A high-low frequency seismic ground motion superposition method considering dam engineering characteristics

Abstract

The application discloses a high-low frequency seismic wave superposition method considering dam engineering characteristics, and belongs to the technical field of seismic wave input. First, the dam natural frequency is calculated according to the regional seismic source parameters of the dam engineering, and the low-frequency vibration simulation range is determined. Then, in combination with the high-frequency seismic wave randomness of the region, a database of high-frequency seismic waves of multiple schemes is simulated, and high-frequency seed seismic waves matching the dam river direction and vertical mode are selected from the database. Next, the low-frequency seed seismic wave is simulated in the low-frequency simulation range, and the wide-band seed seismic wave is synthesized to determine the wide-band target spectrum. Finally, the target spectrum and the target PGA are taken as targets, and the wide-band mixed seismic wave is obtained by using the wavelet time domain response spectrum fitting method. The high-low frequency seismic wave simulation method provided by the method fully considers the frequency component in the dam fundamental frequency range, avoids underestimating the response spectrum due to the lack of frequency component when superposition is performed, considers multiple frequency points by using the wavelet fitting, avoids the energy cavity of the wide-band, and meets the demand of the dam engineering.

Description

Technical Field

[0001] This invention belongs to the field of seismic motion input technology, specifically relating to a method for superimposing high and low frequency seismic motions that takes into account the characteristics of dam engineering. Background Technology

[0002] Appropriate seismic motion input can ensure the reliability of seismic calculations for structures. For important structures such as dams, it is usually necessary to input seismic motion time histories for structural dynamic analysis. However, the number of actual seismic motion records is still relatively small and cannot meet the needs of actual engineering projects. Therefore, artificially simulated seismic motions are needed as a supplement.

[0003] Currently, commonly used seismic motion simulation methods in engineering include stochastic methods and deterministic methods. Stochastic methods (such as the stochastic finite fault method) have the advantage of simulating high-frequency ground motions relatively well; however, they cannot account for the differences between the three components of ground motion, struggle to incorporate the influence of local topographic relief on the simulation, and oversimplify the description of propagation paths and sites, failing to reflect their true characteristics. On the other hand, deterministic methods, such as the spectral element method, can address these issues; however, the required source and detailed crustal structural parameters are difficult to obtain. Furthermore, deterministic methods are often too costly to cover the frequency range usable in engineering, making direct application in engineering difficult. Therefore, it is necessary to superimpose the high-frequency components of ground motions obtained using stochastic methods with the low-frequency components obtained using deterministic methods to obtain broadband ground motions usable in engineering. However, the time histories of ground motions generated by the two methods are difficult to superimpose, and discontinuities in the response spectrum of high-frequency and low-frequency ground motions may exist in the mixed frequency band, causing energy voids in the main frequency component range of dams. Summary of the Invention

[0004] To address the aforementioned shortcomings in existing technologies, the high- and low-frequency ground motion superposition method considering the characteristics of dam engineering provided by this invention solves the problem that existing ground motion simulation methods used in engineering projects are difficult to superimpose the time histories of high- and low-frequency ground motions, and that there is a discontinuity in the response spectrum in the mixed frequency band, resulting in energy voids in the main frequency component segments of the dam.

[0005] To achieve the aforementioned objectives, the technical solution adopted by this invention is: a method for superimposing high- and low-frequency seismic motions considering the characteristics of dam engineering, comprising:

[0006] Based on the source parameters of the dam project area, the natural frequency of the dam is calculated, and then the range of low-frequency vibration simulation is determined.

[0007] Based on the randomness of high-frequency ground motion in the dam project area, a multi-scheme high-frequency ground motion simulation considering parameter uncertainties is carried out, and then a high-frequency ground motion database is constructed.

[0008] In the high-frequency ground motion database, ground motions that simultaneously match the river-direction and vertical vibration modes of the dam are selected as high-frequency seed ground motions.

[0009] Based on the selection of high-frequency seed ground motion, low-frequency ground motion simulation is performed within the low-frequency vibration simulation range to obtain low-frequency seed ground motion.

[0010] High-frequency seed ground motion and low-frequency seed ground motion are combined to form broadband seed ground motion, thereby determining the broadband target spectrum;

[0011] Using the broadband target spectrum and target PGA as targets, a wavelet-based time-domain response spectrum fitting method is used to fit the response spectrum, resulting in a broadband hybrid ground motion that takes into account the characteristics of the dam project.

[0012] Furthermore, the maximum frequency in the low-frequency vibration simulation range ;in, For the dam natural frequency of the first order .

[0013] Furthermore, in the process of constructing a high-frequency seismic database:

[0014] The uncertainties considered include: the existence of seismogenic faults around the dam site, the location of each seismogenic fault, the distribution of source slip, the distribution of initial rupture points, the dip angle, the stress drop, the high-frequency attenuation coefficient, and the uncertainty of the random phase of the random finite fault method under different schemes.

[0015] Furthermore, multi-scheme high-frequency ground motion simulations were conducted to construct a high-frequency ground motion database, including:

[0016] Based on parameter uncertainty, multiple samples are simulated using each set of parameters, and the weight of each parameter is determined according to the parameter distribution. Then, the random finite fault method is used to simulate high-frequency ground motion.

[0017] The PGA and acceleration response spectra obtained from various high-frequency ground motion simulation schemes are sorted in order of magnitude to obtain a database of PGA and acceleration response spectra at different quantiles for high-frequency ground motion.

[0018] Based on the requirements of the dam project, the quantiles of the PGA and acceleration response spectrum with preset guarantee rates are determined, and the corresponding PGA and acceleration response spectrum are used as the target PGA and high-frequency target spectrum, thereby constructing a high-frequency ground motion database.

[0019] Furthermore, ground motions that simultaneously match the dam's longitudinal and vertical vibration modes are selected as high-frequency seed ground motions, including:

[0020] From the high-frequency seismic database Earthquake ground motion is divided into In each group of earthquakes, three earthquakes are randomly assigned to the following directions: downstream, transverse, and vertical.

[0021] Calculate the difference between the l-order frequency spectrum value along the river and the target spectrum value along the river in each group of ground motions, and then select several ground motions in the first and third directions that are closest to the high-frequency target spectrum.

[0022] Calculate the difference between the vertical l-th order frequency spectrum value and the vertical target spectrum value in each group of ground motions, and then select several second and third direction ground motions that are closest to the high-frequency target spectrum;

[0023] The three sets of ground motions with the smallest distance from the high-frequency target spectrum along the river direction within the entire natural frequency range of the dam are selected from the intersection of the first and third direction ground motions and the second and third direction ground motions.

[0024] Furthermore, the distance along the river direction from the high-frequency target spectrum across the entire natural frequency range of the dam. Represented as:

[0025]

[0026] In the formula, This indicates the number of response spectrum periods across the entire natural frequency range of the dam. This represents the response spectrum value of the selected seismic motion along the river. This represents the high-frequency target spectrum with preset quantile values. ~ This indicates the range of the dam's natural frequencies.

[0027] Furthermore, in the process of simulating low-frequency ground motion:

[0028] The maximum effective frequency of the constructed three-dimensional spectral unit numerical model is greater than the maximum value of the high and low frequency superposition frequency band;

[0029] The selected source parameters are consistent with the source parameters of the high-frequency seed ground motions in the high-frequency ground motion database;

[0030] By supplementing high-frequency source components, the spatial distribution of slip on the fault plane is made to conform to... An attenuation model was developed, and the rise time and rupture propagation velocity of the seismic source were determined based on the slip, magnitude, and crustal parameters. A broadband kinematic source model was constructed, and then low-frequency ground motion simulation was performed using the spectral element method.

[0031] Furthermore, broadband seed ground motions are synthesized to determine the broadband target spectrum, including:

[0032] High-frequency seed ground motion and low-frequency seed ground motion are filtered by matching filters with the same parameters, respectively, and high-frequency seed ground motion with frequencies greater than the conversion frequency band and low-frequency seed ground motion with frequencies less than the conversion frequency band are retained.

[0033] The retained high-frequency seed ground motion and low-frequency seed ground motion are superimposed to obtain broadband seed ground motion;

[0034] When the frequency is less than the conversion frequency band, the low-frequency target spectrum in the broadband seed ground motion is used as the broadband target spectrum. When the frequency is greater than the conversion frequency band, the high-frequency target spectrum in the broadband seed ground motion is used as the broadband target spectrum. When the frequency is in the conversion frequency band, the weighted average of the high-frequency target spectrum and the low-frequency target spectrum in the broadband seed ground motion is used as the broadband target spectrum.

[0035] Further, reaction spectrum fitting is performed, including:

[0036] Determine the fitting frequency point covering the conversion frequency band;

[0037] For each fitted frequency point, wavelet functions with no baseline drift in displacement and velocity time histories are selected to adjust the acceleration time histories, thereby achieving response spectrum fitting.

[0038] Furthermore, the formula for adjusting the acceleration time history is:

[0039]

[0040] In the formula, Indicates to Acceleration time history after frequency point adjustment Indicates to Acceleration time history before frequency point adjustment The time indicated by the earthquake motion time history Indicates the first One reaction spectrum period point, Describing wavelet function The amplitude modulation coefficient is calculated using the following formula:

[0041]

[0042] In the formula, , , They represent In the Acceleration response spectrum values ​​at each frequency point and These represent the original time history before adjustment and the time history after adjustment, respectively. The sign of the peak response at the period. This indicates the time corresponding to the original peak response before adjustment.

[0043] The beneficial effects of this invention are as follows:

[0044] (1) In this invention, the frequency components within the fundamental frequency range of the dam are fully considered in both high-frequency and low-frequency ground motion simulations. The high and low frequency ground motions obtained by this method are superimposed within this range and will not cause the response spectrum to be underestimated due to the lack of frequency components in a certain method.

[0045] (2) In this invention, a wavelet-based time-domain response spectrum fitting method is used, and multiple frequency points are fitted simultaneously to improve the convergence speed. The final synthesized broadband ground motion has no energy voids in the frequency conversion segment, ensuring that the broadband ground motion simulation meets the requirements of dam engineering characteristics. Attached Figure Description

[0046] Figure 1 A flowchart of the high- and low-frequency ground motion superposition method considering the characteristics of dam engineering provided by the present invention.

[0047] Figure 2 A block diagram of the high- and low-frequency ground motion superposition method considering the characteristics of dam engineering provided by the present invention.

[0048] Figure 3 This invention provides multiple schemes for high-frequency ground motion simulation.

[0049] Figure 4 Examples of time histories for simulating high-frequency ground motion acceleration using different parameter schemes provided by this invention.

[0050] Figure 5 This invention provides a database of different parameter schemes for simulating high-frequency ground motion acceleration response spectra.

[0051] Figure 6 This invention provides a method for selecting high-frequency seed ground motions based on the fundamental frequency range spectrum value.

[0052] Figure 7 This is an example of a low-frequency simulation spectral element method grid and kinematic source model provided by the present invention.

[0053] Figure 8 The present invention provides a method for superimposing high- and low-frequency seed ground motion time histories to obtain broadband seed ground motion.

[0054] Figure 9 The high and low frequency target spectra and the broadband target spectra obtained by superposition are provided by the present invention.

[0055] Figure 10 The broadband seed ground motion time history and the final ground motion time history fitted to the broadband target spectrum are provided for this invention.

[0056] Figure 11The broadband target spectrum for fitting the time history of the seed ground motion provided by this invention is a broadband seed ground motion. Detailed Implementation

[0057] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0058] This invention provides a method for superimposing high- and low-frequency ground motions that takes into account the characteristics of dam engineering.

[0059] See Figure 1-2 ,include:

[0060] Based on the source parameters of the dam project area, the natural frequency of the dam is calculated, and then the range of low-frequency vibration simulation is determined.

[0061] Based on the randomness of high-frequency ground motion in the dam project area, a multi-scheme high-frequency ground motion simulation considering parameter uncertainties is carried out, and then a high-frequency ground motion database is constructed.

[0062] In the high-frequency ground motion database, ground motions that simultaneously match the river-direction and vertical vibration modes of the dam are selected as high-frequency seed ground motions.

[0063] Based on the selection of high-frequency seed ground motion, low-frequency ground motion simulation is performed within the low-frequency vibration simulation range to obtain low-frequency seed ground motion.

[0064] High-frequency seed ground motion and low-frequency seed ground motion are combined to form broadband seed ground motion, thereby determining the broadband target spectrum;

[0065] Using the broadband target spectrum and target PGA as targets, a wavelet-based time-domain response spectrum fitting method is used to fit the response spectrum, resulting in a broadband hybrid ground motion that takes into account the characteristics of the dam project.

[0066] In this embodiment, the source parameters, including moment magnitude Mw, possible fault location, and fault size (length), are determined based on the seismic tectonic evaluation index and geological exploration data of the dam project site area. ,Width ), Fault depth range (burial depth) ), focal mechanism range (strike direction) Sliding angle ,inclination ) and stress drop range ( ), and information on the crustal structure of the dam project area (density) Longitudinal wave velocity transverse wave velocity ) and terrain information.

[0067] In this embodiment, the natural frequencies of the dam are calculated using response spectrum analysis, and the first n frequencies are respectively... For example, such as Figure 6 The gray area represents the 5th order frequency range in front of a certain dam.

[0068] In this embodiment, the low-frequency simulation range is determined based on the dam's natural frequency, ensuring that the maximum low-frequency simulation frequency is greater than the dam's foundation frequency. Considering overall cost requirements, if the low-frequency simulation range is to cover at least the dam's [missing information - likely a specific frequency range or characteristic], then [missing information - likely a specific frequency range or characteristic]... First frequency The maximum frequency in the low-frequency vibration simulation range is... .

[0069] In this embodiment, during the high-frequency ground motion simulation, due to the randomness of high-frequency ground motion, multiple scenarios of ground motion simulation are performed considering the uncertainties of various parameters when simulating high-frequency components.

[0070] In this embodiment, the parameter uncertainties considered include: the uncertainty of the existence of seismogenic faults around the dam site, the uncertainty of the location of each seismogenic fault, the uncertainty of the distribution of source slip, the uncertainty of the distribution of initial rupture points, the uncertainty of dip angle, the uncertainty of stress drop, the uncertainty of high-frequency attenuation coefficient, and the uncertainty of random phase of the random finite fault method under different schemes.

[0071] Furthermore, the weight of each parameter is determined based on the parameter distribution, and the total weighting coefficient of each scheme is the product of the weight coefficients of each node in that scheme; for example, the specific scheme design is as follows: Figure 3 As shown; in Figure 3 middle, Indicates the number of sites affected One epicenter; Indicates the first The first fault One location option; These are the corresponding weighting coefficients; Indicates the first One initial rupture point location scheme; These are the corresponding weighting coefficients; Indicates the first A scheme for setting up concave and convex shapes; These are the corresponding weighting coefficients; The first inclination angle One possible value; These are the corresponding weighting coefficients; The first stress drop represents the stress drop. One possible value; These are the corresponding weighting coefficients; express The One possible value; These are the corresponding weighting coefficients; The first earthquake represents the first earthquake. One sample; These are the corresponding weighting coefficients.

[0072] In this embodiment, the random finite tomography method is used according to... Figure 3 The schemes respectively conduct high-frequency ground motion simulations to obtain multiple high-frequency ground motion databases; specifically, multiple schemes of high-frequency ground motion simulations are performed to construct a high-frequency ground motion database, including:

[0073] Based on parameter uncertainty, multiple samples are simulated using each set of parameters, and the weight of each parameter is determined according to the parameter distribution. Then, the random finite fault method is used to simulate high-frequency ground motion.

[0074] The PGA and acceleration response spectra obtained from various high-frequency ground motion simulation schemes are sorted in order of magnitude to obtain a database of PGA and acceleration response spectra at different quantiles for high-frequency ground motion.

[0075] Based on the requirements of the dam project, the quantiles of the PGA and acceleration response spectrum with preset guarantee rates are determined, and the corresponding PGA and acceleration response spectrum are used as the target PGA and high-frequency target spectrum, thereby constructing a high-frequency ground motion database.

[0076] For example, the acceleration response spectrum database obtained in this embodiment is as follows: Figure 4 As shown, the high-frequency ground motion database constructed based on this is as follows: Figure 5 As shown, Figure 6 The example given is a high-frequency target spectrum with a quantile of 84%.

[0077] In this embodiment, several ground motions in the high-frequency ground motion database that have response spectral values ​​closest to the high-frequency target spectrum within a certain fundamental frequency range of the dam are selected as high-frequency seed ground motions. Since the random finite fault method can only provide horizontal ground motions and does not distinguish between transverse and longitudinal river orientations, in this embodiment, ground motions that simultaneously match the longitudinal and vertical vibration modes of the dam are selected as high-frequency seed ground motions, including:

[0078] From the high-frequency seismic database Earthquake ground motion is divided into In each group of earthquakes, three earthquakes are randomly assigned to the following directions: downstream, transverse, and vertical.

[0079] Furthermore, if the dam site is more than 10km away from the fault, the vertical ground motion amplitude will be adjusted to 2 / 3 times, and the vertical component of the high-frequency target spectrum will also be adjusted to 2 / 3 times.

[0080] Calculate the difference between the l-order frequency spectrum value along the river and the target spectrum value along the river in each group of ground motions, and then select several ground motions in the first and third directions that are closest to the high-frequency target spectrum.

[0081] For example, select the first 15% of the first three-directional ground motions that are closest to the high-frequency target spectrum;

[0082] Calculate the difference between the vertical l-th order frequency spectrum value and the vertical target spectrum value in each group of ground motions, and then select several second and third direction ground motions that are closest to the high-frequency target spectrum;

[0083] For example, select the top 15% of the second and third directional ground motions that are closest to the high-frequency target spectrum;

[0084] The three sets of ground motions with the smallest distance from the high-frequency target spectrum along the river direction within the entire natural frequency range of the dam are selected from the intersection of the first and third direction ground motions and the second and third direction ground motions.

[0085] In this embodiment, the distance along the river from the high-frequency target spectrum across the entire natural frequency range of the dam is... Represented as:

[0086]

[0087] In the formula, This indicates the number of response spectrum periods across the entire natural frequency range of the dam. This represents the response spectrum value of the selected seismic motion along the river. This represents the high-frequency target spectrum with preset quantile values. ~ This indicates the range of the dam's natural frequencies.

[0088] For example, The high-frequency target spectral value is at the quantile of 84%.

[0089] In this embodiment, during the low-frequency ground motion simulation, a three-dimensional spectral unit numerical model of the study area is established by integrating velocity structure and topographic information, which can reflect complex medium conditions and detailed topography. Based on this:

[0090] The maximum effective frequency of the constructed three-dimensional spectral unit numerical model is greater than the maximum value of the high and low frequency superposition frequency band;

[0091] The selected source parameters are consistent with the source parameters of the high-frequency seed ground motions in the high-frequency ground motion database;

[0092] By supplementing high-frequency source components, the spatial distribution of slip on the fault plane is made to conform to... An attenuation model was developed, and the rise time and rupture propagation velocity of the seismic source were determined based on the slip, magnitude, and crustal parameters. A broadband kinematic source model was constructed, and then low-frequency ground motion simulation was performed using the spectral element method.

[0093] In this embodiment, the spectral element method is used to simulate low-frequency ground motion. The calculated triaxial ground motion of the site is used as the low-frequency seed ground motion, and its response spectrum is calculated as the low-frequency target spectrum.

[0094] For example, Figure 7 Examples of low-frequency simulated spectral element method grid models and kinematic source models are given.

[0095] In this embodiment, synthesizing broadband seed ground motions to determine the broadband target spectrum includes:

[0096] High-frequency seed ground motion and low-frequency seed ground motion are filtered by matching filters with the same parameters, respectively, and high-frequency seed ground motion with frequencies greater than the conversion frequency band and low-frequency seed ground motion with frequencies less than the conversion frequency band are retained.

[0097] The retained high-frequency seed ground motion and low-frequency seed ground motion are superimposed to obtain broadband seed ground motion;

[0098] When the frequency is less than the conversion frequency band, the low-frequency target spectrum in the broadband seed ground motion is used as the broadband target spectrum. When the frequency is greater than the conversion frequency band, the high-frequency target spectrum in the broadband seed ground motion is used as the broadband target spectrum. When the frequency is in the conversion frequency band, the weighted average of the high-frequency target spectrum and the low-frequency target spectrum in the broadband seed ground motion is used as the broadband target spectrum.

[0099] For example, Figure 8 The first, second, and third columns respectively present the filtered downstream high-frequency seed ground motion, low-frequency seed ground motion, and superimposed downstream broadband seed ground motion; Figure 9 The high-frequency and low-frequency target spectra and the superimposed broadband target spectra are given.

[0100] In this embodiment, using a broadband target spectrum and a target PGA as targets, a wavelet-based time-domain response spectrum fitting method is employed for response spectrum fitting, including:

[0101] Determine the fitting frequency point covering the conversion frequency band;

[0102] For each fitted frequency point, wavelet functions with no baseline drift in displacement and velocity time histories are selected to adjust the acceleration time histories, thereby achieving response spectrum fitting.

[0103] In this embodiment, when determining the fitting frequency point, the fitting frequency point should cover the conversion frequency band; for example, such as Figure 11 As shown by the red dot, there are a total of The frequency, at the frequency The target response spectrum at each frequency point is .

[0104] In this embodiment, when performing acceleration time history adjustment, the calculation is performed. In the Acceleration response spectrum values ​​at each frequency point , , The original broadband seed time history was in the first... Acceleration response spectrum values ​​at each frequency point , , .

[0105] In this embodiment, the formula for adjusting the acceleration time history is:

[0106]

[0107] In the formula, Indicates to Acceleration time history after frequency point adjustment Indicates to Acceleration time history before frequency point adjustment The time indicated by the earthquake motion time history Indicates the first One reaction spectrum period point, Describing wavelet function The amplitude modulation coefficient is calculated using the following formula:

[0108]

[0109] In the formula, , , They represent In the Acceleration response spectrum values ​​at each frequency point and These represent the original time history before adjustment and the time history after adjustment, respectively. The sign of the peak response at the period. This indicates the time corresponding to the original peak response before adjustment.

[0110] In this embodiment, Figure 10 A comparison of the ground motion time histories before and after fitting the response spectrum is presented, and the ground motion time-frequency is basically preserved. Figure 11The final response spectrum results are presented. Since both high-frequency and low-frequency ground motion simulations fully consider the frequency components within the dam's fundamental frequency range, the superposition of high and low frequencies within this range will not cause the response spectrum to be underestimated due to the lack of frequency components in a certain method. At the same time, a wavelet-based time-domain response spectrum fitting method is adopted to eliminate the energy voids generated by superposition, ensuring that the broadband ground motion simulation meets the requirements of the dam engineering characteristics.

[0111] Specific embodiments have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

[0112] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for superimposing high- and low-frequency seismic motions considering the engineering characteristics of dams, characterized in that, include: Based on the source parameters of the dam project area, the natural frequency of the dam is calculated, and then the range of low-frequency vibration simulation is determined. Based on the randomness of high-frequency ground motion in the dam project area, a multi-scheme high-frequency ground motion simulation considering parameter uncertainties is carried out, and then a high-frequency ground motion database is constructed. In the high-frequency ground motion database, ground motions that simultaneously match the river-direction and vertical vibration modes of the dam are selected as high-frequency seed ground motions. Based on the selection of high-frequency seed ground motion, low-frequency ground motion simulation is performed within the low-frequency vibration simulation range to obtain low-frequency seed ground motion. High-frequency seed ground motion and low-frequency seed ground motion are combined to form broadband seed ground motion, thereby determining the broadband target spectrum; Using the broadband target spectrum and target PGA as targets, a wavelet-based time-domain response spectrum fitting method is used to fit the response spectrum, resulting in a broadband hybrid ground motion that takes into account the characteristics of the dam project.

2. The high- and low-frequency seismic motion superposition method considering the engineering characteristics of dams according to claim 1, characterized in that, The maximum frequency in the low-frequency vibration simulation range ;in, For the dam natural frequency of the first order .

3. The high- and low-frequency seismic motion superposition method considering the engineering characteristics of dams according to claim 1, characterized in that, During the construction of the high-frequency seismic database: The uncertainties considered include: the existence of seismogenic faults around the dam site, the location of each seismogenic fault, the distribution of source slip, the distribution of initial rupture points, the dip angle, the stress drop, the high-frequency attenuation coefficient, and the uncertainty of the random phase of the random finite fault method under different schemes.

4. The high- and low-frequency seismic motion superposition method considering the engineering characteristics of dams according to claim 1, characterized in that, Perform multi-scheme high-frequency ground motion simulations and construct a high-frequency ground motion database, including: Based on parameter uncertainty, multiple samples are simulated using each set of parameters, and the weight of each parameter is determined according to the parameter distribution. Then, the random finite fault method is used to simulate high-frequency ground motion. The PGA and acceleration response spectra obtained from various high-frequency ground motion simulation schemes are sorted in order of magnitude to obtain a database of PGA and acceleration response spectra at different quantiles for high-frequency ground motion. Based on the requirements of the dam project, the quantiles of the PGA and acceleration response spectrum with preset guarantee rates are determined, and the corresponding PGA and acceleration response spectrum are used as the target PGA and high-frequency target spectrum, thereby constructing a high-frequency ground motion database.

5. The high- and low-frequency seismic motion superposition method considering the engineering characteristics of dams according to claim 4, characterized in that, The seismic motion that simultaneously matches the longitudinal and vertical vibration modes of the dam is selected as the high-frequency seed seismic motion, including: From the high-frequency seismic database Earthquake ground motion is divided into In each group of earthquakes, three earthquakes are randomly assigned to the following directions: downstream, transverse, and vertical. Calculate the difference between the l-order frequency spectrum value along the river and the target spectrum value along the river in each group of ground motions, and then select several ground motions in the first and third directions that are closest to the high-frequency target spectrum. Calculate the difference between the vertical l-th order frequency spectrum value and the vertical target spectrum value in each group of ground motions, and then select several second and third direction ground motions that are closest to the high-frequency target spectrum; The three sets of ground motions with the smallest distance from the high-frequency target spectrum along the river direction within the entire natural frequency range of the dam are selected from the intersection of the first and third direction ground motions and the second and third direction ground motions.

6. The high- and low-frequency seismic motion superposition method considering dam engineering characteristics according to claim 5, characterized in that, The distance along the river from the high-frequency target spectrum across the entire natural frequency range of the dam. Represented as: In the formula, This indicates the number of response spectrum periods across the entire natural frequency range of the dam. This represents the response spectrum value of the selected seismic motion along the river. This represents the high-frequency target spectrum with preset quantile values. ~ This indicates the range of the dam's natural frequencies.

7. The high- and low-frequency seismic motion superposition method considering the engineering characteristics of dams according to claim 1, characterized in that, During the low-frequency ground motion simulation process: The maximum effective frequency of the constructed three-dimensional spectral unit numerical model is greater than the maximum value of the high and low frequency superposition frequency band; The selected source parameters are consistent with the source parameters of the high-frequency seed ground motions in the high-frequency ground motion database; By supplementing high-frequency source components, the spatial distribution of slip on the fault plane is made to conform to... An attenuation model was developed, and the rise time and rupture propagation velocity of the seismic source were determined based on the slip, magnitude, and crustal parameters. A broadband kinematic source model was constructed, and then low-frequency ground motion simulation was performed using the spectral element method.

8. The high- and low-frequency seismic motion superposition method considering the engineering characteristics of dams according to claim 1, characterized in that, Synthesize broadband seed ground motions to determine the broadband target spectrum, including: High-frequency seed ground motion and low-frequency seed ground motion are filtered by matching filters with the same parameters, respectively, and high-frequency seed ground motion with frequencies greater than the conversion frequency band and low-frequency seed ground motion with frequencies less than the conversion frequency band are retained. The retained high-frequency seed ground motion and low-frequency seed ground motion are superimposed to obtain broadband seed ground motion; When the frequency is less than the conversion frequency band, the low-frequency target spectrum in the broadband seed ground motion is used as the broadband target spectrum. When the frequency is greater than the conversion frequency band, the high-frequency target spectrum in the broadband seed ground motion is used as the broadband target spectrum. When the frequency is in the conversion frequency band, the weighted average of the high-frequency target spectrum and the low-frequency target spectrum in the broadband seed ground motion is used as the broadband target spectrum.

9. The high- and low-frequency seismic motion superposition method considering dam engineering characteristics according to claim 1, characterized in that, Performing reaction spectrum fitting includes: Determine the fitting frequency point covering the conversion frequency band; For each fitted frequency point, wavelet functions with no baseline drift in displacement and velocity time histories are selected to adjust the acceleration time histories, thereby achieving response spectrum fitting.

10. The high- and low-frequency seismic motion superposition method considering dam engineering characteristics according to claim 9, characterized in that, The formula for adjusting the acceleration time history is: In the formula, Indicates to Acceleration time history after frequency point adjustment Indicates to Acceleration time history before frequency point adjustment The time indicated by the earthquake motion time history Indicates the first One reaction spectrum period point, Describing wavelet function The amplitude modulation coefficient is calculated using the following formula: In the formula, , , They represent In the Acceleration response spectrum values ​​at each frequency point and These represent the original time history before adjustment and the time history after adjustment, respectively. The sign of the peak response at the period. This indicates the time corresponding to the original peak response before adjustment.

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