Direct economic loss assessment method for corroded building structures based on Taylor series

Abstract

The present invention provides a method for assessing direct economic losses of corroded building structures based on Taylor series, comprising: selecting real main shock and aftershock records as seismic motion inputs, simulating the degradation of reinforced concrete structural materials due to corrosion by mathematical methods, and performing finite element modeling of the corroded reinforced concrete structure based on mathematical methods; performing nonlinear time history analysis on the finite element model of the corroded reinforced concrete structure under the action of main shock and aftershock sequences to obtain damage data of the structure under different corrosion rates; taking logarithms of main shock intensity, aftershock intensity and structural damage parameters, and constructing a generalized probabilistic seismic demand model of the structure by Taylor series expansion; deleting parameter items with lower importance in the generalized probabilistic seismic demand model by step-by-step elimination method to obtain a practical probabilistic seismic demand model that takes into account both accuracy and simplicity; constructing a functional function, and then calculating the median value and interval of the seismic vulnerability of reinforced concrete structures with different corrosion rates, and then obtaining the median value and interval of the economic loss index of the reinforced concrete structure under different corrosion rates based on the direct economic loss coefficient.

Description

Technical Field

[0001] The invention belongs to the technical field of structural seismic toughness assessment, and in particular relates to a method for assessing direct economic losses of corroded building structures based on Taylor series. Background Art

[0002] Reinforced concrete structures are widely used in various infrastructures such as buildings, bridges, tunnels, and offshore platforms. Their excellent mechanical properties and durability make them one of the main materials for modern engineering construction. However, during long-term use, reinforced concrete structures are prone to steel corrosion due to environmental factors (such as humidity, temperature, salinity, pH, etc.) and the properties of the material itself. Corrosion not only leads to a reduction in the cross-sectional area of ​​the steel bars and a decrease in mechanical properties, but also causes cracking and peeling of the concrete protective layer, which seriously affects the overall safety and durability of the structure.

[0003] Existing corrosion detection and assessment methods include visual inspection, ultrasonic testing, electrochemical methods, X-ray testing, etc. Although these methods can assess the corrosion situation to a certain extent, they have some limitations, such as complex and expensive detection equipment, time-consuming and labor-intensive detection process, and the results are greatly affected by human factors. In addition, traditional methods mostly focus on qualitative analysis and local assessment of the degree of corrosion, but lack a systematic quantitative assessment of the economic losses caused by corrosion of the entire structure.

[0004] my country is located in the Pacific Ring of Fire. The casualties and property losses caused by strong earthquakes in recent years are difficult to estimate. Economic loss assessment is an important basis for engineering management and decision-making. Accurately assessing the direct economic losses of corroded reinforced concrete structures is of great significance for formulating reasonable maintenance, reinforcement, and repair strategies, extending the service life of the structure, and saving economic costs. At this stage, there is an urgent need for a systematic and efficient assessment method to conduct a comprehensive quantitative analysis of the economic losses of corroded reinforced concrete structures. Taylor series expansion, as an important mathematical tool, has significant advantages in dealing with complex nonlinear problems. Through Taylor series expansion, complex loss assessment problems can be transformed into polynomial solution problems, thereby simplifying the calculation process and improving assessment efficiency. Summary of the invention

[0005] The present invention adopts the Taylor series expansion method to take into account the square terms, cross product terms and higher-order terms that may affect the calculation results into the demand model, and proves the rationality of the elimination results from a mathematical point of view through the step-by-step elimination method. A direct economic loss index evaluation method for corroded structures based on Taylor series expansion is proposed, which provides a more comprehensive method for direct economic loss analysis considering the combined effects of earthquakes and corrosion in actual engineering projects, and the method is applied to the direct economic loss evaluation of actual engineering structures.

[0006] A method for evaluating direct economic losses of corroded building structures based on Taylor series includes the following steps:

[0007] Step 1: Based on the internationally public earthquake database, select a sufficient number of real main shock and aftershock records as earthquake input; use mathematical methods to simulate the material performance degradation process caused by corrosion, as shown in the following formula:

[0008] (1) Reduction in steel section due to corrosion:

[0009]

[0010] In the formula, A′ s and A s Respectively represent the cross-sectional area of ​​the steel bar after corrosion and without corrosion; π is the pi; D is the diameter of the steel bar without corrosion; η is the corrosion rate.

[0011] (2) Reduction in steel bar strength due to corrosion:

[0012] Yield strength: f′ y =(1-0.5η)f y

[0013] Ultimate tensile strength: f′ u =(1-0.5η)f u

[0014] Ultimate elongation: ε′ u =(1-3η)ε u

[0015] In the formula, f′ y and f y are the yield strength of steel bars after corrosion and without corrosion, respectively; f′ u He f u is the ultimate tensile strength of the steel bar after and without corrosion; ε′ u and ε u It is the ultimate elongation of steel bars after corrosion and without corrosion.

[0016] (3) Concrete degradation due to corrosion:

[0017] Concrete compressive strength:

[0018] The average tensile strain of concrete

[0019] Variation of the width of the concrete beam: b f -b0=n c w cr

[0020] Concrete crack width: w cr =2π(v rs -1)X

[0021] In the formula, f′ c and f c are the compressive strength of concrete after corrosion and without corrosion, respectively; K is a parameter, which is taken as 0.1; ε c0 represents the peak compressive strain; b f and b0 represent the width of the beam after and without corrosion; n c Indicates the number of steel bars in the compression zone; v rs represents the volume expansion rate; X represents the corrosion depth.

[0022] Based on the above mathematical model, a finite element analysis model of the corroded structure is established. The selected main aftershock records are used as input to perform nonlinear time history analysis on the structure to obtain damage data of structures with different corrosion rates under earthquake action;

[0023] Step 2: Take the logarithm of the main shock intensity, aftershock intensity and structural damage parameters, and use Taylor series expansion to construct a generalized probabilistic seismic demand model for the structure, as shown in the following formula:

[0024] Main shock conditions:

[0025] ln[EDP MS (Θ MS )]=θ 0M +θ 1M ln(IM MS )+θ 2M [ln(IM MS )] 2 +θ 3M [ln(IM MS )] 3 +…+σ MS ε

[0026] Main shock and aftershock conditions:

[0027] ln[EDP MA (Θ MA )]=θ 0MA +θ 1MA ln(IM MS )+θ 2MA ln(IM AS )+θ 31MA [ln(IM MS )] 2 +θ 32MA [ln(IM AS )] 2 +θ 33MA [ln(IM MS)·ln(IM AS )]+…+σ MA ε

[0028] Where, IM MS and IM AS Indicates the intensity parameter of the main shock and aftershocks; EDP MS and EDP MA Respectively represent the main shock damage and main aftershock cumulative damage parameters of the structure; θ MS =(θ 0M ,θ 1M ,θ 2M ,θ 3M ,…), Θ MS =(θ MS ,σ MS ), θ MA =(θ 0MA ,θ 1MA ,θ 2MA ,θ 31MA ,…) and Θ MA =(θ MA ,σ MA ) is the model parameter set; σ MS ε and σ MA ε represents the model error.

[0029] Step 3: Use the step-by-step elimination method to delete the less important parameters in the generalized probabilistic seismic demand model. The process is as follows: first calculate the coefficient of variation of each parameter in the generalized probabilistic seismic demand model, delete the parameter with a high coefficient of variation, calculate the coefficient of variation of all parameters after deletion, delete the parameter with a high coefficient of variation again, and repeat the cycle until the formula form can take into account the requirements of accuracy and simplicity, and finally obtain a practical probabilistic seismic demand model;

[0030] Step 4: Construct a functional function as shown below:

[0031] g(IM,Θ)=ln(C)-ln[D(IM,Θ)]

[0032] Where IM is the general name of the earthquake intensity parameter; C represents the resistance parameter of the structure; ln[D(IM,Θ)] represents the demand model of the structure. When ln[D(IM,Θ)]=ln[EDP MS (Θ MS )], indicating that this equation is the function function under the main shock, similarly ln[D(IM,Θ)]=ln[EDP MA (Θ MA )]; Θ is the general name of the model parameters, when Θ = Θ MS This equation represents the function of the main shock under the action of the main shock. Similarly, Θ = Θ MA.

[0033] The median value and range of seismic vulnerability of structures with different corrosion rates are calculated using the first-order second moment method, as shown in the following formula:

[0034] Median value of the vulnerability curve: F(LS|IM,Θ)=P[g(IM,Θ)≤0|IM,Θ]

[0035] Vulnerability curve strip: {Φ[-β(IM)-σ β (IM)],Φ[-β(IM)+σ β (IM)]}

[0036] Where LS represents the limit state of the structure; β(IM) is the reliability index; σ β (IM) is the standard deviation of the reliability index β(IM).

[0037] Based on the direct economic loss coefficient, the median value and range of the economic loss index L(·) of the structure under different corrosion rates are obtained, as shown in the following formula:

[0038]

[0039] Where, DS i and LS i represent the i-th damage state and i-th limit state of the structure respectively; R DS,i Indicates that the structure is in DS i The loss coefficient when .

[0040] Beneficial effects of the present invention: The purpose of the present invention is to solve the drawback that only fixed-mode demand models can be considered in existing economic loss index assessment methods. At present, when calculating the economic loss index, a mathematical model that constructs a structural demand model using a single main shock parameter or a linear addition of main shock and aftershock parameters is used, and it is difficult to expand the form of the demand model. The present invention uses the Taylor series expansion method to take into account the square terms, cross product terms and higher-order terms that may affect the calculation results into the demand model, and proves the rationality of the elimination results from a mathematical perspective through the step-by-step elimination method, solving the problem that it is difficult to expand the form of the demand model in the traditional analysis process.

[0041] The method of the present invention can be used to establish a direct economic loss analysis model for corroded engineering structures, and can evaluate the loss range of engineering structures under earthquakes and corrosion, providing a theoretical basis and a new evaluation method for loss assessment and risk prevention and control in engineering construction. The method uses Taylor series to expand the needs of the structure, and then derives the vulnerability curve of the structure, and finally obtains the direct economic loss index of the structure. The method has the advantages of simple calculation and wide application range, and can provide a scientific basis for the maintenance and management of corroded reinforced concrete structures, and ensure the long-term safe operation of infrastructure. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a flow chart of a method for evaluating direct economic losses of corroded building structures based on Taylor series of the present invention;

[0043] Figure 2 is a diagram of the item deletion process in one embodiment of the present invention - taking the structure of η=0 as an example;

[0044] Figure 3 It is a practical probability demand model-main shock in one embodiment of the present invention;

[0045] Figure 4 It is a practical probability demand model-mainshock-aftershock in one embodiment of the present invention;

[0046] Figure 5 is a vulnerability median value and a strip chart in one embodiment of the present invention;

[0047] In the figure, (a) is the fragility result diagram when the limit state is LS1 and η = 0, (b) is the fragility result diagram when the limit state is LS2 and η = 0, (c) is the fragility result diagram when the limit state is LS3 and η = 0, (d) is the fragility result diagram when the limit state is LS4 and η = 0, (e) is the fragility result diagram when the limit state is LS1 and η = 0.05, (f) is the fragility result diagram when the limit state is LS2 and η = 0.05, (g) is the fragility result diagram when the limit state is LS3 and η = 0.05, (h) is the fragility result diagram when the limit state is LS4 and η = 0.05, (i) (a) is the fragility result diagram when the limit state is LS1 and η = 0.1, (j) is the fragility result diagram when the limit state is LS2 and η = 0.11, (k) is the fragility result diagram when the limit state is LS3 and η = 0.1, (l) is the fragility result diagram when the limit state is LS4 and η = 0.1, (m) is the fragility result diagram when the limit state is LS1 and η = 0.15, (n) is the fragility result diagram when the limit state is LS2 and η = 0.15, (o) is the fragility result diagram when the limit state is LS3 and η = 0.15, (p) is the fragility result diagram when the limit state is LS4 and η = 0.15;

[0048] Figure 6 is the median value and range of the economic loss index in one embodiment of the present invention;

[0049] (a) is the economic loss index when η=0, (b) is the economic loss index when η=0.05, (c) is the economic loss index when η=0.1, and (d) is the economic loss index when η=0.15. DETAILED DESCRIPTION

[0050] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0051] like Figure 1 As shown, the direct economic loss index assessment method for corroded structures based on Taylor series expansion provided in this embodiment solves the drawback of existing economic loss index assessment methods that only fixed mode demand models can be considered, and square terms, cross product terms and higher-order terms that may affect the calculation results are taken into account in the demand model, and the rationality of the elimination results is proved from a mathematical perspective through the step-by-step elimination method. The direct economic loss index assessment method for corroded structures based on Taylor series expansion of the present invention can be used to establish a direct economic loss analysis model for corroded engineering structures, and can evaluate the loss range of engineering structures under earthquakes and corrosion, providing a theoretical basis and a new assessment method for loss assessment and risk prevention and control in engineering construction.

[0052] A method for assessing direct economic losses of corroded building structures based on Taylor series, the specific steps of the method are:

[0053] Step S1, selecting real main shock and aftershock records as seismic input, using mathematical methods to simulate the degradation of structural materials caused by corrosion, and performing finite element modeling of the corroded structure based on mathematical methods; performing nonlinear time history analysis on the finite element model of the corroded structure under the action of the main shock and aftershock sequence, and obtaining damage data of the structure under different corrosion rate conditions.

[0054] Specifically in this embodiment, the above step S1 also includes the following steps:

[0055] S11. Based on the internationally public earthquake database, select a sufficient number of real main shock and aftershock records as earthquake input;

[0056] S12. Select η=0, 0.05, 0.1 and 0.15 to represent four working conditions of no corrosion, slight corrosion, moderate corrosion and severe corrosion respectively, and use mathematical methods to simulate the material performance degradation process caused by corrosion, as shown in the following formula, as shown in the following formula.

[0057] (1) Reduction in steel section due to corrosion:

[0058]

[0059] In the formula, A′ s and A s Respectively represent the cross-sectional area of ​​the steel bar after corrosion and without corrosion; π is the pi; D is the diameter of the steel bar without corrosion; η is the corrosion rate.

[0060] (2) Reduction in steel bar strength due to corrosion:

[0061] Yield strength: f′ y =(1-0.5η)f y

[0062] Ultimate tensile strength: f′ u =(1-0.5η)f u

[0063] Ultimate elongation: ε′ u =(1-3η)ε u

[0064] In the formula, f′ y and f y are the yield strength of steel bars after corrosion and without corrosion, respectively; f′ u He f u is the ultimate tensile strength of the steel bar after and without corrosion; ε′ u and ε u It is the ultimate elongation of steel bars after corrosion and without corrosion.

[0065] (3) Concrete degradation due to corrosion:

[0066] Concrete compressive strength:

[0067] The average tensile strain of concrete

[0068] Variation of the width of the concrete beam: b f -b0=n c w cr

[0069] Concrete crack width: w cr =2π(v rs -1)X

[0070] In the formula, f′ c and f c are the compressive strength of concrete after corrosion and without corrosion, respectively; K is a parameter, which is taken as 0.1; ε c0 represents the peak compressive strain; bf and b0 represent the width of the beam after and without corrosion; n c Indicates the number of steel bars in the compression zone; v rs represents the volume expansion rate; X represents the corrosion depth.

[0071] S13. Based on the above mathematical model, a finite element analysis model of the corroded structure is established. The selected main aftershock records are used as input to perform nonlinear time history analysis on the structure to obtain damage data of structures with different corrosion rates under earthquake action.

[0072] Step S2: Take the logarithm of the main shock intensity, aftershock intensity and structural damage parameter, and construct a generalized probabilistic seismic demand model of the structure by using Taylor series expansion.

[0073] Specifically in this embodiment, the above step S2 also includes the following steps:

[0074] Based on the structural damage data obtained in step 1, the spectral acceleration Sa is used as the ground motion intensity parameter, and the main shock intensity (Sa MS ), aftershock intensity (Sa AS ) and structural damage parameters (DI, DI MS Indicates the main shock damage, DI MA The logarithm of ( ) represents the cumulative damage of the main shock and aftershocks, and the Taylor series expansion method is used to construct the generalized probabilistic seismic demand model of the structure, as shown in the following formula:

[0075] Main shock conditions:

[0076] ln[DI MS (Θ MS )]=θ 0M +θ 1M ln(Sa MS )+θ 2M [ln(Sa MS )] 2 +θ 3M [ln(Sa MS )] 3 +…+σ MS ε

[0077] Main shock and aftershock conditions:

[0078] ln[DI MA (Θ MA )]=θ 0MA +θ 1MA ln(Sa MS )+θ 2MA ln(Sa AS )

[0079] +θ 31MA [ln(SaMS )] 2 +θ 32MA [ln(Sa AS )] 2 +θ 33MA [ln(Sa MS )·ln(Sa AS )]

[0080] +…+σ MA ε

[0081] In the formula, θ MS =(θ 0MA ,θ 1MA ,θ 2MA ,θ 31MA ,…) and Θ MA =(θ MA ,σ MA ) is the model parameter set; σ MS ε and σ MA ε represents the model error.

[0082] Step S3: Use the step-by-step elimination method to delete the less important parameter items in the generalized probabilistic seismic demand model to obtain a practical probabilistic seismic demand model that takes into account both accuracy and simplicity.

[0083] Specifically in this embodiment, the above step S3 also includes the following steps:

[0084] The step-by-step elimination method is used to delete the less important parameters in the generalized probabilistic seismic demand model. The process is as follows: first, the coefficient of variation of each parameter in the generalized probabilistic seismic demand model is calculated, and a parameter with a high coefficient of variation is deleted. The coefficient of variation of all parameters after deletion is calculated again, and a parameter with a high coefficient of variation is deleted again. This cycle is repeated until the formula form can take into account the requirements of both accuracy and simplicity. Taking the structure of η=0 as an example, the deletion process is as follows: Figure 2 As shown in the figure, the final practical probability earthquake demand model is as follows Figure 3 , Figure 4 , as shown in Table 1 and Table 2.

[0085] Table 1θ MS The calculation results

[0086]

[0087] Table 2θ MA The calculation results

[0088]

[0089] Step S4, construct a functional function, and then calculate the median value and range of seismic vulnerability of structures with different corrosion rates, and then obtain the median value and range of economic loss index of structures under different corrosion rates based on the direct economic loss coefficient.

[0090] Specifically in this embodiment, the above step S4 also includes the following steps:

[0091] S41. Construct a functional function as shown below:

[0092] g(IM,Θ)=ln(C)-ln[D(IM,Θ)]

[0093] Where IM is the general name of the earthquake intensity parameter; C represents the resistance parameter of the structure; ln[D(IM,Θ)] represents the demand model of the structure. When ln[D(IM,Θ)]=ln[EDP MS (Θ MS )], indicating that this equation is the function function under the main shock, similarly ln[D(IM,Θ)]=ln[EDP MA (Θ MA )]; Θ is the general name of the model parameters, when Θ = Θ MS This equation represents the function of the main shock, and similarly Θ = Θ MA .

[0094] The median value and range of seismic vulnerability of structures with different corrosion rates are calculated by the first-order second moment method, as shown in the following formula and Figure 5 As shown:

[0095] Median value of the vulnerability curve: F(LS|IM,Θ)=P[g(IM,Θ)≤0|IM,Θ]

[0096] Vulnerability curve strip: {Φ[-β(IM)-σ β (IM)],Φ[-β(IM)+σ β (IM)]}

[0097] Where LS represents the limit state of the structure; β(IM) is the reliability index; σ β (IM) is the standard deviation of the reliability index β(IM).

[0098] Based on the direct economic loss coefficient, the median value and range of the economic loss index L(·) of the structure under different corrosion rates are obtained as follows: Figure 6 As shown:

[0099]

[0100] Where, DS i and LS irepresent the i-th damage state and i-th limit state of the structure respectively; R DS,i Indicates that the structure is in DS i The loss coefficient when .

[0101] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. It should be pointed out that a person skilled in the art can make several improvements and modifications without departing from the technical principles of the present invention, and these improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A method for assessing direct economic losses of corroded building structures based on Taylor series, characterized in that: The steps include: Step 1: Select real main shock and aftershock records as ground motion input, use mathematical methods to simulate the degradation of structural materials caused by corrosion, and perform finite element modeling of the corroded structure based on mathematical methods; perform nonlinear time history analysis on the finite element model of the corroded structure under the action of the main shock and aftershock sequence, and obtain the damage data of the structure under different corrosion rates; Step 2: Take the logarithm of the main shock intensity, aftershock intensity and structural damage parameters, and use Taylor series expansion to construct a generalized probabilistic seismic demand model for the structure; as shown in the following formula: Main shock conditions: ln[EDP MS (I MS )]=θ 0M +θ 1M ln(IM MS )+θ 2M [ln(IM MS )] 2 +θ 3M [ln(IM MS )] 3 +…+s MS e Main shock and aftershock conditions: ln[EDP MA (I MA )]=θ 0MA +θ 1MA ln(IM MS )+θ 2MA ln(IM AS ) +θ 31MA [ln(IM MS )] 2 +θ 32MA [ln(IM AS )] 2 +θ 33MA [ln(IM MS )·ln(IM AS )] +…+s MA e Where, IM MS and IM AS Indicates the intensity parameter of the main shock and aftershocks; EDP MS and EDP MA They represent the main shock damage and main aftershock cumulative damage parameters of the structure respectively; i MS =(θ 0M ,i 1M ,i 2M ,i 3M ,…), T MS =(θ MS ,s MS ),θ MA =(θ 0MA ,i 1MA ,i 2MA ,i 31MA ,…) and Θ MA =(θ MA ,s MA ) for model parameter set; p MS e and s MA e indicates model error; Step 3: Use the step-by-step elimination method to delete the less important parameter items in the generalized probabilistic seismic demand model to obtain a practical probabilistic seismic demand model that takes into account both accuracy and simplicity; The step-by-step elimination method is used to delete the less important parameters in the generalized probabilistic seismic demand model. The process is as follows: first, the coefficient of variation of each parameter in the generalized probabilistic seismic demand model is calculated, and a parameter with a high coefficient of variation is deleted. The coefficient of variation of all parameters after deletion is calculated again, and a parameter with a high coefficient of variation is deleted again. This cycle is repeated until the formula form can take into account the requirements of both accuracy and simplicity, and finally a practical probabilistic seismic demand model is obtained. Step 4: Construct a functional function to calculate the median value and range of seismic vulnerability of structures with different corrosion rates. Based on the direct economic loss coefficient, obtain the median value and range of the economic loss index of structures under different corrosion rates.

2. A method for assessing direct economic losses of corroded building structures based on Taylor series according to claim 1, characterized in that: The step 1 specifically includes: Based on the internationally public earthquake database, a sufficient number of real main shock and aftershock records are selected as earthquake inputs; mathematical methods are used to simulate the material performance degradation process caused by corrosion, as shown in the following formula: (1) Reduction in steel section due to corrosion: In the formula, A s ' and A s Represent the cross-sectional area of ​​the steel bar after corrosion and without corrosion, respectively; π is the pi; D is the diameter of the steel bar without corrosion; η is the corrosion rate; (2) Reduction in steel bar strength due to corrosion: Yield strength: f y '=(1-0.5η)f y Ultimate tensile strength: f u '=(1-0.5η)f u Ultimate elongation: ε u '=(1-3η)ε u In the formula, f y ' and f y are the yield strength of steel bars after corrosion and without corrosion, respectively; f u 'What u is the ultimate tensile strength of the steel bar after and without corrosion; ε u ' and ε u It is the ultimate elongation of the steel bar after corrosion and without corrosion; (3) Concrete degradation due to corrosion: Concrete compressive strength: The average tensile strain of concrete Variation of the width of the concrete beam: b f -b0=n c w cr Concrete crack width: w cr =2π(v rs -1)X In the formula, f c ' and f c are the compressive strength of concrete after corrosion and without corrosion, respectively; K is a parameter, which is taken as 0.1; ε c0 represents the peak compressive strain; b f and b0 represent the width of the beam after and without corrosion; n c Indicates the number of steel bars in the compression zone; v rs represents the volume expansion rate; X represents the corrosion depth; Based on the above mathematical formula, a finite element analysis model of the corroded structure is established, and the selected main shock and aftershock records are used as input to perform nonlinear time history analysis on the structure to obtain damage data of structures with different corrosion rates under earthquake action.

3. The method for evaluating direct economic losses of corroded building structures based on Taylor series according to claim 1, characterized in that: The step 4 specifically includes: Construct the function as shown below: g(IM,Θ)=ln(C)-ln[D(IM,Θ)] Where IM is the general name of the earthquake intensity parameter; C represents the resistance parameter of the structure; ln[D(IM,Θ)] represents the demand model of the structure. When ln[D(IM,Θ)]=ln[EDP MS (Θ MS )], indicating that this equation is the function function under the main shock, similarly ln[D(IM,Θ)]=ln[EDP MA (Θ MA )]; Θ is the general name of the model parameters, when Θ = Θ MS This equation represents the function of the main shock under the action of the main shock. Similarly, Θ = Θ MA ; The median value and range of seismic vulnerability of structures with different corrosion rates are calculated using the first-order second moment method, as shown in the following formula: Median value of the vulnerability curve: F(LS|IM,Θ)=P[g(IM,Θ)≤0|IM,Θ] Vulnerability curve strip: {Φ[-β(IM)-σ β (IM)],Φ[-β(IM)+σ β (IM)]} Where LS represents the limit state of the structure; β(IM) is the reliability index; σ β (IM) is the standard deviation of the reliability index β(IM); Based on the direct economic loss coefficient, the median value and range of the economic loss index L(·) of the structure under different corrosion rates are obtained, as shown in the following formula: Where, DS i and LS i represent the i-th damage state and i-th limit state of the structure respectively; R DS,i Indicates that the structure is in DS i The loss coefficient when .

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