A time history simulation method and system of ground motion in alpine valley sites

Abstract

The application discloses a kind of high mountain and valley site seismic time history simulation method and system, belong to geotechnical earthquake engineering technical field, including the following steps: numerical integration solution;Fast Fourier transform (FFT);Amplification factor solution;Fourier spectrum adjustment;Inverse fast Fourier transform (IFFT);Numerical differentiation solution.The application adopts fast Fourier transform (FFT) to efficiently convert seismic input signal into frequency domain Fourier spectrum, multiply it with displacement amplitude transfer function to obtain Fourier spectrum considering valley topographic effect, reconstructs time domain response based on inverse fast Fourier transform (IFFT), provides an efficient, accurate and engineering generalization scheme for valley topographic effect analysis;Frequency domain processing avoids the discrete error of time domain numerical integration or differentiation, accurately retains the frequency domain characteristics of seismic motion by directly calculating the Fourier spectrum considering topographic amplification effect, ensures the authenticity of topographic amplification effect.

Description

Technical Field

[0001] This invention relates to the field of rock and soil earthquake engineering technology, specifically to a method and system for simulating the time history of ground motion in high mountain and canyon sites. Background Technology

[0002] The seismic wave propagation characteristics of high mountain and canyon sites (valley sites) are extremely complex, exhibiting a prominent topographic effect. This means that after seismic waves propagate into high mountains and canyons, scattering causes amplification, attenuation, and spatial variation in ground motion. On the one hand, the local amplification of ground motion caused by high mountains and canyons can exacerbate earthquake hazards; on the other hand, ground motion in valley sites exhibits spatial variation, with different peak values ​​and phases of seismic waves at different locations within the site. This topographic effect often exacerbates earthquake damage to bridge engineering projects.

[0003] Currently, domestic and international seismic codes for engineering projects have gradually reflected requirements regarding the inconsistency (spatial variation) of seismic motion input; however, the regulations concerning topographic effects are not clear or specific enough. Therefore, it is necessary to provide a method and system for simulating seismic motion time histories in high mountain and canyon sites, to provide a reference for the seismic design of major projects in high mountain and canyon sites that take topographic effects into account. Summary of the Invention

[0004] The technical problem to be solved by this invention is: how to calculate the amplification factor of valley topography on ground motion (relative to flat site) through the seismic wave theory of high mountain and canyon sites, and further obtain the ground motion of valley site considering topographic effect, so as to provide ground motion input considering topographic effect for the seismic analysis of valley bridges, and thus provide a method for time history simulation of ground motion in high mountain and canyon sites.

[0005] The present invention solves the above-mentioned technical problems through the following technical solution, and the present invention includes the following steps:

[0006] S1: Numerical integration solution

[0007] The seismic acceleration time history is numerically integrated twice to obtain the input displacement time history. ;

[0008] S2: FFT Transform

[0009] Input displacement time history Perform a fast Fourier transform to obtain its Fourier spectrum;

[0010] S3: Solving for the magnification factor

[0011] Based on the seismic wave propagation theory of valley sites, the seismic amplification factor at the target location in the valley site at different seismic frequencies is solved, and the displacement amplitude amplification transfer function at the target location in the valley site is obtained. and phase adjustment transfer function ;

[0012] S4: Fourier Spectrum Adjustment

[0013] Multiply the displacement amplitude amplification transfer function of the target location in the valley obtained in step S3 with the Fourier spectrum obtained in step S2 at the corresponding frequency to obtain the Fourier spectrum of the target location considering the valley topographic effect.

[0014] S5: IFFT Transform

[0015] Based on the Fourier spectrum obtained after adjustment in step S4, the output displacement time history at the target location considering the valley terrain amplification effect can be obtained by fast inverse Fourier transform.

[0016] S6: Numerical Differentiation Solution

[0017] Based on the output displacement time history obtained in step S5, the velocity time history is obtained by performing a numerical differentiation. Then, based on the obtained velocity time history, the acceleration time history is obtained by performing a numerical differentiation, thus obtaining the seismic acceleration time history considering the valley topographic effect.

[0018] Furthermore, in step S1, the displacement time history is input. The specific calculation formula is as follows:

[0019] ;

[0020] in, Input the time history of ground motion acceleration.

[0021] Furthermore, in step S2, the displacement time history is input. The formula for calculating the Fast Fourier Transform is as follows:

[0022] ;

[0023] in, Represents the Fourier spectrum, i= , represents the imaginary unit, ω represents the frequency domain variable, and t represents time;

[0024] Fourier spectrum Represented in complex form as follows:

[0025] ;

[0026] in, , These are the Fourier amplitude spectrum and the Fourier phase spectrum, respectively.

[0027] Furthermore, in step S3, the specific formula for calculating the frequency domain seismic amplification factor at the target location in the valley is as follows:

[0028] ;

[0029] in, Indicates the free field displacement amplitude, target point That is, the target location of the valley site.

[0030] Furthermore, in step S4, the phase adjustment transfer function is calculated using the following formula. The calculation formula is as follows:

[0031] .

[0032] Furthermore, in step S4, the formula for calculating the Fourier spectrum at the target location considering the valley topographic effect is as follows:

[0033] ;

[0034] At this moment, the Fourier amplitude spectrum and phase spectrum of the ground motion at the target location become respectively... and .

[0035] Furthermore, in step S5, the formula for calculating the inverse fast Fourier transform of the adjusted Fourier spectrum is as follows:

[0036] ;

[0037] in, This is the output displacement time history at the target location to be simulated, taking into account the amplification effect of the valley terrain.

[0038] Furthermore, in step S6, the displacement time history is output. The specific calculation formula for obtaining the acceleration time history is as follows:

[0039] ;

[0040] in, Seismic acceleration time histories for high mountain and canyon sites taking into account valley topographic effects.

[0041] This invention also provides a seismic motion time history simulation system for high mountain and canyon sites, which uses the above-described method to obtain seismic acceleration time histories considering valley topographic effects, including:

[0042] The numerical integration module is used to perform two numerical integrations on the seismic acceleration time history to obtain the input displacement time history. ;

[0043] The FFT transform module is used to transform the input displacement time history. Perform a fast Fourier transform to obtain its Fourier spectrum;

[0044] The amplification factor calculation module is used to solve for the seismic motion amplification factor at the target location in a valley site at different seismic frequencies, based on the seismic wave propagation theory of valley sites, and to obtain the displacement amplitude amplification transfer function at the target location in the valley site. and phase adjustment transfer function ;

[0045] The Fourier spectrum adjustment module is used to multiply the displacement amplitude amplification transfer function of the target location in the valley obtained in step S3 with the Fourier spectrum obtained in step S2 at the corresponding frequency to obtain the Fourier spectrum at the target location considering the valley topographic effect.

[0046] The IFFT transform module is used to obtain the output displacement time history at the target location, taking into account the valley terrain amplification effect, based on the Fourier spectrum obtained after adjustment in step S4, through inverse fast Fourier transform.

[0047] The differential solution module is used to perform a numerical differential on the output displacement time history obtained in step S5 to obtain the velocity time history, and then perform a numerical differential on the obtained velocity time history to obtain the acceleration time history, thus obtaining the seismic acceleration time history considering the valley topographic effect.

[0048] The present invention has the following advantages over the prior art:

[0049] 1. Compared with the Discrete Fourier Transform (DFT), the Fast Fourier Transform (FFT) and Inverse Fast Fourier Transform (IFFT) used in this invention reduce the computational complexity from O(N²) of the traditional time-domain method to O(NlogN) with the same number of sampling points N. The finite difference / finite element method requires iterative calculations and is time-consuming.

[0050] 2. The Fast Fourier Transform (FFT) and Inverse Fast Fourier Transform (IFFT) frequency-to-time domain conversion used in this invention can accurately preserve the signal amplitude and phase information. The error mainly comes from rounding errors in floating-point operations, which are negligible in most engineering applications. In contrast, the direct integration method can introduce significant errors if the integration step size is not chosen properly, especially for high-frequency oscillation integration. Furthermore, in numerical solutions, grid discretization and time step size affect accuracy, requiring additional convergence analysis.

[0051] 3. With its superlinear computational efficiency, high precision, and ease of frequency domain manipulation, FFT / IFFT has become an irreplaceable tool in signal processing, wave simulation, and other fields. For seismic response analysis of high mountain and canyon sites, it can quickly superimpose frequency domain topographic effects, making it the optimal solution balancing speed and accuracy. Attached Figure Description

[0052] Figure 1 This is a flowchart illustrating the time history simulation method for seismic motion in a high mountain canyon site according to Embodiment 1 of the present invention.

[0053] Figure 2 This is a schematic diagram of the valley site model in Embodiment 2 of the present invention;

[0054] Figure 3 This is a schematic diagram of the valley-bridge coupling model in Embodiment 3 of the present invention;

[0055] Figure 4 This is a schematic diagram of the valley-building coupling model in Embodiment 4 of the present invention;

[0056] Figure 5 This is a schematic diagram of the structure of the earthquake time history simulation device for high mountain and canyon sites in Embodiment 5 of the present invention. Detailed Implementation

[0057] The embodiments of the present invention are described in detail below. These embodiments are implemented based on the technical solution of the present invention, and provide detailed implementation methods and specific operation processes. However, the scope of protection of the present invention is not limited to the following embodiments.

[0058] Example 1

[0059] This embodiment provides a technical solution: a method for simulating the time history of ground motion in a high mountain canyon site, the purpose of which is to obtain the spatially varying ground motion of a valley site given the ground motion acceleration time history input of a flat site.

[0060] The key to establishing this method lies in understanding and applying the topographic amplification factor caused by valleys, as explained below: The wave function series solution of the valley topographic effect uses a steady-state plane wave of unit amplitude as the incident wave. If there were no valley (i.e., only a free field on flat ground), the amplitude of the horizontal surface displacement at different locations under SH wave incidence would always be equal to 2. However, the valley topographic effect causes the amplitude of surface displacement at different locations to fluctuate around the value of 2. In other words, at a certain frequency, if the displacement amplitude at a certain point on the surface is greater than 2, then the ground motion at that point is amplified relative to the free field on the surface; conversely, if it is less than 2, the ground motion is reduced.

[0061] Based on this principle, the amplitude of the valley surface displacement given by the wave function series solution can be divided by 2 to obtain the seismic amplitude amplification factor of the valley topography.

[0062] Dividing the surface displacement phase of the valley by the free field phase yields the seismic phase adjustment factor of the valley topography. The amplitude amplification factor and the phase adjustment factor are collectively referred to as the frequency domain topography amplification factor.

[0063] Based on bedrock ground motion and frequency domain topographic amplification factor, according to Figure 1The illustrated process can further obtain the seismic acceleration, velocity, and displacement time histories at various points on the surface of the valley site. The specific process is as follows:

[0064] Step 1: Perform two numerical integrations on the seismic acceleration time history to obtain the input displacement time history. .

[0065] Step 2: Perform a Fast Fourier Transform (FFT) on the input displacement time history to obtain its Fourier spectrum.

[0066] Step 3: Based on the seismic wave propagation theory of valley sites, solve for the seismic amplification factor at the target location in the valley site under different seismic frequencies, and obtain the displacement amplitude amplification transfer function at the target location in the valley site. and phase adjustment transfer function ;

[0067] Step 4: Multiply the displacement amplitude amplification transfer function of the target location in the valley obtained in Step 3 with the Fourier spectrum obtained in Step 2 at the corresponding frequency to obtain the Fourier spectrum of the target location considering the valley topographic effect.

[0068] Step 5: Based on the Fourier spectrum obtained after adjustment in Step 4, the displacement time history at the target location considering the valley terrain amplification effect can be obtained by fast inverse Fourier transform.

[0069] Step 6: Based on the displacement time history obtained in Step 5, perform a numerical differentiation to obtain the velocity time history.

[0070] Step 7: Based on the velocity time history obtained in Step 6, perform a numerical differentiation to obtain the acceleration time history, which is the seismic acceleration time history considering the valley topographic effect.

[0071] More specifically, in step 1, the bedrock ground motion acceleration time history record is numerically integrated twice to obtain the input displacement time history. :

[0072]

[0073] in, Input the time history of ground motion acceleration.

[0074] More specifically, in step 2, the displacement time history is subjected to a fast Fourier transform to obtain its Fourier spectrum:

[0075] (1)

[0076] in, Let represent the Fourier spectrum, i represent the imaginary unit, ω represent the frequency domain variable, and t represent time.

[0077] The Fourier transform obtained above It is usually a complex number, which can be further expressed as:

[0078] (2)

[0079] in, , These are the Fourier amplitude spectrum and the Fourier phase spectrum, respectively.

[0080] More specifically, in step 3, based on the theory of seismic wave propagation in valley sites, a geometric model is established, the wave equation and boundary conditions are determined, and the seismic amplification factor at the target location in the valley site under different seismic frequencies is solved using analytical or numerical methods.

[0081] The specific method for calculating the seismic amplification factor is as follows:

[0082] Target point The seismic amplification factor is the ratio of the surface displacement amplitude to the free-field displacement amplitude (without topography):

[0083] (3)

[0084] in, This represents the amplitude of the free field displacement.

[0085] Based on the aforementioned terrain magnification factor, the displacement amplitude amplification transfer function of the target location in the valley is obtained. and phase adjustment transfer function . The calculation formula is: Target point That is, the target location of the valley site. For a single frequency The seismic amplification factor at all calculated frequencies for the target location in the valley site constitutes the displacement amplitude amplification transfer function for that location. .

[0086] More specifically, in step 4, the displacement amplitude amplification transfer function of the target location in the valley obtained in step 3 is multiplied with the Fourier spectrum obtained in step 2 at the corresponding frequency to obtain the Fourier spectrum at the target location considering the valley topographic effect:

[0087] (3)

[0088] More specifically, the Fourier amplitude spectrum and phase spectrum of the ground motion at the target location at this time become... and .

[0089] More specifically, in step 5, based on the adjusted Fourier spectrum, the output displacement time history at the target location, considering the valley terrain amplification effect, can be obtained through inverse fast Fourier transform:

[0090] (4)

[0091] in, This refers to the time history of ground motion displacement at the target location in the valley site, taking into account the terrain amplification effect, which is to be simulated.

[0092] More specifically, in step 6, the velocity time history can be obtained by numerically differentiating the ground motion displacement time history of the target location obtained in step 5.

[0093] More specifically, in step 7, the acceleration time history can be obtained by numerically differentiating the target position velocity time history obtained in step 5.

[0094] More specifically, this invention employs Fast Fourier Transform (FFT) to efficiently convert the seismic input signal into a frequency domain Fourier spectrum. By considering the valley topographic effect, it reconstructs the time domain response based on Inverse Fast Fourier Transform (IFFT), providing an efficient, accurate, and engineering-promotable solution for valley topographic effect analysis.

[0095] More specifically, the frequency domain processing of this invention avoids the discrete errors of time domain numerical integration or differentiation, and accurately preserves the frequency domain characteristics of ground motion by directly calculating the Fourier spectrum that takes into account the terrain amplification effect, thus ensuring the authenticity of the terrain amplification effect.

[0096] More specifically, this invention allows for the flexible superposition of multiple transfer functions (such as topographic and soil layer effects) in the frequency domain, avoiding the complex calculations of time-domain convolution and simplifying the analysis process.

[0097] More specifically, the FFT / IFFT algorithm of this invention supports parallel computing (such as GPU acceleration) and optimizes the efficiency of large-scale seismic field simulation.

[0098] Example 2

[0099] Specific implementation example 1 of the present invention is as follows: Figure 2 The first calculation model is presented to analyze the influence of topographic effects on the distribution characteristics of ground motion in valley sites.

[0100] In the calculation model, the Poisson's ratio ν of the medium is 0.25 and the density ρ is 2650 kg / m³. 3 Shear wave velocity V s It is 1773 m / s.

[0101] In this embodiment, the El Centro wave is selected as the SV wave incident for the input ground motion, and the bedrock peak acceleration (PGA) is selected as 0.1g.

[0102] Based on the Fourier spectrum of the input ground motion, the frequency range for calculating the transfer function is selected as 0~20Hz.

[0103] The model selects 7 representative locations as calculation points, with 4 calculation points #1 to #4 evenly distributed on the left bank of the valley and 4 calculation points #4 to #7 evenly distributed on the right bank of the valley.

[0104] Through steps 1-7 above, the peak ground acceleration amplification factor (frequency domain ground motion amplification factor) of the valley calculation point is obtained as shown in Table 1.

[0105] Table 1. Amplification factor of peak ground acceleration in valley areas compared to flat areas

[0106]

[0107] Example 3

[0108] Specific implementation example 2 of the present invention is as follows: Figure 3 The second calculation model is shown to analyze the influence of topographic effects on the seismic motion distribution characteristics of bridge projects in valley sites.

[0109] Approximate the valley to a V-shape and establish... Figure 3 The V-shaped valley-bridge coupled calculation model is shown.

[0110] The V-shaped valley is 832.2m wide and 237m deep, with a bedrock density of 2000kg / m³. 3 The shear wave velocity is 1773 m / s.

[0111] The model's excitation was the measured near-fault seismic wave at Baima, Deyang, during the Wenchuan earthquake.

[0112] The seismic waves were incident horizontally from left to right.

[0113] The frequency range of 0-25Hz was selected based on the Fourier spectrum of the incident seismic wave.

[0114] When the seismic wave is incident horizontally (α = 90°), #1~#3 (wave-facing side) and #4~#6 (wave-back side) are as follows: Figure 3 As shown in Table 1, the peak ground acceleration amplification factor (frequency domain ground motion amplification factor) at each bridge pier is amplified.

[0115] Table 2. Amplification factor of peak ground acceleration in valley sites compared to flat sites

[0116]

[0117] Table 2 shows that when the seismic wave is incident horizontally, the peak ground acceleration at the bridge pier location on the wave-facing side of the valley is significantly amplified compared to the flat site, with the amplification factor reaching up to 1.62 times.

[0118] Furthermore, the peak ground acceleration at the bridge pier location on the back wave side of the valley decreased.

[0119] Example 4

[0120] The following is a specific embodiment of the present invention: Figure 4 The third calculation model is shown, which analyzes the influence of terrain effects on the ground motion distribution characteristics of the valley-building coupling model.

[0121] Establish such as Figure 4 The diagram shows the valley-building coupling calculation model.

[0122] The V-shaped valley is 263.5m wide and 68.2m deep, with a bedrock density of 2000kg / m³. 3 The shear wave velocity is 1773 m / s.

[0123] The input ground motion was selected as El Centro wave as the SH wave incident, and the bedrock peak acceleration (PGA) was selected as 0.1g.

[0124] The seismic waves are incident from left to right.

[0125] The frequency range of 0-20Hz was selected based on the Fourier spectrum of the incident seismic wave.

[0126] When the seismic wave is incident horizontally (α = 45°), monitoring points #1 to #5 are as follows: Figure 5 As shown in Table 3, the peak ground acceleration amplification factor (frequency domain ground motion amplification factor) at various locations in the model is shown in Table 3.

[0127] Table 3. Amplification factor of peak ground acceleration in valley sites compared to flat sites

[0128]

[0129] Table 3 shows that the peak ground acceleration on the wave-facing side of the valley is significantly amplified compared to the flat site, with the amplification factor reaching up to 1.574 times.

[0130] Furthermore, the magnification of the valley floor reached 1.247 times.

[0131] Furthermore, the amplification factor on the back wave side of the valley reaches 0.948 times.

[0132] Furthermore, the magnification at the building foundation is 0.985 times, and the magnification of the building itself is as high as 1.625 times.

[0133] Example 5

[0134] like Figure 5 As shown in the figure, this embodiment provides a seismic time history simulation device for a high mountain canyon site, including a processor and a memory.

[0135] In this embodiment, the processor's input parameter is the measured initial ground motion input from the site, and the output result is the ground motion time history considering site effects. The processor is used to solve differential equations, solve integral equations, perform Fourier transforms, and inverse Fourier transforms.

[0136] In this embodiment, the memory stores one or more calculation programs for the high mountain canyon site seismic time history simulation method of the present invention and multiple intermediate calculation parameters.

[0137] In summary, the above embodiments demonstrate that high mountain and canyon sites have a significant amplification effect on seismic input for major engineering projects. The seismic time history simulation method for high mountain and canyon sites proposed in this invention can provide a reference for the seismic design of major engineering projects in high mountain and canyon sites that takes into account topographic effects.

[0138] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for simulating the time history of seismic ground motion in a high mountain canyon site, characterized in that, Includes the following steps: S1: Numerical integration solution The seismic acceleration time history is numerically integrated twice to obtain the input displacement time history. ; S2: FFT Transform Input displacement time history Perform a fast Fourier transform to obtain its Fourier spectrum; S3: Solving for the magnification factor Based on the seismic wave propagation theory of valley sites, the seismic amplification factor at the target location in the valley site at different seismic frequencies is solved, and the displacement amplitude amplification transfer function at the target location in the valley site is obtained. and phase adjustment transfer function ; S4: Fourier Spectrum Adjustment Multiply the displacement amplitude amplification transfer function of the target location in the valley obtained in step S3 with the Fourier spectrum obtained in step S2 at the corresponding frequency to obtain the Fourier spectrum of the target location considering the valley topographic effect. S5: IFFT Transform Based on the Fourier spectrum obtained after adjustment in step S4, the output displacement time history at the target location considering the valley terrain amplification effect can be obtained by fast inverse Fourier transform. S6: Numerical Differentiation Solution Based on the output displacement time history obtained in step S5, the velocity time history is obtained by performing a numerical differentiation. Then, based on the obtained velocity time history, the acceleration time history is obtained by performing a numerical differentiation. Thus, the seismic acceleration time history considering the valley topographic effect is obtained. In step S2, the displacement time history is input. The formula for calculating the Fast Fourier Transform is as follows: ； in, Represents the Fourier spectrum, i= , represents the imaginary unit, ω represents the frequency domain variable, and t represents time; Fourier spectrum Represented in complex form as follows: ； in, , These are the Fourier amplitude spectrum and the Fourier phase spectrum, respectively. In step S3, the specific formula for calculating the frequency domain seismic amplification factor at the target location in the valley is as follows: ； in, Indicates the free field displacement amplitude, target point That is, the target location of the valley site; In step S4, the phase adjustment transfer function is calculated using the following formula. The calculation formula is as follows: ； In step S4, the formula for calculating the Fourier spectrum at the target location considering the valley topographic effect is as follows: ； At this moment, the Fourier amplitude spectrum and phase spectrum of the ground motion at the target location become respectively... and ; In step S5, the formula for calculating the inverse fast Fourier transform of the adjusted Fourier spectrum is as follows: ； in, This is the output displacement time history at the target location to be simulated, taking into account the amplification effect of the valley terrain; In step S6, the displacement time history is output. The specific calculation formula for obtaining the acceleration time history is as follows: ； in, Seismic acceleration time histories for high mountain and canyon sites taking into account valley topographic effects.

2. The method for simulating seismic motion time history in a high mountain canyon site according to claim 1, characterized in that, In step S1, the displacement time history is input. The specific calculation formula is as follows: ； in, Input the time history of ground motion acceleration.

3. A seismic motion time history simulation system for high mountain and canyon sites, characterized in that, Obtaining the time history of ground motion acceleration considering valley topographic effects using the method of claim 1 or 2 includes: The numerical integration module is used to perform two numerical integrations on the seismic acceleration time history to obtain the input displacement time history. ; The FFT transform module is used to transform the input displacement time history. Perform a fast Fourier transform to obtain its Fourier spectrum; The amplification factor calculation module is used to solve for the seismic motion amplification factor at the target location in a valley site at different seismic frequencies, based on the seismic wave propagation theory of valley sites, and to obtain the displacement amplitude amplification transfer function at the target location in the valley site. and phase adjustment transfer function ; The Fourier spectrum adjustment module is used to multiply the displacement amplitude amplification transfer function of the target location in the valley obtained in step S3 with the Fourier spectrum obtained in step S2 at the corresponding frequency to obtain the Fourier spectrum at the target location considering the valley topographic effect. The IFFT transform module is used to obtain the output displacement time history at the target location, taking into account the valley terrain amplification effect, based on the Fourier spectrum obtained after adjustment in step S4, through inverse fast Fourier transform. The differential solution module is used to perform a numerical differential on the output displacement time history obtained in step S5 to obtain the velocity time history, and then perform a numerical differential on the obtained velocity time history to obtain the acceleration time history, thus obtaining the seismic acceleration time history considering the valley topographic effect.

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