An evaluation method for time-dependent seismic resilience of RC bridge piers under ice force loading

Abstract

A kind of time-varying seismic toughness evaluation method considering ice force load under salt frozen RC pier, belongs to civil engineering bridge seismic design technical field.The present application includes (1) dividing RC pier service area, distinguish salt frozen area and chloride ion erosion area;(2) analysis the time-varying degradation characteristics of each area material, determine the time-varying mechanical parameters;(3) establish the degradation finite element model of different service time;(4) construct the coupling load time history curve containing ice force and seismic characteristics;(5) input model for nonlinear time history analysis, obtain dynamic response data;(6) fitting time-varying seismic vulnerability curve, reveal time-varying law;(7) establish the seismic toughness calculation model, calculate the toughness index of whole life cycle.The method realizes the time effect evaluation of pier toughness under the coupling action of salt frozen environment and ice force-seismic, provides scientific basis for bridge maintenance and reinforcement.

Description

Technical Field

[0001] This invention relates to a method for evaluating the time-varying seismic toughness of reinforced concrete bridge piers, belonging to the field of seismic design technology for civil engineering bridges. Background Technology

[0002] Seismic toughness of a structure specifically refers to its ability to retain its original function and restore that function after an earthquake under the action of a seismic motion of a specific intensity. In recent years, academic understanding in the field of seismic engineering has been continuously deepening, and many scholars have proposed that seismic engineering should move away from the previous single-minded focus on earthquake safety and gradually move towards a development path that "balances safety and toughness." Bridges play a crucial connecting role in transportation systems, and the efficiency of their post-earthquake traffic capacity restoration directly affects the overall reconstruction speed of the disaster-stricken area. Based on this characteristic, bridge seismic toughness is the ability of a bridge to maintain and restore its original traffic capacity, and it can also serve as an important indicator for measuring the seismic performance of bridge structures.

[0003] In cold coastal and inland frozen lake regions, reinforced concrete (RC) bridge piers face the long-term coupling effect of salt-freezing cycles (chloride ion corrosion + freeze-thaw action) and ice loads. Ice loads, a unique form of load in cold aquatic environments, exert continuous vibrations on offshore platforms and bridge piers across sea and rivers through static ice compression, ice flow impact, and freeze-thaw cycles, easily leading to progressive damage such as localized cracking, overall collapse, and cumulative deformation. Under the action of moving ice loads, the design of marine structures with vertical direct contact surfaces must consider the impact of ice-induced vibrations. These ice-induced vibrations, originating from the dynamic interaction between ice and the structure, significantly reduce the safety and durability of the structure. Seismic action, characterized primarily by instantaneous dynamic impacts, induces structural resonance and amplifies vibration effects, leading to sudden damage such as bridge beam collapse and building collapse. Both of these factors, from different dimensions of action, pose severe challenges to the load-bearing capacity and safety reserves of structures. Therefore, in cold regions, systematically exploring the influence of ice loads and seismic action on bridges subjected to salt freezing can not only provide important support for improving the theoretical system of structural design under extreme loads, but also provide scientific basis for disaster prevention and mitigation of projects in cold regions and seismic zones. This has important theoretical value and practical significance for ensuring the long-term safe operation of infrastructure and improving regional disaster prevention and mitigation capabilities.

[0004] Existing research has three problems or shortcomings: First, the material performance degradation model of RC bridge piers in salt-frozen environments is not clear enough; there is a lack of research and application of using ice vibration response spectrum to describe dynamic ice loads; Second, load coupling simply superimposes seismic waves and static ice pressure, without realizing the dynamic coupling of pulsating ice loads and ground motion based on power spectral density function, thus failing to reflect the influence of ice force randomness on structural response; there is a lack of research, both domestically and internationally, on the seismic vulnerability of RC bridge piers in salt-frozen environments under ice-induced force loads and seismic coupling; Third, there is a lack of research on time-varying toughness assessment of bridge piers in this environment based on probabilistic vulnerability and recovery function theory. Summary of the Invention

[0005] This invention proposes a time-varying seismic toughness assessment method and system for RC (reinforced concrete) bridge piers under the influence of salt freezing under ice loads. It is applicable to special environments such as cold tidal zones where salt freezing erosion and ice loads coexist. It can achieve accurate quantitative assessment of the seismic toughness of salt-frozen RC bridge piers throughout their entire life cycle.

[0006] This invention addresses the problems of fuzzy constitutive performance degradation models for bridge piers under the coupled effects of chloride ion corrosion and freeze-thaw cycles, and the failure of seismic performance analyses to consider the long-term icing forces experienced by bridge piers in cold regions. This invention proposes an accurate model for constructing a salt-freezing degradation model of bridge piers, and uses this model to establish a finite element model for numerical simulation, thereby analyzing the seismic performance of reinforced concrete (RC) bridge piers under the combined effects of icing forces and earthquakes in a salt-freezing environment.

[0007] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0008] A method for assessing the time-varying seismic toughness of salt-frozen reinforced concrete bridge piers under ice loads includes the following steps:

[0009] Step S1: Divide the RC bridge piers into atmospheric zone, tidal and splash zone, and underwater submerged zone according to the service environment. The tidal and splash zone is the salt freezing zone, and the atmospheric zone and underwater submerged zone are the chloride ion corrosion zone.

[0010] Step S2: A one-dimensional chloride ion zonal corrosion model is used to analyze the deterioration of reinforcing steel and concrete in the atmospheric and underwater submerged zones. Using 200 freeze-thaw cycles as the limit, the service life of concrete in the actual tidal zone is correlated with the indoor / outdoor freeze-thaw cycle ratio. Annual pore damage is obtained throughout the entire lifespan through macro-microscopic concrete tests. The time-varying stress-strain curve and elastic modulus of salt-frozen concrete are calculated using standard formulas to determine the calculation parameters for the time-varying stress-strain relationship between reinforcing steel and concrete.

[0011] Step S3: Calculate the initial corrosion time and corrosion depth of the steel bars based on the damage model to obtain the time-varying steel bar corrosion rate and yield strength. Calculate the compressive strength of the concrete protective layer after corrosion in the atmospheric and submerged zones. Correct the stress-strain calculation model parameters of the reinforced concrete code to obtain the stress-strain relationship after strength degradation. Based on the microscopic damage degree of concrete and the principle of damage mechanics, incorporate the effect of salt freezing into the damage variables of the concrete constitutive model in the "Standard for Design of Concrete Structures" to determine the calculation parameters of the concrete plastic damage model under different salt freezing alternation cycles.

[0012] Step S4: Input the time-varying degradation data of steel bars and concrete in different areas into ABAQUS material properties to establish finite element models of RC piers after degradation at different service times;

[0013] Step S5: Set the calculation time point and distribute the material mechanical properties at different times during the entire life cycle to the entire pier model;

[0014] Step S6: Based on the power spectral density function (PSD), construct the artificial ice vibration response spectrum using the variable amplitude superposition method;

[0015] Step S7: Based on the seismic ground motion database of the Pacific Earthquake Engineering Research Center in the United States, select the seismic ground motion that matches the seismic hazard analysis results of the area where the bridge pier is located and perform response spectrum amplitude modulation; combine the power spectral density characteristics of the artificial ice vibration response spectrum, and generate the external dynamic load time history curve that simultaneously includes ice force load and seismic action characteristics through signal synthesis technology.

[0016] Step S8: Select the ground motion intensity index, input the artificial ice force time history and the ground motion time history into the bridge pier analysis model, perform nonlinear time history analysis, and record dynamic response data such as displacement, internal force, and damage development at different times;

[0017] Step S9: Based on the nonlinear time history analysis results, a probabilistic statistical method is used, with the seismic ground motion intensity index as the abscissa and the probability of the bridge piers being slightly damaged, moderately damaged, severely damaged, or collapsed as the ordinate, to obtain the seismic vulnerability curve at the current calculation time point by fitting a log-normal distribution.

[0018] Step S10: By combining the seismic vulnerability analysis results at different calculation time points, the vulnerability curve of the bridge piers over time is obtained, revealing the time-varying law of the seismic vulnerability of the bridge piers under the coupled action of salt-freezing environment, ice force, and seismic load.

[0019] Step S11: Determine the structural performance index of seismic toughness, and establish a calculation model of the seismic toughness of bridge piers that considers the salt-freezing environment and ice loads, based on the pre-disaster performance and post-disaster performance.

[0020] Step S12: Based on the seismic toughness calculation model, calculate the pier toughness index at different time points throughout the entire life cycle, and plot the time-dependent toughness curve to provide a scientific basis for bridge maintenance, reinforcement and management decisions.

[0021] Preferably, in step S3, the initial corrosion time of the reinforcing steel is calculated using the Duracrate model derived from the one-dimensional Fick's second law to calculate the chloride ion concentration at any time t and a distance of x millimeters from the concrete surface, and then the initial corrosion time of the reinforcing steel is calculated in reverse. The Duracrate model comprehensively considers the time-varying characteristics of chloride ion diffusion rate and the influence of materials, environment, and curing. The chloride ion concentration calculation formula is as follows:

[0022]

[0023] in, To determine the chloride ion concentration on the concrete surface, by... calculate, The correction factor is used to account for the influence of experimental methods. This is the environmental impact correction factor; This is a correction factor for the impact of maintenance. For the age of concrete; for Chloride ion diffusion coefficient; This is the time decay coefficient; This refers to the water-to-binder ratio; For environmental parameters;

[0024] When the chloride ion concentration reaches a critical value When the steel bars begin to rust, the formula for calculating the initial corrosion time of the steel bars, based on the chloride ion concentration calculation formula, is as follows:

[0025]

[0026] In the formula, This refers to the thickness of the concrete cover, expressed in mm. The initial corrosion time is expressed in years.

[0027] (2) Calculation of the area and depth of steel reinforcement corrosion: Steel reinforcement corrosion is divided into "uniform corrosion" and "pit corrosion";

[0028] Uniform corrosion is outwardly manifested as a decrease in the diameter of the reinforcing bar, and the uniform corrosion area at time t. pass Calculation, where The initial diameter of the reinforcing bar; Let be the residual diameter of the reinforcing bar at time t, and the calculation formula is: ,in Let t be the corrosion depth of the reinforcing bar. Based on Faraday's law and the calculation results of the initial corrosion time of the reinforcing bar, the formula for calculating the corrosion depth of the reinforcing bar can be obtained as follows:

[0029] In the formula, This refers to the density of the reinforcing steel. Unit length; The atomic weight of iron ions is taken as 55.85 g / mol; F is the Faraday constant, with a standard value of 96485 C / mol. The valence is 2; Let be the corrosion current density at time t, through calculate;

[0030] Pitting corrosion occurs in localized areas around the reinforcing bars, and this type of corrosion is prone to occur at cracks in structural members. The area affected by pitting corrosion is [not specified]. Based on pitting depth The calculation is performed for different ranges, specifically as follows:

[0031] when hour, ;

[0032] when hour, ;

[0033] when hour, ;

[0034] in, ; ;

[0035] ; ;

[0036] In the formula, The pitting depth is calculated by correcting for uniform corrosion depth. R is the pitting coefficient;

[0037] (3) Calculation of steel reinforcement material performance degradation: The corrosion rate of steel reinforcement is calculated based on the corrosion area of ​​steel reinforcement, and the yield strength of steel reinforcement after corrosion is calculated using the DU model. and ultimate strength The calculation formula is:

[0038]

[0039] in, The yield strength reduction factor is taken as 0.0049; The ultimate strength reduction factor is taken as 0.0065; The initial yield strength of the steel reinforcement; This represents the initial ultimate strength of the reinforcing steel. The corrosion rate of the reinforcing steel is calculated using the formula... Perform calculations. This represents the initial area of ​​the reinforcing steel.

[0040] (4) Calculation of uniaxial stress-strain curves of concrete, including "uniaxial tensile stress-strain curves" and "uniaxial compressive stress-strain curves", wherein:

[0041] The uniaxial tensile stress-strain curve is calculated using the following formula:

[0042]

[0043]

[0044]

[0045]

[0046] In the formula, Strain in the later stages of damage; Tensile stress in the later stage of damage; This represents the initial elastic modulus of the concrete. The ratio of strain at any location to peak strain; Process parameters for uniaxial tension specimens; These are the parameter values ​​for the descending segment of the uniaxial tensile stress-strain curve of concrete; This represents the uniaxial tensile strength of concrete. Representative value of uniaxial tensile strength Corresponding peak tensile strain of concrete These are parameters for the evolution of uniaxial tensile damage in concrete.

[0047] The uniaxial compressive stress-strain curve is calculated using the following formula:

[0048]

[0049]

[0050]

[0051]

[0052]

[0053] In the formula, The compressive stress is for the later-stage damage state; Process parameters for uniaxially compressed specimens; These are the parameter values ​​for the descending segment of the uniaxial compressive stress-strain curve of concrete. This represents the uniaxial compressive strength of concrete. Representative value of uniaxial compressive strength Peak tensile strain of concrete; These are the parameters for the evolution of uniaxial compressive damage in concrete.

[0054] (5) Calculation of concrete compressive strength degradation under chloride ion attack:

[0055] The formula for calculating the compressive strength of concrete after rust expansion is:

[0056]

[0057] In the formula, A coefficient related to the diameter and roughness of the reinforcing bar, with a value of 0.1; This represents the peak strain of the un-rusted and expanded concrete. The average tensile strain of concrete after rust expansion perpendicular to the direction of force is calculated using the following formula: ,in, , The width of the cross-section without rust expansion. This refers to the number of longitudinal reinforcement bars. The total width of the crack is calculated as follows: Perform calculations. The coefficient of volumetric expansion due to steel corrosion is taken as 2.0. When >3mm, Take 3mm;

[0058] (6) Determination of constitutive and CDP model parameters for concrete damage under salt freezing: Introducing the initial damage factor of salt freezing. The stress-strain relationship of concrete is modified to consider the stress of the later damage state after initial salt-freezing damage. , To account for the strain in the later damage state after initial salt-freezing damage, The total damage caused by salt freezing and load is denoted as under tension. When under pressure Elastic modulus of concrete after salt freeze damage: Inelastic strain , For elastically recovering strain, by calculate.

[0059] Preferred method: In step S6, based on the velocity-related power spectral density function, a variable amplitude superposition method is used.

[0060]

[0061] In the formula:

[0062] express A phase angle that is uniformly distributed between the phase angles;

[0063] Indicates frequency increment Frequency value at the midpoint ;

[0064] The power spectral density function is expressed using the following formula:

[0065]

[0066] In the formula: ; This indicates the average ice speed.

[0067] Preferred method: In step S7, the seismic wave is selected for amplitude modulation, and the ice velocity time history curve is consistent with the duration of the seismic wave;

[0068] (1) Assuming that the single-degree-of-freedom structure is in the linear elastic stage, the pulsating ice force at the point where the structure is hit by ice is proportional to the pulsating ice velocity. The ice velocity time history curve can also be the normalized ice force dimensionless. Based on the single particle motion equation, the ice force acceleration unit is g, and the ice force is numerically normalized.

[0069] (2) Calculate the horizontal ice pressure based on the ice load calculation formula in the highway bridge and culvert design code, and convert the pulsating ice velocity time history curve into the ice pressure time history curve.

[0070] Both of the above methods can describe the impact of ice force on RC bridge piers. Based on the normalized ice force acceleration time history curve or ice pressure time history curve combined with seismic waves, incremental dynamic IDA analysis is performed on the RC bridge piers to obtain the dynamic response of the structure.

[0071] Preferred method: In step S8, the nonlinear dynamic time history analysis uses PGA as the seismic motion parameter. After inputting the corresponding seismic motion time history curve and artificial ice force time history curve into the structural model, nonlinear time history analysis is carried out: First, the seismic motion curve matching the site characteristics is loaded and the load is adjusted according to the PGA level; then, based on the nonlinear constitutive relationship of the structure, the dynamic equilibrium equation is solved by the step-by-step integration method, and the displacement, velocity and other responses are calculated at each time step; during the process, the stress state of the components is tracked simultaneously, the stiffness matrix is ​​updated and the internal force and damage development data are recorded; finally, through the statistical processing of the multi-wave analysis results, the nonlinear dynamic response and damage characteristics of the structure under the action of PGA are obtained.

[0072] Preferred method: The fragility analysis process in step S9 is as follows:

[0073] Eleven natural earthquake waves were selected from the PEER database. A mainshock and aftershock sequence was constructed using the repetition method. Equal-step amplitude modulation was applied to each earthquake wave. The initial value of the peak ground acceleration (PGA) was 0.1g, with a step size of 0.1g. After 14 amplitude modulations, the final amplitude of the PGA was 1.5g. Using the maximum pier top displacement B as the engineering requirement parameter and the PGA as the seismic intensity parameter, the horizontal axis represents the relative displacement ductility ratio. The vertical axis represents the IDA curve of the PGA.

[0074]

[0075] In the formula: B is the maximum relative displacement of the pier top response; This represents the relative displacement of the pier top when the reinforcing steel first yields;

[0076] The peak ground acceleration (PGA) and the corresponding relative displacement ductility ratio for each amplitude modulation level of the ground motion are calculated. Take the logarithm of each, and plot ln(peak acceleration) on the horizontal axis. Using the logarithmic IDA analysis results as the vertical axis, linear regression analysis was performed on the logarithmic IDA analysis results;

[0077] Using XTRACT software, moment-curvature analysis of the pier section is performed to determine different curvature values ​​at the bottom of the pier at different service times, thereby determining the pier damage limit value. Based on the vulnerability function, the exceedance probability of each limit state is obtained, i.e., the vulnerability curve.

[0078] Preferred method: In step S11, static elastoplastic analysis is performed on bridge piers with different service years. A displacement value varying with time is applied to the pier top to obtain the maximum shear force value at the pier bottom. This value is compared with the initial shear force value to obtain the initial performance index Q0. The instantaneous damage value ΔQ is calculated using the product of the exceedance probability and the damage discrete value. The average recovery time under different damage states and the recovery time are used as the basis for the analysis. A recovery function is selected to describe the toughness index, and finally the toughness index is calculated:

[0079]

[0080] In the formula: For the residual function of the bridge system, =Q0-ΔQ is dimensionless; The time of the earthquake; R is the resilience index of the bridge system. The recovery time is calculated based on the exceedance probability obtained from the vulnerability analysis.

[0081] The beneficial effects of this invention are as follows:

[0082] 1. This invention fully considers the time-varying influence of salt-freezing environment (coupling of chloride ion erosion and freeze-thaw cycle) on the performance of RC bridge pier materials. By establishing a salt-freezing time-varying damage model, it can more accurately reflect the performance degradation law of bridge piers throughout their entire life cycle, providing a more reliable basis for subsequent seismic toughness analysis and solving the problem of inaccurate evaluation caused by neglecting the time-varying characteristics of materials in traditional methods.

[0083] 2. This invention innovatively couples pulsating ice load based on power spectral density function with seismic waves. Compared with the traditional simple superposition of loads, it can more realistically reflect the influence of the randomness of ice force and the complexity of ground motion on the stress and response of bridge piers, making the simulation of external dynamic loads closer to actual engineering conditions and improving the scientificity and rationality of load coupling.

[0084] 3. This invention constructs a multi-parameter seismic toughness assessment model, integrating multiple performance indicators before, during, and after a disaster, and combining probabilistic vulnerability theory with the mean of the repair function to comprehensively and accurately assess the seismic toughness of RC bridge piers. This breaks through the limitations of traditional single-parameter and one-sided assessments, providing a more scientific basis for bridge maintenance, reinforcement, and management decisions.

[0085] 4. This invention takes RC bridge piers affected by salt freezing and subjected to ice loads in cold regions as the research object. The method of this invention can accurately evaluate their seismic toughness throughout their entire life cycle, which helps to identify potential seismic weaknesses in bridge piers in advance, formulate more reasonable maintenance strategies, and ensure the safe operation of bridges in cold regions under complex environments. It is of great significance to improve the safety and durability of bridge structures in cold regions. Attached Figure Description

[0086] Figure 1 A model diagram of the zonal degradation of salt-frozen bridge piers under chloride ion erosion and freeze-thaw cycles;

[0087] Figure 2 Flowchart for vulnerability analysis of salt-frozen RC bridge piers considering the effects of ice forces;

[0088] Figure 3 Flowchart for assessing the seismic toughness of salt-frozen reinforced concrete bridge piers considering the effects of ice forces;

[0089] Figure 4 A flowchart of a time-varying seismic toughness assessment method for a salt-frost damage model considering ice loads. Detailed Implementation

[0090] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading the present invention, any modifications of the present invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0091] Specific implementation method one: Combining Figures 1-4 This embodiment describes in detail the time-varying seismic toughness assessment method for RC bridge piers under the influence of salt freezing and ice loads. The implementation object is an RC bridge pier in a cold-region tidal zone. The calculation model is designed according to the "Design Specification for Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts". A circular bridge pier with a diameter of 2m is used, with longitudinal reinforcement diameter of 28mm, longitudinal reinforcement spacing of 12cm, and longitudinal reinforcement ratio of 1.02%. The stirrup diameter is 16mm, stirrup (HRB400) is 0.134%, and stirrup spacing is 15cm. The concrete design strength grade is C40, and the steel reinforcement is HRB400 grade; the concrete cover thickness is 50mm. Specifically, the environmental action zones of the RC bridge pier are divided along the height direction into a 4m atmospheric zone, a 2m tidal zone, and a 4m underwater zone. The embodiment of the present invention will be described in detail below with reference to the accompanying drawings:

[0092] A time-varying seismic toughness assessment method for RC bridge piers considering the effects of salt freezing under ice loads is implemented in three stages, as follows:

[0093] Phase 1: Quantification of time-varying damage to RC bridge piers under salt-freezing conditions.

[0094] (1) Introduce a strength degradation model of bridge piers under salt-freezing environment. Based on the theory of the influence of salt-freezing cycle on concrete performance in concrete materials science and the relevant principle of chloride ion corrosion of steel bars in corrosion science, a finite element model of strength degradation of bridge piers under salt-freezing environment is established by calculating and adjusting relevant parameters.

[0095] (2) The RC bridge piers were divided into atmospheric zone, tidal zone and submerged zone. Based on the environmental characteristics of different zones, chloride ion erosion analysis and salt-freeze erosion analysis were carried out respectively. Among them, the chloride ion erosion analysis used the theory of chloride ion diffusion in concrete to study the diffusion law of chloride ions in concrete; the salt-freeze erosion analysis explored the deterioration of concrete under salt-freeze action based on the mechanism of damage to concrete by freeze-thaw cycle.

[0096] (3) Based on the results of chloride ion corrosion and salt-freezing corrosion, the initial corrosion time of the reinforcing steel and the compressive strength of the concrete over time were determined. This process was determined with reference to relevant studies on the theory of reinforcing steel corrosion kinetics, the law of concrete strength decay, and the theory of damage mechanics.

[0097] (4) Further determine the change of corrosion depth over time, combine the time-varying law of concrete compressive strength, and correct the parameters of the concrete and steel reinforcement constitutive model according to the time-varying parameters to obtain the concrete plastic damage index (CDP). Finally, determine the mechanical properties of the section over time in ABAQUS to provide a basis for subsequent analysis.

[0098] Phase 2: Seismic toughness analysis of bridge piers under the coupling of ice force and seismic load.

[0099] (1) Model selection

[0100] The model constructed using the research content from the previous section is used as the research object.

[0101] (2) Selection of structural requirement parameters and their correlation analysis

[0102] Seismic demand refers to a series of dynamic responses recorded by a structure under seismic loading. A specific index can be used to interpret the structure's resistance and demand when performing seismic vulnerability analysis on a structure. Using different indices for IDA on the same structure can result in analysis results showing that the structure has collapsed under a certain seismic intensity but is still repairable.

[0103] (3) Constructing artificial ice waves and selecting ground motion records. The construction of artificial ice waves is based on the power spectral density function. The artificial ice wave response spectrum is constructed by using the amplitude superposition method with the assumed power spectral density function. The selection of ground motion records is based on the ground motion database of the Pacific Earthquake Engineering Research Center of the United States, selecting appropriate seismic waves and performing amplitude modulation based on the standard response spectrum.

[0104] (4) Distribute different mechanical properties throughout the entire life cycle to the entire pier, set the calculation time point, and establish an RC pier analysis model.

[0105] (5) The time-varying stress performance of the pier is obtained by performing pushover analysis on the cross section. The mechanical performance of the pier affected by salt freezing is described by the base shear force-pier top displacement. The pre-disaster performance of the pier is described by the base shear force ratio.

[0106] (6) Determine the pier damage index, and select the ground motion intensity index, seismic capacity analysis, seismic demand analysis, nonlinear time history analysis and seismic vulnerability analysis.

[0107] (7) Vulnerability Analysis

[0108] This analysis selected 11 natural earthquake waves from the PEER database. A mainshock and aftershock sequence was constructed using the repetition method. Each earthquake wave underwent equal-step amplitude modulation. The initial value of the peak ground acceleration (PGA) was 0.1g, with a step size of 0.1g. After 14 amplitude modulations, the final amplitude of the PGA was 1.5g. Using the maximum pier top displacement B as the engineering requirement parameter and the PGA as the seismic intensity parameter, the horizontal axis represents the relative displacement ductility ratio. The vertical axis represents the IDA curve of the PGA.

[0109]

[0110] In the formula: B is the maximum relative displacement of the pier top response;

[0111] The relative displacement of the pier top when the reinforcing steel yields for the first time

[0112] The peak ground acceleration (PGA) and the corresponding relative displacement ductility ratio for each amplitude modulation level of the ground motion are calculated. Take the logarithm of each, and plot ln(PGA) on the x-axis. Linear regression analysis was performed on the logarithmic IDA results, using the vertical axis as the ordinate.

[0113] Based on the research of domestic and foreign scholars on the classification of structural limit states, the structure is classified into limit states. Using XTRACT software, moment-curvature analysis is performed on the pier section to determine different curvature values ​​at the bottom of the pier, thereby determining the pier damage threshold. Based on probabilistic vulnerability theory, a vulnerability function is obtained, yielding the exceedance probability, i.e., the vulnerability curve, for each limit state.

[0114] ④ In order to combine the three-level fortification target of my country's seismic design code and quantify the damage state of the structure under frequent earthquakes, fortification earthquakes and rare earthquakes, the failure state is further divided on the basis of each limit state, and the failure state probability is calculated based on the exceedance probability of each limit state.

[0115] (8) Through the above analysis, the vulnerability curve of the bridge pier over time is obtained, which intuitively shows the time-varying law of the seismic vulnerability of the bridge pier under the coupled action of ice force and seismic load.

[0116] Phase 3: Time-varying toughness analysis of bridge piers considering salt freezing and ice loads

[0117] (1) Considering salt freezing and ice force loads, based on the definition of seismic toughness, and combining the pre-disaster performance (initial mechanical performance obtained from the first stage) and post-disaster performance (seismic analysis results from the second stage), a calculation model for the seismic toughness of bridge piers is established.

[0118] (2) Determine pre-disaster and post-disaster performance indicators, and evaluate the performance of bridge piers at different stages.

[0119] Pre-disaster performance indicators are characterized by seismic resistance degradation: considering the degradation of bridge pier structural performance caused by chloride ion corrosion, the degradation of bridge pier cross-section durability over service time is used as a time-varying performance indicator with the help of Pushover analysis.

[0120] Based on the vulnerability curve, the probability of different damage states of the bridge is multiplied by the damage index that quantifies the discrete value of the damage state, which is defined as the post-disaster damage performance, thereby quantifying the instantaneous functional loss of the bridge pier.

[0121] By referencing positive and negative exponential functions and sinusoidal functions, a recovery function is constructed to describe the repair methods of bridges after being subjected to earthquakes.

[0122] (3) Analyze the full life cycle performance of the bridge piers and finally obtain the time-varying toughness curve, which clearly shows the change of the seismic toughness of the bridge piers over time, providing a basis for the maintenance, reinforcement and management of the bridge.

[0123] This embodiment proposes a time-varying seismic toughness assessment method for RC bridge piers under frost and ice loads. Through three stages—salt-freeze damage quantification, ice-seismic load coupling, and multi-parameter toughness assessment—it accurately assesses the seismic toughness of bridge piers throughout their entire life cycle. This method can be widely applied in the seismic design of civil engineering bridges, and is particularly suitable for RC bridges in cold regions and tidal zones subjected to the coupled effects of salt-freeze erosion and frost loads, such as cross-sea bridges and bridges spanning frozen lakes. It provides a scientific basis for their design, maintenance, and life-cycle management.

[0124] Specific Implementation Method Two: Combining Figures 1-4 This embodiment describes a method for assessing the time-varying seismic toughness of RC bridge piers under frost conditions considering ice loads, comprising the following steps:

[0125] Step S1: Divide the RC bridge piers into atmospheric zone, tidal and splash zone, and underwater submerged zone according to the service environment. The tidal and splash zone is the salt freezing zone, and the atmospheric zone and underwater submerged zone are the chloride ion corrosion zone.

[0126] Step S2: Analyze the deterioration of steel bars and concrete in atmospheric and underwater immersion zones using a one-dimensional chloride ion zone corrosion model; use 200 freeze-thaw cycles as the limit, and correlate the service time of concrete in the actual tidal zone with the ratio of indoor and outdoor freeze-thaw cycles; obtain the annual pore damage degree throughout the entire life cycle through macro-micro concrete tests, and calculate the time-varying stress-strain curve and elastic modulus of salt-frozen concrete using standard formulas to determine the calculation parameters for the time-varying stress-strain relationship between steel bars and concrete;

[0127] Step S2 is to determine the material degradation parameters: that is:

[0128] 1. For the atmospheric zone and the underwater immersion zone (chloride ion erosion zone), a one-dimensional chloride ion zone corrosion model is used to analyze the deterioration mechanism and process of steel bars and concrete in this zone and obtain basic parameters related to chloride ion diffusion;

[0129] 2. For tidal and splash zones (salt-freezing zones), 200 cycles are set as the limit for freeze-thaw cycles. The relationship between indoor and outdoor freeze-thaw cycle ratio and actual service time is established.

[0130] 3. Conduct macro- and micro-scale tests on concrete to obtain the annual pore damage degree of concrete in the salt-frozen zone throughout its entire life cycle, providing basic data for subsequent calculation of mechanical property parameters.

[0131] Step S3: Calculate the initial corrosion time and corrosion depth of the steel bars based on the damage model to obtain the time-varying steel bar corrosion rate and yield strength. Calculate the compressive strength of the concrete protective layer after corrosion in the atmospheric and submerged zones. Correct the stress-strain calculation model parameters of the reinforced concrete code to obtain the stress-strain relationship after strength degradation. Based on the microscopic damage degree of concrete and the principle of damage mechanics, incorporate the effect of salt freezing into the damage variables of the concrete constitutive model in the "Standard for Design of Concrete Structures" (GB / T50010—2010) to determine the calculation parameters of the concrete plastic damage (CDP) model under different salt freezing alternation cycles.

[0132] Step S3 is to modify the constitutive model, that is:

[0133] 1. Based on the chloride ion corrosion data obtained in step S2, calculate the initial corrosion time and corrosion depth of the steel bars, and further obtain the time-varying steel bar corrosion rate and yield strength throughout the entire life cycle; at the same time, calculate the compressive strength of the protective layer concrete after corrosion in the atmospheric zone and underwater immersion zone.

[0134] 2. Based on the annual pore damage degree of concrete in the salt-frozen zone obtained in step S2, calculate the time-varying stress-strain curve and elastic modulus of the salt-frozen concrete according to the standard formula, and determine the calculation parameters for the time-varying stress-strain relationship between steel reinforcement and concrete in the salt-frozen zone.

[0135] 3. Correct the parameters of the stress-strain calculation model for reinforced concrete to obtain the stress-strain relationship after the material strength degradation in each erosion / salt-freezing zone;

[0136] 4. Based on the microstructure damage degree and damage mechanics principle of concrete, the effect of salt freezing is included in the damage variables of the concrete constitutive model in the "Standard for Design of Concrete Structures" (GB / T50010—2010), and the calculation parameters of the concrete plastic damage (CDP) model under different salt freezing cycles are determined.

[0137] Step S4: Input the time-varying degradation data of steel bars and concrete in different areas into ABAQUS material properties to establish finite element models of RC piers after degradation at different service times;

[0138] Step S5: Set the calculation time point and distribute the material mechanical properties at different times during the entire life cycle to the entire pier model;

[0139] Step S6: Based on the power spectral density function (PSD), construct the artificial ice vibration response spectrum using the variable amplitude superposition method;

[0140] Step S7: Match and fuse the artificial ice vibration response spectrum with the actual ground motion record to obtain the external dynamic load time history that simultaneously includes ice force load and seismic action characteristics. Based on the ground motion database of the Pacific Earthquake Engineering Research Center (PEC) in the United States, select ground motions that match the seismic hazard analysis results of the area where the bridge pier is located (considering magnitude, epicentral distance, spectral characteristics, etc.) and perform amplitude modulation on their response spectra. Combining the power spectral density characteristics of the artificial ice vibration response spectrum, generate an external dynamic load time history curve that simultaneously includes ice force load and seismic action characteristics using signal synthesis technology. This curve can reflect the dynamic characteristics under the combined action of ice force and seismic action.

[0141] Step S8: Select ground motion intensity index (such as peak ground acceleration PGA, spectral acceleration Sa), input the artificial ice force time history and ground motion time history into the bridge pier analysis model, perform nonlinear time history analysis, and record dynamic response data such as displacement, internal force, and damage development at different times;

[0142] Step S9: Based on the nonlinear time history analysis results, a probabilistic statistical method is used, with the seismic ground motion intensity index as the abscissa and the probability of the bridge piers being slightly damaged, moderately damaged, severely damaged, or collapsed as the ordinate, to obtain the seismic vulnerability curve at the current calculation time point by fitting a log-normal distribution.

[0143] Step S10: By combining the seismic vulnerability analysis results at different calculation time points, the vulnerability curve of the bridge piers over time is obtained, revealing the time-varying law of the seismic vulnerability of the bridge piers under the coupled action of salt-freezing environment, ice force, and seismic load.

[0144] Step S11: Determine the structural performance index of seismic toughness, and combine the pre-disaster performance (mechanical performance at different time points obtained from the RC pier time-varying damage quantification model) and the post-disaster performance (damage situation obtained from seismic vulnerability analysis) to establish a calculation model of pier seismic toughness considering salt-freezing environment and ice load.

[0145] Step S12: Based on the seismic toughness calculation model, calculate the pier toughness index at different time points throughout the entire life cycle, and plot the time-dependent toughness curve to provide a scientific basis for bridge maintenance, reinforcement and management decisions.

[0146] Further, in step S3, the initial corrosion time of the reinforcing steel is calculated using the Duracrate model derived from the one-dimensional Fick's second law. This model calculates the chloride ion concentration at any time t and a distance of x millimeters from the concrete surface, and then reverses this calculation to determine the initial corrosion time of the reinforcing steel. The Duracrate model comprehensively considers the time-varying characteristics of chloride ion diffusion rate and the influence of materials, environment, and curing. The formula for calculating the chloride ion concentration is as follows:

[0147]

[0148] in, To determine the chloride ion concentration on the concrete surface, by... calculate, The correction factor is used to account for the influence of experimental methods. This is the environmental impact correction factor; This is a correction factor for the impact of maintenance. For the age of concrete; for Chloride ion diffusion coefficient; This is the time decay coefficient; This refers to the water-to-binder ratio; For environmental parameters;

[0149] When the chloride ion concentration reaches a critical value When the steel bars begin to rust, the formula for calculating the initial corrosion time of the steel bars, based on the chloride ion concentration calculation formula, is as follows:

[0150]

[0151] In the formula, This refers to the thickness of the concrete cover, expressed in mm. The initial corrosion time is expressed in years.

[0152] (2) Calculation of the area and depth of steel reinforcement corrosion: Steel reinforcement corrosion is divided into "uniform corrosion" and "pit corrosion";

[0153] Uniform corrosion is outwardly manifested as a decrease in the diameter of the reinforcing bar, and the uniform corrosion area at time t. pass Calculation, where The initial diameter of the reinforcing bar; Let be the residual diameter of the reinforcing bar at time t. When the service time reaches the initial corrosion time, the calculation formula is: ,in Let t be the corrosion depth of the reinforcing bar. Based on Faraday's law and the calculation results of the initial corrosion time of the reinforcing bar, the formula for calculating the corrosion depth of the reinforcing bar can be obtained as follows:

[0154] In the formula, This refers to the density of the reinforcing steel. Unit length; The atomic weight of iron ions is taken as 55.85 g / mol; F is the Faraday constant, with a standard value of 96485 C / mol. In the electrochemical reaction of steel reinforcement corrosion, iron atoms lose 2 electrons to form a chemical oxidation state. Therefore, the valence value here is 2; Let be the corrosion current density at time t, through calculate;

[0155] Compared to uniform corrosion, pitting corrosion occurs in localized areas around the circumference of reinforcing bars. This type of corrosion is prone to occur at cracks in structural members. Based on pitting depth The calculation is performed for different ranges, specifically as follows:

[0156] when hour, ;

[0157] when hour, ;

[0158] when hour, ;

[0159] in, ; ;

[0160] ; ;

[0161] In the formula, The pitting depth is calculated by correcting for uniform corrosion depth. R is the pitting erosion coefficient, which follows an extreme value type I distribution. Based on standard steel reinforcement (8mm) units, statistical parameters for different steel reinforcements can be calculated through correction. ; ; , The statistical parameters for pit erosion of standard steel reinforcement units are taken as 5.08 and 1.02, respectively. This is the standard length of a rebar unit; for a rebar with a diameter of 8mm, it can be taken as 125mm. To calculate the length of a steel reinforcement unit, a steel reinforcement with a diameter of 28mm can be taken as 200mm;

[0162] (3) Calculation of steel reinforcement material performance degradation: The corrosion rate of steel reinforcement is calculated based on the corrosion area of ​​steel reinforcement, and the yield strength of steel reinforcement after corrosion is calculated using the DU model. and ultimate strength The calculation formula is:

[0163]

[0164] in, The yield strength reduction factor is taken as 0.0049; The ultimate strength reduction factor is taken as 0.0065; The initial yield strength of the steel reinforcement; This represents the initial ultimate strength of the reinforcing steel. The corrosion rate of the reinforcing steel is calculated using the formula... Perform calculations. This represents the initial area of ​​the reinforcing steel.

[0165] (4) Calculation of uniaxial stress-strain curves of concrete, including "uniaxial tensile stress-strain curves" and "uniaxial compressive stress-strain curves", wherein:

[0166] The uniaxial tensile stress-strain curve is calculated using the following formula:

[0167]

[0168]

[0169]

[0170]

[0171] In the formula, Strain in the later stages of damage; Tensile stress in the later stage of damage; This represents the initial elastic modulus of the concrete. The ratio of strain at any location to peak strain; Process parameters for uniaxial tension specimens; The parameter values ​​for the descending segment of the uniaxial tensile stress-strain curve of concrete can be taken from Table 1. This represents the uniaxial tensile strength of concrete. Representative value of uniaxial tensile strength The corresponding peak tensile strain of concrete can be obtained from Table 1; These are parameters for the evolution of uniaxial tensile damage in concrete.

[0172] Table 1. Parameter values ​​for uniaxial tensile stress-strain curves of concrete.

[0173]

[0174] The uniaxial compressive stress-strain curve is calculated using the following formula:

[0175]

[0176]

[0177]

[0178]

[0179]

[0180] In the formula, The compressive stress is for the later-stage damage state; Process parameters for uniaxially compressed specimens; The parameter values ​​for the descending segment of the uniaxial compressive stress-strain curve of concrete can be taken from Table 2. This represents the uniaxial compressive strength of concrete. Representative value of uniaxial compressive strength The peak tensile strain of concrete can be obtained from Table 2. These are the parameters for the evolution of uniaxial compressive damage in concrete.

[0181] Table 2. Parameter values ​​for uniaxial compressive stress-strain curves of concrete.

[0182]

[0183] (5) Calculation of concrete compressive strength degradation under chloride ion attack:

[0184] The impact of salt freezing on concrete in this area only considers the degradation of concrete cover strength due to chloride ion corrosion. As steel corrosion continues to deepen, corrosion products accumulate, and cracks extend to the surface of the concrete cover. Cracking of the concrete cover leads to spalling or complete detachment, ultimately resulting in a decrease in the strength of the reinforced concrete structure. Coronelli et al. established a calculation formula for the degradation of the compressive strength of concrete structures with protective covers: The formula for calculating the compressive strength of concrete after rust expansion is:

[0185]

[0186] In the formula, A coefficient related to the diameter and roughness of the reinforcing bar, with a value of 0.1; This represents the peak strain of the un-rusted and expanded concrete. The average tensile strain of concrete after rust expansion perpendicular to the direction of force is calculated using the following formula: ,in, , The width of the cross-section without rust expansion. This refers to the number of longitudinal reinforcement bars. The total width of the crack is calculated as follows: Perform calculations. The coefficient of volumetric expansion due to steel corrosion is taken as 2.0. When >3mm, Take 3mm;

[0187] (6) Considering the initial damage (microstructural damage) and later damage (macromechanical damage) of concrete under salt freezing, the standard value is modified for the pore damage degree of salt freezing, the constitutive relationship of concrete damage under salt freezing is constructed, and the concrete damaged plasticity (CDP) index of concrete subjected to initial salt freezing damage is determined.

[0188] Based on the standard concrete constitutive model provided in the specifications, this paper uses the stress of the later-stage damage state unaffected by erosion, considers the initial damage from salt freezing, and introduces the concept of a damage factor to modify the stress-strain relationship of concrete. Taking into account the influence of salt freezing on the degree of micro-damage, the damage model calculation in this paper adopts a damage evolution model for hydraulic concrete structures that considers the initial micro-damage from salt freezing.

[0189] Determination of Constitutive and CDP Model Parameters for Concrete Damage under Salt-Freezing Conditions: Introducing Initial Salt-Freezing Damage Factor The stress-strain relationship of concrete is modified to consider the stress of the later damage state after initial salt-freezing damage. , To account for the strain in the later damage state after initial salt-freezing damage, The total damage caused by salt freezing and load is denoted as under tension. When under pressure Elastic modulus of concrete after salt freeze damage: Inelastic strain , For elastically recovering strain, by calculate.

[0190] Furthermore, in step S6, based on the velocity-related power spectral density function, a variable amplitude superposition method is used:

[0191]

[0192] In the formula:

[0193] express A phase angle that is uniformly distributed between the phase angles;

[0194] Indicates frequency increment Frequency value at the midpoint ;

[0195] The power spectral density function is expressed using the following formula:

[0196]

[0197] In the formula: ; This indicates the average ice speed.

[0198] By adjusting the ice velocity value, setting an appropriate time step, random phase angle, frequency range, and number of discrete points, a large number of different random waves are obtained and superimposed to simulate the real ice velocity time history curve. The random seeding points are fixed to make it reproducible, and the accuracy and applicability of the artificial ice waves are verified by comparing them with actual ice waves.

[0199] (7) The following correlation exists between indoor and outdoor freeze-thaw cycles of concrete:

[0200]

[0201] In the formula: For the service life of concrete structures; The number of rapid freeze-thaw cycles in a laboratory environment is taken as the limit of 200 cycles. The number of freeze-thaw cycles per year for concrete structures under actual conditions is taken as 27 actual freeze-thaw cycles. The freeze-thaw ratio is set to 18.5.

[0202] According to the "Test Procedure for Hydraulic Concrete" (SL / T352—2020), the mix design was carried out, and several 100mm standard test blocks were made. After soaking in salt solution, the test blocks were subjected to indoor quick-freezing tests to observe the degree of damage to their porosity compared with the initial value. Furthermore, the experimental data were fitted to analyze the pore damage degree of concrete with different service years (t) under different salt-freezing cycles and indoor-outdoor freeze-thaw cycle ratios. Finally, the following microscopic damage evolution model of concrete based on porosity was derived:

[0203] .

[0204] Further, in step S7, the seismic wave is selected for amplitude modulation, and the ice velocity time history curve is consistent with the duration of the seismic wave;

[0205] (1) Assuming that the single-degree-of-freedom structure is in the linear elastic stage, the pulsating ice force at the point where the structure is hit by ice is proportional to the pulsating ice velocity. The ice velocity time history curve can also be the normalized ice force dimensionless. Based on the single-particle motion equation, the ice force acceleration unit is g, and the ice force is numerically normalized. In this case, the ice force acceleration time history curve is highly consistent with the seismic wave.

[0206] (2) Calculate the horizontal ice pressure based on the ice load calculation formula in the highway bridge and culvert design code, and convert the pulsating ice velocity time history curve into the ice pressure time history curve.

[0207] Both of the above methods can describe the impact of ice force on RC bridge piers. Based on the normalized ice force acceleration time history curve or ice pressure time history curve combined with seismic waves, incremental dynamic IDA analysis is performed on the RC bridge piers to obtain the dynamic response of the structure.

[0208] Further, in step S8, the nonlinear dynamic time history analysis uses the PGA as the seismic motion parameter. After inputting the corresponding seismic motion time history curve and artificial ice force time history curve into the structural model, nonlinear time history analysis is carried out: first, the seismic motion curve matching the site characteristics is loaded and the load is adjusted according to the PGA level; then, based on the nonlinear constitutive relationship of the structure, the dynamic equilibrium equation is solved by the step-by-step integration method, and the displacement, velocity and other responses are calculated at each time step; during the process, the stress state of the components is tracked simultaneously, the stiffness matrix is ​​updated and the internal force and damage development data are recorded; finally, through the statistical processing of the multi-wave analysis results, the nonlinear dynamic response and damage characteristics of the structure under the action of the PGA are obtained.

[0209] Further, the vulnerability analysis process in step S9 is as follows:

[0210] Eleven natural earthquake waves were selected from the PEER database. A mainshock and aftershock sequence was constructed using the repetition method. Equal-step amplitude modulation was applied to each earthquake wave. The initial value of the peak ground acceleration (PGA) was 0.1g, with a step size of 0.1g. After 14 amplitude modulations, the final amplitude of the PGA was 1.5g. Using the maximum pier top displacement B as the engineering requirement parameter and the PGA as the seismic intensity parameter, the horizontal axis represents the relative displacement ductility ratio. The vertical axis represents the IDA curve of the PGA.

[0211]

[0212] In the formula: B is the maximum relative displacement of the pier top response; This represents the relative displacement of the pier top when the reinforcing steel first yields;

[0213] The peak ground acceleration (PGA) and the corresponding relative displacement ductility ratio for each amplitude modulation level of the ground motion are calculated. Take the logarithm of each, and plot ln(peak acceleration) on the horizontal axis. Using the logarithmic IDA analysis results as the vertical axis, linear regression analysis was performed on the logarithmic IDA analysis results;

[0214] Based on the research of domestic and foreign scholars on the classification of structural limit states, the structure is classified into limit states. Using XTRACT software, moment-curvature analysis is performed on the pier cross-section to determine different curvature values ​​at the bottom of the pier at different service times, thereby determining the pier damage threshold. Based on the vulnerability function, the exceedance probability, i.e., the vulnerability curve, is obtained for each limit state.

[0215] Further, in step S11, static elastoplastic analysis is performed on bridge piers with different service years. Displacement values ​​varying with time are applied to the pier top to obtain the maximum shear force at the pier bottom. This is compared with the initial shear force value to obtain the initial performance index Q0. Based on statistical data on damage dispersion and recovery time from domestic and international scholars, the instantaneous damage value ΔQ is calculated using the product of the exceedance probability and the damage dispersion. The average recovery time under different damage states and the recovery time are then used. A recovery function is selected to describe the toughness index, and finally the toughness index is calculated:

[0216]

[0217] In the formula:

[0218] For the residual function of the bridge system, =Q0-ΔQ is dimensionless; The time of the earthquake; R is the resilience index of the bridge system. The recovery time is calculated based on the exceedance probability obtained from vulnerability analysis.

[0219] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for evaluating the time-varying seismic toughness of salt-frozen reinforced concrete bridge piers under ice loads, characterized in that, Includes the following steps: Step S1: Divide the RC bridge piers into atmospheric zone, tidal and splash zone, and underwater submerged zone according to the service environment. The tidal and splash zone is the salt freezing zone, and the atmospheric zone and underwater submerged zone are the chloride ion corrosion zone. Step S2: Determine material degradation parameters: Use a one-dimensional chloride ion zone corrosion model to analyze the degradation of steel bars and concrete in the atmospheric and underwater submerged zones; use 200 cycles as the limit of freeze-thaw cycles and correlate the service time of concrete in the actual tidal zone with the ratio of indoor and outdoor freeze-thaw cycles; obtain the annual pore damage degree throughout the entire life cycle through macro-micro concrete tests, and calculate the time-varying stress-strain curve and elastic modulus of salt-frozen concrete using standard formulas to determine the calculation parameters for the time-varying stress-strain relationship between steel bars and concrete; Step S3: Correct the concrete constitutive model: Calculate the initial corrosion time and corrosion depth of the steel bars based on the damage model to obtain the time-varying steel bar corrosion rate and yield strength. Calculate the compressive strength of the concrete cover after corrosion in the atmospheric and submerged zones. Correct the stress-strain calculation model parameters of the reinforced concrete code to obtain the stress-strain relationship after strength degradation. Based on the principles of concrete microstructure damage degree and damage mechanics, the influence of salt freezing is included in the damage variables of the concrete constitutive model in the "Standard for Design of Concrete Structures", and the calculation parameters of the concrete plastic damage model under different salt freezing alternation cycles are determined. Step S4: Input the time-varying degradation data of steel bars and concrete in different areas into ABAQUS material properties to establish finite element models of RC piers after degradation at different service times; Step S5: Set the calculation time point and distribute the material mechanical properties at different times during the entire life cycle to the entire pier model; Step S6: Based on the power spectral density function (PSD), construct the artificial ice vibration response spectrum using the variable amplitude superposition method; Step S7: Based on the seismic ground motion database of the Pacific Earthquake Engineering Research Center in the United States, select the seismic ground motion that matches the seismic hazard analysis results of the area where the bridge pier is located and perform response spectrum amplitude modulation; combine the power spectral density characteristics of the artificial ice vibration response spectrum, and generate the external dynamic load time history curve that simultaneously includes ice force load and seismic action characteristics through signal synthesis technology. Step S8: Select the ground motion intensity index, input the artificial ice force time history and the ground motion time history into the bridge pier analysis model, perform nonlinear time history analysis, and record dynamic response data such as displacement, internal force, and damage development at different times; Step S9: Based on the nonlinear time history analysis results, a probabilistic statistical method is used, with the seismic ground motion intensity index as the abscissa and the probability of the bridge piers being slightly damaged, moderately damaged, severely damaged, or collapsed as the ordinate, to obtain the seismic vulnerability curve at the current calculation time point by fitting a log-normal distribution. Step S10: By combining the seismic vulnerability analysis results at different calculation time points, the vulnerability curve of the bridge piers over time is obtained, revealing the time-varying law of the seismic vulnerability of the bridge piers under the coupled action of salt-freezing environment, ice force, and seismic load. Step S11: Determine the structural performance index of seismic toughness, and establish a calculation model of the seismic toughness of bridge piers that considers the salt-freezing environment and ice loads, based on the pre-disaster performance and post-disaster performance. Step S12: Based on the seismic toughness calculation model, calculate the pier toughness index at different time points throughout the entire life cycle, and plot the time-dependent toughness curve to provide a scientific basis for bridge maintenance, reinforcement and management decisions.

2. The method for evaluating the time-varying seismic toughness of salt-frozen RC bridge piers considering ice loads as described in claim 1, characterized in that: In steps S2 and S3: (1) Calculation of initial corrosion time of steel bars: The Duracrate model is based on the one-dimensional Fick's second law to calculate the time t and distance from the concrete surface at any time t. The chloride ion concentration at millimeters was used to calculate the initial corrosion time of the steel bars. The Duracrite model comprehensively considers the time-varying characteristics of chloride ion diffusion rate and the influence of materials, environment, and maintenance. The formula for calculating chloride ion concentration is as follows: in, The chloride ion concentration on the concrete surface is determined by... calculate, The correction factor is used to account for the influence of experimental methods. This is the environmental impact correction factor; Correction factor for maintenance impact; The concrete age; for Chloride ion diffusion coefficient; This is the time decay coefficient; This refers to the water-to-binder ratio; For environmental parameters; When the chloride ion concentration reaches a critical value When the steel bars begin to rust, the formula for calculating the initial corrosion time of the steel bars, based on the chloride ion concentration calculation formula, is as follows: In the formula, This refers to the thickness of the concrete protective layer, expressed in mm. The initial corrosion time is expressed in years. (2) Calculation of the area and depth of steel reinforcement corrosion: Steel reinforcement corrosion is divided into "uniform corrosion" and "pit corrosion"; Uniform corrosion is outwardly manifested as a decrease in the diameter of the reinforcing bar, and the uniform corrosion area at time t. pass Calculation, where The initial diameter of the reinforcing bar; Let be the residual diameter of the reinforcing bar at time t, and the calculation formula is: ,in Let t be the corrosion depth of the reinforcing bar. Based on Faraday's law and the calculation results of the initial corrosion time of the reinforcing bar, the formula for calculating the corrosion depth of the reinforcing bar can be obtained as follows: In the formula, This indicates the mass of the steel reinforcement loss, expressed in grams (g). This refers to the density of the reinforcing steel. Unit length; The atomic weight of iron ions is taken as 55.85 g / mol; F is the Faraday constant, with a standard value of 96485 C / mol. The valence is 2; Let be the corrosion current density at time t, through calculate; Pitting corrosion occurs in localized areas around the reinforcing bars, and this type of corrosion is prone to occur at cracks in structural members. The area affected by pitting corrosion is [not specified]. Based on pitting depth The calculation is performed for different ranges, specifically as follows: when hour, ; when hour, ; when hour, ; in, ; ; ； ； In the formula, The pitting depth is calculated by correcting for uniform corrosion depth. R is the pitting coefficient; (3) Calculation of steel reinforcement material performance degradation: The corrosion rate of steel reinforcement is calculated based on the corrosion area of ​​steel reinforcement, and the yield strength of steel reinforcement after corrosion is calculated using the DU model. and ultimate strength The calculation formula is: in, The yield strength reduction factor is taken as 0.0049; The ultimate strength reduction factor is taken as 0.0065; The initial yield strength of the steel reinforcement; This represents the initial ultimate strength of the reinforcing steel. The corrosion rate of the reinforcing steel is calculated using the formula... Perform calculations. This represents the initial area of ​​the reinforcing steel. (4) Calculation of uniaxial stress-strain curves of concrete, including "uniaxial tensile stress-strain curves" and "uniaxial compressive stress-strain curves", wherein: The uniaxial tensile stress-strain curve is calculated using the following formula: In the formula, Strain in the later stages of damage; Tensile stress in the later stage of damage; This represents the initial elastic modulus of the concrete. The ratio of strain at any location to peak strain; Process parameters for uniaxial tension specimens; These are the parameter values ​​for the descending segment of the uniaxial tensile stress-strain curve of concrete; This represents the uniaxial tensile strength of concrete. Representative value of uniaxial tensile strength The corresponding peak tensile strain in concrete; These are parameters for the evolution of uniaxial tensile damage in concrete. The uniaxial compressive stress-strain curve is calculated using the following formula: In the formula, The compressive stress is for the later-stage damage state; Process parameters for uniaxially compressed specimens; These are the parameter values ​​for the descending segment of the uniaxial compressive stress-strain curve of concrete. This represents the uniaxial compressive strength of concrete. Representative value of uniaxial compressive strength Peak tensile strain of concrete; These are the parameters for the evolution of uniaxial compressive damage in concrete. This represents the elastic modulus corresponding to the peak compressive strain of concrete, expressed in MPa. (5) Calculation of concrete compressive strength degradation under chloride ion attack: The formula for calculating the compressive strength of concrete after rust expansion is: In the formula, A coefficient related to the diameter and roughness of the reinforcing bar, with a value of 0.1; This represents the peak strain of the un-rusted and expanded concrete. The average tensile strain of concrete after rust expansion perpendicular to the direction of force is calculated using the following formula: ,in, , The width of the cross-section without rust expansion. This refers to the number of longitudinal reinforcement bars. The total width of the crack is calculated as follows: Perform calculations. The coefficient of volumetric expansion due to steel corrosion is taken as 2.

0. When >3mm, Take 3mm; (6) Determination of constitutive and CDP model parameters for concrete damage under salt freezing: Introducing the initial damage factor of salt freezing. The stress-strain relationship of concrete is modified to consider the stress of the later damage state after initial salt-freezing damage. , To account for the stress in the later stage of the initial salt-freezing damage, This represents the initial microstructural damage of concrete under salt-freezing conditions. To account for the strain in the later damage state after initial salt-freezing damage, The total damage caused by salt freezing and load, under tension. When under pressure , These are parameters for the evolution of uniaxial tensile damage in concrete. For parameters related to the uniaxial compressive damage evolution of concrete; elastic modulus of concrete after salt-frost damage: Inelastic strain , For elastically recovering strain, by calculate.

3. The method for evaluating the time-varying seismic toughness of salt-frozen RC bridge piers considering ice loads as described in claim 1, characterized in that: In step S6, based on the velocity-related power spectral density function, a variable amplitude superposition method is used: In the formula: express A phase angle that is uniformly distributed between the phase angles; Indicates frequency increment Frequency value at the midpoint ; n is the frequency in Hz, and n is the frequency value at the midpoint of each frequency increment Δn interval. Δn is the frequency increment in Hz, which is the frequency step size within the discrete frequency range of the ice speed. The power spectral density function is expressed using the following formula: In the formula: ; This indicates the average ice speed.

4. The method for evaluating the time-varying seismic toughness of salt-frozen RC bridge piers considering ice loads as described in claim 1, characterized in that: In step S7, the seismic wave is selected for amplitude modulation, and the ice velocity time history curve is consistent with the duration of the seismic wave. (1) Assuming that the single-degree-of-freedom structure is in the linear elastic stage, the pulsating ice force at the point where the structure is hit by ice is proportional to the pulsating ice velocity. The ice velocity time history curve can also be the normalized ice force dimensionless. Based on the single particle motion equation, the ice force acceleration unit is g, and the ice force is numerically normalized. (2) Calculate the horizontal ice pressure based on the ice load calculation formula in the highway bridge and culvert design code, and convert the pulsating ice velocity time history curve into the ice pressure time history curve. Both of the above methods can describe the impact of ice force on RC bridge piers. Based on the normalized ice force acceleration time history curve or ice pressure time history curve combined with seismic waves, incremental dynamic IDA analysis is performed on the RC bridge piers to obtain the dynamic response of the structure.

5. The method for evaluating the time-varying seismic toughness of salt-frozen RC bridge piers considering ice loads as described in claim 1, characterized in that: In step S8, the nonlinear dynamic time history analysis uses the PGA as the seismic motion parameter. After inputting the corresponding seismic motion time history curve and artificial ice force time history curve into the structural model, nonlinear time history analysis is carried out: first, the seismic motion curve matching the site characteristics is loaded and the load is adjusted according to the PGA level; then, based on the nonlinear constitutive relationship of the structure, the dynamic equilibrium equation is solved by the step-by-step integration method, and the displacement, velocity and other responses are calculated at each time step; during the process, the stress state of the components is tracked simultaneously, the stiffness matrix is ​​updated and the internal force and damage development data are recorded; finally, through the statistical processing of the multi-wave analysis results, the nonlinear dynamic response and damage characteristics of the structure under the action of the PGA are obtained.

6. The method for evaluating the time-varying seismic toughness of salt-frozen RC bridge piers considering ice loads as described in claim 1, characterized in that: The fragility analysis process in step S9 is as follows: Eleven natural earthquake waves were selected from the PEER database. A mainshock and aftershock sequence was constructed using the repetition method. Equal-step amplitude modulation was applied to each earthquake wave. The initial value of the peak ground acceleration (PGA) was 0.1g, with a step size of 0.1g. After 14 amplitude modulations, the final amplitude of the PGA was 1.5g. Using the maximum pier top displacement B as the engineering requirement parameter and the PGA as the seismic intensity parameter, the horizontal axis represents the relative displacement ductility ratio. The vertical axis represents the IDA curve of the PGA; In the formula: B is the maximum relative displacement of the pier top response; This represents the relative displacement of the pier top when the reinforcing steel first yields; The peak ground acceleration (PGA) and the corresponding relative displacement ductility ratio for each amplitude modulation level of the ground motion are calculated. Take the logarithm of each, and plot ln(peak acceleration) on the horizontal axis. Using the logarithmic IDA analysis results as the vertical axis, linear regression analysis was performed on the logarithmic IDA analysis results; Using XTRACT software, moment-curvature analysis of the pier section is performed to determine different curvature values ​​at the bottom of the pier at different service times, thereby determining the pier damage limit value. Based on the vulnerability function, the exceedance probability of each limit state is obtained, i.e., the vulnerability curve.

7. The method for evaluating the time-varying seismic toughness of salt-frozen RC bridge piers considering ice loads as described in claim 1, characterized in that: In step S11, static elastoplastic analysis is performed on bridge piers with different service years. Displacement values ​​varying with time are applied to the pier top to obtain the maximum shear force at the pier bottom. This is compared with the initial shear force value to obtain the initial performance index Q0. The instantaneous damage value ΔQ is calculated using the product of the exceedance probability and the damage discrete value. The average recovery time under different damage states and the recovery time are used as the basis for the analysis. A recovery function is selected to describe the toughness index, and finally the toughness index is calculated: In the formula: For the residual function of the bridge system, =Q0-ΔQ is dimensionless; The time when the earthquake occurred; R is the toughness index of the bridge system; The recovery time is calculated based on the exceedance probability obtained from the vulnerability analysis.

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