A method for artificially synthesizing seismic waves in liquefiable ground

Abstract

The application discloses a method for synthesizing liquefied site seismic waves artificially and relates to the technical field of geotechnical earthquake engineering. The method comprises the following steps: obtaining seismic waves through site response analysis and decomposing the seismic waves to obtain corresponding response spectra; inputting the response spectra into a seismic ground motion model to output new seismic waves; decomposing the new seismic waves to obtain the amplitude and frequency of different modal waves of the seismic waves; adjusting the frequency of different modal waves by introducing a phase method; synthesizing the adjusted waves into response spectra, overcoming the problem of large high-frequency errors by using a relative error formula, and then judging the energy possessed in the response spectra, outputting seismic waves meeting the requirements, and re-iterating seismic waves not meeting the requirements back to the foregoing steps until the seismic waves meet the requirements. The method overcomes the shortage of samples in existing seismic data, effectively fills the problem of lacking effective seismic waves in the process of doing liquefied site structure seismic resistance, and has the advantages of high efficiency and high accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of geotechnical earthquake engineering, and more particularly to a method for artificially synthesizing seismic waves in liquefied sites. Background Art

[0002] Due to a lack of original data on field earthquake liquefaction, the empirical formula for liquefaction identification based on the Standard Penetration Test (SPT) in the Code for Seismic Design of Buildings (GB50011-2010, 2016 edition) has certain limitations and local specificities. Therefore, it is urgent to understand site liquefaction from a new perspective and propose a new liquefaction identification theory to provide strong support for disaster prevention and mitigation in engineering fields such as seismic risk assessment of sand liquefaction sites, reinforcement design of foundations within liquefiable sites, and seismic design of various foundations and retaining structures within liquefiable sites. In 2004, Academician Hu Yuxian's team analyzed surface, subsurface, and vertical records obtained at the Wildlife liquefaction site during the 1987 Superstition Hills earthquake in the United States and proposed a liquefaction site identification method based on the Hilbert-Huang Transform. This method requires a large number of earthquake records.

[0003] At present, there are three main ways to obtain seismic waves: one is to directly use the seismic waves recorded by the strong motion instrument at the actual site; the second is to select the measured earthquake records with similar site conditions, and modify their spectrum by adjusting the acceleration amplitude and time scale to meet the seismic requirements of the actual site; the third is to fit the spectrum phase according to the specifications to produce artificial synthetic seismic waves.

[0004] While some typical strong-seismic signals can be used for site liquefaction analysis, the existing seismic signals still cannot meet the actual computational analysis requirements due to the significant differences between the site conditions in the area where the strong-seismic instruments are located and those in my country. Therefore, it is very necessary to artificially synthesize the seismic signals of liquefaction site earthquakes. Summary of the Invention

[0005] In order to overcome the defects and shortcomings of the above-mentioned prior art, the present invention provides a method for artificially synthesizing seismic waves in liquefaction sites. The purpose of the present invention is to address the problem of lack of earthquake records that meet the requirements when using finite element software for seismic design of liquefaction site structures. A method for artificially synthesizing seismic waves with simple operation, good fit between the synthesized artificial response spectrum and the standard response spectrum, and high convergence accuracy is provided to overcome the shortage of samples in the existing seismic data and effectively fill the problem of lack of effective seismic waves when performing seismic design of liquefaction site structures.

[0006] In order to solve the above problems in the prior art, the present invention is implemented through the following technical solutions.

[0007] The present invention provides a method for artificially synthesizing seismic waves in a liquefied site, the method comprising the following steps:

[0008] S1. Seismic waves are obtained through site response analysis;

[0009] S2. Decomposing the obtained seismic wave to obtain its corresponding response spectrum;

[0010] S3, substituting the seismic wave response spectrum decomposed in step S2 into the earthquake ground motion model, and outputting a new seismic wave through the earthquake ground motion model;

[0011] S4, decomposing the new seismic wave obtained in step S3 to obtain the amplitude and frequency of different modal waves of the seismic wave;

[0012] S5. The frequencies of different modal waves are adjusted by introducing phases;

[0013] S6. The adjusted waves are synthesized into a response spectrum again, and the relative error formula is used to overcome the problem of large high-frequency errors. Then, the energy in the response spectrum is used to make a judgment, and the seismic waves that meet the requirements are output. The seismic waves that do not meet the requirements are iterated back to step S2 until they meet the requirements.

[0014] Further preferably, step S1 specifically includes:

[0015] S101. Create a site profile using the equivalent linear site response program based on the seismic site investigation report.

[0016] S102. According to the soil shear wave velocity and bulk density recorded in the on-site investigation report, set the corresponding dynamic modulus attenuation curve and hysteretic damping ratio curve;

[0017] S103. Input bedrock seismic waves; obtain seismic waves through site response analysis.

[0018] More preferably, in step S103, if there is no bedrock seismic wave, data obtained by deconvolution of the surface seismic record is used as the bedrock seismic wave input.

[0019] More preferably, in step S1, a site response analysis method is used to obtain multiple liquefaction site seismic waves.

[0020] More preferably, in step S2, each of the aforementioned seismic waves is decomposed to obtain a response spectrum of the seismic wave.

[0021] Further preferably, in step S3, the earthquake ground motion model is the Clough-Penzin model.

[0022] More preferably, the specific expression of the earthquake ground motion model is as follows:

[0023] ;

[0024] Where, represents the Clough-Penzien random earthquake motion model, represents the ground motion frequency, and represent the damping ratio and predominant frequency of soil respectively; and is the secondary filter parameter, is the spectral intensity factor, usually taken as = , =0.1~0.2 .

[0025] Further preferably, in step S4, the new seismic wave obtained in step S3 is subjected to empirical mode decomposition (EMD) to obtain amplitudes and frequencies of different modal waves of the seismic wave.

[0026] More preferably, the seismic wave expression obtained by EMD decomposition is as follows:

[0027] ;

[0028] in, is the amplitude, is the transient frequency, and t is the time.

[0029] Further preferably, in step S5, the frequencies of different modal waves are adjusted by introducing a phase method, specifically,

[0030] Add random phase to the obtained seismic wave expression to change the frequency, etc. The expression after adding the phase is as follows:

[0031] ;

[0032] in, is the amplitude, is the transient frequency, is the phase, .

[0033] Further preferably, in step S6, a relative error formula is used to overcome the problem of large high-frequency error. Specifically, after the frequency adjustment is completed, the following response spectrum error formula is used to overcome the problem of large high-frequency error after frequency adjustment:

[0034] ;

[0035] in, is the frequency obtained after frequency modulation, and T is the period.

[0036] Further preferably, in step S6, the judgment is made based on the energy in the response spectrum, and the judgment formula is as follows:

[0037] ;

[0038] in, represents the acceleration of seismic waves, when When the conditions are met, the seismic wave can be output; if the conditions are not met, the obtained response spectrum is iterated back to step S2 and continues to cycle until the conditions are met before it can be output.

[0039] Compared with the prior art, the present invention has the following beneficial technical effects:

[0040] 1. The seismic waves obtained by the present invention have the characteristics of actual liquefaction site seismic waves and can be used for seismic analysis of liquefaction site structures. Moreover, a considerable number of artificially synthesized liquefaction site seismic waves can be obtained through continuous cyclic adjustment.

[0041] 2. The advantages of the present invention are that the present invention is applicable to the synthesis of seismic waves in liquefied sites under any conditions, and has the advantages of strong applicability, high accuracy, fast synthetic wave speed, and a large number of synthetic seismic waves. It provides more comprehensive information for detecting the seismic design of structures in liquefied sites in numerical simulations, thereby improving the reliability of the seismic design of structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 This is a flow chart of a method for artificially synthesizing seismic waves in liquefaction sites according to the present invention;

[0043] Figure 2 It is the seismic wave and acceleration response spectrum obtained through site response analysis;

[0044] Figure 3 The seismic wave and acceleration response spectrum output by the Clough-Penzin model;

[0045] Figure 4 Different modal waveforms obtained by EMD decomposition of seismic waves output by the Clough-Penzin model;

[0046] Figure 5 It is the seismic wave and acceleration response spectrum that meet the conditions after adjustment. DETAILED DESCRIPTION

[0047] Typical embodiments embodying the features and advantages of the present invention will be described in detail in the following description. The present invention can have various changes in different embodiments without departing from the scope of the present invention, and the descriptions and illustrations therein are essentially for illustrative purposes only and are not used to limit the present invention.

[0048] Example 1

[0049] As a preferred embodiment of the present invention, refer to the attached Figure 1 As shown, this embodiment discloses a method for artificially synthesizing seismic waves in a liquefaction site, the method comprising the following steps:

[0050] S1. Seismic waves are obtained through site response analysis;

[0051] S2. Decomposing the obtained seismic wave to obtain its corresponding response spectrum;

[0052] S3, substituting the seismic wave response spectrum decomposed in step S2 into the earthquake ground motion model, and outputting a new seismic wave through the earthquake ground motion model;

[0053] S4, decomposing the new seismic wave obtained in step S3 to obtain the amplitude and frequency of different modal waves of the seismic wave;

[0054] S5. The frequencies of different modal waves are adjusted by introducing phases;

[0055] S6. The adjusted waves are synthesized into a response spectrum again, and the relative error formula is used to overcome the problem of large high-frequency errors. Then, the energy in the response spectrum is used to make a judgment, and the seismic waves that meet the requirements are output. The seismic waves that do not meet the requirements are iterated back to step S2 until they meet the requirements.

[0056] Example 2

[0057] As another preferred embodiment of the present invention, this embodiment is based on the above embodiment 1 and further supplements and elaborates on the technical solution of the present invention. In this embodiment, step S1 specifically includes:

[0058] S101. Create a site profile using the equivalent linear site response program based on the seismic site investigation report.

[0059] S102. According to the soil shear wave velocity and bulk density recorded in the on-site investigation report, set the corresponding dynamic modulus attenuation curve and hysteretic damping ratio curve;

[0060] S103. Input bedrock seismic waves; obtain seismic waves through site response analysis.

[0061] Furthermore, if there is no bedrock seismic wave, the data obtained by deconvolution of the surface seismic record is used as the bedrock seismic wave input.

[0062] Example 3

[0063] As another preferred embodiment of the present invention, refer to the attached Figure 1 As shown, this embodiment is a further detailed supplement and elaboration of the technical solution of the present invention on the basis of the above-mentioned embodiment 1 or embodiment 2. In this embodiment, a plurality of liquefaction site seismic waves are obtained by using a site response analysis method. Each of the aforementioned seismic waves is decomposed to obtain the response spectrum of the seismic wave. A new seismic wave is produced after the response spectrum of the seismic wave is input into the Clough-Penzin model. After the obtained seismic wave is subjected to EMD decomposition, different modal waves are obtained. After obtaining the amplitude and frequency of different modal waves, a random phase angle is introduced to adjust the frequency of different modal waves, and finally the response spectrum is synthesized. The response spectrum relative error formula is used to overcome the problem of large high-frequency errors, and the energy of the wave is used to determine whether the synthesized seismic wave meets the conditions. The seismic wave that meets the conditions is output, and the seismic wave that does not meet the conditions is substituted back into the above-mentioned steps for adjustment until it meets the requirements and is output.

[0064] Example 4

[0065] As another preferred embodiment of the present invention, this embodiment is a further detailed supplement and elaboration of the technical solution of the present invention on the basis of the above-mentioned embodiment 1, embodiment 2 or embodiment 3.

[0066] As an example, in step S3, the earthquake ground motion model is the Clough-Penzin model. The specific expression of the earthquake ground motion model is as follows:

[0067] ;

[0068] Where, represents the Clough-Penzien random earthquake motion model, represents the ground motion frequency, and represent the damping ratio and predominant frequency of soil respectively; and is the secondary filter parameter, is the spectral intensity factor, usually taken as = , =0.1~0.2 .

[0069] As an implementation of this embodiment, in step S4, the new seismic wave obtained in step S3 is subjected to empirical mode decomposition (EMD) to obtain the amplitude and frequency of different modal waves of the seismic wave. The seismic wave expression obtained by EMD decomposition is as follows:

[0070] ;

[0071] in, is the amplitude, is the transient frequency, and t is the time.

[0072] As another preferred implementation of this embodiment, in step S5, the frequencies of different modal waves are adjusted by introducing a phase method, specifically,

[0073] Add random phase to the obtained seismic wave expression to change the frequency, etc. The expression after adding the phase is as follows:

[0074] ;

[0075] in, is the amplitude, is the transient frequency, is the phase, .

[0076] As another preferred implementation of this embodiment, in step S6, a relative error formula is used to overcome the problem of large high-frequency error. Specifically, after the frequency adjustment is completed, the following response spectrum error formula is used to overcome the problem of large high-frequency error after frequency adjustment:

[0077] ;

[0078] in, is the frequency obtained after frequency modulation, and T is the period.

[0079] In step S6, the energy in the response spectrum is used for judgment. The judgment formula is as follows:

[0080] ;

[0081] in, represents the acceleration of seismic waves, when When the conditions are met, the seismic wave can be output; if the conditions are not met, the obtained response spectrum is iterated back to step S2 and continues to cycle until the conditions are met before it can be output.

[0082] Example 5

[0083] As another preferred embodiment of the present invention, this embodiment uses the 1989 Lomas Prieta earthquake as an example, taking Treasure Island (located northwest of San Francisco, USA) as an example. Based on the field survey report (as shown in Table 1), an equivalent linear site response program is used to create a site profile. The corresponding dynamic modulus attenuation curve and hysteretic damping ratio curve are set according to the shear wave velocity and bulk density of the soil layer. The bedrock seismic wave is input and the site response analysis is performed. Only one liquefaction site earthquake record is selected to obtain the acceleration response spectrum corresponding to the seismic wave through Duharmel integration, as shown in Figure 1. Figure 2 shown.

[0084] Table 1 Treasure Island site profile and soil layer parameters

[0085] .

[0086] Specifically, the obtained seismic wave response spectrum is brought into the Clough-Penzien model, a new seismic wave is generated by the model, and the response spectrum of the seismic wave is obtained by Duharmel integration. The seismic wave obtained by the Clough-Penzien model is as follows: Figure 3 .

[0087] Specifically, through EMD Figure 3 The earthquake record shown is decomposed into 10 different modal components, such as Figure 4 .

[0088] By introducing random phase angles, the frequencies and values ​​of different modal waves of seismic waves are adjusted. ,in .

[0089] Specifically, the adjusted modal waves are synthesized into seismic wave response spectra, and the problem of large high-frequency errors after frequency modulation is overcome by the response spectrum error formula.

[0090] Specifically, after the above processing, the energy of the seismic wave response spectrum is judged. If the conditions are met, the seismic wave can be output; if the conditions are not met, the obtained response spectrum is iterated back to the previous steps and continues to cycle until the conditions are met ( ) before it can be output, such as Figure 5 .

[0091] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. The present invention can be appropriately modified and changed. Any modifications, equivalent replacements, improvements, etc. made within the specifications and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for artificially synthesizing seismic waves in a liquefied site, characterized in that: The method The following steps are included: S1. Seismic waves are obtained through site response analysis; S2. Decomposing the obtained seismic wave to obtain its corresponding response spectrum; S3, substituting the seismic wave response spectrum decomposed in step S2 into the earthquake ground motion model, and outputting a new seismic wave through the earthquake ground motion model; S4, decomposing the new seismic wave obtained in step S3 to obtain the amplitude and frequency of different modal waves of the seismic wave; S5. Adjust the frequencies of different modal waves by introducing phases; S6. The adjusted waves are synthesized into a response spectrum again, and the relative error formula is used to overcome the problem of large high-frequency errors. Then, the energy in the response spectrum is used to make a judgment, and the seismic waves that meet the requirements are output. The seismic waves that do not meet the requirements are iterated back to step S2 until they meet the requirements.

2. The method for artificially synthesizing seismic waves in a liquefied site according to claim 1, wherein: Step S1 specifically includes: S101. Create a site profile using the equivalent linear site response program based on the seismic site investigation report. S102. According to the soil shear wave velocity and bulk density recorded in the on-site investigation report, set the corresponding dynamic modulus attenuation curve and hysteretic damping ratio curve; S103. Input bedrock seismic waves; obtain seismic waves through site response analysis.

3. A method for artificially synthesizing seismic waves in a liquefaction site according to claim 1 or 2, characterized in that: In step S1, a site response analysis method is used to obtain multiple liquefaction site seismic waves; each of the aforementioned seismic waves is decomposed to obtain a response spectrum of the seismic wave.

4. A method for artificially synthesizing seismic waves in a liquefied site according to claim 1 or 2, characterized in that: In step S3, the earthquake ground motion model is the Clough-Penzien model.

5. The method for artificially synthesizing seismic waves in a liquefied site according to claim 4, characterized in that: The specific expression of the earthquake ground motion model is as follows: ； Where, represents the Clough-Penzien random earthquake motion model, represents the ground motion frequency, and represent the damping ratio and predominant frequency of soil respectively; and is the secondary filter parameter, is the spectrum intensity factor, take = , =0.1~0.2 .

6. The method for artificially synthesizing seismic waves in a liquefied site according to claim 1 or 2, characterized in that: In step S4, the new seismic wave obtained in step S3 is subjected to empirical mode decomposition to obtain the amplitudes and frequencies of different modal waves of the seismic wave.

7. The method for artificially synthesizing seismic waves in a liquefied site according to claim 6, characterized in that: The seismic wave expression obtained through empirical mode decomposition is as follows: ； in, is the amplitude, is the transient frequency, and t is the time.

8. The method for artificially synthesizing seismic waves in a liquefied site according to claim 7, characterized in that: In step S5, the frequencies of different modal waves are adjusted by introducing the phase method, specifically, A random phase is added to the obtained seismic wave expression to change the frequency. The expression after adding the phase is as follows: ； in, is the amplitude, is the transient frequency, is the phase, .

9. The method for artificially synthesizing seismic waves in a liquefied site according to claim 1 or 2, characterized in that: In step S6, the relative error formula is used to overcome the problem of large high-frequency error. Specifically, after the frequency adjustment is completed, the following response spectrum error formula is used to overcome the problem of large high-frequency error after frequency adjustment: ； in, is the frequency obtained after frequency modulation, and T is the period.

10. The method for artificially synthesizing seismic waves in a liquefied site according to claim 1 or 2, characterized in that: In step S6, the energy in the response spectrum is used for judgment. The judgment formula is as follows: ； in, represents the acceleration of seismic waves, when When the conditions are met, the seismic wave can be output; if the conditions are not met, the obtained response spectrum is iterated back to step S2 and continues to cycle until the conditions are met before it can be output.

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