A method for assessing the impact toughness of corroded reinforced steel bridge structures after a ship collision

Abstract

This invention relates to the field of transportation infrastructure maintenance technology, specifically disclosing a method for assessing the impact toughness of corroded reinforced concrete bridge structures after a ship collision. The method includes the following steps: first, establishing a finite element model of the corroded bridge pier based on a theoretical degradation model of corroded reinforced concrete; second, simulating a ship collision using the equivalent static method to determine the dynamic damage factors of the ship; third, considering sudden external forces, performing nonlinear static and nonlinear dynamic analyses of the structure to obtain the bridge's functional loss function, and then calculating the bridge's functional function; fourth, constructing a response surface proxy model to predict the dynamic response; fifth, determining the criteria for judging the bridge's structural damage state; sixth, calculating the vulnerability of the corroded bridge through Monte Carlo simulation; and finally, calculating the structural impact toughness index based on the bridge's functional loss function, combined with repair time and recovery function. The method proposed in this invention fills the gap in assessing the impact toughness of coastal corroded bridge piers, providing a scientific basis for bridge safety assessment and maintenance decisions, and is of great significance for ensuring the safe operation of bridges.

Description

Technical Field

[0001] This invention relates to the field of transportation infrastructure maintenance technology, and in particular to a method for assessing the impact toughness of a rusted steel bridge structure after a ship collision. Background Technology

[0002] For coastal bridges, ship collisions are among the most severe loads, easily causing serious damage or even collapse, disrupting transportation systems and leading to safety incidents. During an impact, bridge piers may suffer shear failure or even total overturning, and the superstructure faces the risk of beam collapse, severely challenging the overall structural integrity. Such accidents not only directly cause severe bridge damage or even complete collapse, but also result in significant casualties, disruption of critical transportation routes, economic losses, and social impacts, posing a serious threat to the resilience and reliability of transportation systems. Therefore, researching the structural performance degradation of bridges after ship collisions and their ability to repair themselves to their initial state after an impact is particularly important.

[0003] Current research on structural toughness primarily focuses on a structure's ability to resist external disasters or its recovery efficiency after being affected by disasters. Toughness is evaluated from four aspects: redundancy, robustness, speed, and strategy. Toughness assessment is relatively limited in the engineering field, and engineering research on toughness is concentrated on seismic toughness. Regarding seismic toughness, various quantitative methods have been proposed. For example, a simplified probabilistic risk assessment method quantifies a building's seismic resistance by introducing the average annual repair time. Other studies have considered the coupling effect of earthquakes and corrosive environments, using a probabilistic framework to assess the toughness of aged reinforced concrete (RC) bridge piers with different failure modes. In contrast, research on the impact of other disasters (such as ship collisions, floods, hurricanes, explosions, and tsunamis) on bridge toughness is significantly insufficient. For example, in the field of coastal bridges, some studies have proposed quantitative expressions specifically for assessing the wave toughness of bridges based on the performance-based earthquake engineering (PBEE) framework; for coastal reinforced concrete bridges, some studies have established methods for assessing their toughness under multiple disasters by combining multiple indicators such as repair time, repair cost and carbon footprint; and in terms of blast disasters, reviews have summarized the core scientific questions and challenges in the research on the blast toughness of critical infrastructure.

[0004] Coastal bridges are constantly subjected to seawater erosion and the impact of waves. Cracks appear on the surface of the concrete structure, accelerating the corrosion of reinforced concrete by chloride ions. When the chloride ion concentration on the surface of the reinforcing steel exceeds a certain critical value, the passivation film on the steel surface is destroyed, leading to steel corrosion. Studies have shown that steel corrosion reduces the yield strength and effective cross-sectional area of ​​the steel. The rust produced on the surface of the corroded steel is several times the volume of the steel section loss, causing cracks in the concrete cover due to rust expansion, resulting in deterioration of the concrete structure's performance. Most scholars have made some progress in the study of the effects of single corrosion and the toughness assessment under the coupled effects of corrosion and earthquakes, but research on the impact toughness assessment of coastal bridge piers that are prone to corrosion is somewhat lacking. Summary of the Invention

[0005] The purpose of this invention is to provide a method for assessing the impact toughness of corroded reinforced steel bridge structures after a ship collision. This method addresses the problems of insufficient research, inaccurate assessment, and lack of quantitative basis for assessing the impact toughness of easily corroded bridge piers in coastal areas after a ship collision. Through comprehensive assessment using multiple methods, it achieves accurate simulation and quantification, fills a research gap, provides a scientific basis for bridge safety assessment and maintenance decisions, and ensures the safe operation of bridges.

[0006] To achieve the above objectives, the present invention provides a method for assessing the impact toughness of a corroded reinforced steel bridge structure after a ship collision, comprising the following steps:

[0007] S1. A finite element model of a corroded bridge pier was established based on the theoretical degradation model of corroded reinforced concrete.

[0008] S2. The equivalent static method is used to simulate ship impact and determine the dynamic damage factors of the ship.

[0009] S3. Considering the sudden external force, perform nonlinear static analysis and nonlinear dynamic analysis of the structure to obtain the bridge function loss function, and then calculate the bridge function function based on the bridge function loss function.

[0010] S4. Construct a response surface proxy model to predict dynamic response;

[0011] S5. Determine the criteria for judging the damage status of bridge structures;

[0012] S6. Calculate the vulnerability of corroded bridges using Monte Carlo simulation;

[0013] S7. Calculate the structural impact toughness index based on the bridge function loss function, combined with the repair time and recovery function.

[0014] Preferably, in S1, when establishing the finite element model of the corroded bridge pier, the structural performance deterioration caused by steel corrosion is considered, including the reduction of the effective cross-sectional area of ​​the steel, the reduction of the yield strength and ultimate strength of the steel, the reduction of the bond strength between the steel and the concrete, and the reduction of the tensile strength of the concrete after corrosion expansion.

[0015] Considering the diameter of the reinforcing steel bars in the bridge piers and the corrosion rate, the corrosion condition of the bridge piers is assessed, and the corrosion rate is calculated using the following formula:

[0016] ;

[0017] In the formula, For steel reinforcement corrosion rate, The diameter of the uncorroded steel bar. The diameter of the corroded steel bar;

[0018] A constitutive model of corroded steel reinforcement was used to simulate the mechanical properties of steel reinforcement exposed and corroded in an atmospheric environment. The characteristic parameters of the constitutive model were taken as follows:

[0019] ;

[0020] ;

[0021] ;

[0022] ;

[0023] In the formula, , These represent the effective cross-sectional area and ultimate strain of the uncorroded steel bars, respectively. , These are the yield strength and ultimate strength of the uncorroded steel bars, respectively. , These are the yield strength and ultimate strength of the corroded steel bars, respectively. , These represent the effective cross-sectional area and ultimate strain of the corroded steel bars, respectively.

[0024] The reduction in bond-slip strength between steel reinforcement and concrete caused by corrosion was simulated using a coefficient reduction method. The bond-slip strength relationship is as follows:

[0025] ;

[0026] ;

[0027] In the formula, This relates to the bond-slip relationship between corroded steel bars and concrete. This represents the bond-slip relationship between the uncorroded reinforcing steel and the concrete. The factor that reduces the bond strength between corroded steel bars and concrete;

[0028] A reduction factor is introduced to simulate the strength degradation of the concrete cover. The calculation model is as follows:

[0029] ;

[0030] ;

[0031] In the formula, , These represent the compressive strength of the protective concrete layer before and after steel reinforcement corrosion, respectively. Take 0.1; The average tensile strain caused by rust expansion and cracking of the protective concrete layer; This represents the compressive strain corresponding to the maximum stress in uncorroded concrete. This refers to the number of main reinforcement bars within the cross-section of the pier column. The diameter of the uncorroded main reinforcing bar; The perimeter of the cross-section of the pier specimen;

[0032] Based on the Mander model, the core area concrete strength was calculated using a constitutive model of concrete confined with circular corroded stirrups, as follows:

[0033] ;

[0034] ;

[0035] ;

[0036] ;

[0037] In the formula, The volumetric reinforcement ratio of transverse steel bars in corrosion-resisting concrete; The volumetric reinforcement ratio of transverse steel bars in uncorroded confined concrete; This represents the yield strength of the transverse reinforcement. The yield strength of the corroded transverse reinforcing steel; For effective lateral constraint stress; This refers to the compressive strength of unconfined concrete. The compressive strength of corrosion-restrained concrete; The coefficient for reducing the yield strength of corroded transverse reinforcing bars; The stress correction coefficient is obtained after regression analysis of the test data; This is the constraint effectiveness coefficient.

[0038] Preferably, in S2, the equivalent static method is used to simulate the ship impact and determine the dynamic damage factors of the ship, including the barge impact force, full load displacement, and ship impact speed. The formula for calculating the barge impact force is as follows:

[0039] ;

[0040] In the formula, F The design value for the barge impact force. M For full load displacement, V The speed at which the ship struck.

[0041] 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 from the nonlinear static analysis of the corroded pier is selected as the index of the remaining function of the structure. The quantification formula of the initial corrosion pier function loss function under different corrosion rates is as follows:

[0042] ;

[0043] In the formula, This represents the maximum vertical bearing capacity of the bridge pier in its uncorroded state. The maximum vertical bearing capacity of the structure is time-varying.

[0044] Loss function of concrete subjected to impact under corroded conditions The vulnerability curves corresponding to different states are used for calculation, which 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:

[0045] ;

[0046] In the formula, j= 1, 2, 3, 4, and 5 correspond to five damage status levels; This represents the structural damage ratio under the corresponding conditions. For state j The probability of structural failure under different conditions is calculated based on the failure probability.

[0047] ;

[0048] In the formula, For state j Probability of substructure failure;

[0049] The bridge function is calculated based on the initial corrosion pier function and the impact-induced pier function. Its expression is:

[0050] ;

[0051] In the formula, C Corrosion intensity; This is the loss function of concrete subjected to impact under corrosion conditions; The initial corrosion pier functional loss function, It is a step function. For recovery function, t It is a time variable.

[0052] Preferably, in S4, a surrogate model is constructed using the Response Surface Method (RSM) to predict the dynamic response. Specifically:

[0053] The BBD method in response surface methodology was adopted, and Design-Expert software was used to design and analyze different working conditions. Corrosion rate, impact velocity and impact tonnage were used as independent variables of response, and residual bearing capacity was used as dependent variable for three-factor, three-level design analysis.

[0054] Preferably, in S5, the structural compressive ultimate bearing capacity is selected as the ultimate limit state standard, and the following values ​​are taken respectively: , , , The limit values ​​correspond to 10%, 20%, 40%, and 70% of the ultimate compressive bearing capacity, based on the range of loss of the structure's ultimate compressive bearing capacity. The criteria for determining the damage state are as follows:

[0055] like If the damage rate is less than 10%, the damage status is considered basically intact.

[0056] If 10%≤ If the damage is less than 20%, the damage status is considered minor.

[0057] If 20%≤ If the damage is less than 40%, the damage status is moderate.

[0058] If 40%≤ If the damage rate is less than 70%, the damage status is considered severe.

[0059] like If ≥70%, the damage condition is collapse;

[0060] in, , To compensate for the remaining load-bearing capacity after damage, This refers to the ultimate compressive bearing capacity of the structure.

[0061] Preferably, in S6, based on the statistical distribution of the cross-sectional resistance of concrete components and the statistical distribution of ship tonnage, the failure probability of each damage state is obtained using Monte Carlo simulation, and finally the vulnerability curve of the ship impacting the bridge pier is obtained.

[0062] 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 service state. The bridge repair time is related to the damage state of the bridge. The greater the damage, the longer the repair time. The recovery time for different damage states is obtained based on the repair time.

[0063] The resilience assessment is performed using a negative exponential recovery function, calculated as follows:

[0064] ;

[0065] In the formula, a and b These are two constants fitted through data, and they are related to the damage state and the recovery state. t OE The time when the collision occurred; T RE This refers to the repair time for the structure after a ship collision.

[0066] Therefore, the present invention employs the above-mentioned method for assessing the impact toughness of a corroded reinforced steel bridge structure after a ship collision, and the beneficial effects are as follows:

[0067] (1) This invention 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, and combines the equivalent static method to accurately simulate the mechanical behavior of the bridge. Through comprehensive evaluation by multiple methods, the results are ensured to be scientific and reliable.

[0068] (2) In view of the lack of research on the impact toughness assessment of coastal bridge piers after being hit by ships, this invention provides a complete assessment scheme and improves the theoretical system in related fields.

[0069] (3) This 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.

[0070] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0071] Figure 1 This is an overall flowchart of an embodiment of the present invention, which describes a method for assessing the impact toughness of a corroded steel bridge structure after being struck by a ship.

[0072] Figure 2 This is a diagram illustrating the disaster resistance toughness of a corroded reinforced concrete structure, representing an embodiment of the present invention's method for assessing the impact toughness of a corroded reinforced concrete bridge structure after a ship collision.

[0073] Figure 3This is a flowchart illustrating the vulnerability analysis of an embodiment of the present invention, which describes a method for assessing the impact toughness of a corroded reinforced steel bridge structure after a ship collision.

[0074] Figure 4 This is a finite element diagram of a bridge pier according to an embodiment of the method for evaluating the impact toughness of a corroded steel bridge structure after being struck by a ship, as proposed by the present invention.

[0075] Figure 5 This is a structural stability stress cloud diagram under four working conditions of an embodiment of the method for evaluating the impact toughness of a corroded steel bridge structure after being struck by a ship, wherein (a) is the working condition of 7.5%-100t-3m / s, (b) is the working condition of 7.5%-700t-0.5m / s, (c) is the working condition of 15%-400t-3m / s, and (d) is the working condition of 15%-700t-1.75m / s.

[0076] Figure 6 This invention provides a method for evaluating the impact toughness of a corroded steel bridge structure after a ship collision, which includes stress cloud diagrams of a pier under vertical load failure under four working conditions. (a) is the working condition of 7.5%-100t-3m / s, (b) is the working condition of 7.5%-700t-0.5m / s, (c) is the working condition of 15%-400t-3m / s, and (d) is the working condition of 15%-700t-1.75m / s.

[0077] Figure 7 This invention provides an embodiment of a method for evaluating the impact toughness of a corroded reinforced steel bridge structure after a ship collision, showing the failure probabilities of bridge piers at different impact velocities for different levels, where (a) represents a corrosion rate of 0%, (b) represents a corrosion rate of 7.5%, and (c) represents a corrosion rate of 15%.

[0078] Figure 8 This is a graph showing the probability of pier failure under different damage states corresponding to different impact velocities when the corrosion rate is 0%, according to an embodiment of the method for evaluating the impact toughness of a corroded steel bridge structure after being hit by a ship, based on an embodiment of the present invention.

[0079] Figure 9 This is an example of an embodiment of the method for evaluating the impact toughness of a corroded steel bridge structure after being struck by a ship, showing the impact toughness curves of the bridge pier at different impact velocities. Detailed Implementation

[0080] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0081] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0082] This invention establishes a finite element model of a rusted bridge pier based on a theoretical degradation model of rusted reinforced concrete. Considering the sudden external force, nonlinear static analysis and nonlinear dynamic analysis of the structure are performed to obtain the bridge's functional loss function. Combining the recovery time and recovery function of the system under different damage states, the residual toughness of the rusted bridge pier structure is quantified.

[0083] like Figure 1 As shown, a method for assessing the impact toughness of a corroded reinforced steel bridge structure after a ship collision includes the following steps:

[0084] S1. A finite element model of a rusted bridge pier was established based on the theoretical degradation model of rusted reinforced concrete.

[0085] Coastal bridges are subject to long-term exposure to sea winds and waves, which accelerates chloride ion corrosion, leading to internal steel reinforcement corrosion and external concrete cracking due to rust expansion, thus reducing the overall structural performance. Therefore, this invention, in establishing the finite element model of the corroded bridge piers, considers the following four aspects of structural performance degradation caused by steel reinforcement corrosion: reduction in the effective cross-sectional area of ​​the steel reinforcement, reduction in the yield strength and ultimate strength of the steel reinforcement, reduction in the bond strength between the steel reinforcement and concrete, and reduction in the tensile strength of the concrete after rust expansion.

[0086] Since chloride ions corrode the protective layer, causing steel reinforcement corrosion, the corrosion status of bridge piers over relevant years is assessed, taking into account the diameter of the steel reinforcement and the corrosion rate. The corrosion rate is calculated using the following formula:

[0087] ;

[0088] In the formula, For steel reinforcement corrosion rate, The diameter of the uncorroded steel bar. The diameter of the corroded steel bar.

[0089] Corrosion reduces the yield strength, ultimate strength, and ultimate elongation of reinforcing steel. A constitutive model of corroded reinforcing steel is used to simulate the mechanical properties of steel naturally exposed and corroded in an atmospheric environment. The characteristic parameters of the constitutive model are taken as follows:

[0090] ;

[0091] ;

[0092] ;

[0093] ;

[0094] In the formula, , These represent the effective cross-sectional area and ultimate strain of the uncorroded steel bars, respectively. , These are the yield strength and ultimate strength of the uncorroded steel bars, respectively. , These are the yield strength and ultimate strength of the corroded steel bars, respectively. , These represent the effective cross-sectional area and ultimate strain of the corroded steel bars, respectively.

[0095] In coastal environments, chloride and sulfate ions easily corrode bridge structures, leading to a decline in structural performance. The reduced bond-slip strength between steel reinforcement and concrete is simulated using a coefficient reduction method. The bond-slip strength relationship is as follows:

[0096] ;

[0097] ;

[0098] In the formula, This relates to the bond-slip relationship between corroded steel bars and concrete. This represents the bond-slip relationship between the uncorroded reinforcing steel and the concrete. The factor that reduces the bond strength between corroded steel bars and concrete.

[0099] Reinforcing steel corrosion produces rust products, reducing bond-slip strength and causing cracking of the concrete cover due to rust expansion, leading to a decline 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:

[0100] ;

[0101] ;

[0102] In the formula, , These represent the compressive strength of the protective concrete layer before and after steel reinforcement corrosion, respectively. Take 0.1; The average tensile strain caused by rust expansion and cracking of the protective concrete layer; This represents the compressive strain corresponding to the maximum stress in uncorroded concrete. This refers to the number of main reinforcement bars within the cross-section of the pier column. The diameter of the uncorroded main reinforcing bar; The perimeter of the cross-section of the pier column specimen is given.

[0103] Because the confinement effect of stirrups on concrete increases the tensile and compressive strength of the core area concrete, corrosion reduces the confinement coefficient of the stirrups. This invention uses a constitutive model of concrete confined by circular corroded stirrups, based on the Mander model, to calculate the concrete strength in the core area, as follows:

[0104] ;

[0105] ;

[0106] ;

[0107] ;

[0108] In the formula, The volumetric reinforcement ratio of transverse steel bars in corrosion-resisting concrete; The volumetric reinforcement ratio of transverse steel bars in uncorroded confined concrete; This represents the yield strength of the transverse reinforcement. The yield strength of the corroded transverse reinforcing steel; For effective lateral constraint stress; This refers to the compressive strength of unconfined concrete. The compressive strength of corrosion-restrained concrete; The coefficient for reducing the yield strength of corroded transverse reinforcing bars; The stress correction coefficient is obtained after regression analysis of the test data; This is the constraint effectiveness coefficient.

[0109] S2. The equivalent static method is used to simulate ship impact and determine the dynamic damage factors of the ship.

[0110] There are three main methods for calculating ship impacts: equivalent static method, simplified dynamic calculation model, and high-precision finite element simulation. Since the equivalent static method is simple to calculate and easy to use, this invention uses the equivalent static method to simulate ship impacts and determine the dynamic damage factors of the ship, including barge impact force, full load displacement, and ship impact speed.

[0111] Since the simulated vessel in this invention is a barge, whose mass is much smaller than that of a ship, the barge impact force is calculated using a fitting formula obtained through mathematical statistics. The calculation formula is as follows:

[0112] ;

[0113] In the formula, F The design value for the barge impact force. M The full load displacement is (t). V The impact speed of the ship is (m / s).

[0114] S3. Considering the sudden external force, perform nonlinear static analysis and nonlinear dynamic analysis of the structure 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. Based on the bridge function loss function, the bridge function function is then calculated.

[0115] This invention quantifies the remaining function of reinforced concrete structures with different degrees of corrosion through nonlinear static analysis. The ultimate compressive bearing capacity obtained from nonlinear static analysis of corroded bridge piers is selected as the index of structural remaining function. The quantification formula of the function loss function of the initial corroded bridge pier under different corrosion rates is as follows:

[0116] ;

[0117] In the formula, This represents the maximum vertical bearing capacity of the bridge pier in its uncorroded state. The maximum vertical bearing capacity of the structure is time-varying.

[0118] Loss function of concrete subjected to impact under corroded conditions The vulnerability curves corresponding to different states can be used for calculation, which 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:

[0119] ;

[0120] In the formula, j= 1, 2, 3, 4, and 5 correspond to five damage levels, ranging from basically intact to collapsed. To determine the structural damage ratio under the corresponding conditions, this invention takes the median value of the range of each damage state interval; For state j The probability of substructure failure is calculated based on the failure probability under different conditions:

[0121] ;

[0122] In the formula, For state j The probability of structural failure is derived from the remaining bearing capacity of the pier obtained through nonlinear dynamic analysis of barge impacts on the pier under different working conditions, followed by vulnerability analysis under different damage states. Over the past few decades, most researchers have proposed that the toughness of a structure largely depends on the time-varying system function of the structure after a catastrophic event. This invention references seismic toughness assessment, defining the disaster toughness of corroded reinforced concrete structures under earthquake conditions as shown in the diagram. Figure 2 As shown.

[0123] Bridge Function It is a normalized structural function function. The system function of a structure is evaluated through its impact resistance. For reinforced concrete structures, the impact toughness of the structure can be quantified by the following formula:

[0124] ;

[0125] In the formula, RFor structural impact resistance; t It is a time variable; t OE The time when the collision occurred; T RE This refers to the repair time for the structure after a ship collision.

[0126] Bridge Function Defined as:

[0127] ;

[0128] In the formula, The functional loss function of concrete subjected to impact under corrosion conditions; For recovery functions; It is a step function.

[0129] This invention considers the initial corrosion of bridge piers, where the bridge's functional functions have already degraded before an impact disaster occurs. The invention then modifies the bridge's functional functions... Redefining:

[0130] ;

[0131] In the formula, C Corrosion intensity; The functional loss function of concrete subjected to impact under corrosion conditions; The initial corrosion pier functional loss function, It is a step function. For recovery function, t It is a time variable.

[0132] S4. Utilize the Response Surface Methodology (RSM) to construct a surrogate model for dynamic response prediction. Specifically:

[0133] The BBD method in response surface methodology was adopted, and Design-Expert software was used to design and analyze different working conditions. Corrosion rate, impact velocity and impact tonnage were used as independent variables of response, and residual bearing capacity was used as dependent variable for three-factor, three-level design analysis.

[0134] S5. Determine the criteria for judging the damage status of bridge structures;

[0135] Structural vulnerability refers to the conditional probability that a structure will exceed a predetermined limit state under disasters of varying intensities. This index is used to quantitatively describe the relationship between disaster load intensity and the degree of structural damage. The probability that the dynamic response of a structure exceeds a predetermined limit state under disaster loading can be expressed as:

[0136] ;

[0137] In the formula, For different states j Probability of substructure failure The ultimate compressive bearing capacity of the structure. For the ship's impact speed, For structures under different damage states j The limit state below.

[0138] Since bridge piers are an important component of bridge structures, their core function is to stably bear and effectively transfer vertical loads from the superstructure. Therefore, the vertical bearing capacity of bridge piers can be used as an important evaluation indicator after damage.

[0139] That is, the ultimate compressive bearing capacity of the structure is selected as the ultimate limit state standard, and four ultimate limits are selected according to the loss ratio level, and respectively... , , , The limit values ​​correspond to 10%, 20%, 40%, and 70% of the ultimate compressive bearing capacity. As shown in Table 1, the range of losses based on the ultimate compressive bearing capacity of the structure... The criteria for determining the damage state are as follows:

[0140] like If the damage rate is less than 10%, the damage status is considered basically intact.

[0141] If 10%≤ If the damage is less than 20%, the damage status is considered minor.

[0142] If 20%≤ If the damage is less than 40%, the damage status is moderate.

[0143] If 40%≤ If the damage rate is less than 70%, the damage status is considered severe.

[0144] like If ≥70%, the damage state is collapse.

[0145] Table 1 Damage Status Range Values

[0146] ;

[0147] in, , To compensate for the remaining load-bearing capacity after damage, This refers to the ultimate compressive bearing capacity of the structure.

[0148] S6. Calculate the vulnerability of corroded bridges using Monte Carlo simulation.

[0149] Vulnerability analysis requires obtaining mechanical response data of the structure under different working conditions. However, simulation calculations using the finite element method are too costly. Figure 3 As shown, this invention uses the above-mentioned response surface methodology (RSM) to obtain a surrogate model for dynamic response prediction; then, based on the statistical distribution of the cross-sectional resistance of concrete components and the statistical distribution of ship tonnage, Monte Carlo simulation is used to obtain the failure probability of each damage state, and finally the vulnerability curve of the ship impacting the bridge pier is obtained.

[0150] S7. Calculate the structural impact toughness index based on the bridge function loss function, namely the initial corrosion pier function loss and impact function loss function, combined with the repair time and recovery function.

[0151] Repair time refers to the time it takes for a bridge to be repaired from a damaged state to a normal usable state. Bridge repair time is related to the damage state of the bridge. The greater the damage, the longer the repair time, i.e., the maintenance time. The repair times for different damage states are given as 0d, 0d, 2d, 21.2d and 60d. Among them, the repair time for the two damage states of basically intact and slightly damaged is given as 0d.

[0152] Functional recovery functions are primarily used to describe the gradual recovery of a bridge's performance or function over time after a disaster. However, the repair process involves numerous factors, such as resource allocation, funding, personnel deployment, repair strategies, and seasonal conditions. This invention exemplifies three empirical functional recovery functions, namely the triangular functional recovery function. Negative exponential function of function recovery and linear function recovery function The calculation formula is as follows:

[0153] ;

[0154] ;

[0155] ;

[0156] In the formula, a and b These are two constants fitted through data, and they are related to the damage state and the recovery state. t OE The time when the collision occurred; T RE This refers to the repair time for the structure after a ship collision.

[0157] A linear recovery function represents the simplest form of recovery when there are no prior preparations for available resources and disaster preparedness measures. When available resources are prepared in advance, the recovery speed increases with the initial influx of resources, but decreases as the recovery process progresses; a negative exponential recovery function can be used in this case. When disaster preparedness and recovery capabilities are limited, but the recovery system begins to operate and the recovery speed increases once disaster preparedness departments allocate resources for gradual recovery, a triangular recovery function can be used. Based on practical considerations, this invention uses a negative exponential recovery function for resilience assessment.

[0158] Example 1

[0159] (1) Establishment of finite element model of bridge pier

[0160] During a ship-bridge pier collision, the impact time is short, and the main dynamic response occurs on the pier. Calculating a detailed full-bridge model would be costly. Therefore, this embodiment uses a single pier model instead of the entire bridge model for analysis. The superstructure experiences inertia during impact; assuming a rigid mass block replaces the superstructure, and considering that the weight of the rigid mass block depends on 10% of the pier's vertical compressive bearing capacity, the finite element model of the pier is as follows: Figure 4 As shown. The bridge pier is 15m high and 1.4m in diameter. The concrete grade is C40, the longitudinal reinforcement and stirrups 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 bridge pier is ignored. The lower part is subject to fixed boundary conditions, and the upper part is free of vertical degrees of freedom.

[0161] (2) Material Model

[0162] The plastic damage model (CPD) of finite element software was used to simulate the behavior of concrete. The concrete material was represented by an eight-node hexahedral linear reduced volume element C3D8R, and the concrete damage parameters were calculated using the Sidoroff energy equivalence principle.

[0163] The reinforcing steel is modeled using an elastoplastic model, and the element is a two-node spatial linear beam element B31. The concrete material parameters are shown in Table 2.

[0164] Table 2 Concrete material parameters

[0165] ;

[0166] in, Density, unit: ; E This refers to the elastic modulus, expressed in MPa. Poisson's ratio; Eccentricity; It is the ratio of biaxial ultimate compressive strength to uniaxial ultimate compressive strength; KThis is the ratio of the second stress invariant on the tensile meridional plane to that on the compressive meridional plane; It is the expansion angle; is the viscosity coefficient.

[0167] The bond-slip relationship between steel reinforcement and concrete is achieved by setting up connector elements between the longitudinal reinforcement nodes and the corresponding concrete nodes and defining their interface properties. Since the direction of steel reinforcement slippage is perpendicular to the cross section direction, the translation type is selected as Cartesian in the connection type. At the same time, the two directions perpendicular to the steel reinforcement axis are defined as rigid connections. The nonlinear force in the direction parallel to the steel reinforcement axis can be calculated by multiplying the surface area of ​​the steel reinforcement node element by the stress.

[0168] (3) Calculation of working conditions

[0169] Simulation calculations for ship impacts on bridge piers require consideration of ship parameter selection. This embodiment considers ship impact speed and tonnage as the ship variables, with the impact height assumed to be the middle of the pier. The main focus is on the impact of ships impacting corroded bridge piers in Class III and IV waterways. According to relevant standards, the maximum design tonnage for Class III and IV waterways corresponds to 1000t and 500t respectively. Regarding the impact speed, statistics show that the average speed of barges impacting bridges in inland waterways is approximately 2 m / s. The minimum impact speed for bridge collision analysis specified in the AASHTO standard is 0.514 m / s. Therefore, the impact speed in this embodiment will be within the range of 0.5 m / s to 3 m / s.

[0170] The main structural response parameters obtained from the above analysis are corrosion rate, impact velocity, and impact tonnage. In order to save computational costs and improve efficiency, a surrogate model is established using the response surface methodology to predict the dynamic response. The Box-Behnken (BBD) design method in the response surface methodology is adopted. Design-Expert software is used to design and analyze different working conditions. Corrosion rate, impact velocity, and impact tonnage are used as independent variables of the response, and the remaining bearing capacity is used as the dependent variable for three-factor, three-level design analysis, as shown in Table 3.

[0171] Table 3 Response Surface Experiment Factors and Levels

[0172] ;

[0173] (4) Damage results from finite element simulation

[0174] 1. Nonlinear static analysis

[0175] Vertical axial compression simulation was conducted on a corroded bridge pier to investigate the residual vertical bearing capacity of corroded reinforced concrete under different corrosion degrees. The axial compression simulation employed nonlinear static analysis, with the pier bottom constrained to prevent abrupt changes in numerical calculations caused by load application. A smoothed-step curve was used to apply the vertical load. The pier reaction force reached a peak and then decreased with the gradual application of the vertical load; this peak value was taken as the residual load of the pier. Based on the corroded reinforced concrete model, axial compression experiments were conducted on corroded reinforced concrete models with corrosion rates of 0%, 7.5%, and 15%, respectively, using smoothed-step curve loads. The coupled constraint reaction forces of the corroded reinforced concrete corresponding to different axial compression displacements were extracted. In the initial state of the pier (corrosion rate of 0%), the residual bearing capacity of the pier can be obtained using the formula for calculating the compressive bearing capacity of the normal section of a reinforced concrete axially compressed member, as follows:

[0176] ;

[0177] In the formula, It is an axial force; The stability coefficient for axially compressed components is 0.95 in this embodiment; This refers to the axial compressive strength of concrete. For longitudinal reinforcement compressive strength, The gross cross-sectional area of ​​the component. This represents the cross-sectional area of ​​all longitudinal reinforcing bars.

[0178] 2. Nonlinear dynamic analysis

[0179] Using the BBD design method with corrosion rate, impact velocity, and impact tonnage as independent variables and remaining bearing capacity as the dependent variable, a three-factor, three-level design analysis was conducted, resulting in 17 working conditions. Nonlinear dynamic analysis was performed using finite element software. When considering ship impact loads, an equivalent static method was employed. First, a mass block gravity load was applied to the top to replace the bridge superstructure. Second, an equivalent static ship impact load was applied to the middle of the piers until the structure stabilized. Again, to prevent abrupt changes in simulation values, a smoothed-step load curve was used. Finally, a vertical load was applied to the piers, and the peak value of the coupled constraint reaction force of the piers was taken as the remaining bearing capacity of the structure.

[0180] The damage characteristics of concrete and steel reinforcement under different working conditions, including after the structure stabilizes under equivalent static load and after the structure fails under progressive vertical load, are as follows: Figures 5-6 As shown in the figure, this embodiment presents stress cloud diagrams for structural stability and structural damage under four working conditions, wherein... Figure 5 (a) in Figure 5 (d) in the figure represents the structural stability stress cloud diagram.

[0181] According to the comparison of stress cloud diagrams, the increased degree of corrosion and the 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, and the stress response in the middle is greater than that at both ends. Moreover, the failure mode of the pier shows a shear failure trend.

[0182] like Figure 6 (a) in Figure 6 (d) in the figure is the stress cloud diagram of the bridge pier under vertical load failure. After the structure stabilizes, vertical loads are gradually applied until the structure fails. Before failure, the coupled reaction force of the structure reaches its maximum value and then rapidly decays.

[0183] (5) Response Proxy Model

[0184] The remaining bearing capacity of the structure under different working conditions can be calculated based on nonlinear dynamic analysis. The absolute value of the peak bearing capacity is taken as the response value. All working condition response values ​​are summarized and analyzed. The analysis is carried out using a three-factor influence surface. The three influencing factors are corrosion rate (A), ship tonnage (B), and ship speed (C). The objective function is the remaining bearing capacity (R) of the bridge pier column. The working condition design and response values ​​are shown in Table 4.

[0185] Table 4 Response Surface Experimental Design

[0186] ;

[0187] Using corrosion rate, ship tonnage, and speed as response variables, and the remaining bearing capacity of bridge piers as the objective function, the data in Table 4 were analyzed and processed to obtain the variance analysis of the regression equation based on the Box-Behnken matrix sampling method, as shown in Table 5.

[0188] Table 5. Analysis of variance of the three-factor response surface regression model

[0189] ;

[0190] Analyzing the regression analysis results in Table 5, the p-value of Model is less than 0.001, indicating that the model fit is highly significant and has a very good fit. According to the significance experiment of regression variance analysis, when the p-value of each parameter's statistical characteristic is less than 0.05, the parameter can be considered a significant parameter, meaning that this parameter is the main factor affecting the accuracy of the model. Therefore, based on the analysis results of the regression model in Table 5, factors AB, AC, and B... 2 For insignificant model terms, based on the above results, a polynomial is selected to perform regression fitting between the response values ​​and each factor, thus obtaining the response surface function model, as shown in the following equation:

[0191] ;

[0192] The statistical parameters of the model fit are shown in Table 6 below:

[0193] Table 6 Statistical Indicators for Response Surface Model Fit

[0194] ;

[0195] As shown in Table 6, 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 can explain more than 98% of the response value variation and has 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 does not exhibit overfitting and the prediction results are in good agreement with the experimental data. The signal-to-noise ratio (Adeq Precision = 46.38) is much higher than the threshold of 4, proving that the model can effectively distinguish noise interference.

[0196] (6) Vulnerability Analysis

[0197] The vertical bearing capacity of the bridge piers is determined based on their damage indices. The remaining structural bearing capacity under different working conditions can be calculated using a response surface surrogate model. When calculating the vulnerability of bridge structures, the randomness of basic parameters needs to be considered. Since this embodiment mainly studies the impact of ship impacts on corroded bridge piers in Class III and IV waterways, based on the maximum tonnage of ships designed for the waterway, it can be assumed that the probability distribution of ship tonnage is normally distributed with a coefficient of variation of 0.3. For different damage levels, the pier section resistance can be obtained by multiplying the initial structural bearing capacity by the degree of damage; the coefficient of variation for the section resistance is 0.080~0.085.

[0198] The vulnerability of bridge piers after a ship collision is defined as the vulnerability of bridge piers to damage caused by a ship's speed. V Under the impact of a ship collision, the probability of the pier reaching or exceeding a certain limit state or performance level is calculated. Based on determining the degree of damage under the working condition, the number of sample points reaching each damage level at each specified ship speed is further counted and divided by the number of Monte Carlo samplings N to obtain the probability of the pier reaching different damage levels at that speed. Finally, by connecting the probabilities of the pier being at different damage levels under different ship collision speeds at different damage levels, a vulnerability curve can be plotted, such as... Figure 7 As shown in the figure, due to the 0% corrosion rate, relatively small impact velocity and impact tonnage, the failure probability of structural collapse and severe damage is almost zero. Furthermore, based on the failure probability curves for different states, the probability of structural failure under different limit states is calculated. When the corrosion rate is 0%, the probability of structural failure under different limit states is as follows: Figure 8 As shown, the probability of structural failure is calculated from the failure probability. Therefore, when the corrosion rate is 0%, the probability of structural collapse and severe damage caused by impact velocity and impact tonnage under the present invention is also close to 0.

[0199] The vulnerability curves of ship impacts on bridge piers under different damage conditions show that the more severe the corrosion, the higher the probability of the bridge pier failing to reach the same damage level under the same impact conditions. The impact becomes increasingly significant as the impact speed gradually increases and the corrosion degree worsens.

[0200] (7) Impact toughness assessment

[0201] The initial damage under corrosion conditions is determined by nonlinear static analysis of the bridge piers. Then, nonlinear dynamic analysis is used to determine the impact of different working conditions on the performance of the corroded bridge piers. The toughness of the bridge piers is quantified by combining the recovery time and recovery function of the structure under different damage levels.

[0202] 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 situation determined by nonlinear static analysis. Furthermore, as the impact velocity increases, the impact load increases, leading to a reduction in the structure's impact toughness. Under the same external load, the impact toughness decreases with increasing corrosion rate, but the influence of corrosion rate on the pier's impact toughness gradually weakens.

[0203] Therefore, this invention employs the aforementioned method for assessing the impact toughness of corroded reinforced steel bridge structures after a ship collision. By establishing a finite element model of the bridge pier considering the influence of steel corrosion, and using the equivalent static method to simulate a ship impact, this invention comprehensively utilizes nonlinear analysis, response surface methodology, Monte Carlo simulation, and other techniques to determine the criteria for judging the damage state of the bridge structure and quantify the structural impact toughness index. This method fully considers the complex mechanical behavior and various uncertainties of bridge structures under corrosion and ship collisions. The assessment process is scientifically rigorous, and the results are accurate and reliable, providing an effective approach for the safety assessment and toughness improvement of corroded reinforced steel bridge structures under ship collision disasters.

[0204] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions 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 impact toughness of a corroded reinforced steel bridge structure after a ship collision, characterized in that, Includes the following steps: S1. A finite element model of a corroded bridge pier was established based on the theoretical degradation model of corroded reinforced concrete. S2. The equivalent static method is used to simulate ship impact and determine the dynamic damage factors of the ship. S3. Considering the sudden external force, perform nonlinear static analysis and nonlinear dynamic analysis of the structure to obtain the bridge function loss function, and then calculate the bridge function function 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 using Monte Carlo simulation; S7. Calculate the structural impact toughness index based on the bridge function loss function, combined with the repair time and recovery function; 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 from the nonlinear static analysis of the corroded pier is selected as the index of the remaining function of the structure. The quantitative formula of the initial corrosion pier function loss function under different corrosion rates is as follows: ； In the formula, This represents the maximum vertical bearing capacity of the bridge pier in its uncorroded state. The maximum vertical bearing capacity of the structure is time-varying. Loss function of concrete subjected to impact under corroded conditions The vulnerability curves corresponding to different states are used for calculation, which 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: ； In the formula, = 1, 2, 3, 4, and 5 correspond to five damage status levels; This represents the structural damage ratio under the corresponding conditions. For state The probability of structural failure under different conditions is calculated based on the failure probability. ； In the formula, For state Probability of substructure failure; The bridge function is calculated based on the initial corrosion pier function and the impact-induced pier function. Its expression is: ； In the formula, Corrosion intensity; This is the loss function of concrete subjected to impact under corrosion conditions; Let the initial corroded bridge pier functional loss function be... It is a step function. For recovery function, It is a time variable; In S7, repair time refers to the time it takes for a bridge to be repaired from a damaged state to a normal usable state. The bridge repair time is related to the damage state of the bridge. The greater the damage, the longer the repair time. The recovery time for different damage states is derived from the repair time. The resilience assessment is performed using a negative exponential recovery function, calculated as follows: ； In the formula, and These are two constants fitted through data, and they are related to the damage state and the recovery state. The time when the collision occurred; This refers to the repair time for the structure after a ship collision.

2. The method for evaluating the impact toughness of a corroded reinforced steel bridge structure after a ship collision, as described in claim 1, is characterized in that... In S1, when establishing the finite element model of the corroded bridge pier, the structural performance deterioration caused by steel corrosion is considered, including the reduction of the effective cross-sectional area of ​​the steel, the reduction of the yield strength and ultimate strength of the steel, the reduction of the bond strength between the steel and the concrete, and the reduction of the tensile strength of the concrete after corrosion expansion. Considering the diameter of the reinforcing steel bars in the bridge piers and the corrosion rate, the corrosion condition of the bridge piers is assessed, and the corrosion rate is calculated using the following formula: ； In the formula, For steel reinforcement corrosion rate, The diameter of the uncorroded steel bar. The diameter of the corroded steel bar; A constitutive model of corroded steel reinforcement was used to simulate the mechanical properties of steel reinforcement exposed and corroded in an atmospheric environment. The characteristic parameters of the constitutive model were taken as follows: ； ； ； ； In the formula, , These represent the effective cross-sectional area and ultimate strain of the uncorroded steel bars, respectively. , These are the yield strength and ultimate strength of the uncorroded steel bars, respectively. , These are the yield strength and ultimate strength of the corroded steel bars, respectively. , These represent the effective cross-sectional area and ultimate strain of the corroded steel bars, respectively. The reduction in bond-slip strength between steel reinforcement and concrete caused by corrosion was simulated using a coefficient reduction method. The bond-slip strength relationship is as follows: ； ； Where, This relates to the bond-slip relationship between corroded steel bars and concrete. This represents the bond-slip relationship between the uncorroded reinforcing steel and the concrete. The factor that reduces the bond strength between corroded steel bars and concrete; A reduction factor is introduced to simulate the strength degradation of the concrete cover. The calculation model is as follows: ； ； In the formula, , These represent the compressive strength of the protective concrete layer before and after steel reinforcement corrosion, respectively. Take 0.1; The average tensile strain caused by rust expansion and cracking of the protective concrete layer; This represents the compressive strain corresponding to the maximum stress in uncorroded concrete. This refers to the number of main reinforcement bars within the cross-section of the pier column. The diameter of the uncorroded main reinforcing bar; The perimeter of the cross-section of the pier specimen; Based on the Mander model, the core area concrete strength was calculated using a constitutive model of concrete confined with circular corroded stirrups, as follows: ； ； ； ； Where, The volumetric reinforcement ratio of transverse steel bars in corrosion-resisting concrete; The volumetric reinforcement ratio of transverse steel bars in uncorroded confined concrete; This represents the yield strength of the transverse reinforcement. The yield strength of the corroded transverse reinforcing steel; For effective lateral constraint stress; This refers to the compressive strength of unconfined concrete. The compressive strength of corrosion-restrained concrete; The coefficient for reducing the yield strength of corroded transverse reinforcing bars; The stress correction coefficient is obtained after regression analysis of the test data; This is the constraint effectiveness coefficient.

3. The method for evaluating the impact toughness of a corroded reinforced steel bridge structure after a ship collision, as described in claim 1, is characterized in that... In S2, the equivalent static method is used to simulate ship impact and determine the dynamic damage factors of the ship, including barge impact force, full load displacement, and ship impact speed. The formula for calculating barge impact force is as follows: ； In the formula, The design value for the barge impact force. For full load drainage, The speed at which the ship struck.

4. The method for evaluating the impact toughness of a corroded reinforced steel bridge structure after a ship collision, as described in claim 1, is characterized in that... In S4, a surrogate model is constructed using the Response Surface Method (RSM) to predict dynamic responses. Specifically: The BBD method in response surface methodology was adopted, and Design-Expert software was used to design and analyze different working conditions. Corrosion rate, impact velocity and impact tonnage were used as independent variables of response, and residual bearing capacity was used as dependent variable for three-factor, three-level design analysis.

5. The method for evaluating the impact toughness of a corroded reinforced steel bridge structure after a ship collision, as described in claim 1, is characterized in that... In S5, the ultimate compressive bearing capacity of the structure is selected as the ultimate limit state standard, and the following values ​​are taken respectively: , , , The limit values ​​correspond to 10%, 20%, 40%, and 70% of the ultimate compressive bearing capacity, based on the range of loss of the structure's ultimate compressive bearing capacity. The criteria for determining the damage state are as follows: like If the damage rate is less than 10%, the damage status is considered basically intact. If 10%≤ If the damage is less than 20%, the damage status is considered minor. If 20%≤ If the damage is less than 40%, the damage status is moderate. If 40%≤ If the damage rate is less than 70%, the damage status is considered severe. like If ≥70%, the damage condition is collapse; in, , To compensate for the remaining load-bearing capacity after damage, This refers to the ultimate compressive bearing capacity of the structure.

6. The method for evaluating the impact toughness of a corroded reinforced steel bridge structure after a ship collision, as described in claim 1, is characterized in that... In S6, based on the statistical distribution of the cross-sectional resistance of concrete components and the statistical distribution of ship tonnage, the failure probability of each damage state is obtained using Monte Carlo simulation, and finally the vulnerability curve of ship impacting bridge pier is obtained.

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