Earthquake vulnerability analysis method for buried pipeline based on three-parameter square normal distribution

Abstract

The application discloses a buried pipeline seismic vulnerability analysis method based on a three-parameter square normal distribution, belongs to the field of civil engineering and earthquake engineering, and solves the problem that an existing lognormal distribution model cannot accurately reflect the skewness characteristics of structural response data, thereby leading to the calculation deviation of failure probability, and the method comprises the following steps: generating seismic input data, establishing a buried pipeline finite element model, performing nonlinear time-history analysis, extracting pipeline response data, calculating the failure probability of the buried pipeline under different seismic intensity based on the three-parameter square normal distribution, and drawing a vulnerability curve; the application builds a complete system covering seismic simulation-buried pipeline response analysis-seismic vulnerability analysis, improves the calculation precision of the seismic failure probability of the buried pipeline by introducing the three-parameter square normal distribution which can accurately reflect the skewness characteristics of the structural response data, and thus a seismic vulnerability model with wider application range and higher precision is provided.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of civil engineering and earthquake engineering, and particularly relates to a buried pipeline seismic vulnerability analysis method based on a three-parameter square normal distribution. BACKGROUND

[0002] Buried pipelines are an important part of urban infrastructure, and are prone to damage such as pipe body fracture and buckling in earthquakes, leading to failure of key lifeline systems such as water supply and drainage, gas and oil transportation, and causing serious economic losses and secondary disasters. Therefore, accurate seismic vulnerability assessment of buried pipelines is the key to improving their seismic capacity and strengthening risk management.

[0003] Currently, seismic vulnerability analysis usually uses the probabilistic seismic demand analysis (PSDA) framework to calculate the failure probability of structures. This framework assumes that the structural response follows a lognormal distribution, but actual structural response data often has significant skewness characteristics that cannot be accurately reflected by the lognormal distribution, resulting in deviations in failure probability calculations and affecting the accuracy and reliability of seismic risk assessment.

[0004] In view of this, the present application proposes a buried pipeline seismic vulnerability analysis method based on a three-parameter square normal distribution. This method first generates artificial ground motions that meet the target spectrum based on the random process spectral representation method; then establishes a finite element model of the buried pipeline and performs nonlinear time history analysis to obtain pipeline response data; finally, based on the three-parameter square normal distribution, the probability distribution of the response data is fitted, the failure probability of the pipeline under different ground motion intensities is calculated, and the vulnerability curve is drawn. The present application introduces the three-parameter square normal distribution which can accurately reflect the skewness characteristics of the structural response data, thereby improving the accuracy of the buried pipeline seismic vulnerability analysis and providing a scientific basis for seismic design and seismic disaster risk assessment. SUMMARY

[0005] The present application aims to address the shortcomings of existing seismic vulnerability analysis methods and proposes a buried pipeline seismic vulnerability analysis method based on a three-parameter square normal distribution, which solves the problem that existing lognormal distribution models cannot accurately reflect the skewness characteristics of structural response data, thereby causing deviations in failure probability calculations.

[0006] The method is implemented firstly to establish a random process model of non-stationary ground motion by using a random process spectrum representation method, generate artificial ground motion conforming to the target response spectrum; then a buried pipeline finite element model is established to simulate the dynamic response of the pipeline under the action of the earthquake, the axial peak strain is taken as the engineering demand parameter and the pipeline response data is extracted; finally, the probability distribution of the response data is fitted based on a three-parameter square normal distribution, the failure probability of the pipeline under different ground motion intensities is calculated, and the vulnerability curve is drawn. The embodiment of the application builds a complete system covering ground motion simulation-buried pipeline response analysis-seismic vulnerability analysis to improve the accuracy of the calculation of the seismic failure probability of the buried pipeline, solves the problem that the lognormal distribution is difficult to accurately reflect the skewness characteristics of the structural response data, thereby improving the calculation accuracy of the failure probability, and making the vulnerability curve more in line with the actual damage distribution characteristics of the buried pipeline. Compared with the traditional method, the method provides a seismic vulnerability model with wider application range and higher accuracy, and provides a scientific basis for seismic design, seismic risk management and post-disaster assessment.

[0007] The buried pipeline seismic vulnerability analysis method based on the three-parameter square normal distribution is realized, and specifically includes:

[0008] S1, determining the site characteristics according to the position of the pipeline, and generating ground motion data conforming to the target response spectrum based on the random process spectrum representation method;

[0009] S2, constructing a buried pipeline finite element model, applying seismic action, and performing nonlinear seismic response analysis to extract pipeline response data;

[0010] S3, selecting a ground motion intensity index and an engineering demand parameter, determining a damage index in combination with the pipeline characteristics, and constructing a limit state function of the buried pipeline;

[0011] S4, establishing a buried pipeline failure probability calculation method based on a three-parameter square normal distribution model under different ground motion intensities;

[0012] S5, constructing a buried pipeline seismic vulnerability function and drawing a vulnerability curve based on a logistic regression model and taking the ground motion intensity index as the independent variable.

[0013] The site characteristics are determined according to the position of the pipeline, and the ground motion data conforming to the target response spectrum are generated based on the random process spectrum representation method, including:

[0014] S101, determining the site characteristics according to the position of the pipeline, and selecting an acceleration response spectrum conforming to the target site requirements ;

[0015] S102, constructing an initial input power spectrum by using an empirical spectrum conversion relationship ;

[0016]

[0017] where, is the structural damping ratio; denotes the circular frequency; denotes the target response spectrum for a period ; denotes the duration of ground motion; denotes the probability that the structural response does not exceed the target response spectrum.

[0018] S103, introduce the amplitude modulation function to represent the evolutionary spectrum is:

[0019]

[0020] where, the three-section time envelope function is expressed as follows:

[0021]

[0022] where, and are the start and end times of the strong motion duration, respectively; is the tail decay rate coefficient. These parameters depend on factors such as site, magnitude, and epicentral distance.

[0023] S104, discretize the evolutionary spectrum into N frequency points within the frequency range , and generate a non-stationary process spectrum representation method;

[0024]

[0025] where, is the evolutionary power spectrum; is the frequency step size, and are the maximum and minimum cutoff values of the frequency, respectively; ; is a random phase angle that follows independent uniform distributions.

[0026] S105, calculate the average acceleration response spectrum of the ground motion sample , and compare it with the target spectrum , define its relative error index as

[0027]

[0028] S106, if the relative error exceeds 5%, update the evolutionary spectrum:

[0029]

[0030] where the superscript (n) of the evolutionary spectral density represents the nth iteration. k k

[0031] Repeat the above steps until the requirements are met.

[0032] The buried pipeline finite element model is constructed, seismic action is applied, nonlinear seismic response analysis is carried out, and pipeline response data are extracted, including:

[0033] S201, using ABAQUS finite element software, using beam element to simulate pipeline, using nonlinear soil spring element to simulate pipe-soil interaction, constructing buried pipeline finite element model;

[0034] S202, the seismic acceleration time history is processed and applied to the model soil spring node set, nonlinear time history analysis is carried out, and pipeline seismic response is obtained;

[0035] S203, writing Python general program, batch extracting response data of specified section of pipeline.

[0036] The seismic intensity index and engineering demand parameter are selected, the damage index is determined combined with pipeline characteristics, the limit state function of buried pipeline is constructed, including:

[0037]

[0038] wherein, represents the limit state function; R (X) represents the resistance or carrying capacity of the structure; and S (X) represents the load effect, i.e. the seismic response of the pipeline; represents the critical failure threshold of the pipeline; represents the axial peak strain of the pipeline under the action of earthquake; X represents an uncertainty parameter, when , i.e. the seismic response of the pipeline exceeds its resistance or carrying capacity.

[0039] The buried pipeline failure probability calculation method based on the three-parameter square normal distribution model under different seismic intensity is established, and the expression is:

[0040]

[0041] wherein, is the response of the pipeline under the action of earthquake (i.e. seismic demand parameter ), represents the demand response value of the pipeline obtained under the first seismic input; ​​to be a specific damage state (i.e. damage index) of the pipeline; to be a ground motion intensity index; , and are the mean, standard deviation and skewness of the structural response data, respectively; represents the failure probability of the pipeline exceeding a specific damage state under a given ground motion intensity.

[0042] The seismic vulnerability curve of the buried pipeline is drawn based on the logistic regression model with the ground motion intensity index IM as the independent variable, and the vulnerability curve function is represented as follows:

[0043]

[0044] wherein, and are the logistic regression coefficients.

[0045] Compared with the prior art, the embodiments of the present application have the following beneficial effects:

[0046] The embodiments of the present application construct a complete system covering seismic motion simulation-buried pipeline response analysis-seismic vulnerability analysis to improve the accuracy of the calculation of the seismic failure probability of the buried pipeline, and the present application solves the problem that the existing lognormal distribution cannot accurately reflect the skewness characteristics of the structural response data by introducing a three-parameter square normal distribution, improves the calculation accuracy of the failure probability, and makes the vulnerability curve more consistent with the actual damage distribution characteristics of the buried pipeline. Compared with the traditional vulnerability analysis method, the method has a wider application range and higher accuracy, and can provide a scientific basis for seismic design, seismic risk management and post-disaster assessment.

[0047] The specific implementation steps of the present application are as follows: first, a random process spectrum representation method is used to establish a random process model of non-stationary ground motion to generate artificial ground motion conforming to the target response spectrum; then, a finite element model of the buried pipeline is established to simulate the dynamic response of the pipeline under the action of the earthquake, the axial peak strain is taken as the engineering demand parameter, and the pipeline response data is extracted; finally, the probability distribution of the response data is fitted based on the three-parameter square normal distribution, the failure probability of the pipeline under different ground motion intensities is calculated, and the vulnerability curve is drawn. BRIEF DESCRIPTION OF DRAWINGS

[0048] Figure 1 is the implementation process schematic diagram of the buried pipeline seismic vulnerability analysis method based on the three-parameter square normal distribution provided by the present application.

[0049] Figure 2 shows a comparison chart of the average response spectrum of the artificial ground motion generated based on the random process spectrum representation method and the target response spectrum set in the Chinese code for seismic design of buildings GB50011-2016.

[0050] Figure 3 A sample graph of ground motion is shown in the embodiments of the present application.

[0051] Figure 4 A schematic diagram of a finite element model of a buried pipeline established in the embodiments of the present application is shown.

[0052] Figure 5 A fitting of the probability distribution of the pipeline response value in the failure interval under the action of ground motion is shown.

[0053] Figure 6 A seismic vulnerability curve of a buried pipeline in the embodiments of the present application is shown. DETAILED DESCRIPTION

[0054] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs; the terminology used in the description herein is for describing particular embodiments only and is not intended to be limiting upon the application; the description and the drawings are to be regarded as illustrative in nature and definitions in the specification are to be interpreted consistent with the foregoing. The terms "comprising," "having," "including," and "containing" are to be construed as open-ended terms (i.e., meaning "including, but not limited to,") unless otherwise noted. The terms "first," "second," and the like, as used herein do not have any specific meaning unless otherwise noted.

[0055] Reference herein to "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the application. The appearances of the phrase "in an embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are they necessarily all directed to the same embodiment, or to a single alternative embodiment. It is expressly understood that any of the embodiments described herein can be combined with any of the other embodiments.

[0056] In the prior art, the lognormal distribution model cannot accurately reflect the skewness characteristics of the structural response data, thereby leading to deviation in the calculation of failure probability and affecting the reliability of structural risk assessment. Therefore, the application provides a buried pipeline seismic vulnerability analysis method based on a three-parameter square normal distribution. In brief, when the method is implemented, firstly, a random process spectrum representation method is used to establish a random process model of non-stationary ground motion to generate artificial ground motion conforming to the target response spectrum; then, a buried pipeline finite element model considering pipe-soil interaction is established to simulate the dynamic response of the pipeline under the action of the earthquake, the axial peak strain is selected as the engineering demand parameter, and the pipeline response data is extracted, the probability distribution fitting is performed on the response data based on the three-parameter square normal distribution, the failure probability of the pipeline under different ground motion intensities is calculated, and the vulnerability curve is drawn. The embodiment of the application establishes a complete system covering ground motion simulation-buried pipeline response analysis-seismic vulnerability analysis to improve the accuracy of the calculation of the seismic failure probability of the buried pipeline, and solves the problem that the lognormal distribution cannot accurately reflect the skewness characteristics of the structural response data, thereby improving the calculation accuracy of the failure probability and making the vulnerability curve more consistent with the actual damage distribution characteristics of the buried pipeline. Compared with the traditional method, the method provides a seismic vulnerability model with wider application range and higher accuracy, and provides a scientific basis for seismic design, seismic risk management and post-disaster assessment.

[0057] The embodiment of the application provides a buried pipeline seismic vulnerability analysis method based on a three-parameter square normal distribution, Figure 1 The implementation process schematic diagram of the buried pipeline seismic vulnerability analysis method based on a three-parameter square normal distribution is shown, and the buried pipeline seismic vulnerability analysis method based on a three-parameter square normal distribution is implemented in the following specific steps:

[0058] S1, determining the site characteristics according to the position of the pipeline, and generating ground motion data conforming to the target response spectrum based on the random process spectrum representation method;

[0059] S2, constructing a buried pipeline finite element model, applying ground motion, performing nonlinear seismic response analysis, and extracting pipeline response data;

[0060] S3, selecting a ground motion intensity index and an engineering demand parameter, determining a damage index in combination with the pipeline characteristics, and constructing a limit state function of the buried pipeline;

[0061] S4, establishing a buried pipeline failure probability calculation method based on a three-parameter square normal distribution model under different ground motion intensities;

[0062] S5, based on a logistic regression model, taking the ground motion intensity index as the independent variable, constructing a buried pipeline seismic vulnerability function and drawing a vulnerability curve.

[0063] The embodiment of the application constructs a complete system covering seismic motion simulation-structure response analysis-seismic vulnerability analysis to improve the calculation accuracy of the seismic failure probability of the buried pipeline, and introduces a deviation parameter to correct the deviation in view of the problem that the existing lognormal distribution model cannot accurately reflect the skewness characteristics of the structure response data, thereby improving the calculation accuracy of the failure probability of the buried pipeline and making the vulnerability curve more in line with the actual damage distribution characteristics of the buried pipeline.

[0064] In the embodiment of the application, the method for generating seismic motion input data comprises:

[0065] S101, determining the site characteristics according to the position of the pipeline, and selecting the acceleration response spectrum meeting the requirements of the target site ;

[0066] S102, constructing an initial input power spectrum by using an empirical spectrum conversion relationship ;

[0067]

[0068] In the formula, is the structural damping ratio; represents the circular frequency; represents the target response spectrum when the period is ; represents the duration of the seismic motion; represents the probability that the structure response does not exceed the target response spectrum.

[0069] S103, introducing an amplitude modulation function to represent the evolutionary spectrum ;

[0070]

[0071] In the formula, the three-section time envelope function is expressed as follows:

[0072]

[0073] In the formula, and are the start and end times of the strong motion duration stage, respectively; is the tail decay rate coefficient. These parameters depend on factors such as the site, magnitude and epicentral distance.

[0074] S104, performing the evolutionary spectrum in the frequency range The inner dispersion is N frequency points, and the non-stationary process is generated by a random process spectrum representation method;

[0075]

[0076] In the formula, is the evolutionary power spectrum; is the frequency step, and are the maximum and minimum truncation values of the frequency respectively; ; is a random phase angle, and the uniform distribution of each other is independent.

[0077] S105, the average acceleration response spectrum of the ground motion sample is calculated , and compared with the target spectrum , and the relative error index is;

[0078]

[0079] S106, if the relative error exceeds 5%, the evolutionary spectrum is updated:

[0080]

[0081] In the formula, the superscript of the evolutionary spectrum density ( k ) represents the first iteration. k

[0082] Repeat the above steps until the requirements are met.

[0083] Figure 2 The average response spectrum of the artificial ground motion generated based on the random process spectrum representation method is shown in the comparison chart of the target response spectrum set by the Chinese building anti-seismic design specification GB50011-2016, wherein, Figure 2 The colored curve in the figure is the acceleration response spectrum of the ground motion sample, and from Figure 2 It can be seen that the overall trend of the average response spectrum of the generated artificial ground motion is in good agreement with the specification, indicating that the method can effectively simulate artificial ground motion in accordance with the characteristics of the target response spectrum. And Figure 3 The figure shows the ground motion sample in the embodiment of the application, Figure 3 The curve legend in the figure represents the ground motion acceleration time history sample.

[0084] In the embodiment of the application, the three-parameter square normal distribution-based buried pipeline seismic vulnerability analysis method is provided, Figure 4 The finite element model schematic diagram established in the embodiment of the application is shown, and the three-parameter square normal distribution-based buried pipeline seismic vulnerability analysis method comprises:

[0085] ​​S201, using ABAQUS finite element software, using beam element to simulate pipeline, using nonlinear soil spring element to simulate pipe-soil interaction, and constructing a buried pipeline finite element model;

[0086] S202, the ground motion acceleration time history is processed by a traveling wave and is applied to the model soil spring node set, nonlinear time history analysis is carried out, and the pipeline seismic response is obtained;

[0087] S203, a python general program is written, and the response data of the specified cross section of the pipeline is batch extracted.

[0088] In the embodiment of the application, the seismic intensity index and the engineering demand parameter are selected, the damage index is determined in combination with the pipeline characteristics, the limit state function of the buried pipeline is constructed, and specifically includes:

[0089] S301, according to the response characteristics and historical seismic damage data of the buried pipeline under the action of the earthquake, the peak acceleration (PGA) is selected as the seismic intensity index and the axial peak strain is selected as the engineering demand parameter;

[0090] S302, the limit state function of the buried pipeline is determined by considering the historical seismic damage data and the engineering demand parameter:

[0091]

[0092] Wherein, The limit state function is represented by f (X) ; R (X) represents the resistance or carrying capacity of the structure; and S (X) represents the load effect, that is, the seismic response of the pipeline; represents the critical failure threshold of the pipeline; represents the axial peak strain of the pipeline under the action of the earthquake; and X represents an uncertainty parameter, when , that is, failure occurs, that is, the seismic response of the pipeline exceeds its resistance or carrying capacity.

[0093] In the embodiment of the application, the pipeline response data under different seismic intensities (PGA) is counted, the response data is distributed fitted by using a three-parameter square normal distribution model, Figure 5 a response distribution fitting schematic diagram of the pipeline under the action of the earthquake is shown, and a buried pipeline failure probability calculation method based on a three-parameter square normal distribution model under different ground motion intensities is established, wherein the buried pipeline failure probability expression based on the three-parameter square normal distribution is:

[0094]

[0095] Wherein, is the response of the pipeline under the action of the earthquake (that is, the seismic demand parameter ), represents the demand response value of the pipeline obtained under the seismic input of the first represents the demand response value of the pipeline obtained under the seismic input of the first represents a specific damage state (i.e., a damage index) of the pipeline; represents a seismic intensity index; 、 and respectively represent the mean, standard deviation and skewness of the structural response data; represents the failure probability of the pipeline exceeding a specific damage state under a given seismic intensity.

[0096] In the embodiment of the present application, the seismic vulnerability function of the buried pipeline is constructed based on the logistic regression model with the seismic intensity index IM as the independent variable, and the seismic vulnerability curve of the buried pipeline is drawn based on the logistic regression model with the seismic intensity index IM as the independent variable, and the seismic vulnerability curve function is represented as follows:

[0097]

[0098] wherein, and are the logistic regression coefficients.

[0099] It should be noted that, Figure 6 The seismic vulnerability curve of the buried pipeline in the embodiment of the present application is shown, the failure probability results of the seismic vulnerability model based on the three-parameter square normal distribution and the lognormal distribution are compared, and the Monte Carlo simulation results are verified. The results show that the seismic vulnerability model based on the three-parameter square normal distribution has higher calculation accuracy. The method effectively improves the accuracy of the seismic vulnerability evaluation of the buried pipeline, and provides a more reliable scientific basis for seismic design and seismic risk management.

[0100] The present application provides a buried pipeline seismic vulnerability analysis method based on a three-parameter square normal distribution. The method first generates artificial seismic waves conforming to the target spectrum based on the random process spectrum representation method; then establishes a finite element model of the buried pipeline and performs nonlinear time history analysis to obtain pipeline response data; finally, the probability distribution of the response data is fitted based on the three-parameter square normal distribution, the failure probability of the pipeline under different seismic intensities is calculated, and the vulnerability curve is drawn.

[0101] In summary, the application provides a buried pipeline seismic vulnerability analysis method based on a three-parameter square normal distribution, and the embodiment of the application constructs a complete system covering seismic motion simulation, buried pipeline response analysis and seismic vulnerability analysis. The application solves the problem that the existing lognormal distribution model cannot accurately reflect the skewness characteristics of structural response data, thereby leading to calculation deviation of failure probability. By introducing the three-parameter square normal distribution which can accurately represent the skewness characteristics of structural response data, the calculation accuracy of the seismic failure probability of the buried pipeline is improved, and the vulnerability curve is more consistent with the actual damage distribution characteristics of the buried pipeline. Compared with the traditional method, the method provides a seismic vulnerability model with wider application range and higher accuracy, and provides a scientific basis for seismic design, seismic risk management and post-disaster assessment.

[0102] It should be noted that, for the foregoing embodiments, in order to simply describe, they are all expressed as a series of action combinations, but those skilled in the art should know that the application is not limited by the order of the described actions, because according to the application, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should know that the embodiments described in the specification all belong to preferred embodiments, and the actions and modules involved are not necessarily necessary for the application.

[0103] The above embodiments are only used to illustrate the technical solutions of the present application, and not to limit the protection scope of the application. Obviously, the described embodiments are only some of the embodiments of the present application, not all the embodiments. Based on these embodiments, all other embodiments obtained by those of ordinary skill in the art without creative labor fall within the scope of the present application. Although the present application has been described in detail with reference to the above embodiments, those of ordinary skill in the art can still combine, add or delete the features in the embodiments of the present application according to the circumstances without creative labor, so as to obtain different other technical solutions which do not deviate from the concept of the present application in essence. These technical solutions also belong to the scope of the present application.

Claims

1. A method for seismic fragility analysis of buried pipelines based on a three-parameter square normal distribution, characterized in that, The method comprises: S1, determining site characteristics according to the location of the pipeline, generating ground motion data conforming to the target response spectrum based on random process spectrum representation method; S2, constructing a finite element model of the buried pipeline, applying ground motion, performing nonlinear seismic response analysis, and extracting pipeline response data; S3, selecting ground motion intensity indicators and engineering demand parameters, determining damage indicators in combination with pipeline characteristics, and constructing limit state functions of the buried pipeline; S4, establishing a buried pipeline failure probability calculation method based on a three-parameter square normal distribution model under different ground motion intensities; S5, based on the logistic regression model, taking the ground motion intensity indicator as the independent variable, constructing the seismic vulnerability function of the buried pipeline and drawing the vulnerability curve; The determination of site characteristics according to the location of the pipeline, and the generation of ground motion data conforming to the target response spectrum based on the random process spectrum representation method, comprises: S101, determine the site characteristics according to the location of the pipeline, select the acceleration response spectrum S that meets the requirements of the target site a (T); S102, constructing an initial input power spectrum S(ω) using an empirical spectrum conversion relationship; where ξ is the structural damping ratio; ω = 2π / T represents the circular frequency; S a (T) represents the target response spectrum for a period of T; T d represents the duration of ground motion; p represents the probability that the structural response does not exceed the target response spectrum; S103, an amplitude modulation function g(t) is introduced to represent the evolution spectrum S x (ω, t) is: S x (ω,t) = |g(t)| 2 S(ω) Wherein, the expression of the three-section time envelope function g(t) is as follows: where t a and t b are the start and end times of the strong motion duration, respectively; c is the tail decay rate coefficient, and the above parameters depend on site, magnitude and epicentral distance factors; S104, discretize the evolutionary spectrum into N points within the frequency range [ω min ,ω max ] to generate a non-stationary process by a random process spectral representation method; where S x (ω n ,t) is the evolved power spectrum; Δω = (ω max - ω min ) / N is the frequency step size, ω max and ω min are the maximum and minimum cut-off values of the frequency, respectively; ω n = nΔω; are random phase angles that are mutually independent and uniformly distributed over [0, 2π]. S105, calculate the average acceleration response spectrum S of the ground motion sample a (T), and compare it with the target spectrum S a (T), and the relative error index is: S106, if the relative error exceeds 5%, update the evolution spectrum: Wherein, the superscript (k) of the evolution spectrum density represents the kth iteration; Repeat the above steps until the requirements are met.

2. The method for buried pipeline seismic fragility analysis based on three-parameter square normal distribution according to claim 1, characterized in that: The construction of the finite element model of the buried pipeline, the application of ground motion, the nonlinear seismic response analysis, and the extraction of pipeline response data, comprise: S201, using ABAQUS finite element software, using beam elements to simulate the pipeline, using nonlinear soil spring elements to simulate the pipe-soil interaction, and constructing a finite element model of the buried pipeline; S202, performing non-linear time history analysis by applying the ground motion acceleration time history to the model soil spring node set, and obtaining the seismic response of the pipeline; S203, writing a Python general program to batch extract the response data of the specified section of the pipeline.

3. The method for buried pipeline seismic fragility analysis based on three-parameter square normal distribution according to claim 1, characterized in that: Selecting ground motion intensity indicators and engineering demand parameters, determining damage indicators in combination with pipeline characteristics, and constructing limit state functions of the buried pipeline, comprise: S301, selecting ground motion intensity indicators and engineering demand parameters according to the response characteristics of the buried pipeline under seismic action and historical earthquake damage data; S302, considering historical earthquake damage data and engineering demand parameters to determine the limit state function of the buried pipeline: G(X) = R(X) - S(X) = ε cr - ε c where G(X) represents the limit state function; R(X) represents the resistance or carrying capacity of the structure; and S(X) represents the load effect, i.e., the seismic response of the pipeline; ε cr represents the critical failure threshold of the pipeline; ε c represents the axial peak strain of the pipeline under seismic action; and X represents the uncertainty parameter, and when G(X)≤0, it means that failure occurs, i.e., the seismic response of the pipeline exceeds its resistance or carrying capacity.

4. The method for buried pipeline seismic fragility analysis based on three-parameter square normal distribution according to claim 1, characterized in that: When establishing a buried pipeline failure probability calculation method based on a three-parameter square normal distribution model under different ground motion intensities, the buried pipeline failure probability expression based on a three-parameter square normal distribution is: where D is the response of the pipeline under seismic action, EDP i represents the demand response value of the pipeline under the ith seismic input; d is the specific damage state of the pipeline; IM is the seismic intensity index; μ, σ and α3 are the mean, standard deviation and skewness of the structural response data, respectively; P(D≥d|IM=x) represents the failure probability of the pipeline exceeding a specific damage state under a given seismic intensity.

5. The method for buried pipeline seismic fragility analysis based on three-parameter square normal distribution according to claim 4, characterized in that: When constructing the seismic vulnerability function of the buried pipeline and drawing the vulnerability curve based on the logistic regression model, taking the seismic intensity indicator IM as the independent variable, drawing the seismic vulnerability curve of the buried pipeline based on the logistic regression model, and the vulnerability curve function is expressed as follows: Wherein, β1 and β2 are the logistic regression coefficients.

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