, the critical velocity for scour to occur is determined by a hydraulic calculation model. The river velocity distribution under different flow conditions is simulated to establish a quantitative relationship between velocity and flow rate. Based on this, the critical flow rate threshold for the risk of bridge foundation scour is determined. q 0, quantifying historical flood events exceeding the critical flow threshold; (2) Combine the Markov model to describe the scour accumulation process, determine the probability of flood events that can cause scour, and then construct a time-varying scour depth calculation model, and combine the scour depth with bridge samples; (3) A refined nonlinear finite element model of the bridge was established using OpenSees. Seismic loads and bridge scour depth were added. The nonlinear time history analysis method was used to realize the coupling calculation of seismic motion time history and bridge sample. The response peak values ​​of bridge components under different seismic conditions were extracted to obtain the bridge scour earthquake time-varying vulnerability curve and vulnerability surface. (4) The recovery process of bridges after disasters is represented by three typical functional recovery models, and then the disaster resistance of bridges is calculated to evaluate the bridge resilience under scour earthquake action.

[0009] The specific construction method of the time-varying scour depth calculation model in step (2) includes: (2.1) Based on the peak-splitting method, select the flow rate exceeding the critical flow threshold. q The probability of a flood event occurring is estimated by fitting a homogeneous Poisson process to the historical flood events with a value of 0. (2.2) Divide the scour depth into a finite number of discrete states, and combine flood hazard, hydrological information and river hydraulic conditions to solve the flood sample transition probability matrix based on Monte Carlo simulation; (1) In the formula, Represents the flood sample transition probability matrix. Indicates a flood event q The conditional transition matrix of 1, N sample This represents the number of flood samples. (2.3) Based on the transition probability matrix, the probability mass distribution, complementary cumulative distribution and expected value of scour depth over the whole life are obtained (i.e., the average scour depth of the bridge at different times). Based on the probability mass distribution, the average scour depth over the whole life is obtained. Based on the average scour depth value, the time-varying scour depth of the bridge is obtained by fitting, thus constructing a time-varying scour depth calculation model.

[0010] Step (3) of constructing the time-varying vulnerability of scour earthquakes specifically includes: Seismic vulnerability analysis aims to establish seismic motion intensity parameters ( IM ) and damage state threshold ( LS The probability mapping relationship of ) quantifies different IM Under horizontal conditions, bridge components or systems reach the specified damage limit state. LSi The exceedance probability of seismic vulnerability; the seismic vulnerability function is usually expressed in conditional probability form: (2) In the formula, S D To meet the actual seismic requirements of bridge components, S C|LSi Damage limit state for bridge components LSi, IM These are the parameters for seismic intensity. For the coupled effects of bridge scour and earthquake disasters, the vulnerability function of bridge components and systems can be expressed as: (3) In the formula, H This represents the probability distribution of scour depth at different time periods; based on this function model, the time-varying vulnerability curve of bridge scour during earthquakes can be generated.

[0011] Generally speaking, S D and S C|LSi If we consider that they are linearly correlated on a logarithmic scale, then the above formula can be expressed in the following form: (4) In the formula, μ D and μ C|LSi These are the ground motion intensity parameters ( IM The median estimates of the demand and capacity of the function; βD This represents the dispersion or logarithmic standard deviation of earthquake demand. β C|LSi Φ(·) represents the dispersion or logarithmic standard deviation of the seismic resistance of the structure; Φ(·) represents the standard normal cumulative distribution function.

[0012] Earthquake demand average μ D With seismic intensity parameters IM Obligation to follow an exponential relationship: (5) In the formula, a and b The parameters are determined based on logarithmic regression.

[0013] As a hybrid system composed of multiple components (piers, bearings, superstructure, etc.), the overall seismic performance of a bridge cannot be simply described by the superposition of the vulnerability of individual components. The first-order limit estimation method assumes that the failure modes of each component are positively correlated, and the functional relationship is as follows: (6) In the formula, P fi For the first i The probability of damage to each component; P sys This represents the overall probability of damage to the bridge. Based on the probability limit theory, the vulnerability parameters of each component of the bridge are input into the calculation model of equation (4), and the vulnerability surface of the overall bridge system can be obtained by using the first-order and second-order limit methods.

[0014] The bridge toughness assessment method under scour earthquake loading described in step (4) specifically includes: Seismic toughness ( R This represents the ability of a structural system to recover its required function after an earthquake event. It is usually assessed through the post-earthquake function of the structure at a specific time, and its functional relationship is as follows: (7) In the formula, t 0 represents the time when the earthquake occurred; t h This is the observation point after the structural repair; Q ( τ The post-earthquake function of the structure is typically between 0 and 1. Q ( τ A value of 1 indicates that the structure and function are intact; Q ( τ )and Q (k) ( τRelated to, through 4 damage states Q (k) ( τ The result is obtained by superposition, as shown in formula (9).

[0015] Based on relevant standards, engineering experience, and the characteristics of bridges, bridge toughness is classified into three levels, as detailed in Table 1.

[0016] Table 1. Criteria for Rating Bridge Toughness Level In this invention, a typical functional recovery model is used to represent the recovery process of bridges after a disaster. Given that the functional recovery process of a bridge depends on its damage state, over time... τ Time k The functional recovery function for each damage state (DS) is expressed as follows: Q (k) ( τ ), can be expressed in general form: (8) In the formula, k The numbers 1, 2, 3, and 4 represent minor, moderate, severe, and complete damage, respectively. Q r Residual function, characterizing the level of remaining function retained by the structure under seismic loading; R f (·) is the structural function recovery function, which describes the dynamic process of system function reconstruction over time after a disaster; Q t The target function after the structural repair is completed reflects the degree to which the actual function after repair conforms to the design goal; H (·) represents the piecewise step function of Haweside; t 0 represents the time when the earthquake occurred; δ i To delay the repair time; δ r The duration of the repair process.

[0017] For a bridge at a specific disaster intensity level, its resilience can be represented by adding the products of the vulnerability curves for each damage state and the expected function curve. When considering the uncertainty of the recovery process, the expected function (i.e., the aforementioned...) Q ( τ The curve is the mean functional recovery curve, which can be expressed as: (9) (10) In the formula, Q (k) ( τ ) for the firstk Functional curves of structures related to damage states; P ds,k This represents the probability of the structure occurring under different damage states; P ds,0 This represents the probability of the structure occurring without damage. P f,k For the structure in the first k The failure probability under each damage state.

[0018] Generally, the extent of performance degradation in engineering systems caused by seismic excitation is positively correlated with the difficulty of functional reconstruction. Due to differences in the degree of damage, different recovery strategies may be adopted for bridges after an earthquake. This invention employs three types of recovery functions to quantify the bridge recovery process: In the formula, ω Indicates the morphological characteristics of the curve; η These are time points in the recovery process; R n f (·) represents the structural function recovery function under minor damage; R s f (·) represents the structural function recovery function under moderate damage; R p f (·) represents the structural function recovery function under severe and complete damage.

[0019] Compared with the prior art, the present invention has the following beneficial effects: This invention focuses on the coupled scenario of scour and earthquake, breaking through the traditional single-hazard assessment paradigm. It fully considers the dynamic evolution of scour, cumulative earthquake damage, and the coupling effect between the two throughout the bridge's life cycle. By integrating multidisciplinary technologies, it constructs a systematic assessment framework, solving the problems of insufficient analysis of coupling mechanisms, inadequate characterization of time-varying effects, and low practicality of existing methods. Its substantial features and significant effects also include: (1) Construct a vulnerability analysis system with multiple disaster coupling: Establish a bridge refinement model that considers the scour effect, and construct a vulnerability function by integrating the cumulative earthquake damage. Compared with the traditional single disaster vulnerability analysis, this system can quantify the impact of scour depth on the seismic response of bridges during different service periods. (2) Establish a scientific quantitative model of disaster resilience: Based on three typical functional recovery models, combined with the exceedance probability and expected function curve of different damage states, the post-disaster recovery process of bridges is quantified. Compared with the traditional resilience assessment that ignores the differences in the recovery process, this model avoids overestimating the seismic resilience of bridges under long-term service or high-intensity earthquakes. (3) Enhance the engineering practical value of multi-hazard assessment: This method is based on actual hydrological data, standard formulas and open source platforms, and can be directly applied to engineering practice, forming a complete technology chain from risk identification, performance assessment to resilience quantification, overcoming the limitations of existing multi-hazard assessment methods that are highly theoretical but lack practical application. Attached Figure Description

[0020] Figure 1 This is a flowchart of the bridge toughness assessment method under multiple disasters including scour and earthquake, as described in an embodiment of the present invention.

[0021] Figure 2 This is a schematic diagram of the bridge structure described in an embodiment of the present invention. The numerical units in the diagram are cm.

[0022] Figure 3 This is a sequence diagram of the daily average flow of the river as described in an embodiment of the present invention.

[0023] Figure 4 This is a peak flow diagram of floods exceeding the threshold as described in an embodiment of the present invention.

[0024] Figure 5 This is a transition probability matrix diagram of the flood sample described in an embodiment of the present invention.

[0025] Figure 6 shows the calculation results of the Markov process according to the embodiment of the present invention, wherein Figure 6(a) is the probability mass function of scour depth and Figure 6(b) is the complementary cumulative distribution function of scour depth.

[0026] Figure 7 This is a graph showing the calculation results of the mean and standard deviation of the time-varying scour depth as described in an embodiment of the present invention.

[0027] Figure 8 This is the seismic response spectrum selected according to the embodiments of the present invention.

[0028] Figure 9 shows the seismic response requirements of the bridge components under different lifespans according to the embodiments of the present invention, wherein Figure 9(a) is the pier bottom curvature requirement diagram and Figure 9(b) is the support displacement requirement diagram.

[0029] Figure 10 shows the log-linear regression results of different structural responses according to the embodiments of the present invention, wherein Figure 10(a) is the regression diagram of the curvature of the pier bottom and Figure 10(b) is the regression diagram of the displacement of the support.

[0030] Figure 11 This is a time-varying seismic vulnerability curve of a bridge pier as described in an embodiment of the present invention, wherein... Figure 11 (a) is a minor injury. Figure 11 (b) is a moderate injury. Figure 11 (c) indicates severe injury. Figure 11 (d) is complete destruction.

[0031] Figure 12 This is a time-varying seismic vulnerability curve of the support described in an embodiment of the present invention, wherein... Figure 12 (a) is a minor injury. Figure 12 (b) is a moderate injury. Figure 12 (c) indicates severe injury. Figure 12 (d) is complete destruction.

[0032] Figure 13 This is a seismic vulnerability surface diagram of the bridge system described in an embodiment of the present invention, wherein... Figure 13 (a) is a minor injury. Figure 13 (b) is a moderate injury. Figure 13 (c) indicates severe injury. Figure 13 (d) is complete destruction.

[0033] Figure 14 This is a schematic diagram illustrating the structural toughness and post-event recovery process under an earthquake event as described in an embodiment of the present invention.

[0034] Figure 15 The above are the functional recovery curves of the bridge under different seismic intensities as described in the embodiments of the present invention, wherein... Figure 15 (a) is a functional recovery curve under a 0.2g seismic motion. Figure 15 (b) is the functional recovery curve under a 0.5g seismic motion. Figure 15 (c) is the functional recovery curve under a 0.8g earthquake.

[0035] Figure 16 This is a diagram showing the seismic toughness of bridges under different ground motion intensities as described in an embodiment of the present invention. Detailed Implementation

[0036] The technical solution of the present invention will be explained and described in detail below with reference to the accompanying drawings and specific embodiments.

[0037] This invention provides a method for assessing the toughness of bridges under scour-earthquake multi-hazard conditions. This method is based on the OpenSees platform and utilizes a refined finite element model of pile-foundation bridges that considers scour effects. It includes structural vulnerability analysis and toughness assessment procedures, such as... Figure 1 The diagram shown is a flowchart of one implementation of this method.

[0038] To reveal the time-varying degradation patterns and multi-hazard failure mechanisms of structural performance under scour-seismic coupling, it is necessary to conduct multi-hazard response analysis of bridges. Existing studies mostly analyze the two types of hazards independently, lacking performance evaluation methods that consider their coupling effect; moreover, most results only address seismic responses at fixed scour depths, neglecting the spatiotemporal uncertainties of ground motion parameters and scour depth throughout the entire lifespan. Therefore, this invention proposes a multi-hazard performance evaluation method for cross-river bridges under scour-seismic conditions. First, the time-varying probability distribution of scour depth is calculated; then, a refined nonlinear finite element model of the entire bridge is constructed; finally, performance indicators of key components such as piers and bearings are defined through a demand-capacity analysis framework, establishing vulnerability curves for scour-affected components and the system, and assessing seismic toughness during the service life.

[0039] Example I. Analysis of Time-Varying Scour Depth of Bridges The prototype bridge for the example is a near-shore highway bridge with a river estuary width of 800m. The riverbed surface material consists of fine sand and gravel with a relative density of 1.65 and a median particle size of 2mm. The river channel is clean and straight, and the Manning roughness coefficient is taken as 0.025. This example selects a three-span continuous concrete box girder bridge to verify and analyze the bridge toughness assessment framework under the above-mentioned scour-earthquake multi-hazard action. The bridge span arrangement is 3×50m, and the bridge layout and geometric dimensions are as follows. Figure 2 As shown. The main girder is a C50 concrete box girder, 26.5m wide and 2.8m high. The piers are circular double-column piers commonly used in highway bridges, without crossbeams or cap beams. The pier diameter is 2.5m and the pier height is 17m. The longitudinal reinforcement of the piers uses 32mm diameter HRB400 steel bars; 16mm ring stirrups are used, with a stirrup spacing of 15cm. The supports are spherical steel supports. Each pier has a foundation, which is made of C30 concrete. Under each foundation are 2×2 bored piles (4 in total), made of C30 underwater concrete, with a pile diameter of 1.5m and a pile length of 24m. The pile foundations are embedded in a 30m thick sand layer with a unit weight of 15.6kN / m³ and an internal friction angle of 35.6°.

[0040] like Figure 3 As shown, the hydrological station near the bridge site recorded the daily average flow values ​​of the river from January 1, 1940 to January 1, 2020. When the flood flow exceeds the scour threshold flow, the scour depth increases. Therefore, for wider river channels with relatively regular cross-sections, the threshold flow can be directly calculated using the "Specifications for Hydrological Survey and Design of Highway Engineering" (JTG C30-2015) and the Manning formula. q 0 is 590m 3 / s. For example... Figure 4 As shown, historical flood events exceeding the threshold are selected according to the peak-splitting method.

[0041] The scour state transition matrix is ​​calculated using discrete-time and discrete-state Markov processes. Flood events with independent and stationary increments are modeled using homogeneous Poisson processes. To calculate the scour state transition matrix, a set of... N s = 23 scouring state, discrete scouring depth is 0.5m. For example Figure 5 As shown, the state transition matrix is ​​obtained through Monte Carlo simulation, and the calculation formula is as follows: In the formula, Represents the state transition matrix; Indicates a flood event q The conditional state transition matrix of 1; N sample This represents the number of flood samples.

[0042] As shown in Figure 6, the unconditional probability mass function and complementary cumulative distribution function of the scour depth at different times can be obtained from the state transition matrix. It can be seen that the probability distribution of the scour depth is relatively dispersed in the early stages, but as time increases, the probability mass shifts towards higher values ​​of the scour depth and gradually stabilizes. Simultaneously, the average scour depth at different times can be obtained from the probability mass function, and the time-varying scour depth of the bridge can be fitted from the average value. The changes of the mean and standard deviation of the scour depth over time are shown in Figure 6. Figure 7 As shown, the average scour depth increases over time, but the rate of increase decreases, reaching an average of 8.73 m after 100 years.

[0043] II. Performance Evaluation under Multiple Hazards of Scour and Earthquake To quantitatively reveal the impact mechanism of scour uncertainty on the seismic performance of bridges, a refined nonlinear finite element model of the entire bridge is first required to provide basic data samples for subsequent seismic demand analysis. This invention utilizes the secondary development capabilities of the OpenSees platform to construct a nonlinear dynamic analysis model of the bridge considering pile-soil interaction and scour boundary conditions, laying the numerical simulation foundation for multi-hazard coupled response analysis.

[0044] A nonlinear finite element analysis model of the bridge was constructed using OpenSees software. Elastic beam-column elements, nonlinear beam-column elements, and zero-length elements were used to simulate the seismic response characteristics of the components. The main girder and cap beam were simulated using elastic beam-column elements, and their geometric properties were determined through section property analysis. The pier components were modeled using nonlinear beam-column elements, and the mechanical behavior of the steel reinforcement and concrete was characterized using a fiber section model. The Concrete 01 constitutive model was used to characterize the concrete material, incorporating the effect of stirrup confinement; the Steel 02 constitutive model was used to simulate the longitudinal reinforcement. The supports were implemented using zero-length elements, and their horizontal mechanical properties were described using an ideal elastoplastic constitutive relation. To account for soil-structure interaction, each pile node used a nonlinear zero-length element. py , tz and qz Soil spring elements. These elements simulate lateral soil resistance, axial pile friction, and pile bottom support resistance. In the OpenSees model, uniaxial materials PySimple1, TzSimple1, and QzSimple1 are used for simulation, respectively.

[0045] In bridge performance evaluation, the quantification of pier damage status typically employs a two-parameter criterion system based on deformation capacity, specifically including two key indicators: displacement ductility and cross-sectional curvature ductility. For bridge bearings, current methods mostly use relative deformation or displacement to characterize bearing damage. As shown in Table 2, the curvature ductility ratio is used as the required parameter for the pier response, while relative displacement is used as the damage indicator for plate rubber bearings.

[0046] Table 2 Definitions of Limit States under Scour Seismic Hazards for Different Components In vulnerability calculations based on incremental dynamic analysis, the selection of the number of ground motion samples must balance computational efficiency and statistical reliability. Considering the site conditions of the bridge in this embodiment, the study selected 19 far-field ground motion records with epicentral distances greater than 10 km from the Pacific Earthquake Engineering Research Center (PEER) database, and adjusted the proportions using peak ground acceleration (PGA) as an indicator. Figure 8 As shown.

[0047] Using a time-varying scour depth calculation model based on Markov processes, the probability distribution of scour depth for bridges at different lifespans can be obtained. As shown in Figure 9, nonlinear time-history analyses were performed on finite element models of bridges at different lifespans (0 years, 5 years, 10 years, 20 years, 50 years, and 100 years). Using PGA as the seismic intensity index, the calculation results of the seismic response requirements of the main bridge components at different lifespans were analyzed. Figure 9(a) shows the probabilistic seismic demand models for pier base curvature established using PGA when the bridge lifespan is 0 years, 20 years, and 50 years. Figure 9(b) shows the probabilistic seismic demand models for support displacement established using PGA when the bridge lifespan is 0 years, 20 years, and 50 years.

[0048] Log-linear regression analysis was performed on the extracted structural response values ​​to construct a probabilistic seismic demand model considering the time-varying effects of scour. Figure 10(a) shows the probabilistic seismic demand model for pier base curvature. Figure 10(b) shows the probabilistic seismic demand model for support displacement. The results show that both pier curvature ductility and support relative displacement increase with increasing PGA. The pier base section curvature ductility ratio is significantly positively correlated with PGA, and the curvature demand increases rapidly with increasing seismic intensity. Scour depth also shows a strong correlation with support peak displacement, and its influence on the probabilistic seismic demand model for support peak displacement is more significant.

[0049] The time-varying vulnerability characteristics of bridge piers, such as Figure 11 As shown in the figure, the vulnerability of the bridge piers increases significantly with earthquake intensity, and the probability of exceeding the threshold increases monotonically with the increase of peak ground acceleration and the accumulation of service years. Scour depth has a relatively small impact on the vulnerability probability of the bridge piers; with the increase of scour depth, the probability of the bridge pier reaching various damage states increases slightly, and the increase is more significant with the increase of damage level. The time-varying vulnerability characteristics of the bearings are as follows: Figure 12 As shown, bearing vulnerability increases significantly with earthquake intensity, and its exceedance probability monotonically increases with peak ground acceleration and service life. Scour depth has a significant impact on bearing vulnerability probability; with increasing scour depth, the probability of the bearing reaching various damage states increases significantly, and the increase is even more pronounced with increasing damage level.

[0050] Based on this, by inputting the vulnerability parameters of each pier and bearing into the calculation model according to the probability limit theory, the vulnerability surface of the overall bridge system can be obtained by using the first-order and second-order limit methods. Figure 13The time-varying vulnerability surfaces of the bridge under four damage states, calculated using the first-order limit method, are displayed. Analysis shows that the upper limit of system vulnerability increases significantly with earthquake intensity, with the maximum vulnerability reaching 100% for any damage state. Compared to support vulnerability, the time-varying amplitude of bridge system vulnerability is reduced, which is essentially due to the coupling effect of multiple component failure modes. The system damage probability is jointly determined by multiple failure paths, such as pier bending failure and excessive support displacement; the stiffness degradation effect of individual components is partially buffered by structural redundancy.

[0051] III. Disaster Resilience Assessment under Scour-Earthquake Loading Figure 14 This explains the concept of seismic toughness of structures under earthquake events. t An earthquake occurs at time 0, and the structural function instantly drops from 1 to... Q r During the period from the end of the earthquake to the start of repairs, the structural function remained at [value missing]. Q r The state remains unchanged; this period is called the delayed repair time. δ i The repair started at [time]. t s The target function can be restored by taking repair measures within the repair time. Q t .in, t e This indicates the completion time of the repair process, while δ r This corresponds to the duration of the repair process.

[0052] Based on the vulnerability analysis results, different scour conditions have varying impacts on the seismic performance of bridges. Therefore, it is crucial to comprehensively assess these effects through seismic toughness evaluation. The toughness analysis considers and calculates the loss of bridge function over service life. Given the complexity of the functional recovery process, which is often accompanied by randomness, primarily manifested in the residual structural function and recovery time, this analysis is particularly important.

[0053] Table 3 presents the probability distribution of key parameters for functional recovery curves under different injury states. Using these probability distributions, Monte Carlo simulations were conducted to obtain samples of key parameters for the functional recovery curves corresponding to a given injury state. Then, each set of sampled key parameters was substituted into the functional recovery function to obtain the bridge function at a specific time point under a given injury state in each simulation. Finally, by averaging the bridge function at each time point in the Monte Carlo simulations, the expected functional curve associated with each injury state could be generated.

[0054] Table 3 Random variables in the recovery model under different injury states The resilience index of a bridge during its service life is calculated by measuring the area under the recovery curve. Based on the generated vulnerability curve, Monte Carlo simulations are performed to calculate the average recovery curve. By generating 10,000 samples and setting a time range of 400 days, a full simulation of these recovery models is performed to obtain the average functional recovery curve of the bridge. Seismic toughness can then be calculated based on the average recovery curve. Since the structural function is related to the vulnerability probability under the seismic intensity conditions of the bridge's location, three levels of seismic intensity indices (peak ground acceleration of 0.2g, 0.5g, and 0.8g) are selected for comparative analysis.

[0055] Figure 15 The functional status of bridges affected by scour after earthquakes was compared under three seismic intensities (peak ground acceleration of 0.2g, 0.5g, and 0.8g). For example... Figure 15 As shown, under scour conditions, bridge function depends on its service life. In scour scenarios, within the same recovery time, bridge function decreases with increasing service life. With continued use, older bridges retain less function due to severe scour effects. Furthermore, bridge function is related to seismic intensity. Clearly, within a given recovery time, a larger peak ground acceleration reduces bridge function.

[0056] Figure 16 This study demonstrates the seismic toughness of bridges affected by scour during their service life. It can be observed that scour has a significant impact on the toughness of bridges during their service life. The effect of scour on the bridge toughness index varies depending on the peak ground acceleration (PGA). When the PGA is less than 0.1g, the impact of scour on the toughness index is relatively small before the bridge reaches 100 years of service life. For bridges under scour conditions, the change in toughness during their service life depends on the service time and the intensity of the seismic events.

[0057] Bridge resilience is classified into three levels, with detailed classification standards shown in Table 1. Figure 16 As shown in the figure, the bridge's resilience is dynamically divided into three warning zones: Level 1, Level 2, and Level 3. It can be seen from the figure that when the bridge's lifespan is 0 years, a peak ground acceleration of 0.57g will cause its resilience level to drop from Level 1 to Level 2; when the bridge's lifespan reaches 100 years, a peak ground acceleration of only 0.36g is needed to cause the resilience level to drop from Level 1 to Level 2. Corresponding alarm response measures will be taken for different warning levels.

[0058] Regardless of earthquake intensity, bridges subjected to scour scenarios exhibit a more significant decrease in toughness over their lifespan compared to bridges unaffected by scour. This is because bridge performance is influenced by the depth of scour. For bridges under scour scenarios, at peak ground accelerations of 0.4g and 0.8g, their toughness indicators decrease by approximately 31% and 68%, respectively, over a 100-year service life. Therefore, neglecting the effects of scour may lead to an overestimation of a bridge's seismic toughness under high-intensity earthquakes or after long-term service.

[0059] The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, various improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for assessing bridge toughness under scour-earthquake multi-hazard loading, characterized in that, Includes the following steps: (1) Based on the sediment initiation velocity, combined with the hydraulic characteristics and bridge geometry, the critical velocity for scour to occur is determined by a hydraulic calculation model. The river velocity distribution under different flow conditions is simulated to establish a quantitative relationship between velocity and flow rate. Based on this, the critical flow rate threshold for the risk of bridge foundation scour is determined. q 0, quantifying historical flood events exceeding the critical flow threshold; (2) Combine the Markov model to describe the scour accumulation process, determine the probability of flood events that can cause scour, and then construct a time-varying scour depth calculation model, and combine the scour depth with bridge samples; (3) A refined nonlinear finite element model of the bridge was established using OpenSees. Seismic loads and bridge scour depth were added. The nonlinear time history analysis method was used to realize the coupling calculation of seismic motion time history and bridge sample. The response peak values ​​of bridge components under different seismic conditions were extracted to obtain the bridge scour earthquake time-varying vulnerability curve and vulnerability surface. (4) The recovery process of bridges after disasters is represented by three typical functional recovery models, and then the disaster resistance of bridges is calculated to evaluate the bridge resilience under scour earthquake action.

2. The bridge toughness assessment method under scour-earthquake multi-hazard loading as described in claim 1, characterized in that, Step (2) specifically includes: (2.1) Based on the peak-splitting method, select the flow rate exceeding the critical flow threshold. q The probability of a flood event occurring is estimated by fitting a homogeneous Poisson process to the historical flood events with a value of 0. (2.2) Divide the scour depth into a finite number of discrete states, and combine flood hazard, hydrological information and river hydraulic conditions to solve the flood sample transition probability matrix based on Monte Carlo simulation; （1） In the formula, Represents the flood sample transition probability matrix. Indicates a flood event q The conditional transition matrix of 1, N sample This represents the number of flood samples. (2.3) Based on the transition probability matrix, the probability mass distribution, complementary cumulative distribution and expected value of scour depth over the whole life are obtained. Based on the probability mass distribution, the average scour depth over the whole life is obtained. Based on the average scour depth value, the time-varying scour depth of the bridge is obtained by fitting. A time-varying scour depth calculation model is constructed.

3. The bridge toughness assessment method under scour-earthquake multi-hazard loading as described in claim 1, characterized in that, Step (3) of constructing the time-varying vulnerability of scour earthquakes specifically includes: By establishing seismic intensity parameters IM With damage state threshold LS The probability mapping relationship, quantifying different IM Bridge components or systems reaching a specified damage limit state under horizontal conditions LSi The exceedance probability, the seismic vulnerability function is expressed in conditional probability form: （2） In the formula, S D To meet the actual seismic requirements of bridge components, S C|LSi Damage limit state for bridge components LSi,IM These are the parameters for seismic intensity. For the coupled effects of bridge scour and earthquake disasters, the vulnerability function of bridge components and systems can be expressed as: （3） In the formula, H The probability distribution of scour depth at different time periods is given; based on this function model, the time-varying vulnerability curve of bridge scour during earthquakes is generated. because S D and S C|LSi If the correlation is linear on a logarithmic scale, the above formula can be expressed as follows: （4） In the formula, μ D and μ C|LSi Seismic intensity parameters IM Median estimates of the demand and capacity of the function; β D This represents the dispersion or logarithmic standard deviation of earthquake demand. β C|LSi Φ(·) represents the dispersion or logarithmic standard deviation of the structure's seismic resistance; Φ(·) represents the standard normal cumulative distribution function. Earthquake demand average μ D With seismic intensity parameters IM Obligation to follow an exponential relationship: （5） In the formula, a and b The parameters are determined based on logarithmic regression; As a hybrid system composed of multiple components connected in series and parallel, the overall seismic performance of a bridge is estimated using the first-order limit method, assuming that the failure modes of each component are positively correlated. The functional relationship is as follows: （6） In the formula, P fi For the first i The probability of damage to each component; P sys This represents the overall probability of damage to the bridge. Based on the probability limit theory, the vulnerability parameters of each component of the bridge are input into the calculation model of equation (4) to obtain the vulnerability surface of the overall bridge system solved by the first-order and second-order limit methods.

4. The bridge toughness assessment method under scour-earthquake multi-hazard loading as described in claim 1, characterized in that, The bridge toughness assessment method under scour earthquake loading described in step (4) specifically includes: Seismic toughness R This represents the structural system's ability to recover its required function after an earthquake event, assessed through the post-earthquake function of the structure at a specific time point, and its functional relationship is as follows: （7） In the formula, t 0 represents the time when the earthquake occurred; t h This is the observation point after the structural repair; Q ( τ The post-earthquake function of the structure is typically between 0 and 1. Q ( τ A value of 1 indicates that the structure and function are intact; In time τ Time k The functional recovery function of a damage state DS is expressed as follows: Q (k) ( τ ), generally expressed as: （8） In the formula, k The numbers 1, 2, 3, and 4 represent minor, moderate, severe, and complete damage, respectively. Q r Residual function, characterizing the level of remaining function retained by the structure under seismic loading; R f (·) is the structural function recovery function, which describes the dynamic process of system function reconstruction over time after a disaster; Q t The target function after the structural repair is completed reflects the degree to which the actual function after repair conforms to the design goal; H (·) represents the piecewise step function of Haweside; t 0 represents the time when the earthquake occurred; δ i To delay the repair time; δ r The duration of the repair process; Bridge resilience at a specific disaster intensity level is represented by adding the products of the vulnerability curves for each damage state and the expected function curve, where the expected function... Q ( τ The curve is the mean functional recovery curve, expressed as: （9） （10） In the formula, Q (k) ( τ ) for the first k Functional curves of structures related to damage states; P ds,k This represents the probability of the structure occurring under different damage states; P ds,0 This represents the probability of the structure occurring without damage. P f,k For the structure in the first k The failure probability under each damage state.

5. The bridge toughness assessment method under scour-earthquake multi-hazard loading as described in claim 4, characterized in that, The bridge toughness described in step (4) is divided into three levels, wherein the third level... D R The warning value is [0, 0.5), and the warning color is red; Level II D R The value is [0.5, 0.8), and the warning color is orange; Level 1 D R The value is [0.8, 1), and the warning color is green.

6. The bridge toughness assessment method under scour-earthquake multi-hazard loading as described in claim 4, characterized in that, In step (4), the bridge restoration process is quantified using three types of restoration functions: In the formula, ω Indicates the morphological characteristics of the curve; η These are time points in the recovery process; R n f (·) represents the structural function recovery function under minor damage; R s f (·) represents the structural function recovery function under moderate damage; R p f (·) represents the structural function recovery function under severe and complete damage.

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