An evaluation method for applicability of a seismic wave tuning method in elastic time history analysis

Abstract

The present application relates to the technical field of elastic time history analysis, in particular to a method for evaluating the applicability of seismic wave conditioning methods in elastic time history analysis. The method comprises the following steps: defining an evaluation index of the applicability of seismic record conditioning methods; calculating a reliability index of the seismic wave conditioning method; and calculating a dispersion index of the seismic wave conditioning method. The present application can effectively compare various seismic wave conditioning methods, and also provide a basis for optimizing the seismic wave conditioning method.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of elastic time history analysis, and particularly relates to a method for evaluating the applicability of a seismic wave selection method in elastic time history analysis. BACKGROUND

[0002] In structural seismic design, the design response spectrum is a statistical seismic response spectrum obtained through four stages of averaging, regularization, smoothing and empiricism. For some important buildings, elastic time history analysis is needed as a supplementary calculation. The seismic record selection method in elastic time history analysis should not only avoid excessive dispersion of structural response, but also ensure the safety level of the calculation results.

[0003] The current specifications of major countries have their own seismic wave selection methods. In addition, different seismic wave selection methods have been proposed in existing researches, such as selecting waves according to site, selecting waves according to site characteristic period, selecting waves according to response spectrum double frequency band, and selecting waves according to response spectrum characteristic period area before and after. However, there is no uniform conclusion on the advantages and disadvantages of the existing seismic wave selection methods. Establishing a quantitative evaluation method for the applicability of seismic wave selection methods in elastic time history analysis can effectively compare various seismic wave selection methods, and also provide a basis for the optimization of seismic wave selection methods. SUMMARY

[0004] In view of the defects in the prior art, the purpose of the present application is to provide a method for evaluating the applicability of a seismic wave selection method in elastic time history analysis, which can solve the problem that the applicability of a seismic wave selection method in elastic time history analysis cannot be quantitatively evaluated in the prior art.

[0005] To achieve the above purpose, the technical solution adopted by the present application is as follows:

[0006] The present application provides a method for evaluating the applicability of a seismic wave selection method in elastic time history analysis, comprising the following steps:

[0007] Define the applicability evaluation index of the seismic record selection method:

[0008] The present application uses reliability index and dispersion index as the applicability index of the seismic record selection method in elastic time history analysis. The reliability index is used to evaluate the safety level of the selection method, and the dispersion index is used to evaluate the feasibility of the selection method.

[0009] Calculate the reliability index of the seismic wave selection method:

[0010] The reliability index of the seismic wave selection method in elastic time history analysis can be calculated as follows,

[0011]

[0012] In the formula, x is the value of PGA, when considering bidirectional horizontal earthquake, x Take the geometric mean of two horizontal direction PGA; is the reliability index of the seismic wave selection method; the seismic wave selection method reliability equation ; is the probability density function of the ground peak acceleration PGA.

[0013] The dispersion index of the seismic wave selection method is calculated:

[0014] The confidence interval of the probability of the occurrence of the effective seismic wave under a certain significance level α can be expressed as,

[0015]

[0016] In the formula, is the frequency of the occurrence of the effective seismic wave in the seismic wave sample; N is the sample quantity of the seismic wave; is the reliability coefficient.

[0017] According to the size of the obtained reliability index value of the seismic wave selection method, the greater the reliability index indicates that the result obtained by the selection method is more economical, and vice versa, which indicates that the result obtained by the selection method is more conservative.

[0018] According to the size of the obtained dispersion index value of the seismic wave selection method, the greater the dispersion index indicates that the result obtained by the selection method is more stable, and vice versa, which indicates that the result obtained by the selection method has greater volatility and is not convenient for design.

[0019] The present application can effectively compare various seismic wave selection methods, and also provide a basis for optimization of the seismic wave selection method. BRIEF DESCRIPTION OF DRAWINGS

[0020] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiment description. The drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the premise of the drawings.

[0021] Figure 1 is the overall flowchart of the embodiment of the present application;

[0022] Figure 2 (a) is the plan view of the multi-layer frame structure of the embodiment of the present application;

[0023] Figure 2 (b) is the plan view of the multi-layer frame structure of the embodiment of the present application; ​

[0024] Figure 3 For the embodiment of the application, the regression model of the structural base shear PSDM (main direction) is provided.

[0025] Figure 4 For the embodiment of the application, the reliability curve of the brewing method (main direction) is provided. DETAILED DESCRIPTION

[0026] To make the purposes, technical solutions and advantages of the embodiments of the application clearer, the technical solutions in the embodiments of the application will be described clearly and completely below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are part of the embodiments of the application, rather than all the embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by a person of ordinary skill in the art without creative work belong to the protection scope of the application.

[0027] Figure 1 For the embodiment of the application, the evaluation method for the applicability of the seismic wave brewing method in elastic time history analysis is provided. As shown in the following formula: Figure 1

[0028] The embodiments of the application will be described in further detail below with reference to the drawings.

[0029] The application provides an evaluation method for the applicability of a seismic wave brewing method, comprising the following steps:

[0030] S1: defining the applicability evaluation index of the seismic record brewing method:

[0031] The application adopts the reliability index and the discreteness index as the applicability index of the seismic record brewing method in elastic time history analysis. The reliability index is used to evaluate the safety level of the brewing method, and the discreteness index is used to evaluate the feasibility of the brewing method.

[0032] S2: calculating the reliability index of the seismic wave brewing method;

[0033] S21: establishing the reliability equation for evaluating the seismic wave brewing method;

[0034] Referring to the concepts of “small earthquake elasticity” and “medium earthquake non-yielding” in seismic performance design, the performance requirement of “small earthquake elasticity” is generally met by bearing capacity design in structural design, and the “medium earthquake non-yielding” has a higher requirement for the bearing capacity of the structure, which is not required for ordinary structures. For ordinary structures, elastic time history checking is a supplementary checking for “small earthquake elasticity”, and the structural response caused by the selected seismic wave should be less than the structural bearing capacity designed according to “medium earthquake non-yielding”. In this paper, the safety level of the brewing method is evaluated by the total base shear in the main direction of the structure, and the total base shear corresponding to the seismic performance of “medium earthquake non-yielding” is ​As the limit state of the reliability of the seismic wave selection method, the total base shear of the structure calculated by the elastic time history analysis under the condition of a given ground peak acceleration (PGA) is less than The conditional probability defined as the reliability equation of the seismic wave selection method is that the total base shear of the structure calculated by the elastic time history analysis under the condition of a given ground peak acceleration (PGA) is less than The reliability equation of the seismic wave selection method can be written as,

[0035]

[0036] In the formula, Q is the total base shear of the structure in a specific principal direction calculated by the elastic time history analysis.

[0037] S22: Calculate the reliability index of the applicability of the seismic wave selection method;

[0038] The application quantifies the seismic demand of the structure by the base shear Q of the structure, and establishes a conditional probability model of the seismic demand under the condition of a specified PGA, i.e., a probabilistic seismic demand model (PSDM). The maximum seismic demand m Ft of the structure can be obtained by regression analysis of the response of the structure, and the regression equation can be written as,

[0039]

[0040] In the formula, a and b are regression parameters; x is the value of PGA, when considering bidirectional horizontal earthquake, x the geometric mean of the two horizontal direction PGAs is taken.

[0041] It is assumed that obeys a lognormal distribution, then obeys a normal distribution, and the reliability equation of the seismic wave selection method can be expressed by the cumulative distribution function of the standard normal distribution as:

[0042]

[0043]

[0044] In the formula, is the logarithmic standard deviation of the total base shear ; is the total base shear of the structure under the th seismic wave in the elastic time history analysis; j is the number of simulations. M

[0045] The reliability index of the seismic wave selection method in the elastic time history analysis can be calculated according to the following formula, ​

[0046]

[0047] In the formula, is the reliability index of the seismic wave selection method; is the probability density function of the ground peak acceleration PGA, and the cumulative distribution function of PGA can be derived.

[0048] Wherein, the seismic intensity and the corresponding ground peak acceleration PGA conform to the cumulative distribution function described by the scale transformation method of extreme value distribution, which can be written as:

[0049]

[0050] In the formula, c 1, c 2, c 3 are coefficients, the values of which are related to the seismic intensity; x is the value of the ground peak acceleration PGA.

[0051] S3: Calculate the dispersion index of the seismic wave selection method;

[0052] Assuming that the seismic wave causing the total shear force of the structure base greater than is an invalid seismic wave, and the seismic wave less than is an effective seismic wave, all seismic records in the earthquake library can be divided into two sets: the effective seismic wave set and the invalid seismic wave set, and the selection process of the seismic wave can be regarded as a Bernoulli trial between the two sets. According to the De Moivre-Laplace local limit theorem, there are

[0053]

[0054] In the formula, N E is the number of effective seismic records; N is the total number of seismic records; P s is the probability of the occurrence of effective seismic records.

[0055] From the above formula, it can be seen that obeys the standard normal distribution, and , then it can be concluded that

[0056]

[0057] In the formula, is the frequency value of the occurrence of effective seismic records in the seismic record sample.

[0058] At a certain significance level α, the probability of an effective vibration record occurring. The confidence interval is determined by the number of samples from seismic ground motion records. N Represented as,

[0059]

[0060] In the formula, This represents the reliability coefficient.

[0061] Calculation example

[0062] The example of this invention is a Class A multi-layered frame structure symmetrically arranged in two principal axis directions. For example... Figure 2 As shown, the multi-story frame has a single span of 6m in both main axis directions; the story height is 3.0m, and there are eight stories. The concrete strength grade of the frame columns is C35, and the concrete strength grade of the frame beams and floor slabs is C30; the frame column cross-section dimensions are 600mm x 600mm, the main beam dimensions are 250mm x 550mm, the secondary beam dimensions are 200mm x 500mm, and the floor slab thickness is 100mm; the seismic fortification intensity is 6 degrees (the example is a Class A building, treated as a seismic fortification intensity increased by one degree); the seismic design group is Group 1, and the site category is III; the basic wind pressure is 0.35kN / m³. 2 The ground roughness is classified as Class C; in addition to the structure's self-weight, the additional dead load is taken as 2.0 kN / m. 2 The live load is taken as 2.0 kN / m. 2 .

[0063] This invention compares and illustrates the amplitude modulation method in the American Building Load Code ASCE 7-10 (hereinafter referred to as the ASCE 7-10 method) and the selection method in my country's Seismic Design Code GB50011-2010 (hereinafter referred to as the "Code for Seismic Design") as examples. Elastic time history analysis is performed on seismic waves selected using the ASCE 7-10 method and the Code for Seismic Design, and the reliability and dispersion indices of the seismic wave selection method are calculated according to the method of this invention.

[0064] like Figure 3 As shown, the PSDM (Probabilistic Seismic Demand Model) calculated based on the amplitude-adjusted seismic records using the ASCE7-10 method has a higher good of fit; when the PGA value is the same, the seismic records adjusted by the ASCE7-10 method result in greater base shear force on the structure. Figure 4As shown, the reliability curves of the two methods are quite similar. However, according to statistical results, the median of the reliability equation corresponding to the ASCE7-10 method is larger, while the dispersion is smaller (ASCE7-10 method reliability equation: median 1.47, logarithmic error 0.68; "Code for Seismic Design of Buildings" method reliability equation: median 1.43, logarithmic error 0.70). The applicability indices of the two selection methods are shown in Table 1.

[0065] Table 1 Applicability Indicators of Selection Methods

[0066] As shown in Table 1, for earthquakes of intensity 6 degrees in my country, the reliability of the two amplitude modulation methods is at the same level; the probability of occurrence of effective ground motion records calculated using the seismic design code is as follows: The confidence interval is wider, but the calculated probability of a valid vibration record is lower. Significantly higher than the ASCE7-10 method. Combined Figure 4 From the results, it can be inferred that... Using the ASCE7-10 method as a boundary, the structural base shear force caused by earthquake records after amplitude adjustment is more likely to be greater than that of the seismic records after amplitude adjustment. This result also reflects that the ASCE 7-10 method is more suitable for areas with higher earthquake intensity. The earthquake intensity and frequency in the United States are higher than in my country, and the seismic design provisions in ASCE 7-10 are mostly aimed at ensuring the safety of structures under high-intensity earthquakes. Furthermore, the ASCE 7-10 method requires the use of only natural ground motion records, while the seismic design code allows the use of artificial ground motion records. The earthquake records used in this analysis are all natural earthquake records; using some artificial ground motion records can reduce the dispersion of the results obtained according to the seismic design code to a certain extent.

[0067] In summary, the ASCE7-10 method is more complex. Elastic time-history analysis using seismic records selected according to the ASCE7-10 method yields a larger base shear force with less dispersion, making the ASCE7-10 method more suitable for areas with higher seismic intensity. The seismic design code (GB 50011-2012) method is simpler. Elastic time-history analysis using seismic records selected according to the GB 50011-2012 method yields a smaller base shear force with greater dispersion, requiring the use of some manual records to reduce the dispersion of the base shear force.

Claims

1. An evaluation method of applicability of seismic wave conditioning method in elastic time history analysis, comprising the following steps: 1) defining the evaluation index of applicability of seismic record conditioning method: using reliability index and dispersion index as the evaluation index of seismic record conditioning method in elastic time history analysis; the reliability index is used to evaluate the safety level of the conditioning method; the dispersion index is used to evaluate the feasibility of the conditioning method; 2) calculating the reliability index of seismic wave conditioning method: the reliability index of seismic wave conditioning method in elastic time history analysis is calculated according to the following formula, In the formula, is a cumulative distribution function of a standard normal distribution; x is a value of the ground peak acceleration PGA when considering bidirectional horizontal earthquake, x is a geometric mean of two horizontal direction PGAs; is a reliability index of the seismic wave conditioning method; is a reliability equation of the seismic wave conditioning method; is a probability density function of the ground peak acceleration PGA; wherein the reliability equation of seismic wave conditioning method is expressed as the cumulative distribution function of standard normal distribution: ， where F t is the total base shear in a particular principal direction calculated from the elastic time history analysis; is the total base shear of the structure under the i-th seismic wave in the elastic time history analysis; t is the logarithmic standard deviation of F tj ; F Ft is the total base shear of the structure under the i-th seismic wave in the elastic time history analysis; j is the total base shear of the structure under the i-th seismic wave in the elastic time history analysis; M is the number of simulations; is the total base shear corresponding to the performance of non-yielding under the medium earthquake; m Ft is the maximum seismic demand, a and b are regression parameters, x is the value of PGA, when considering the two-way horizontal earthquake, x take the geometric mean of the two horizontal direction PGA; 3) calculating the dispersion index of seismic wave conditioning method: The probability of occurrence of an effective seismic wave at a certain level of significance α The confidence interval of the probability of occurrence of an effective seismic wave can be expressed as, wherein is the frequency of occurrence of valid seismic waves in the sample of seismic waves; N is the number of samples of seismic waves; is the reliability factor.

2. The method according to claim 1, wherein the method is characterized by: according to the size of the reliability index value of seismic wave conditioning method obtained in step 2), the greater the reliability index, the more economical the result obtained by the conditioning method, and vice versa; according to the size of the dispersion index value of seismic wave conditioning method obtained in step 3), the greater the dispersion index, the more stable the result obtained by the conditioning method, and vice versa.

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