Method and device for calculating the vulnerability of structures with circular dangerous sections

Abstract

The present invention discloses a method and device for calculating the vulnerability of a structure with an annular dangerous section. The method includes the following steps: determining the annular dangerous section of the structure and its failure mode according to the stress characteristics of the annular dangerous section of the structure; confirming the structural bearing capacity factor and its variability according to the annular dangerous section and its failure mode; confirming the structural response factor and its variability according to the annular dangerous section and its failure mode; and obtaining the median ground acceleration capacity and variability of the structure according to the structural bearing capacity factor and its variability, the structural response factor and its variability, and the separation of variables method. The method and device are applicable to all structures with annular dangerous sections, and perform vulnerability calculations for nuclear power plants with the most dangerous walls being cylindrical walls and the most dangerous sections being annular sections, and make the earthquake PSA analysis results of nuclear power plants more accurate. The method is easy to operate, and its calculation process is closer to the actual plant, and the calculation results are more accurate and reliable.

Description

Technical Field

[0001] The invention belongs to the technical field of building structures, and in particular relates to a method and a device for calculating the vulnerability of a structure suitable for an annular dangerous section. Background Art

[0002] The nuclear fuel in a nuclear power plant is highly radioactive. Once its safety is destroyed or even leaks due to an earthquake, it will cause serious disasters with immeasurable consequences. Therefore, earthquakes are one of the main external disasters faced by nuclear power plants. Probabilistic Safety Assessment (PSA) analysis is an earthquake probability analysis of earthquakes and disasters in nuclear power plants. By evaluating the overall risk of nuclear power plants under different intensities, it identifies possible weaknesses in seismic design, thereby providing a comprehensive earthquake risk insight for nuclear power plants. Its three basic components include seismic hazard analysis, seismic vulnerability analysis, and power plant response analysis. Seismic vulnerability analysis evaluates the conditional failure probability of nuclear power plant SSC under given earthquake ground motion intensity conditions by making the best estimate of the seismic response and seismic resistance of nuclear power plant structures, systems and equipment (SSC) under seismic conditions. The purpose of structure seismic vulnerability analysis is to estimate the capacity of structures relative to earthquake acceleration parameters (such as PGA).

[0003] The seismic vulnerability of a structure can be expressed as the best estimate of the median ground acceleration capacity A m And the relationship between the two random variables. The two random variables can be expressed by two logarithmic standard deviations: random uncertainty β R and epistemic uncertainty β U The ground acceleration capability A can be expressed as:

[0004] A=A m e R e U (1)

[0005] Among them, e R and e U are random variables with a median value of 1.0, representing the inherent randomness about the median (also called random uncertainty) and the uncertainty in the level of knowledge (also called epistemic uncertainty). In this model, e R and e U is a log-normal distribution, corresponding to a log-standard deviation β R and β U .

[0006] For each ground acceleration value a, the seismic vulnerability f can be expressed by (2):

[0007]

[0008] Where: Q = P[f < f′|a], which represents the subjective probability (confidence level) of conditional failure probability f < f′ when the peak ground acceleration is a; Φ -1 [.] is the inverse function of the standard normal cumulative distribution. From equation (2), we can get the following earthquake vulnerability curve: Figure 1 .

[0009] The calculation of seismic vulnerability of structures is a key link in the PSA analysis of nuclear power plants. Therefore, it is necessary to ensure that the median seismic capacity A of the most dangerous section of the structure can be accurately calculated. m and its standard deviation of variability β R and β U The median seismic capacity can be obtained by multiplying the strength factor of the most dangerous section by the seismic acceleration PGA.

[0010] The guideline TR-103959[1] recommends the use of the separation of variables method to calculate the seismic vulnerability of structures. According to this guideline, the median ground acceleration capacity A of the structure is m It can be expressed as the product of two factors and the site-specific PGA:

[0011] A m =F C ·F SR ·PGA ref (3)

[0012] where F c is the structural bearing capacity factor of the most dangerous section, F SR is the most dangerous cross-sectional structural response factor, PGA ref PGA for a specific site of the project.

[0013] The variability (logarithmic standard deviation) of earthquake vulnerability can be obtained by taking the square root of the sum of the squares of the uncertainties.

[0014]

[0015]

[0016] where β R_C and β U_C is the random uncertainty and epistemic uncertainty of the structural bearing capacity of the most dangerous section; β R_SR and β U_SR is the random uncertainty and epistemic uncertainty of the structural response factor of the most dangerous section.

[0017] In summary, the analysis of the seismic vulnerability of structures requires accurate calculation of the structural bearing capacity factor (F c ), structural response factor (F SR ), random uncertainty and epistemic uncertainty of structural bearing capacity (β R_C and β U_C ), random uncertainty and epistemic uncertainty of structural response factors (β R_SR and β U_SR ).

[0018] In the existing guidelines for earthquake PSA analysis, there are no regulations for earthquake vulnerability analysis of circular dangerous sections, and there is no systematic calculation method for its safety factor and variability. Among the many types of nuclear power plants, some important walls of the reactor building are built in a cylindrical form (such as the containment shell and the primary and secondary shielding walls of the internal structure), and the dangerous section of the cylindrical wall is a circular section. However, there are no relevant guidelines for reference in the calculation of the vulnerability of circular cross-section earthquake PSA analysis structures. Therefore, it is necessary to invent a method for calculating the vulnerability of structures suitable for circular dangerous sections, which is convenient for structural analysts to calculate the vulnerability of plants with cylindrical walls, so as to ensure the accuracy of earthquake PSA analysis. Summary of the invention

[0019] The technical problem to be solved by the present invention is to provide a method and device for calculating the vulnerability of structures with annular dangerous sections in view of the above-mentioned deficiencies in the prior art, so as to be able to calculate the vulnerability of nuclear power plants where the most dangerous walls are cylindrical walls and the most dangerous sections are annular sections, and to make the earthquake PSA analysis results of nuclear power plants more accurate.

[0020] The technical solution adopted to solve the technical problem of the present invention is to provide a method for calculating the vulnerability of structures applicable to annular dangerous sections, comprising the following steps:

[0021] According to the stress characteristics of the circular section of the structure, determine the circular dangerous section of the structure and its failure mode;

[0022] According to the annular dangerous section and its failure mode, the structural bearing capacity factor and its variability are confirmed;

[0023] According to the annular dangerous section and its failure mode, the structural response factor and its variability are confirmed;

[0024] According to the structural bearing capacity factor and its variability, the structural response factor and its variability, the median ground acceleration capacity A of the structure is obtained according to the separation of variables method. m and variability β R and β U .

[0025] Among the many reactor types in nuclear power plants, some important walls of the reactor building are built in a cylindrical form (such as the containment shell and the primary and secondary shielding walls of the internal structure), and the dangerous section of the cylindrical wall is a circular section.

[0026] Preferably, the failure modes of the annular dangerous section of the structure are determined to include: tangential shear failure mode and bending failure mode.

[0027] Preferably, the step of confirming the structural bearing capacity factor and its variability according to the annular dangerous section and its failure mode specifically comprises the following steps:

[0028] (a) Determine the structural strength factor and its variability;

[0029] (ii) Determine the inelastic energy absorption factor and its variability;

[0030] (iii) Determine the structural bearing capacity factor and its variability of the annular dangerous section based on the structural strength factor and its variability, the inelastic energy absorption factor and its variability.

[0031] Preferably, the step (i) of determining the structural strength factor and its variability specifically comprises the following steps:

[0032] iCalculate the tangential shear failure factor;

[0033] ii Calculate the bending failure factor;

[0034] iii. Determine the variability of the structural strength factor.

[0035] Preferably, the step (ii) of determining the inelastic energy absorption factor and its variability specifically comprises the following steps:

[0036] Determine the inelastic energy absorption factor: F u =1.25;

[0037] Determine the random uncertainty of the inelastic energy absorption factor: β r_u =0.00;

[0038] Determine the epistemic uncertainty of the inelastic energy absorption factor: β u_u =0.00.

[0039] Preferably, the step (iii) of determining the structural bearing capacity factor and its variability of the annular dangerous section according to the structural strength factor and its variability, the inelastic energy absorption factor and its variability specifically comprises the following steps:

[0040] Determine the structural bearing capacity factor, the calculation formula is as follows F C =F s ·F u , where Fc is the structural bearing capacity factor of the annular dangerous section, F s is the strength factor of the structural bearing capacity of the annular dangerous section, F u is the inelastic energy absorption factor;

[0041] Determine the random uncertainty β of the structural bearing capacity factor r_C =0;

[0042] Determine the epistemic uncertainty of the structural bearing capacity factor, the calculation formula is expressed as follows Among them, β μ_c is the epistemic uncertainty of the structural bearing capacity factor, β μ_Fs is the epistemic uncertainty of the strength factor of the annular dangerous section, β μ_μ The epistemic uncertainty is the inelastic energy absorption factor.

[0043] Preferably, the tangential shear failure factor F of the final annular dangerous section in step i is Vs The calculation formula is as follows:

[0044]

[0045] Among them, F Vs1 The median earthquake stress is less than Shear failure factor, f′ c is the median compressive strength of concrete, D s is the demand value of the annular dangerous section under the reference earthquake action, ν u1 is the median earthquake stress.

[0046] Preferably, the earthquake median stress is less than Shear failure factor F Vs1 The calculation formula is as follows:

[0047] Among them, C is the bearing capacity value of the circular dangerous section, D NS is the cross-sectional demand value under non-seismic action, D S is the demand value of the section under the reference earthquake action, ΔC S is the reduction in bearing capacity caused by the reference earthquake. Preferably, the earthquake median stress ν u1 The calculation formula is as follows:

[0048] v u1 =F Vs1 ·D S =CF Vs1 ·ΔC S -D NS

[0049] Preferably, the step ii of calculating the bending failure factor specifically comprises the following steps:

[0050] The tensile or compressive bending bearing capacity of the circular cross section is only related to the material strength and the calculated area. Therefore, the internal force of the cross section under the earthquake action will not cause the change of the bearing capacity value. The bending resistance of the cross section needs to consider the axial force and bending moment. Therefore, the bending failure factor F of the circular dangerous cross section is determined. Bs The calculation can be obtained by the following two formulas:

[0051] F Bs ·N demend地震 =N capacity -N demend非地震 (9)

[0052] F Bs ·M demend地震 =M capacity -M demend非地震 (10)

[0053] Among them, F BS is the bending failure strength factor of the annular dangerous section, N demand地震 is the axial force of the circular dangerous section of the structure under the reference earthquake, M demand地震 is the bending moment of the circular dangerous section of the structure under the reference earthquake, N demand非地震 is the axial force of the annular dangerous section of the structure under the action of dead load, live load and prestressed non-seismic conditions in the seismic probabilistic safety assessment (PSA) analysis stage, M demand非地震 is the bending moment of the annular dangerous section of the structure under the action of dead load, live load and prestressed non-seismic conditions in the seismic probabilistic safety assessment (PSA) analysis stage, N capacity is the axial force bearing capacity of the annular dangerous section, M capacity is the moment bearing capacity of the annular dangerous section;

[0054] a. According to the principle of plane section assumption, the axial force value N of the annular dangerous section is determined according to the stress-strain distribution relationship of the material annular dangerous section. capacity Total bearing capacity of bending moment M capacity ;

[0055] The total bearing capacity of axial force and moment of concrete, steel bars and prestressed steel tendons is superimposed as shown in the following formula:

[0056] Axial force: N capacity (c) = N concrete (c)+N steel (c)+N prestress (c) (22)

[0057] Bending moment: M capacity (c) = M concrete (c)+Msteel (c)+M prestress (c) (23)

[0058] Where c is the distance from the neutral axis to the outer radius, i.e. the height of the concrete compression zone, N concrete (c) is the axial force on the concrete, N steel (c) is the axial force on the steel bar, N prestress (c) is the axial force on the prestressed steel tendon, M concrete (c) is the total moment bearing capacity of concrete, M steel (c) is the total moment bearing capacity of the steel bar, M prestress (c) is the total moment bearing capacity of the prestressed steel tendons;

[0059] Substituting equations (22) and (23) into equations (9) and (10), we obtain the following formula:

[0060] F Bs ·N demand地震 =N concrete (c)+N steel (c)+N prestress (c)-N demand非地震 (twenty four)

[0061] F Bs ·M demand地震 =M concrete (c)+M steel (c)+M prestress (c)-M demand非地震 (25)

[0062] Formulas (24) and (25) constitute the equation containing the neutral axis position distance c and the annular dangerous section bending failure strength factor F Bs The equation group is solved to obtain the bending failure strength factor F of the annular dangerous section. Bs value;

[0063] The strength factor Fs of the structural bearing capacity of the final annular dangerous section is the minimum value of the shear failure strength factor and the bending failure strength factor:

[0064] F S =min(F Vs ,F Bs ) (26),

[0065] Among them, F Vs is the shear failure strength factor.

[0066] Preferably, the step iii of determining the variability of the intensity factor specifically comprises the following steps:

[0067] 1) Determine the uncertainty β of the material strength value u_mat , and its calculation formula is as follows:

[0068]

[0069] Among them, Fs is the strength factor of the structural bearing capacity of the annular dangerous section, F s_mβ is the intensity factor related to the intensity value;

[0070] 2) Determine the uncertainty β of the strength calculation formula u_eqn , and its calculation formula is as follows:

[0071]

[0072] Among them, F s_eβ is the intensity factor associated with the calculation formula;

[0073] Determining the epistemic uncertainty β of the strength factor of the circular dangerous section u_Fs , can be calculated by the following formula:

[0074]

[0075] Preferably, the step of confirming the structural response factor and its variability according to the annular dangerous section and its failure mode specifically comprises the following steps:

[0076] (i) Identify ground motion factors and their variability;

[0077] (ii) confirm the structural damping factor and its variability;

[0078] (iii) confirm the structural model factors and their variability;

[0079] (iv) confirm the mode superposition factors and their variability;

[0080] (v) Confirm the earthquake time history fitting factors and their variability;

[0081] (vi) identify base-structure interaction factors and their variability;

[0082] (vii) Identify the spatial combination factors of seismic components and their variability;

[0083] (viii) Confirm the structural response factors and their variability.

[0084] Preferably, the step (i) of confirming the ground motion factor and its variability specifically comprises the following steps:

[0085] ia. Confirm the response spectrum and its uncertainty;

[0086] ib. Confirm the horizontal peak response and its uncertainty;

[0087] ic. Identify the vertical seismic components and their uncertainties.

[0088] Confirm the ground motion factor F GM : F GM =F SS ·F HD ·F VC (1)

[0089] Among them, F SS is the response spectrum shape factor, F HD is the horizontal peak response factor, F VC is the vertical earthquake component factor;

[0090] Determine the random uncertainty β of the ground motion factor r_GM :

[0091]

[0092] Among them, β r_SS is the random uncertainty of the response spectrum shape factor, β r_HD is the random uncertainty of the horizontal peak response factor, β r_VC is the random uncertainty of the vertical seismic component factor;

[0093] Confirm the epistemic uncertainty β of the ground motion factor u_GM :

[0094]

[0095] Among them, β u_SS is the epistemic uncertainty of the response spectrum shape factor, β u_HD is the epistemic uncertainty of the horizontal peak response factor, β u_VC is the epistemic uncertainty of the vertical seismic component factor.

[0096] Preferably, the step (ii) of confirming the structural damping factor and its variability specifically comprises the following steps:

[0097] When the structure is destroyed, it is considered that the steel bar has exceeded its yield state and the prestress has exceeded the yield state but has not reached the prestress failure. The damping will become larger. The calculation formula of the structural damping factor and its variability is:

[0098]

[0099] β r_SD =0

[0100]

[0101] Among them, F SD is the structural damping factor, Sa -σ To reduce the main frequency response spectrum of the reference earthquake structure with a standard deviation damping ratio, Sa ξ is the main frequency response spectrum of the reference earthquake structure under the median damping ratio, β r_SD is the random uncertainty of the structural damping factor, β u_SD is the epistemic uncertainty of the structural damping factor

[0102] Preferably, the step (iii) of confirming the structural model factors and their variability specifically comprises the following steps:

[0103] iiia. Confirm the frequency and its cognitive uncertainty, and consider the uncertainty of the model by adjusting the model's main frequency by 15% above and below. The analysis model in the initial stage is used as the median structure model, the model corresponding to 1.15 times the main frequency is used as the upper limit structure model, and the model corresponding to 0.85 times the main frequency is used as the lower limit structure model. Repeat the calculation process of the intensity factor respectively, and its cognitive uncertainty is calculated as follows:

[0104] The frequency factor takes the value of 1 and the random uncertainty is 0.

[0105] β u_M_F is the epistemic uncertainty of the frequency factor, F 频率中值 is the average value of the intensity factor calculated for the three models, F 频率上限值 Envelope values ​​of intensity factors calculated for the three models;

[0106] iiib. Confirm the vibration mode and its epistemic uncertainty. The vibration mode response factor and its random uncertainty can be 1 and 0. The epistemic uncertainty of the containment model can be 0.05 and that of the internal structure can be 0.15.

[0107] iiic. Confirm the torsion and its epistemic uncertainty. The reactor building configuration is cylindrical and approximately symmetrical. The frequencies in the two horizontal directions are approximately equal. It can be considered that the torsion effect is very small. The factor and random uncertainty of the torsion effect are 1 and 0 respectively, and the epistemic uncertainty is 0.05.

[0108] Confirm the structural model factor F M : F M =F M_F ·F M_MS ·F M_T (6)

[0109] Among them, F M_F is the frequency factor, F M_MS is the vibration factor, F M_T is the torsion factor;

[0110] Confirm the random uncertainty β of the structural model factor r_M :

[0111]

[0112] Among them, β r_M_F is the random uncertainty of the frequency factor, β r_M_MS is the random uncertainty of the vibration factor, β r_M_T is the random uncertainty of the torsion factor;

[0113] Confirm the epistemic uncertainty of the structural model factors β u_M :

[0114]

[0115] Among them, β u_M_F is the frequency factor epistemic uncertainty, β u_M_MS is the epistemic uncertainty of the vibration factor, β u_M_T Epistemic uncertainty as a reversal factor

[0116] Preferably, step (iv) determines the modal superposition factor and its variability. According to the guideline [1], the modal superposition factor and the epistemic uncertainty are 1 and 0 respectively, and the recommended value of random uncertainty can be from 0.05 for simple models to 0.15 for complex models.

[0117] Preferably, the step (v) confirms the earthquake time history fitting factors and their variability,

[0118] Using different artificial fitting time histories to perform structural time history analysis, repeating the intensity factor calculation process will result in different intensity factor values, and their epistemic uncertainty β r_TH The calculation formula is as follows:

[0119]

[0120] Among them, F thAve To calculate the average value of the intensity factor, F thUp is the envelope value of the calculated intensity factor. The time history fitting factor is 1 and the epistemic uncertainty is 0.

[0121] Preferably, the step (vi) of confirming the basis-structure interaction factors and their variability specifically comprises the following steps:

[0122] via.Confirmation of ground motion inconsistencies and their uncertainties;

[0123] vib. Confirm vertical spatial changes and their uncertainties;

[0124] vic. Confirm the soil-structure interaction and its uncertainty. Repeating the strength factor calculation process with different foundation soil parameters will result in different strength factor values, and its epistemic uncertainty β u_SSI The calculation formula is as follows:

[0125]

[0126] Among them, F SSI中值 is the average value of all calculated intensity factors, F SSI上限值 is the envelope value of all calculated intensity factors.

[0127] The soil-structure interaction factor takes the value of 1, and its random uncertainty is 0;

[0128] Basic structure factor F FSI : F FSI =F GMI ·F VS ·F SSI (11)

[0129] Among them, F GMI is the ground motion inconsistency factor, F VS is the vertical spatial variation factor, F SSI is the soil-structure interaction factor;

[0130] Random uncertainty of the underlying structure factor β r_FSI :

[0131] Among them, β r_GMI is the ground motion inconsistency random uncertainty, β r_VS is the random uncertainty of vertical spatial variation, β r_SSI is the random uncertainty of soil-structure interaction;

[0132] Epistemic uncertainty of the underlying structural factor β u_FSI :

[0133] Among them, β u_GMI is the epistemic uncertainty of ground motion inconsistency, β u_VS is the vertical spatial variation epistemic uncertainty, β u_SSI Epistemic uncertainty for soil-structure interactions.

[0134] Preferably, the step (vii) confirms the spatial combination factor of the earthquake components and their variability, and calculates the intensity factor by summing up the absolute values ​​of the earthquake forces in the three directions (X, Y, Z) as the earthquake demand force, with the cognitive uncertainty β r_ES The calculation formula is as follows:

[0135]

[0136] Among them, F s地震分量中值 is the calculated intensity factor, F S_EC Structural strength factor calculated to confirm the structural bearing capacity factor;

[0137] The spatial combination factor and epistemic uncertainty of the earthquake components are 1 and 0 respectively.

[0138] Preferably, the step (viii) confirming the structural response factor and its variability specifically comprises the following steps:

[0139] Structural response factor F SR : F SR =F GM ·F SD ·F M ·F MC ·F TH ·F FSI ·F EC (15)

[0140] Among them, F GM is the ground motion factor, F SD is the structural damping factor, F M is the structural model factor, F MC is the mode superposition factor, F TH is the earthquake time history fitting factor, F FSI is the basic structure factor, F EC is the spatial combination factor of the seismic component;

[0141] Random uncertainty of structural response factor β r_SR :

[0142]

[0143] Among them, β r_GM is the random uncertainty of the ground motion factor, β r_SD is the random uncertainty of the structural damping factor, β r_M is the random uncertainty of the structural model factors, β r_MC is the random uncertainty of the vibration mode superposition factor, β r_TH is the random uncertainty of the earthquake time history fitting factor, β r_FSI is the random uncertainty of the basic structure factor, β r_EC is the random uncertainty of the spatial combination factor of the seismic component;

[0144] Epistemic uncertainty of structural response factor β u_SR :

[0145]

[0146] Among them, β u_GM is the epistemic uncertainty of the ground motion factor, β u_SD is the epistemic uncertainty of the structural damping factor, β u_M is the epistemic uncertainty of the structural model factors, β u_MC is the epistemic uncertainty of the mode superposition factor, β u_TH is the epistemic uncertainty of the earthquake time history fitting factor, β u_FSI is the epistemic uncertainty of the underlying structural factor, β u_EC is the epistemic uncertainty of the spatial combination factor of the seismic components.

[0147] The present invention also provides a device for calculating the vulnerability of structures applicable to annular dangerous sections, comprising:

[0148] Failure unit, according to the stress characteristics of the circular section of the structure, determine the circular dangerous section of the structure and its failure mode;

[0149] The first variation unit confirms the structural bearing capacity factor and its variability based on the annular dangerous section and its failure mode determined by the failure unit;

[0150] The second variation unit confirms the structural response factor and its variability based on the annular dangerous section and its failure mode determined by the failure unit;

[0151] Separate the variable unit, according to the structural bearing capacity factor and its variability confirmed by the first variation unit, and the structural response factor and its variability confirmed by the second variation unit, and according to the separation variable method, the median ground acceleration capacity A of the structure is obtained. m and variability β R and β U .

[0152] The method and device for calculating the vulnerability of structures with annular dangerous sections in the present invention are applicable to all structures with annular dangerous sections, and can calculate the vulnerability of nuclear power plants with cylindrical walls as the most dangerous walls and annular sections as the most dangerous sections, and make the earthquake PSA analysis results of nuclear power plants more accurate. The method of the present invention is easy to operate, the calculation process is closer to the actual plant, and the calculation results are more accurate and reliable. BRIEF DESCRIPTION OF THE DRAWINGS

[0153] Figure 1 It is a schematic diagram of the seismic vulnerability curve of a structure in the prior art;

[0154] Figure 2It is a flow chart of a method for calculating the vulnerability of a structure applicable to an annular dangerous section in Embodiment 1 of the present invention;

[0155] Figure 3 It is a schematic diagram of the structure of the device for calculating the vulnerability of structures applicable to annular dangerous sections in embodiments 1 and 2 of the present invention. DETAILED DESCRIPTION

[0156] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0157] The embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be understood as limiting the present invention.

[0158] Example 1

[0159] like Figure 2 As shown, this embodiment provides a method for calculating the vulnerability of a structure applicable to an annular dangerous section, comprising the following steps:

[0160] S1 Determine the dangerous circular section of the structure and its failure mode according to the stress characteristics of the circular section of the structure;

[0161] S2 confirms the structural bearing capacity factor and its variability based on the annular dangerous section and its failure mode;

[0162] S3 confirms the structural response factor and its variability based on the annular dangerous section and its failure mode;

[0163] S4 According to the structural bearing capacity factor and its variability, the structural response factor and its variability, and the separation of variables method, the median ground acceleration capacity A of the structure is obtained. m and variability β R and β U .

[0164] Among the many reactor types in nuclear power plants, some important walls of the reactor building are built in a cylindrical form (such as the containment shell and the primary and secondary shielding walls of the internal structure), and the dangerous section of the cylindrical wall is a circular section.

[0165] like Figure 3 As shown, this embodiment also provides a device for calculating the vulnerability of structures applicable to annular dangerous sections, including:

[0166] Failure unit, according to the stress characteristics of the circular section of the structure, determine the circular dangerous section of the structure and its failure mode;

[0167] The first variation unit confirms the structural bearing capacity factor and its variability based on the annular dangerous section and its failure mode determined by the failure unit;

[0168] The second variation unit confirms the structural response factor and its variability based on the annular dangerous section and its failure mode determined by the failure unit;

[0169] Separate the variable unit, according to the structural bearing capacity factor and its variability confirmed by the first variation unit, and the structural response factor and its variability confirmed by the second variation unit, and according to the separation variable method, the median ground acceleration capacity A of the structure is obtained. m and variability β R and β U .

[0170] The method and device for calculating the vulnerability of structures with annular dangerous sections in this embodiment are applicable to all structures with annular dangerous sections. They can calculate the vulnerability of nuclear power plants with cylindrical walls as the most dangerous walls and annular sections as the most dangerous sections, and make the earthquake PSA analysis results of nuclear power plants more accurate. The method of this embodiment is easy to operate, the calculation process is closer to the actual plant, and the calculation results are more accurate and reliable.

[0171] Example 2

[0172] Among the many reactor types in nuclear power plants, some important walls of the reactor building are built in a cylindrical form (such as the containment shell and the primary and secondary shielding walls of the internal structure), and the dangerous section of the cylindrical wall is a circular section.

[0173] This embodiment provides a method for calculating the vulnerability of a structure applicable to an annular dangerous section, comprising the following steps:

[0174] (1) According to the stress characteristics of the circular section of the structure, determine the circular dangerous section of the structure and its failure mode; first, it is necessary to determine the most dangerous section of the entire plant and its failure mode. According to the stress characteristics of the circular section, its failure mode is mainly tangential shear failure mode and bending failure mode.

[0175] (2) According to the annular dangerous section and its failure mode, confirm the structural bearing capacity factor and its variability; according to Table 2-1 of the standard "EPRI 103959", the structural bearing capacity can be divided into two cases: strength and inelastic energy absorption, and their safety factors and variability are calculated respectively. According to the failure mode, the strength factor is the smaller value of the tangential shear failure factor and the bending failure factor. Specifically, the following steps are included:

[0176] (I) Determine the structural strength factor and its variability, including the following steps:

[0177] According to the failure mode of the annular section, the structural strength factor of the annular dangerous section is divided into two types: tangential shear failure factor and bending failure factor.

[0178] EPRI 103959 gives the following relationship:

[0179] F s ·D S =CF s ·ΔC S -D NS (1)

[0180] Among them, C is the bearing capacity value of the circular dangerous section, D NS is the demand value of the annular dangerous section under non-seismic action, D S is the demand value of the annular dangerous section under the reference earthquake action, ΔC S The bearing capacity value is reduced due to the reference earthquake.

[0181] Intensity factor F S The calculation formula is as follows:

[0182]

[0183] iCalculation of tangential shear failure factor F Vs

[0184] The invention refers to the provisions of "EPRI 6041" to deduce the calculation method of the shear failure strength factor of the annular section of the vulnerability of the seismic PSA analysis structure.

[0185] According to Appendix N of EPRI 6041, the various terms of intensity factor can be calculated as follows:

[0186] a. Dangerous section bearing capacity value C:

[0187]

[0188] Among them, f′ c is the median compressive strength of concrete, f y is the median yield strength of steel bars, ρ h is the circumferential reinforcement ratio of the dangerous section, ρ m is the axial reinforcement ratio of the section.

[0189] b. Section demand value D for non-seismic action NS :

[0190]

[0191] Among them, σh非地震 is the hoop stress caused by non-seismic forces, σ m非地震 It is the axial stress caused by non-seismic force. Non-seismic force refers to the cross-sectional stress of the structure under non-seismic conditions such as dead load, live load, prestress, etc. during the PSA analysis stage.

[0192] c. Reference earthquake demand value D S :

[0193]

[0194] Among them, V s A is the tangential shear force at the dangerous section of the structure under the reference earthquake, s The effective shear area of ​​the cross section can be calculated by referring to the relevant formula in Appendix N of the guideline "EPRI TR-6041".

[0195] d. Reference earthquake-induced reduction in bearing capacity ΔC S :

[0196]

[0197] Among them, σ h地震 is the hoop stress of the dangerous section of the structure under the reference earthquake, σ m地震 is the axial stress of the dangerous section of the structure under the reference earthquake.

[0198] Substituting equations (3), (4), (5), and (6) into equation (2), we can obtain the shear failure factor F of the annular dangerous section: Vs1 .

[0199] The median earthquake stress is less than Shear failure factor F Vs1 The calculation formula is as follows:

[0200] D NS is the cross-sectional demand value under non-seismic action, D S is the demand value of the section under the reference earthquake action, ΔC S To refer to the reduction in bearing capacity caused by earthquake,

[0201] Introducing the shear failure factor F Vs1 The earthquake median stress ν u1 The calculation formula is as follows:

[0202] v u1 =F Vs1 ·D S =CF Vs1 ·ΔC S -D NS (7)

[0203] Where C is the bearing capacity of the circular dangerous section, ⊿C s D is the reduction in bearing capacity caused by the reference earthquake. NS is the demand value of the annular dangerous section under non-seismic action, D S is the demand value of the section under reference earthquake action.

[0204] Since EPRI 6041 stipulates that the earthquake median stress ν u Provision of limited values Therefore The final annular dangerous section tangential shear failure factor F Vs , and its calculation formula is as follows:

[0205]

[0206] Among them, F Vs1 The median earthquake stress is less than Shear failure factor, f c ' is the median compressive strength of concrete, D s is the demand value of the annular dangerous section under the reference earthquake action, ν u1 is the median earthquake stress.

[0207] ii. Calculate the bending failure factor, specifically including the following steps:

[0208] According to the GB50010-2010 standard, the bending or compression bearing capacity of a circular cross-section is only related to the material strength and the calculated area. Therefore, the internal force of the cross-section under the earthquake action will not cause a change in the bearing capacity value, that is, F s ·ΔC S The bending resistance of the normal section needs to consider the axial force and bending moment, and combined with the meaning of the other terms in formula (1), the bending failure factor F of the annular dangerous section is determined as Bs The calculation can be obtained by the following two formulas:

[0209] F Bs ·N demend地震 =N capacity -N demend非地震 (9)

[0210] F Bs ·M demend地震 =M capacity -M demend非地震 (10)

[0211] Among them, F BS is the bending failure strength factor of the annular dangerous section, N demand地震 M is the axial force of the circular dangerous section of the structure under the reference earthquake, demand地震is the bending moment of the circular dangerous section of the structure under the reference earthquake, N demand非地震 is the axial force of the annular dangerous section of the structure under the action of dead load, live load and prestressed non-seismic conditions in the seismic probabilistic safety assessment (PSA) analysis stage, M demand非地震 is the bending moment of the annular dangerous section of the structure under the action of dead load, live load and prestressed non-seismic conditions in the seismic probabilistic safety assessment (PSA) analysis stage, N capacity is the axial force bearing capacity of the annular dangerous section, M capacity is the moment bearing capacity of the annular dangerous section;

[0212] a. According to the principle of plane section assumption, the expression can be derived based on the stress-strain distribution relationship of the material's annular dangerous section to determine the axial force value N of the annular dangerous section. capacity Total bearing capacity of bending moment M capacity ;

[0213] According to the stress-strain distribution diagram of the annular section, the concrete compressive bearing capacity, steel tensile bearing capacity, and prestressed steel tendon tensile bearing capacity at the dangerous section are all organized as a function of the neutral wheelbase outer radius distance c. The bearing capacity can be divided into axial force and bending moment. In the derivation process, the axial force is considered positive in tension, and the bending moment is considered positive in counterclockwise rotation along a horizontal axis. The calculation formula is as follows:

[0214] F Bs ·N demand地震 =N concrete (c)+N steel (c)+N prestress (c)-N demand非地震 (twenty four)

[0215] F Bs ·M demand地震 =M concrete (c)+M steel (c)+M prestress (c)-M demand非地震 (25)

[0216] Formulas (24) and (25) constitute the equation containing the neutral axis position distance c and the annular dangerous section bending failure strength factor F Bs The equation group is solved to obtain the bending failure strength factor F of the annular dangerous section. Bs value;

[0217] The strength factor Fs of the structural bearing capacity of the final annular dangerous section is the minimum value of the shear failure strength factor and the bending failure strength factor:

[0218] F S =min(F Vs ,F Bs ) (26),

[0219] Among them, F Vs is the shear failure strength factor.

[0220] iii. Determine the variability of the structural strength factor, specifically including the following steps:

[0221] The influence of randomness, i.e., β, is not considered in the analysis of structural bearing capacity. r Take 0.

[0222] Epistemic uncertainty β u The analysis takes into account the uncertainty of material strength (including the uncertainty of the median compressive strength of concrete and the uncertainty of the median tensile strength of steel bars) and the uncertainty of the strength calculation formula.

[0223] 1) Determine the uncertainty β of the material strength value u_mat

[0224] The strength factor is calculated based on the median compressive strength of concrete and the median tensile strength of steel. To take into account the uncertainty, the median compressive strength of concrete is converted into a strength value with one standard deviation reduced: Convert the median tensile strength of the steel bars to a strength value that is one standard deviation less: Repeating the process of sections (i) and (ii) using the same low value of the material strength will yield the strength factor F related to the strength value. s_mβ ,

[0225] Determine the uncertainty β of the material strength value u_mat , and its calculation formula is as follows:

[0226]

[0227] Among them, Fs is the strength factor of the structural bearing capacity of the annular dangerous section, F s_mβ is the intensity factor related to the intensity value;

[0228] 2) Determine the uncertainty β of the strength calculation formula u_eqn ,

[0229] 《EPRI 6041》 calculates the reference seismic demand value D S A factor of 0.85 is taken into account. Formula (1) can be transformed into: Repeating the process of sections (1) and (2) can obtain the intensity factor F related to the calculation formula s_eβ , and finally determine the uncertainty β of the strength calculation formula u_eqn , and its calculation formula is as follows:

[0230]

[0231] Among them, Fs_eβ is the intensity factor associated with the calculation formula;

[0232] Determining the epistemic uncertainty β of the strength factor of the circular dangerous section u_Fs , can be calculated by the following formula:

[0233]

[0234] (ii) Determining the inelastic energy absorption factor and its variability, specifically comprising the following steps:

[0235] According to EPRI 6041, the cylindrical wall has sufficient ductility even when the section is damaged. A more conservative inelastic energy absorption factor of 1.25 is desirable, and the effect of cognitive uncertainty is not considered because it is more conservative.

[0236] Determine the inelastic energy absorption factor: F u =1.25;

[0237] Determine the random uncertainty of the inelastic energy absorption factor: β r_u =0.00;

[0238] Determine the epistemic uncertainty of the inelastic energy absorption factor: β u_u =0.00.

[0239] (III) Determine the structural bearing capacity factor and its variability of the annular dangerous section based on the structural strength factor and its variability, the inelastic energy absorption factor and its variability, and specifically include the following steps:

[0240] Determine the structural bearing capacity factor, the calculation formula is as follows F C =F s ·F u , where Fc is the structural bearing capacity factor of the annular dangerous section, Fs is the strength factor of the structural bearing capacity of the annular dangerous section, and Fu is the inelastic energy absorption factor;

[0241] Determine the random uncertainty β of the structural bearing capacity factor r_C =0;

[0242] Determine the epistemic uncertainty of the structural bearing capacity factor, the calculation formula is expressed as follows Among them, βμ_c is the epistemic uncertainty of the structural bearing capacity factor, βμ_Fs is the epistemic uncertainty of the strength factor of the annular dangerous section, and βμ_μ is the epistemic uncertainty of the inelastic energy absorption factor.

[0243] (3) According to the annular dangerous section and its failure mode, the structural response factor and its variability are confirmed, which specifically includes the following steps:

[0244] According to Table 3-1 of EPRI 103959, the structural response factor F SR The following variables need to be considered:

[0245] Ground Movement

[0246] Structural damping

[0247] Structural model

[0248] Mode superposition

[0249] Earthquake time history fitting

[0250] Base-Structure Interaction

[0251] Spatial combination of seismic components

[0252] (i) Confirming the ground motion factors and their variability includes the following steps:

[0253] According to the standard "EPRI 103959", the ground motion response factor considers the response spectrum, horizontal peak response and vertical seismic component respectively.

[0254] ia. Confirm the response spectrum and its epistemic uncertainty

[0255] According to the provisions of EPRI 1019200, when the earthquake hazard analysis of a nuclear power plant has taken into account the variability of wave crests and troughs and the uncertainty of the earthquake hazard spectrum, in order to avoid repeated consideration, the response spectrum factor can be taken as 1 and its variability can be 0.

[0256] ib. Confirm the horizontal peak response and its cognitive uncertainty

[0257] EPRI 103959 gives four cases of horizontal peak response, and one of them can be selected to calculate the factors and variability.

[0258] Case 1: Special direction response.

[0259] Case 2: Collinear vector reactions.

[0260] Case 3: Generalized vector reaction.

[0261] Case 4: Longest directional response.

[0262] In case 1, the factor is 1, βr is 0.18, and βu is 0. Cases 2, 3, and 4 use log-normal distribution. The factors and variability are determined by performing mathematical statistics on a certain number of random numbers. The specific calculation can be based on formulas 3-1, 3-2, and 3-3 of the standard "EPRI 103959".

[0263] Case 4 is a special case where symmetry plays an important role. The annular dangerous section is approximately symmetrical in both the horizontal X and Y directions, so the calculation results of Case 4 are selected as the factors and variability of the peak response in the horizontal direction.

[0264] ic. Confirm the vertical seismic components and their epistemic uncertainties, which specifically includes the following steps:

[0265] Since the horizontal seismic force of the reference earthquake in the vulnerability analysis of the annular dangerous section is higher than the vertical seismic force, the vertical seismic component factor and its variability can be 1 and 0.

[0266] Confirm the ground motion factor F GM : F GM =F SS ·F HD ·F VC (1)

[0267] Among them, F SS is the response spectrum shape factor, F HD is the horizontal peak response factor, F VC is the vertical earthquake component factor;

[0268] Determine the random uncertainty β of the ground motion factor r_GM :

[0269]

[0270] Among them, β r_SS is the random uncertainty of the response spectrum shape factor, β r_HD is the random uncertainty of the horizontal peak response factor, β r_VC is the random uncertainty of the vertical seismic component factor;

[0271] Confirm the epistemic uncertainty β of the ground motion factor u_GM :

[0272]

[0273] Among them, β u_SS is the epistemic uncertainty of the response spectrum shape factor, β u_HD is the epistemic uncertainty of the horizontal peak response factor, β u_VC is the epistemic uncertainty of the vertical seismic component factor.

[0274] (ii) Confirming the structural damping factor and its variability; specifically including the following steps:

[0275] When the structure is destroyed, it is considered that the steel bar has exceeded its yield state and the prestress has exceeded the yield state but has not reached the prestress failure. The damping will become larger. The calculation formula of the structural damping factor and its variability is:

[0276]

[0277] Among them, F SD is the structural damping factor, Sa -σ To reduce the main frequency response spectrum of the reference earthquake structure with a standard deviation damping ratio, Sa ξ is the main frequency response spectrum of the reference earthquake structure under the median damping ratio, β r_SD is the random uncertainty of the structural damping factor, β u_SD is the epistemic uncertainty of the structural damping factor.

[0278] (iii) Confirming the structural model factors and their variability; specifically, the following steps are included:

[0279] According to EPRI 103959, structural model factors are divided into frequency, mode shape and torsion.

[0280] iiia. Confirmation frequency and its epistemic uncertainty

[0281] According to Chapter 6 of ASCE4-16, the uncertainty of the model is considered by adjusting the model frequency up and down by 15%. The analysis model in the preliminary stage is used as the median structural model, the model corresponding to 1.15 times the main frequency is used as the upper limit structural model, and the model corresponding to 0.85 times the main frequency is used as the lower limit structural model. The calculation process of the intensity factor is repeated respectively. The average value of the intensity factor calculated by the three models is used as the median frequency, the envelope value is used as the upper limit value of the frequency, the frequency factor value is 1, the random uncertainty is 0, and the frequency and its cognitive uncertainty are confirmed. The cognitive uncertainty is calculated as follows:

[0282]

[0283] β u_M_F is the epistemic uncertainty of the frequency factor, F 频率中值 is the average value of the intensity factor calculated for the three models, F 频率上限值 Envelope values ​​of intensity factors calculated for the three models;

[0284] iiib. Confirm the vibration mode and its cognitive uncertainty

[0285] According to EPRI 103959, the modal response factor and its random uncertainty can be 1 and 0, and the recommended value of epistemic uncertainty can range from 0.05 for simple models to 0.15 for complex models. The simple containment model can be 0.05, and the internal structure can be 0.15.

[0286] iiic. Confirm the twist and its epistemic uncertainty, including the following steps:

[0287] Whether it is the containment building or the internal structure building, its configuration is cylindrical and approximately symmetrical, and the frequencies in the two horizontal directions are approximately equal, so the torsion effect can be considered to be very small. The conservative factor and random uncertainty considering the torsion effect are taken as 1 and 0 respectively, and the epistemic uncertainty is taken as 0.05.

[0288] Confirm the structural model factor F M : F M =F M_F ·F M_MS ·F M_T (6)

[0289] Among them, F M_F is the frequency factor, F M_MS is the vibration factor, F M_T is the torsion factor;

[0290] Confirm the random uncertainty β of the structural model factor r_M :

[0291]

[0292] Among them, β r_M_F is the random uncertainty of the frequency factor, β r_M_MS is the random uncertainty of the vibration factor, β r_M_T is the random uncertainty of the torsion factor;

[0293] Confirm the epistemic uncertainty of the structural model factors β u_M :

[0294]

[0295] Among them, β u_M_F is the frequency factor epistemic uncertainty, β u_M_MS is the epistemic uncertainty of the vibration factor, β u_M_T The reversal factor is cognitive uncertainty.

[0296] (iv) Confirmation of the modal superposition factor and its variability

[0297] According to EPRI 103959, when different earthquake records are used for time history analysis, different wave forms will be generated due to the different phase numbers used in Fourier transform. At this time, it is necessary to consider the superposition of response vibration modes. According to the guidelines, the vibration mode superposition factor and epistemic uncertainty are 1 and 0 respectively, and the random uncertainty β r_MC The recommended value ranges from 0.05 for simple models to 0.15 for complex models. Frequency domain analysis does not need to consider this item.

[0298] (v) Confirm earthquake time history fitting factors and their variability

[0299] According to EPRI 103959, the influence of the time history fitting factor needs to be considered when using different artificial fitting time histories for time history analysis, but this is not considered in response spectrum analysis. Using different artificial fitting time histories for structural time history analysis, repeating the intensity factor calculation process will result in different intensity factor values. The average value of these intensity factors is used as the median value of the time history fitting, and the envelope value is used as the upper limit of the time history fitting. The time history fitting factor is taken as 1 and the epistemic uncertainty is 0. Confirm the epistemic uncertainty β of the earthquake time history fitting factor and its variability. r_TH The calculation formula is as follows:

[0300]

[0301] Among them, F thAve To calculate the average value of the intensity factor, F thUp is the envelope value for calculating the intensity factor.

[0302] (vi) Confirming the base-structure interaction factors and their variability, including the following steps:

[0303] According to EPRI 103959, foundation-structure interaction factors are divided into ground motion inconsistency, vertical spatial variation and soil-structure interaction.

[0304] via.Confirming ground motion inconsistency and its epistemic uncertainty

[0305] At present, the inconsistency of input motion is not considered in the process of structural analysis of nuclear power plants. This item can be ignored, that is, the factor is 1 and the variability is 0.

[0306] vib. Confirm vertical spatial changes and their cognitive uncertainty

[0307] In a soil site, the free-field seismic motion will decrease with the increase of soil depth. At this time, the factors of vertical spatial change and their variability can be considered based on the soil conditions of the site; this item is not considered in bedrock sites.

[0308] vic. Identification of soil-structure interaction and its epistemic uncertainty

[0309] According to EPRI 103959, the influence of this item needs to be considered when considering different foundation soil parameters for reference seismic analysis and internal force extraction. Repeating the intensity factor calculation process in the previous section with different foundation soil parameters will result in different intensity factor values. The average value of these intensity factors is taken as the SSI median value, and the envelope value is taken as the SSI upper limit value. The SSI factor value is 1 and the random uncertainty is 0, confirming the soil-structure interaction and its epistemic uncertainty, and its epistemic uncertainty β u_SSI The calculation formula is as follows:

[0310]

[0311] Among them, F SSI中值 is the average value of all calculated intensity factors, F SSI上限值 is the envelope value of all calculated intensity factors;

[0312] Basic structure factor F FSI : F FSI =F GMI ·F VS ·F SSI (11)

[0313] Among them, F GMI is the ground motion inconsistency factor, F VS is the vertical spatial variation factor, F SSI is the soil-structure interaction factor;

[0314] Random uncertainty of the underlying structure factor β r_FSI :

[0315] Among them, β r_GMI is the ground motion inconsistency random uncertainty, β r_VS is the random uncertainty of vertical spatial variation, β r_SSI is the random uncertainty of soil-structure interaction;

[0316] Epistemic uncertainty of the underlying structural factor β u_FSI :

[0317] Among them, β u_GMI is the epistemic uncertainty of ground motion inconsistency, β u_VS is the vertical spatial variation epistemic uncertainty, β u_SSI Epistemic uncertainty for soil-structure interactions.

[0318] (vii) Identify the spatial combination factors of earthquake components and their variability

[0319] According to EPRI 103959, when formula (1)(F s ·D S =CF s ·ΔC S -D NS ) is obtained by combining the three directional seismic components according to SRSS or Newmark. The absolute value of the seismic forces in the three directions (X, Y, Z) is added and the intensity factor calculation process in the previous section is repeated to obtain the upper limit intensity factor F of the seismic component. S_EC , taking the intensity factor calculated in the previous section as the median intensity of the earthquake component, according to EPRI103959, the sum of the absolute values ​​of the earthquake response is 2.3 standard deviations of the median, confirming the spatial combination factor of the earthquake component and its variability, and its epistemic uncertainty β r_ES The calculation formula is as follows:

[0320]

[0321] Among them, F s地震分量中值 is the calculated intensity factor, F S_EC This is the structural strength factor calculated in step (ii).

[0322] The spatial combination factor and epistemic uncertainty of the earthquake components are 1 and 0, respectively.

[0323] (viii) Confirming the structural response factor and its variability, including the following steps:

[0324] Structural response factor F SR : F SR =F GM ·F SD ·F M ·F MC ·F TH ·F FSI ·F EC (15)

[0325] Among them, F GM is the ground motion factor, F SD is the structural damping factor, F M is the structural model factor, F MC is the mode superposition factor, F TH is the earthquake time history fitting factor, F FSI is the basic structure factor, F EC is the spatial combination factor of the seismic component;

[0326] Random uncertainty of structural response factor β r_SR :

[0327]

[0328] Among them, β r_GM is the random uncertainty of the ground motion factor, β r_SD is the random uncertainty of the structural damping factor, β r_M is the random uncertainty of the structural model factors, β r_MC is the random uncertainty of the vibration mode superposition factor, β r_TH is the random uncertainty of the earthquake time history fitting factor, β r_FSI is the random uncertainty of the basic structure factor, β r_EC is the random uncertainty of the spatial combination factor of the seismic component;

[0329] Epistemic uncertainty of structural response factor β u_SR :

[0330]

[0331] Among them, β u_GM is the epistemic uncertainty of the ground motion factor, β u_SD is the epistemic uncertainty of the structural damping factor, β u_M is the epistemic uncertainty of the structural model factors, β u_MC is the epistemic uncertainty of the mode superposition factor, β u_TH is the epistemic uncertainty of the earthquake time history fitting factor, β u_FSI is the epistemic uncertainty of the underlying structural factor, β u_EC is the epistemic uncertainty of the spatial combination factor of the seismic components.

[0332] like Figure 3 As shown, this embodiment also provides a device for calculating the vulnerability of structures applicable to annular dangerous sections, including:

[0333] Failure unit, according to the stress characteristics of the circular section of the structure, determine the circular dangerous section of the structure and its failure mode;

[0334] The first variation unit confirms the structural bearing capacity factor and its variability based on the annular dangerous section and its failure mode determined by the failure unit;

[0335] The second variation unit confirms the structural response factor and its variability based on the annular dangerous section and its failure mode determined by the failure unit;

[0336] Separate the variable unit, according to the structural bearing capacity factor and its variability confirmed by the first variation unit, and the structural response factor and its variability confirmed by the second variation unit, and according to the separation variable method, the median ground acceleration capacity A of the structure is obtained. m and variability β R and βU .

[0337] The calculation method and device for the vulnerability of structures applicable to annular dangerous sections in this embodiment have the following beneficial effects:

[0338] (1) It is applicable to all structures with circular dangerous sections, and can be used to calculate the fragility of nuclear power plants with cylindrical walls as the most dangerous wall and circular sections as the most dangerous section, and to make the earthquake PSA analysis results of nuclear power plants more accurate. The method of this embodiment is easy to operate, and its calculation process is closer to the actual plant, and the calculation results are more accurate and reliable.

[0339] (2) The calculation and analysis of the shear failure factor of the annular section is obtained. This embodiment refers to the provisions of the seismic margin analysis specification to derive the calculation method of the shear failure factor of the annular section of the seismic vulnerability of the structure.

[0340] (3) The calculation and analysis of the bending failure factor suitable for the ring section is obtained. According to the provisions of the specification and the stress-strain distribution relationship of concrete, steel bars and prestressed steel strands in the ring section, the calculation method suitable for the bending failure factor of the ring section is derived.

[0341] It is to be understood that the above embodiments are merely exemplary embodiments used to illustrate the principles of the present invention, but the present invention is not limited thereto. For those of ordinary skill in the art, various modifications and improvements can be made without departing from the spirit and essence of the present invention, and these modifications and improvements are also considered to be within the scope of protection of the present invention.

Claims

1. A method for calculating the vulnerability of structures applicable to annular dangerous sections, characterized in that: The following steps are involved: According to the stress characteristics of the circular section of the structure, the circular dangerous section of the structure and its failure mode are determined. The failure modes of the circular dangerous section of the structure include: tangential shear failure mode and bending failure mode; According to the annular dangerous section and its failure mode, the structural bearing capacity factor and its variability are confirmed, which specifically includes the following steps: (I) Determine the structural strength factor and its variability, including the following steps: iCalculate the tangential shear failure factor, and finally the tangential shear failure factor F of the annular dangerous section Vs The calculation formula is as follows: Among them, F Vs1 The median earthquake stress is less than Shear failure factor, f c ' is the median compressive strength of concrete, D s is the demand value of the annular dangerous section under the reference earthquake action, ν u1 is the earthquake median stress, which is less than Shear failure factor F Vs1 The calculation formula is as follows: Among them, C is the bearing capacity value of the circular dangerous section, D NS is the cross-sectional demand value under non-seismic action, D S is the demand value of the section under the reference earthquake action, ΔC S To refer to the reduction in bearing capacity caused by earthquake, Earthquake median stress ν u1 The calculation formula is as follows: v u1 =F Vs1 ·D S =C-F Vs1 ·ΔC S -D NS ; ii. Calculate the bending failure factor, specifically including the following steps: The tensile or compressive bending bearing capacity of the circular cross section is only related to the material strength and the calculated area. Therefore, the internal force of the cross section under the earthquake action will not cause the change of the bearing capacity value. The bending resistance of the cross section needs to consider the axial force and the bending moment. Therefore, the bending failure factor F of the circular dangerous cross section is determined. Bs The calculation can be obtained by the following two formulas: F Bs ·N demend地震 =N capacity -N demend非地震 (9) F Bs ·M demend地震 =M capacity -M demend非地震 (10) Among them, F BS is the bending failure strength factor of the annular dangerous section, N demand地震 is the axial force of the circular dangerous section of the structure under the reference earthquake, M demand地震 is the bending moment of the circular dangerous section of the structure under the reference earthquake, N demand非地震 M is the axial force of the annular dangerous section of the structure under the action of dead load, live load and prestressed non-seismic conditions in the earthquake probabilistic safety assessment analysis stage. demand非地震 is the bending moment of the annular dangerous section of the structure under the action of dead load, live load and prestressed non-seismic conditions in the earthquake probabilistic safety assessment analysis stage, N capacity is the axial force bearing capacity of the annular dangerous section, M capacity is the moment bearing capacity of the annular dangerous section; iii. Determine the variability of the structural strength factor, which specifically includes the following steps: 1) determine the uncertainty of the material strength value; 2) Determine the uncertainty of the strength calculation formula, and finally the structural strength factor Fs of the annular dangerous section takes the minimum value of the shear failure strength factor and the bending failure strength factor: F S =min(F Vs ,F Bs )(26), Among them, F Vs is the shear failure strength factor; (ii) Determining the inelastic energy absorption factor and its variability, specifically comprising the following steps: Determine the inelastic energy absorption factor: F u =1.25; Determine the random uncertainty of the inelastic energy absorption factor: β r_u =0.00; Determine the epistemic uncertainty of the inelastic energy absorption factor: β u_u =0.00; (iii) Determine the structural bearing capacity factor and its variability of the annular dangerous section based on the structural strength factor and its variability, the inelastic energy absorption factor and its variability; According to the annular dangerous section and its failure mode, the confirmation of the structural response factor and its variability specifically includes the following steps: (i) Identify ground motion factors and their variability; (ii) confirm the structural damping factor and its variability; (iii) confirm the structural model factors and their variability; (iv) confirm the mode superposition factors and their variability; (v) Confirm the earthquake time history fitting factors and their variability; (vi) identify base-structure interaction factors and their variability; (vii) Identify the spatial combination factors of seismic components and their variability; (viii) confirming the factors and their variability obtained according to steps (i) to (vii), and confirming the structural response factors and their variability; According to the structural bearing capacity factor and its variability, the structural response factor and its variability, the median ground acceleration capacity and variability of the structure are obtained according to the separation of variables method.

2. The method for calculating the vulnerability of structures applicable to annular dangerous sections according to claim 1 is characterized in that: The step (iii) of determining the structural bearing capacity factor and its variability of the annular dangerous section according to the structural strength factor and its variability, the inelastic energy absorption factor and its variability specifically comprises the following steps: Determine the structural bearing capacity factor, the calculation formula is as follows F C =F s ·F u , where F c is the structural bearing capacity factor of the circular dangerous section, F s is the structural strength factor of the annular dangerous section, F u is the inelastic energy absorption factor; Determine the random uncertainty β of the structural bearing capacity factor r_C =0; Determine the epistemic uncertainty of the structural bearing capacity factor, the calculation formula is expressed as follows Among them, β μ_c is the epistemic uncertainty of the structural bearing capacity factor, β μ_Fs is the epistemic uncertainty of the strength factor of the annular dangerous section, β μ_μ The epistemic uncertainty is the inelastic energy absorption factor.

3. The method for calculating the vulnerability of structures applicable to annular dangerous sections according to claim 1 is characterized in that: Axial force value of annular dangerous section N capacity Total bearing capacity of the moment M capacity The method of determining is as follows: a. According to the principle of plane section assumption, the axial force value N of the annular dangerous section is determined according to the stress-strain distribution relationship of the material annular dangerous section. capacity Total bearing capacity of the moment M capacity ; The total bearing capacity of axial force and moment of concrete, steel bars and prestressed steel tendons is superimposed as shown in the following formula: Axial force: N capacity (c) = N concrete (c)+N steel (c)+N prestress (c)(22) Bending moment: M capacity (c) = M concrete (c)+M steel (c)+M prestress (c)(23) Where c is the distance from the neutral axis to the outer radius, i.e. the height of the concrete compression zone, N concrete (c) is the axial force on the concrete, N steel (c) is the axial force on the steel bar, N prestress (c) is the axial force on the prestressed steel tendon, M concrete (c) is the total moment bearing capacity of concrete, M steel (c) is the total moment bearing capacity of the steel bar, M prestress (c) is the total moment bearing capacity of the prestressed steel tendons; Substituting equations (22) and (23) into equations (9) and (10), we obtain the following formula: F Bs ·N demand地震 =N concrete (c)+N steel (c)+N prestress (c)-N demand非地震 (24) F Bs ·M demand地震 =M concrete (c)+M steel (c)+M prestress (c)-M demand非地震 (25) Formulas (24) and (25) constitute the equation containing the neutral axis position distance c and the annular dangerous section bending failure strength factor F Bs The equation group is solved to obtain the bending failure strength factor F of the annular dangerous section. Bs value.

4. The method for calculating the vulnerability of structures applicable to annular dangerous sections according to claim 1 is characterized in that: The step iii of determining the variability of the intensity factor specifically comprises the following steps: 1) Determine the uncertainty β of the material strength value u_mat , and its calculation formula is as follows: Among them, Fs is the structural strength factor of the annular dangerous section, F s_mβ is the intensity factor related to the intensity value; 2) Determine the uncertainty β of the strength calculation formula u_eqn , and its calculation formula is as follows: Among them, F s_eβ is the intensity factor associated with the calculation formula; Determining the epistemic uncertainty β of the strength factor of the circular dangerous section u_Fs , can be calculated by the following formula:

5. The method for calculating the vulnerability of structures applicable to annular dangerous sections according to claim 1 is characterized in that: The step (i) of confirming the ground motion factor and its variability specifically comprises the following steps: ia. Confirm the response spectrum and its uncertainty; ib. Confirm the horizontal peak response and its uncertainty; ic. Identify vertical seismic components and their uncertainties; Confirm the ground motion factor F GM :F GM =F SS ·F HD ·F VC (1) Among them, F SS is the response spectrum shape factor, F HD is the horizontal peak response factor, F VC is the vertical earthquake component factor; Determine the random uncertainty β of the ground motion factor r_GM : Among them, β r_SS is the random uncertainty of the response spectrum shape factor, β r_HD is the random uncertainty of the horizontal peak response factor, β r_VC is the random uncertainty of the vertical seismic component factor; Confirm the epistemic uncertainty β of the ground motion factor u_GM : Among them, β u_SS is the epistemic uncertainty of the response spectrum shape factor, β u_HD is the epistemic uncertainty of the horizontal peak response factor, β u_VC is the epistemic uncertainty of the vertical seismic component factor.

6. The method for calculating the vulnerability of structures applicable to annular dangerous sections according to claim 1 is characterized in that: The step (ii) of confirming the structural damping factor and its variability specifically comprises the following steps: When the structure is destroyed, it is considered that the steel bar has exceeded its yield state and the prestress has exceeded the yield state but has not reached the prestress failure. The damping will become larger. The calculation formula of the structural damping factor and its variability is: β r_SD ＝0 Among them, F SD is the structural damping factor, Sa -σ To reduce the main frequency response spectrum of the reference earthquake structure with a standard deviation damping ratio, Sa ξ is the main frequency response spectrum of the reference earthquake structure under the median damping ratio, β r_SD is the random uncertainty of the structural damping factor, β u_SD is the epistemic uncertainty of the structural damping factor.

7. The method for calculating the vulnerability of structures applicable to annular dangerous sections according to claim 1 is characterized in that: The step (iii) of confirming the structural model factors and their variability specifically comprises the following steps: iiia. Confirm the frequency and its epistemic uncertainty. Consider the uncertainty of the model by adjusting the model frequency by 15% above and below. Take the analysis model in the initial stage as the median structure model, the model corresponding to 1.15 times the main frequency as the upper limit structure model, and the model corresponding to 0.85 times the main frequency as the lower limit structure model. Repeat the calculation process of the intensity factor. The epistemic uncertainty is calculated as follows: The frequency factor takes the value of 1, and the random uncertainty takes the value of 0. β u_M_F is the epistemic uncertainty of the frequency factor, F 频率中值 is the average value of the intensity factor calculated for the three models, F 频率上限值 Envelope values ​​of intensity factors calculated for the three models; iiib. Confirm the vibration mode and its epistemic uncertainty. The vibration mode response factor and its random uncertainty can be 1 and 0. The epistemic uncertainty of the containment model can be 0.05 and that of the internal structure can be 0.

15. iiic. Confirm the torsion and its epistemic uncertainty. The reactor building configuration is cylindrical and approximately symmetrical. The frequencies in the two horizontal directions are approximately equal. It can be considered that the torsion effect is very small. The factor and random uncertainty of the torsion effect are 1 and 0 respectively, and the epistemic uncertainty is 0.05: Confirm the structural model factor F M :F M =F M_F ·F M_MS ·F M_T (6) Among them, F M_F is the frequency factor, F M_MS is the vibration factor, F M_T is the torsion factor; Confirm the random uncertainty β of the structural model factor r_M : Among them, β r_M_F is the random uncertainty of the frequency factor, β r_M_MS is the random uncertainty of the vibration factor, β r_M_T is the random uncertainty of the torsion factor; Confirm the epistemic uncertainty of the structural model factors β u_M : Among them, β u_M_F is the frequency factor epistemic uncertainty, β u_M_MS is the epistemic uncertainty of the vibration factor, β u_M_T The reversal factor is epistemic uncertainty.

8. The method for calculating the vulnerability of structures applicable to annular dangerous sections according to claim 1 is characterized in that: The step (iv) confirms the modal superposition factor and its variability. According to the guidelines, the modal superposition factor and the epistemic uncertainty are 1 and 0 respectively, and the recommended value of random uncertainty can be from 0.05 for simple models to 0.15 for complex models.

9. The method for calculating the vulnerability of structures applicable to annular dangerous sections according to claim 1 is characterized in that: The step (v) confirms the earthquake time history fitting factor and its variability, uses different artificial fitting time histories to perform structural time history analysis, and repeats the intensity factor calculation process to obtain different intensity factor values, whose random uncertainty β r_TH The calculation formula is as follows: Among them, F thAve To calculate the average value of the intensity factor, F thUp To calculate the envelope value of the intensity factor, The time history fitting factor takes the value of 1 and the epistemic uncertainty takes the value of 0.

10. The method for calculating the vulnerability of structures applicable to annular dangerous sections according to claim 1, characterized in that: The step (vi) of confirming the base-structure interaction factor and its variability specifically comprises the following steps: via.Confirmation of ground motion inconsistencies and their uncertainties; vib. Confirm vertical spatial changes and their uncertainties; vic. Confirm the soil-structure interaction and its uncertainty. Repeating the strength factor calculation process with different foundation soil parameters will result in different strength factor values, and its epistemic uncertainty β u_SSI The calculation formula is as follows: Among them, F SSI中值 is the average value of all calculated intensity factors, F SSI上限值 is the envelope value of all calculated intensity factors, The soil-structure interaction factor takes the value of 1 and its random uncertainty is 0. Basic structure factor F FSI :F FSI =F GMI ·F VS ·F SSI (11) Among them, F GMI is the ground motion inconsistency factor, F VS is the vertical spatial variation factor, F SSI is the soil-structure interaction factor; Random uncertainty of the underlying structure factor β r_FSI : Among them, β r_GMI is the ground motion inconsistency random uncertainty, β r_VS is the random uncertainty of vertical spatial variation, β r_SSI is the random uncertainty of soil-structure interaction; Epistemic uncertainty of the underlying structural factor β u_FSI : Among them, β u_GMI is the epistemic uncertainty of ground motion inconsistency, β u_VS is the vertical spatial variation epistemic uncertainty, β u_SSI Epistemic uncertainty for soil-structure interactions.

11. The method for calculating the vulnerability of structures applicable to annular dangerous sections according to claim 1, characterized in that: The step (vii) confirms The spatial combination factor of the earthquake components and their variability are summed up to calculate the intensity factor of the earthquake demand force. The random uncertainty β r_EC The calculation formula is as follows: Among them, F s地震分量中值 is the calculated intensity factor, F S_EC Structural strength factor calculated to confirm the structural bearing capacity factor; The spatial combination factor and epistemic uncertainty of the earthquake components are 1 and 0, respectively.

12. The method for calculating the vulnerability of structures applicable to annular dangerous sections according to claim 1, characterized in that: The step (viii) confirms the structural response factor and its variability, specifically comprising the following steps: Structural response factor F SR :F SR =F GM ·F SD ·F M ·F MC ·F TH ·F FSI ·F EC (15) Among them, F GM is the ground motion factor, F SD is the structural damping factor, F M is the structural model factor, F MC is the mode superposition factor, F TH is the earthquake time history fitting factor, F FSI is the basic structure factor, F EC is the spatial combination factor of the seismic component; Random uncertainty of structural response factor β r_SR : Among them, β r_GM is the random uncertainty of the ground motion factor, β r_SD is the random uncertainty of the structural damping factor, β r_M is the random uncertainty of the structural model factors, β r_MC is the random uncertainty of the vibration mode superposition factor, β r_TH is the random uncertainty of the earthquake time history fitting factor, β r_FSI is the random uncertainty of the basic structure factor, β r_EC is the random uncertainty of the spatial combination factor of the seismic component; Epistemic uncertainty of structural response factor β u_SR : Among them, β u_GM is the epistemic uncertainty of the ground motion factor, β u_SD is the epistemic uncertainty of the structural damping factor, β u_M is the epistemic uncertainty of the structural model factors, β u_MC is the epistemic uncertainty of the mode superposition factor, β u_TH is the epistemic uncertainty of the earthquake time history fitting factor, β u_FSI is the epistemic uncertainty of the underlying structural factor, β u_EC is the epistemic uncertainty of the spatial combination factor of the seismic components.

13. A device for calculating the vulnerability of structures in annular dangerous sections according to any one of claims 1 to 12, characterized in that: include: The failure unit determines the dangerous annular section of the structure and its failure mode according to the stress characteristics of the annular section of the structure. The failure modes of the dangerous annular section of the structure include: tangential shear failure mode and bending failure mode; The first variation unit confirms the structural bearing capacity factor and its variability based on the annular dangerous section and its failure mode determined by the failure unit; The second variation unit confirms the structural response factor and its variability based on the annular dangerous section and its failure mode determined by the failure unit; The variable unit is separated, and the median ground acceleration capacity and variability of the structure are obtained according to the structural bearing capacity factor and its variability confirmed by the first variation unit and the structural response factor and its variability confirmed by the second variation unit, and the separation of variables method is used.

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