Method for evaluating anti-collision toughness of rusted steel bar bridge structure after ship collision

Abstract

The invention relates to the technical field of traffic infrastructure maintenance, and particularly discloses a method for evaluating the anti-collision toughness of a rusted steel bar bridge structure after ship collision, and the method comprises the following steps: firstly, building a rusted bridge pier finite element model based on a rusted steel bar concrete theoretical degradation model; simulating ship collision by adopting an equivalent static method, and determining dynamic damage factors of the ship; structural nonlinear static analysis and nonlinear dynamic analysis are conducted by considering sudden external force to obtain a bridge function loss function, and then a bridge function is calculated; constructing a response surface agent model to perform dynamic response prediction; determining a bridge structure damage state judgment criterion; the vulnerability of the rusted bridge is calculated through Monte Carlo simulation; and according to the bridge function loss function, combining the repair time and the recovery function to calculate a structure anti-collision toughness index. The method provided by the invention fills up the blank of ship collision resistance toughness evaluation of the coastal rusted bridge pier, provides a scientific basis for bridge safety evaluation and maintenance decision, and is of great significance for guaranteeing safe operation of the bridge.

Description

Technical Field

[0001] The present invention relates to the technical field of transportation infrastructure maintenance, and in particular to a method for evaluating the collision toughness of a corroded steel bar bridge structure after being hit by a ship. Background Art

[0002] For coastal bridges, ship impacts are one of the extreme loads that can easily cause serious damage or even collapse of bridges, resulting in safety accidents and impacting the transportation system. During an impact, bridge piers may suffer shear damage or even overturn as a whole, and the superstructure is at risk of falling beams, posing a serious challenge to the integrity of the overall structure. Such accidents not only directly lead to serious damage to the bridge or even its total collapse, but also cause significant casualties, block key transportation routes, cause economic losses and social impacts, and pose a serious threat to the resilience and reliability of the transportation system. Therefore, it is particularly important to study the degradation of structural performance after a ship impact with a bridge and its ability to be repaired to its original state after the collision.

[0003] Current research on structural resilience focuses primarily on a structure's ability to withstand external disasters or its efficiency in recovering after a disaster. Resilience is primarily evaluated based on four key aspects: redundancy, robustness, rapidity, and strategic nature. Resilience assessment is relatively understudied in the engineering field, and this research has primarily focused on earthquake resilience. Furthermore, various quantitative methods have been proposed for earthquake resilience. For example, a simplified probabilistic risk assessment method quantifies a building's seismic capacity by incorporating an average annual repair time. Other studies, considering the coupling effects of earthquakes and corrosion environments, employed a probabilistic framework to assess the resilience of aged reinforced concrete (RC) bridge piers with different failure modes. In contrast, research on the impact of other disasters (such as ship impacts, floods, hurricanes, explosions, and tsunamis) on bridge resilience is significantly insufficient. For example: In the field of coastal bridges, some studies have proposed a quantitative expression specifically for evaluating the resilience of bridges to waves based on the performance-based earthquake engineering (PBEE) framework; for coastal reinforced concrete bridges, some studies have combined multiple indicators such as repair time, repair cost and carbon footprint to establish a method to evaluate their resilience under multiple disasters; in terms of explosion hazards, a review has been published that has refined the core scientific issues and challenges in the research on the explosion resilience of critical infrastructure.

[0004] Coastal bridges are constantly eroded by seawater and waves, creating cracks on the concrete surface that accelerate chloride ion corrosion of reinforced concrete structures. When the chloride ion concentration on the steel bar surface exceeds a certain critical value, the passive film on the steel bar surface is damaged, causing steel corrosion. Studies have shown that steel corrosion reduces the yield strength of the steel bar and reduces the effective cross-sectional area. The rust produced on the steel bar surface after corrosion is several times the volume of the steel section loss, causing cracks on the surface of the concrete cover due to rust expansion, resulting in deterioration of the concrete structure performance. Most researchers have made some progress in studying the effects of single corrosion and toughness assessment under the coupled effects of corrosion and earthquakes. However, research on the impact toughness assessment of coastal bridge piers, which are prone to corrosion, is somewhat insufficient. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for evaluating the anti-collision toughness of a corroded reinforced steel bridge structure after a ship collision, which solves the problems of insufficient research on the anti-collision toughness evaluation of coastal easily corroded bridge piers after a ship collision, inaccurate evaluation, and lack of quantitative basis; through comprehensive evaluation using multiple methods, accurate simulation and quantification are achieved, filling the research gap, providing a scientific basis for bridge safety assessment and maintenance decision-making, and ensuring the safe operation of bridges.

[0006] To achieve the above object, the present invention provides a method for evaluating the collision toughness of a corroded steel bar bridge structure after a ship collision, comprising the following steps: S1. Establish a finite element model of corroded bridge piers based on the theoretical degradation model of corroded reinforced concrete; S2. Use the equivalent static method to simulate ship collision and determine the dynamic damage factors of the ship; S3. Considering the sudden external force, nonlinear static analysis and nonlinear dynamic analysis of the structure are performed to obtain the bridge function loss function, and then the bridge function function is calculated based on the bridge function loss function; S4. Construct a response surface proxy model to predict dynamic response; S5. Determine the criteria for judging the damage status of bridge structures; S6. Calculate the vulnerability of corroded bridges through Monte Carlo simulation; S7. Calculate the structural crash toughness index based on the bridge function loss function, combined with the repair time and recovery function.

[0007] Preferably, in S1, when establishing the finite element model of the corroded bridge pier, the structural performance degradation caused by steel bar corrosion is taken into account, including a reduction in the effective cross-sectional area of the steel bar, a reduction in the yield strength and ultimate strength of the steel bar, a reduction in the bond strength between the steel bar and concrete, and a reduction in the tensile strength of the concrete after corrosion expansion; Considering the diameter and corrosion rate of the pier steel bars, the corrosion condition of the piers was evaluated. The corrosion rate was calculated as follows: ; Where, is the steel corrosion rate, is the diameter of the uncorroded steel bar, is the diameter of the corroded steel bar; The constitutive model of corroded steel bar material is used to simulate the mechanical properties of naturally corroded steel bars in an atmospheric environment. The characteristic parameters of the constitutive model are as follows: ; ; ; ; Where, , are the effective cross-sectional area and ultimate strain of the uncorroded steel bars, respectively; , are the yield strength and ultimate strength of uncorroded steel bars, respectively; , are the yield strength and ultimate strength of the corroded steel bars, respectively; , are the effective cross-sectional area and ultimate strain of the corroded steel bars, respectively; The reduction in bond slip strength between steel bars and concrete caused by corrosion is simulated by coefficient reduction. The relationship between bond slip strength is as follows: ; ; Where, is the bond-slip relationship between corroded steel bars and concrete, is the bond-slip relationship between uncorroded steel bars and concrete, is the bond strength reduction coefficient between the corroded steel bars and concrete; The reduction factor is introduced to simulate the strength degradation of the concrete cover. The calculation model is as follows: ; ; Where, , are the compressive strength of the cover concrete before and after steel bar corrosion; Take 0.1; is the average tensile strain caused by corrosion expansion and cracking of the cover concrete; is the compressive strain corresponding to the maximum stress of the uncorroded concrete; is the number of main reinforcements in the cross section of the pier column; is the diameter of the uncorroded main reinforcement; is the cross-sectional perimeter of the pier specimen; The core area concrete strength is calculated based on the Mander model using the constitutive model of concrete confined by circular corroded stirrups as follows: ; ; ; ; Where, is the volumetric reinforcement ratio of transverse reinforcement in corrosion-confined concrete; is the volumetric reinforcement ratio of the transverse reinforcement of the uncorroded confined concrete; is the yield strength of the transverse reinforcement; is the yield strength of the corroded transverse reinforcement; is the effective lateral restraint stress; is the compressive strength of unconfined concrete; is the compressive strength of corrosion-confined concrete; is the yield strength reduction factor of the corroded transverse reinforcement; is the stress correction coefficient obtained after regression analysis of the test data; is the constraint effectiveness coefficient.

[0008] Preferably, in S2, the equivalent static method is used to simulate the ship collision to determine the dynamic damage factors of the ship, including the barge impact force, full load displacement and ship impact speed. The barge impact force calculation formula is as follows: ; Where, F is the design value of the barge impact force, M is the full load displacement, V is the ship impact speed.

[0009] Preferably, in S3, the bridge function loss function includes the initial corrosion pier function loss function and the impact function loss function. Considering the initial corrosion of the pier, the ultimate compressive bearing capacity obtained by nonlinear static analysis of the corroded pier is selected as the indicator of the residual function of the structure, and the quantitative formula of the initial corrosion pier function loss function under different corrosion rates is as follows: ; Where, is the maximum vertical bearing capacity of the pier in the uncorroded state; is the time-varying maximum vertical bearing capacity of the structure; Loss function of concrete subjected to impact under corrosion conditions The calculation is performed through the fragility curves corresponding to different states, that is, the product of the probability of structural failure under different damage states and the structural damage ratio under the corresponding state, as shown in the following formula: ; Where, j= 1, 2, 3, 4, and 5 correspond to five levels of damage status; is the structural damage ratio under the corresponding state; Status j The probability of structural damage under different states is calculated based on the damage probability: ; Where, Status j The probability of structural damage; Calculate the bridge function function based on the initial corrosion pier function loss function and the pier impact function loss function , whose expression is: ; Where, C is the corrosion strength; is the loss function of concrete subjected to impact in the case of corrosion; is the functional loss function of the initial corroded bridge pier, is a step function, is the recovery function, t is the time variable.

[0010] Preferably, in S4, a response surface method (RSM) is used to construct an agent model for dynamic response prediction, specifically: The BBD method in the response surface methodology was adopted, and the Design-Expert software was used to design and analyze different working conditions. A three-factor three-level design analysis was carried out with the corrosion rate, impact velocity and impact tonnage as the response independent variables and the residual bearing capacity as the dependent variable.

[0011] Preferably, in S5, the ultimate compressive bearing capacity of the structure is selected as the limit state standard, and the 、 、 、 The limit value corresponds to 10%, 20%, 40%, and 70% of the ultimate compressive bearing capacity, according to the loss range of the ultimate compressive bearing capacity of the structure. Determine the damage status and the judgment criteria are as follows: like <10%, the damage status is basically intact; If 10%≤ <20%, the damage status is slight damage; If 20%≤ <40%, the damage status is moderate damage; If 40%≤ <70%, the damage status is severe damage; like ≥70%, the damage state is collapse; in, , is the residual bearing capacity after damage, is the ultimate compressive bearing capacity of the structure.

[0012] Preferably, in S6, the failure probability of each damage state is obtained by Monte Carlo simulation based on the statistical distribution of the cross-sectional resistance of the concrete component and the statistical distribution of the ship tonnage, and finally a fragility curve of the ship hitting the bridge pier is obtained.

[0013] Preferably, in S7, the repair time refers to the time it takes for the bridge to be repaired from a damaged state to a normal use state. The repair time of the bridge is related to the damage state of the bridge. The greater the damage, the longer the repair time. The recovery time of different damage states is obtained based on the repair time. The negative exponential recovery function is used to evaluate the toughness, and the calculation formula is as follows: ; Where, a and b are two constants fitted through the data, which are related to the damage state and the recovery state; t OE is the time when the impact event occurred; T RE It is the time it takes for the structure to be repaired after a ship collision.

[0014] Therefore, the present invention adopts the above-mentioned method for evaluating the collision toughness of a corroded steel bar bridge structure after a ship collision, and the beneficial effects are as follows: (1) This paper constructs a finite element model based on the theoretical degradation model of corroded reinforced concrete, comprehensively considers the factors of steel corrosion and ship impact, combines the equivalent static method, accurately simulates the mechanical behavior of the bridge, and comprehensively evaluates it through multiple methods to ensure that the results are scientific and reliable.

[0015] (2) This invention addresses the current situation of insufficient research on the impact toughness assessment of coastal piers prone to corrosion after being hit by ships, provides a complete assessment solution, and improves the theoretical system in related fields.

[0016] (3) The present invention clarifies the influence of factors such as corrosion degree and impact speed on the impact toughness of bridge piers, providing guidance for bridge design optimization, maintenance strategy formulation and emergency management, reducing safety risks and ensuring operational safety.

[0017] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 This is an overall flow chart of an embodiment of a method for evaluating the collision toughness of a corroded steel bar bridge structure after a ship collision according to the present invention; Figure 2 This is a definition diagram of the disaster resilience of a corroded reinforced concrete structure according to an embodiment of a method for evaluating the collision resilience of a corroded reinforced concrete bridge structure after a ship collision; Figure 3 This is a vulnerability analysis flow chart of an embodiment of a method for evaluating the collision toughness of a corroded steel bar bridge structure after a ship collision according to the present invention; Figure 4 This is a finite element diagram of a bridge pier according to an embodiment of a method for evaluating the collision toughness of a corroded steel bar bridge structure after a ship collision; Figure 5 These are structural stability stress cloud diagrams under four working conditions of an embodiment of a method for evaluating the collision toughness of a corroded steel bar bridge structure after a ship collision, wherein (a) is a working condition of 7.5%-100t-3m / s, (b) is a working condition of 7.5%-700t-0.5m / s, (c) is a working condition of 15%-400t-3m / s, and (d) is a working condition of 15%-700t-1.75m / s; Figure 6 These are stress cloud diagrams of a bridge pier under vertical load failure structure under four working conditions of an embodiment of a method for evaluating the collision toughness of a corroded steel bar bridge structure after a ship collision according to the present invention, wherein (a) is a working condition of 7.5%-100t-3m / s, (b) is a working condition of 7.5%-700t-0.5m / s, (c) is a working condition of 15%-400t-3m / s, and (d) is a working condition of 15%-700t-1.75m / s; Figure 7 The following are the failure probabilities of bridge piers of different levels at different impact velocities according to an embodiment of a method for evaluating the collision toughness of a corroded steel bar bridge structure after a ship collision, wherein (a) represents a corrosion rate of 0%, (b) represents a corrosion rate of 7.5%, and (c) represents a corrosion rate of 15%. Figure 8 This is a graph showing the probability of pier failure under different damage conditions corresponding to different impact velocities when the corrosion rate is 0% according to an embodiment of a method for evaluating the collision toughness of a corroded steel bar bridge structure after a ship collision; Figure 9 This is a graph showing the impact toughness of bridge piers at different impact speeds according to an embodiment of a method for evaluating the collision toughness of a corroded steel bar bridge structure after being hit by a ship. DETAILED DESCRIPTION

[0019] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0020] Unless otherwise defined, technical or scientific terms used in the present invention shall have the same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs.

[0021] The present invention establishes a finite element model of corroded bridge piers based on the theoretical degradation model of corroded reinforced concrete. Taking into account the sudden external force, the structural nonlinear static analysis and nonlinear dynamic analysis are performed to obtain the bridge function loss function. The residual toughness of the corroded bridge pier structure is quantified by combining the recovery time and recovery function of the system under different damage states.

[0022] like Figure 1 As shown, a method for evaluating the collision toughness of a corroded steel bar bridge structure after a ship collision comprises the following steps: S1. Establish a finite element model of corroded bridge piers based on the theoretical degradation model of corroded reinforced concrete.

[0023] Long-term exposure to ocean winds and waves on coastal bridges accelerates chloride ion corrosion, leading to internal steel corrosion and external concrete cracking due to corrosion expansion, degrading the overall structural performance. Therefore, when developing the finite element model of corroded bridge piers, this paper considers the following four factors that contribute to structural degradation due to steel corrosion: a reduction in effective cross-sectional area of steel, a decrease in steel yield and ultimate strength, a decrease in steel-concrete bond strength, and a reduction in concrete tensile strength due to corrosion expansion.

[0024] Since chloride ions erode the protective layer and cause steel bar corrosion, the corrosion of bridge piers over relevant years was evaluated by considering the diameter and corrosion rate of the steel bars. The corrosion rate was calculated as follows: ; Where, is the steel corrosion rate, is the diameter of the uncorroded steel bar, is the diameter of the corroded steel bar.

[0025] Corrosion reduces the mechanical properties of steel bars, such as yield strength, ultimate strength, and ultimate elongation. The constitutive model of corroded steel bars is used to simulate the mechanical properties of naturally corroded steel bars in an atmospheric environment. The characteristic parameters of the constitutive model are as follows: ; ; ; ; Where, , are the effective cross-sectional area and ultimate strain of the uncorroded steel bars, respectively; , are the yield strength and ultimate strength of uncorroded steel bars, respectively; , are the yield strength and ultimate strength of the corroded steel bars, respectively; , are the effective cross-sectional area and ultimate strain of the corroded steel bars, respectively.

[0026] In coastal environments, chloride ions and sulfate ions can easily corrode bridge structures, causing degradation of structural performance. The reduction in the bond-slip strength between steel bars and concrete is simulated by coefficient reduction. The bond-slip strength relationship is as follows: ; ; Where, is the bond-slip relationship between corroded steel bars and concrete, is the bond-slip relationship between uncorroded steel bars and concrete, is the coefficient of reduction in bond strength between corroded steel bars and concrete.

[0027] Rebar corrosion produces rust, which reduces the bond-slip strength and also causes cracking of the concrete cover due to rust expansion, resulting in a decrease in the mechanical properties of the concrete cover. A reduction factor is introduced to simulate the strength degradation of the concrete cover. The calculation model is as follows: ; ; Where, , are the compressive strength of the cover concrete before and after steel bar corrosion; Take 0.1; is the average tensile strain caused by corrosion expansion and cracking of the cover concrete; is the compressive strain corresponding to the maximum stress of the uncorroded concrete; is the number of main reinforcements in the cross section of the pier column; is the diameter of the uncorroded main reinforcement; is the cross-sectional perimeter of the pier specimen.

[0028] Due to the restraining effect of the stirrups on the concrete, the tensile and compressive strength of the core area concrete is improved. Corrosion causes the restraint coefficient of the stirrups to decrease. Based on the Mander model, the present invention uses the constitutive model of concrete restrained by circular corroded stirrups to calculate the strength of the core area concrete as follows: ; ; ; ; Where, is the volumetric reinforcement ratio of transverse reinforcement in corrosion-confined concrete; is the volumetric reinforcement ratio of the transverse reinforcement of the uncorroded confined concrete; is the yield strength of the transverse reinforcement; is the yield strength of the corroded transverse reinforcement; is the effective lateral restraint stress; is the compressive strength of unconfined concrete; is the compressive strength of corrosion-confined concrete; is the yield strength reduction factor of the corroded transverse reinforcement; is the stress correction coefficient obtained after regression analysis of the test data; is the constraint effectiveness coefficient.

[0029] S2. Use the equivalent static method to simulate ship collision and determine the dynamic damage factors of the ship.

[0030] There are three main ship collision calculation methods: equivalent static method, simplified dynamic calculation model, and high-precision finite element simulation. The equivalent static method is easy to use because of its simple calculation formula. Therefore, the present invention uses the equivalent static method to simulate ship collision and determine the dynamic damage factors of the ship, including the barge impact force, full load displacement and ship impact speed.

[0031] Since the simulated ship in the present invention is a barge, which has a much smaller mass than a ship, the barge impact force is calculated using a fitting formula obtained through mathematical statistics of barge collisions. The calculation formula is as follows: ; Where, F is the design value of the barge impact force, M is the full load displacement (t), V is the ship impact speed (m / s).

[0032] S3. Considering the sudden external force, the nonlinear static analysis and nonlinear dynamic analysis of the structure are performed to obtain the bridge function loss function. The bridge function loss function includes the initial corrosion pier function loss function and the impact function loss function. The bridge function function is then calculated based on the bridge function loss function.

[0033] The present invention quantifies the residual function of reinforced concrete structures with different degrees of corrosion through nonlinear static analysis. The ultimate compressive bearing capacity obtained through nonlinear static analysis of corroded bridge piers is used as an indicator of the residual function of the structure. The quantitative formula for the functional loss function of initially corroded bridge piers under different corrosion rates is as follows: ; Where, is the maximum vertical bearing capacity of the pier in the uncorroded state; is the time-varying maximum vertical bearing capacity of the structure.

[0034] Loss function of concrete subjected to impact under corrosion conditions It can be calculated through the fragility curves corresponding to different states, that is, the product of the probability of structural failure under different damage states and the structural damage ratio under the corresponding state, as shown in the following formula: ; Where, j= 1, 2, 3, 4, and 5 correspond to five damage levels from basically intact to collapsed; is the structural damage ratio under the corresponding state, and the present invention takes the median value of each damage state interval; Status j The probability of structural damage under different conditions is calculated based on the damage probability: ; Where, Status j The probability of structural damage under different working conditions is obtained by nonlinear dynamic analysis of the residual bearing capacity of the piers under different working conditions, and then the vulnerability analysis under different damage conditions is obtained. In the past few decades, most researchers have proposed that the toughness of the structure depends to a large extent on the time-varying system function of the structure after the disaster event. The present invention refers to the seismic toughness assessment. In the event of an earthquake, the definition of the disaster toughness of the corroded reinforced concrete structure is as shown in the figure Figure 2 shown.

[0035] Bridge Function It is a normalized structural function. The system function of a structure is evaluated by its collision resistance. For reinforced concrete structures, the collision toughness of the structure can be quantified by the following formula: ; Where, R It is the structural impact toughness; t is the time variable; t OE is the time when the impact event occurred; T RE It is the time it takes for the structure to be repaired after a ship collision.

[0036] Bridge Function Defined as: ; Where, is the functional loss function of concrete subjected to impact in the case of corrosion; is the recovery function; is a step function.

[0037] The present invention takes into account the initial corrosion of the bridge piers. The functional function of the bridge has already degraded before the impact disaster occurs. Redefine as: ; Where, C is the corrosion strength; is the functional loss function of concrete subjected to impact in the case of corrosion; is the functional loss function of the initial corroded bridge pier, is a step function, is the recovery function, t is the time variable.

[0038] S4. Use the response surface method (RSM) to build a proxy model for dynamic response prediction. Specifically: The BBD method in the response surface methodology was adopted, and the Design-Expert software was used to design and analyze different working conditions. A three-factor three-level design analysis was carried out with the corrosion rate, impact velocity and impact tonnage as the response independent variables and the residual bearing capacity as the dependent variable.

[0039] S5. Determine the criteria for judging the damage status of bridge structures; Structural vulnerability refers to the conditional probability of a structure exceeding a predetermined limit state under the action of disasters of varying intensities. This indicator is used to quantitatively describe the relationship between the intensity of the disaster load and the degree of structural damage. The probability that the dynamic response of a structure under a disaster exceeds the predetermined limit state can be expressed as: ; Where, For different states j The probability of structural damage is is the ultimate compressive bearing capacity of the structure, is the ship impact speed, The structure in different damage states j The lower limit state.

[0040] Since bridge piers are an important part of the bridge structure, their core function is to stably bear and effectively transmit the vertical loads from the superstructure. Therefore, the vertical bearing capacity of bridge piers can be used as an important evaluation indicator after they are damaged.

[0041] That is, the ultimate compressive bearing capacity of the structure is selected as the limit state standard, and four limit states are selected according to the loss ratio level. 、 、 、 The limit values correspond to 10%, 20%, 40%, and 70% of the ultimate compressive bearing capacity. As shown in Table 1, according to the range of loss of the ultimate compressive bearing capacity of the structure Determine the damage status and the judgment criteria are as follows: like <10%, the damage status is basically intact; If 10%≤ <20%, the damage status is slight damage; If 20%≤ <40%, the damage status is moderate damage; If 40%≤ <70%, the damage status is severe damage; like ≥70%, the damage state is collapse.

[0042] Table 1 Damage status range values ;

[0043] in, , is the residual bearing capacity after damage, is the ultimate compressive bearing capacity of the structure.

[0044] S6. Calculate the vulnerability of corroded bridges through Monte Carlo simulation.

[0045] Fragility analysis requires obtaining mechanical response data of the structure under different working conditions. The cost of simulation calculation using finite element method is too high. Figure 3 As shown, the present invention adopts the above-mentioned response surface methodology (RSM) to obtain a proxy model for dynamic response prediction; then, based on the statistical distribution of the cross-sectional resistance of the concrete component and the statistical distribution of the ship tonnage, the failure probability of each damage state is obtained by Monte Carlo simulation, and finally the fragility curve of the ship hitting the bridge pier is obtained.

[0046] S7. Calculate the structural anti-collision toughness index based on the bridge function loss function, i.e., the initial corrosion pier function loss and the impact function loss function, combined with the repair time and recovery function.

[0047] Repair time refers to the time it takes to restore a bridge from a damaged state to a normal usable state. The repair time is related to the damage state of the bridge. The greater the degree of damage, the longer the required repair time, i.e., the maintenance and repair time. The repair times for different damage states are given as 0d, 0d, 2d, 21.2d, and 60d. Among them, the repair time for both the basically intact and slightly damaged damage states is given as 0d.

[0048] Functional recovery function is mainly used to describe the process of gradual recovery of the performance or function of a bridge after a disaster. However, the repair process takes into account too many factors, such as material allocation, funds, personnel allocation, repair strategy and seasonal environment. This paper cites three empirical functional recovery functions, namely triangular functional recovery function , negative exponential function recovery function and linear function recovery function , and its calculation formula is as follows: ; ; ; Where, a and b are two constants fitted through the data, which are related to the damage state and the recovery state; t OE is the time when the impact event occurred; T RE It is the time it takes for the structure to be repaired after a ship collision.

[0049] The linear recovery function is the simplest form of recovery when there are no advance preparations for available resources or disaster prevention and emergency measures. When available resources are prepared in advance, the recovery speed accelerates with the initial inflow of resources, but the recovery speed decreases as the recovery process progresses, so a negative exponential recovery function can be used. When disaster prevention and emergency response capabilities and recovery are limited, but once the disaster prevention and emergency department allocates resources to gradually restore the system, the recovery system will begin to operate, increasing the recovery speed, so a triangular recovery function can be used. Based on actual conditions, this invention uses a negative exponential recovery function for resilience assessment.

[0050] Example 1

[0051] (1) Establishment of finite element model of bridge pier

[0052] During the ship-to-bridge collision process, the impact duration is short and the main dynamic response is on the pier. Therefore, the calculation cost of a detailed whole-bridge model is high. Therefore, this embodiment uses a single pier model instead of the whole-bridge model for analysis. The superstructure will produce inertia during the impact process. Assuming that the superstructure is replaced by a rigid mass block, the gravity of the rigid mass block depends on 10% of the vertical compressive bearing capacity of the pier. The finite element model of the pier is as follows: Figure 4 As shown in the figure, the pier is 15m high and 1.4m in diameter. The concrete grade is C40, the longitudinal reinforcement and stirrup grade are HRB400, the longitudinal reinforcement diameter is 28mm, the reinforcement ratio is 1.12%, the stirrup diameter is 16mm, and the spacing is 200mm. The pile-soil effect at the bottom of the pier is ignored. The boundary condition at the bottom is fixed constraint, and the vertical degrees of freedom at the top are released.

[0053] (2) Material model

[0054] The concrete behavior was simulated using the CPD model of finite element software. The concrete material used was the eight-node hexahedral linear reduced volume element C3D8R. The concrete damage parameters were calculated using the Sidoroff energy equivalence principle.

[0055] The steel bar adopts the elastic-plastic model, the element adopts the two-node spatial linear beam element B31, and the concrete material parameters are shown in Table 2.

[0056] Table 2 Concrete material parameters ;

[0057] in, is the density, in units of ; E is the elastic modulus, in MPa; is Poisson's ratio; is the eccentricity; is the ratio of the biaxial ultimate compressive strength to the uniaxial ultimate compressive strength; K is the ratio of the second stress invariant on the tensile meridian plane to that on the compressive meridian plane; is the expansion angle; is the viscosity coefficient.

[0058] The bond-slip relationship between steel bars and concrete is achieved by establishing a connector element between the longitudinal reinforcement node and the corresponding concrete node and defining its interface properties. Since the steel bar slips in the direction perpendicular to the cross section, the translation type is selected as Cartesian in the Connection Type. At the same time, the two directions perpendicular to the axis of the steel bar are defined as rigid connections. The nonlinear force parallel to the axis of the steel bar can be calculated by multiplying the surface area of the steel bar node element by the stress.

[0059] (3) Calculation conditions

[0060] The simulation calculation of a ship impacting a bridge pier requires consideration of the selection of ship parameters. Since the ship variables considered in this example are the ship's impact velocity and tonnage, the impact height is defaulted to the middle of the pier. Furthermore, the study focuses on the impact of ships impacting corroded piers in Class III and IV waterways. According to relevant standards, the maximum tonnage of ships designed for Class III and IV waterways corresponds to a tonnage of 1000t and 500t. Regarding the impact velocity, statistics show that the average impact velocity of inland waterway barges striking bridges is approximately 2m / s. The minimum impact velocity for bridge collision analysis specified in the AASHTO specification is 0.514m / s. Therefore, the impact velocity in this example will be within the range of 0.5m / s to 3m / s.

[0061] The main structural response parameters obtained through the above analysis are corrosion rate, impact velocity and impact tonnage. In order to save calculation cost and improve efficiency, the response surface method is used to establish a proxy model for dynamic response prediction. The Box-Behnken (BBD) design method in the response surface method is adopted. By using Design-Expert software to perform different working condition designs and analyses, the corrosion rate, impact velocity and impact tonnage are used as response independent variables, and the residual bearing capacity is used as the dependent variable to perform a three-factor three-level design analysis, as shown in Table 3.

[0062] Table 3 Response surface experiment factors and levels ;

[0063] (4) Finite element simulation damage results

[0064] 1. Nonlinear static analysis

[0065] A vertical axial compression simulation was carried out on the corroded bridge piers to explore the vertical residual bearing capacity of corroded reinforced concrete under different degrees of corrosion. The axial compression simulation adopted nonlinear static analysis, and the constraint method of the pier bottom was consolidation to prevent the load application from causing a sudden change in the numerical calculation. The load curve used a smooth step curve to apply the vertical load. The pier reaction force reached a peak value as the vertical load was gradually applied, and then decreased, and this peak value was used as the residual load of the pier. Based on the corroded reinforced concrete model, axial compression experiments were carried out by applying a smooth step curve load to the corroded reinforced concrete model with corrosion rates of 0%, 7.5% and 15%. The coupled constraint reaction force of the corroded reinforced concrete corresponding to different axial compression displacements was extracted. When the corrosion rate is 0%, that is, the initial state of the pier, the residual bearing capacity of the pier can be obtained according to the calculation formula of the compressive bearing capacity of the positive section of the reinforced concrete axially compressed member, as shown below: ; Where, is the axial force; is the stability coefficient of the axial compression member, which is 0.95 in this embodiment; is the axial compressive strength of concrete; is the compressive strength of the longitudinal reinforcement, is the gross cross-sectional area of the component, is the cross-sectional area of all longitudinal reinforcements.

[0066] 2. Nonlinear dynamic analysis

[0067] Using the BBD design method, a three-factor, three-level design analysis was conducted with corrosion rate, impact velocity, and impact tonnage as independent variables and residual bearing capacity as the dependent variable, resulting in 17 load conditions. Nonlinear dynamic analysis was then performed using finite element software. The equivalent static method was employed to account for ship impact loads. First, a mass gravity load was applied to the top to replace the bridge superstructure. Next, a static load equivalent to ship impact was applied to the middle of the pier until the structure stabilized. To prevent sudden changes in simulation values, a smooth step load curve was used. Finally, vertical loads were applied to the piers, and the peak value of the pier coupling constraint reaction was taken as the residual bearing capacity of the structure.

[0068] Under different working conditions, the concrete and steel damage characteristics of the structure failure after the equivalent static load is applied to stabilize the structure and the vertical load is gradually applied are as follows: Figure 5-Figure 6 As shown, this embodiment provides stress cloud diagrams of structural stability and structural damage under four working conditions, where Figure 5 (a) in - Figure 5 (d) in the figure are the structural stability stress cloud diagrams.

[0069] According to the comparison of stress cloud maps, the increased degree of corrosion and greater impact kinetic energy will lead to greater structural stress when the structure is stable. The ship impact location is in the middle of the pier, the stress response in the middle is greater than that at both ends, and the failure form of the pier tends to be shear failure.

[0070] like Figure 6 (a) in - Figure 6 (d) in the figure is the stress cloud diagram of the bridge pier structure failing under vertical load. After the structure stabilizes, vertical load is gradually applied until the structure fails. Before failure, the structural coupling reaction force reaches its maximum value and then decays rapidly.

[0071] (5) Response Agent Model

[0072] Based on nonlinear dynamic analysis, the residual bearing capacity of the structure under different working conditions can be calculated. The absolute value of the peak bearing capacity is taken as the response value. The response values of all working conditions are summarized for analysis. The analysis is based on the three-factor influence surface. The three influencing factors are corrosion rate (A), ship tonnage (B), and ship speed (C). The objective function is the residual bearing capacity of the pier column (R). The working condition design and response values are shown in Table 4.

[0073] Table 4 Response surface experimental design ;

[0074] Taking the corrosion rate, ship tonnage, and speed as the response variables and the residual load of the pier column as the objective function, the data in Table 4 were analyzed and processed, and the variance analysis of the regression equation based on the Box-Behnken matrix sampling method was obtained, as shown in Table 5.

[0075] Table 5 Analysis of variance of three-factor response surface regression model ;

[0076] The regression analysis results in Table 5 show that the Model P value is less than 0.001, indicating that the model fit is highly significant and has a good fit. According to the regression variance analysis significance experiment, when the significance level P value of each parameter statistical characteristic quantity is less than 0.05, it can be concluded that this parameter is a significant parameter, that is, this parameter is the main factor affecting the accuracy of the model. Based on this, from the various analysis results of the regression model in Table 5, it can be seen that factors AB, AC, and B 2 For non-significant model items, based on the above results, we select polynomials to perform regression fitting between the response value and each factor, and then we can get the response surface function model. As shown in the following formula: ; The statistical parameters of model goodness of fit are shown in Table 6 below: Table 6 Response surface model fitting statistics ;

[0077] Table 6 shows that the model's coefficient of determination (R² = 0.9944) and adjusted coefficient of determination (Adjusted R² = 0.9871) are both close to 1, indicating that the model explains over 98% of the response variation and exhibits high fitting accuracy. The difference between the predicted coefficient of determination (Predicted R² = 0.9096) and the adjusted R² is 0.0775 (<0.2), indicating that the model is not overfitting and that the prediction results are consistent with the experimental data. The signal-to-noise ratio (Adeq Precision = 46.38) is well above the threshold of 4, demonstrating that the model can effectively discriminate between noise interference.

[0078] (6) Vulnerability analysis

[0079] The vertical bearing capacity of the piers is determined based on the damage index of the piers. The residual bearing capacity of the structure under different working conditions can be calculated using a response surface proxy model. When calculating the vulnerability of bridge structures, the randomness of basic parameters must be considered. Since this example primarily studies the impact of ships impacting corroded piers in Class III and IV waterways, based on the maximum tonnage of ships designed for the waterway, a normal probability distribution with a coefficient of variation of 0.3 can be assumed. For different damage levels, the cross-sectional resistance of the piers can be calculated by multiplying the initial structural bearing capacity by the degree of damage. The coefficient of variation of the cross-sectional resistance is 0.080-0.085.

[0080] The vulnerability of a bridge pier after a ship collision is defined as the vulnerability of the bridge pier to the ship's speed. VThe probability of the pier reaching or exceeding a certain limit state or performance level under the action of a ship collision is calculated. Based on the determination of the damage degree of the working condition, the number of sample points reaching each level of damage degree at each specified ship speed is further counted and divided by the number of Monte Carlo sampling times N, thereby obtaining the probability of the pier reaching different damage degrees at the speed. Finally, the probabilities of the pier being at different damage degrees under each ship speed collision at different damage levels are connected to draw a vulnerability curve, as shown in the figure below. Figure 7 As shown in the figure. Since the corrosion rate is 0%, the impact speed and impact tonnage are relatively small, making the failure probability of structural collapse and severe damage state almost close to 0. And according to the failure probability curve of different states, the probability of structural damage under different limit states is calculated. When the corrosion rate is 0%, the probability of structural damage under different limit states is as follows: Figure 8 The probability of structural damage is calculated from the failure probability, so when the corrosion rate is 0%, the probability of structural collapse and severe damage caused by the impact velocity and impact tonnage under the present invention is almost close to 0.

[0081] The vulnerability curves for ships impacting bridge piers under different damage states show that the more severe the corrosion, the higher the probability of failure of the pier at the same damage level under the same impact conditions. The impact becomes more pronounced as the impact velocity increases and the corrosion level worsens.

[0082] (7) Impact toughness assessment

[0083] The initial damage of the pier under corrosion is determined by nonlinear static analysis, and the impact of different working conditions on the performance of the corroded pier is determined by nonlinear dynamic analysis. The toughness of the pier is quantified by combining the recovery time and recovery function of the structure under different damage levels.

[0084] from Figure 9 It can be seen that the more severe the corrosion, the greater the initial loss of toughness, which is consistent with the damage determined by nonlinear static analysis. Furthermore, as the impact velocity increases, the impact load increases, causing the structure's impact toughness to begin to decrease. Under the same external load, impact toughness decreases with increasing corrosion rate, but the impact of corrosion rate on the impact toughness of the pier gradually weakens.

[0085] Therefore, the present invention adopts the above-mentioned method for evaluating the impact toughness of a corroded steel bridge structure after a ship collision. By establishing a finite element model of the bridge pier that takes into account the influence of steel corrosion, using the equivalent static method to simulate ship collisions, and comprehensively applying nonlinear analysis, response surface methodology, Monte Carlo simulation and other means, the damage state judgment criteria of the bridge structure are determined and the impact toughness index of the structure is quantified. This method fully considers the complex mechanical behavior and various uncertainties of the bridge structure under the effects of corrosion and ship collisions. The evaluation process is scientific and rigorous, and the results are accurate and reliable. It provides an effective way to evaluate the safety and improve the toughness of corroded steel bridge structures under ship collision disasters.

[0086] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for evaluating the collision toughness of a corroded steel bar bridge structure after a ship collision, characterized in that: The following steps are involved: S1. Establish a finite element model of corroded bridge piers based on the theoretical degradation model of corroded reinforced concrete; S2. Use the equivalent static method to simulate ship collision and determine the dynamic damage factors of the ship; S3. Considering the sudden external force, nonlinear static analysis and nonlinear dynamic analysis of the structure are performed to obtain the bridge function loss function, and then the bridge function function is calculated based on the bridge function loss function; S4. Construct a response surface proxy model to predict dynamic response; S5. Determine the criteria for judging the damage status of bridge structures; S6. Calculate the vulnerability of corroded bridges through Monte Carlo simulation; S7. Calculate the structural crash toughness index based on the bridge function loss function, combined with the repair time and recovery function.

2. The method for evaluating the collision toughness of a corroded steel bar bridge structure after a ship collision according to claim 1 is characterized in that: In S1, when establishing the finite element model of the corroded bridge pier, the structural performance degradation caused by steel bar corrosion was considered, including the reduction of the effective cross-sectional area of the steel bar, the reduction of the yield strength and ultimate strength of the steel bar, the reduction of the bond strength between the steel bar and concrete, and the reduction of the tensile strength of the concrete after corrosion expansion; Considering the diameter and corrosion rate of the pier steel bars, the corrosion condition of the piers was evaluated. The corrosion rate was calculated as follows: ； Where, is the steel corrosion rate, is the diameter of the uncorroded steel bar, is the diameter of the corroded steel bar; The constitutive model of corroded steel bar material is used to simulate the mechanical properties of naturally corroded steel bars in an atmospheric environment. The characteristic parameters of the constitutive model are as follows: ； ； ； ； Where, , are the effective cross-sectional area and ultimate strain of the uncorroded steel bars, respectively; , are the yield strength and ultimate strength of uncorroded steel bars, respectively; , are the yield strength and ultimate strength of the corroded steel bars, respectively; , are the effective cross-sectional area and ultimate strain of the corroded steel bars, respectively; The reduction in bond slip strength between steel bars and concrete caused by corrosion is simulated by coefficient reduction. The relationship between bond slip strength is as follows: ； ； Where, is the bond-slip relationship between corroded steel bars and concrete, is the bond-slip relationship between uncorroded steel bars and concrete, is the bond strength reduction coefficient between the corroded steel bars and concrete; The reduction factor is introduced to simulate the strength degradation of the concrete cover. The calculation model is as follows: ； ； Where, , are the compressive strength of the cover concrete before and after steel bar corrosion; Take 0.1; is the average tensile strain caused by corrosion expansion and cracking of the cover concrete; is the compressive strain corresponding to the maximum stress of the uncorroded concrete; is the number of main reinforcements in the cross section of the pier column; is the diameter of the uncorroded main reinforcement; is the cross-sectional perimeter of the pier specimen; The core area concrete strength is calculated based on the Mander model using the constitutive model of concrete confined by circular corroded stirrups as follows: ； ； ； ； Where, is the volumetric reinforcement ratio of transverse reinforcement in corrosion-confined concrete; is the volumetric reinforcement ratio of the transverse reinforcement of the uncorroded confined concrete; is the yield strength of the transverse reinforcement; is the yield strength of the corroded transverse reinforcement; is the effective lateral restraint stress; is the compressive strength of unconfined concrete; is the compressive strength of corrosion-confined concrete; is the yield strength reduction factor of the corroded transverse reinforcement; is the stress correction coefficient obtained after regression analysis of the test data; is the constraint effectiveness coefficient.

3. The method for evaluating the collision toughness of a corroded steel bar bridge structure after a ship collision according to claim 1 is characterized in that: In S2, the equivalent static method is used to simulate ship collisions and determine the dynamic damage factors of the ship, including the barge impact force, full load displacement, and ship impact speed. The barge impact force calculation formula is as follows: ； Where, F is the design value of the barge impact force, M is the full load displacement, V is the ship impact speed.

4. The method for evaluating the collision toughness of a corroded steel bar bridge structure after a ship collision according to claim 1 is characterized in that: In S3, the bridge function loss function includes the initial corrosion pier function loss function and the impact function loss function. Considering the initial corrosion of the pier, the ultimate compressive bearing capacity obtained by nonlinear static analysis of the corroded pier is used as the indicator of the structure's residual function. The quantitative formula of the initial corrosion pier function loss function under different corrosion rates is as follows: ； Where, is the maximum vertical bearing capacity of the pier in the uncorroded state; is the time-varying maximum vertical bearing capacity of the structure; Loss function of concrete subjected to impact under corrosion conditions The calculation is performed through the fragility curves corresponding to different states, that is, the product of the probability of structural failure under different damage states and the structural damage ratio under the corresponding state, as shown in the following formula: ； Where, Corresponding to five levels of injury status; is the structural damage ratio under the corresponding state; Status The probability of structural damage under different states is calculated based on the damage probability: ； Where, Status The probability of structural damage; Calculate the bridge function function based on the initial corrosion pier function loss function and the pier impact function loss function , whose expression is: ； Where, C is the corrosion strength; is the loss function of concrete subjected to impact in the case of corrosion; is the functional loss function of the initial corroded bridge pier, is a step function, is the recovery function, t is the time variable.

5. The method for evaluating the collision toughness of a corroded steel bar bridge structure after a ship collision according to claim 1 is characterized in that: In S4, the response surface methodology (RSM) is used to construct a proxy model for dynamic response prediction. Specifically: The BBD method in the response surface methodology was adopted, and the Design-Expert software was used to design and analyze different working conditions. A three-factor three-level design analysis was carried out with the corrosion rate, impact velocity and impact tonnage as the response independent variables and the residual bearing capacity as the dependent variable.

6. The method for evaluating the collision toughness of a corroded steel bar bridge structure after a ship collision according to claim 1 is characterized in that: In S5, the ultimate compressive bearing capacity of the structure is selected as the limit state standard, and the 、 、 、 The limit value corresponds to 10%, 20%, 40%, and 70% of the ultimate compressive bearing capacity, according to the loss range of the ultimate compressive bearing capacity of the structure. Determine the damage status and the judgment criteria are as follows: like <10%, the damage status is basically intact; If 10%≤ <20%, the damage status is slight damage; If 20%≤ <40%, the damage status is moderate damage; If 40%≤ <70%, the damage status is severe damage; like ≥70%, the damage state is collapse; in, , is the residual bearing capacity after damage, is the ultimate compressive bearing capacity of the structure.

7. The method for evaluating the collision toughness of a corroded steel bar bridge structure after a ship collision according to claim 1 is characterized in that: In S6, based on the statistical distribution of concrete component cross-sectional resistance and ship tonnage, Monte Carlo simulation was used to obtain the failure probability of each damage state, and finally the fragility curve of the ship hitting the bridge pier was obtained.

8. The method for evaluating the collision toughness of a corroded steel bar bridge structure after a ship collision according to claim 1 is characterized in that: In S7, the repair time refers to the time it takes for a bridge to be repaired from a damaged state to a normal use state. The repair time of a bridge is related to the damage state of the bridge. The greater the damage, the longer the repair time. The recovery time of different damage states can be obtained based on the repair time. The negative exponential recovery function is used to evaluate the toughness, and the calculation formula is as follows: ； Where, and b are two constants fitted through the data, which are related to the damage state and the recovery state; t OE is the time when the impact event occurred; T RE It is the time it takes to repair the structure after a ship collision.

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