Broadband seismic oscillation synthesis method for cross-fault linear engineering

Abstract

The invention relates to the technical field of seismic engineering, and discloses a broadband seismic oscillation artificial synthesis method for cross-fault linear engineering, which is suitable for seismic oscillation input and anti-seismic performance evaluation of linear engineering such as bridges, tunnels, highways and railways which pass through active fault zones. According to the method, based on a set earthquake scene, a high-frequency non-stationary seismic oscillation component, a permanent displacement component related to a sliding impulse effect and a speed pulse component related to a directional effect are simulated respectively, and broadband seismic oscillation with high and low frequency coupling, spatial coherence and inconsistent input characteristics is constructed through frequency domain synthesis. The method not only can accurately reproduce the specific permanent displacement and directional speed pulse characteristics of near-fault seismic oscillation, but also can effectively describe the non-consistency difference of the seismic oscillation on the two sides of the fault in the aspects of amplitude, frequency and response mode, and the non-consistency difference is represented as the difference of the reverse symmetric displacement of the strike-slip fault and the displacement of the upper and lower walls of the tilt-slip fault.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of earthquake engineering, and particularly relates to a wideband ground motion artificial synthesis method for cross-fault linear engineering, which is suitable for the seismic design and performance evaluation of cross-fault linear engineering such as bridges, tunnels, highways and railways. BACKGROUND

[0002] Ground motion input is a core link in seismic analysis and earthquake disaster simulation, and directly affects the accuracy of structural response and the reliability of seismic performance evaluation. In recent years, with the rapid advancement of China's economic construction, especially the construction of a large number of transportation infrastructure in the southwest high-intensity and high-altitude areas, bridges, tunnels, highways and railways and other linear engineering inevitably cross active fault zones. In the process of seismic rupture propagation, influenced by the complex rupture mechanism of the seismic source, the ground motion on both sides of the fault usually shows significant differences in amplitude, frequency component and energy distribution, which is called non-uniform input of ground motion. The main sources include three aspects: first, the surface permanent displacement caused by the slippage effect, which shows that there is a non-zero residual displacement in the displacement record; second, the velocity pulse caused by the directionality of the source rupture propagation, which often appears in the velocity record in the normal direction of the fault, and has the characteristics of suddenness, long period and large amplitude; third, the spatially coherent high-frequency vibration caused by the complexity of the source and the difference in the propagation path. The above factors together exacerbate the stress complexity and response uncertainty of cross-fault linear engineering in earthquakes.

[0003] However, the current traditional ground motion synthesis and input methods, such as spectral superposition method, random vibration method, single-point input and uniform input, do not fully consider the permanent displacement and velocity pulse characteristics in the near-fault region, and have limitations in expressing the difference and coherence of the input ground motion on both sides of the fault, which is difficult to meet the refined seismic analysis needs of cross-fault linear engineering. Although some countries and regions have proposed principles and recommendations for considering fault deformation or displacement in seismic design codes, such as the ASCE 7-22 standard in the United States, which recommends considering the allowable displacement evaluation of permanent ground deformation, and the Highway Bridge Seismic Design Specification (JTG / T 2231-01-2020) in China, which proposes fault avoidance and limiting measures, but there is still no complete ground motion input modeling technology and standard system for cross-fault linear engineering, especially in the aspect of directional velocity pulse and permanent displacement effect superposition modeling. Therefore, it is urgent to develop a wideband ground motion artificial synthesis method for cross-fault linear engineering. SUMMARY

[0004] In view of the deficiencies in the prior art, the present application provides a wideband ground motion artificial synthesis method for cross-fault linear engineering, which comprises the following steps:

[0005] S1: Earthquake scenario and station parameter setting, setting the magnitude of the target earthquake, fault type, geometric parameters, station location and site conditions;

[0006] S2: High-frequency component HF simulation, using wavelet packet transform combined with spectral representation method (WPT-SRM) to generate multi-point high-frequency ground motion with non-stationarity and spatial coherence;

[0007] S3: Permanent displacement component LF-FS simulation related to slip, calling slip parameter prediction model to determine amplitude, period and starting time, using mathematical functions to generate displacement, velocity and acceleration time history;

[0008] S4: Directional velocity pulse component LF-FD simulation, calling directional parameter prediction model to determine amplitude, period, oscillation coefficient, phase and starting time, using mathematical functions to generate velocity, acceleration and displacement time history;

[0009] S5: Wideband synthesis, according to the cross frequency, the HF and LF components are frequency domain spliced, the acceleration time history on both sides of the fault is obtained by inverse Fourier transform, and the velocity and displacement time history is obtained by integration;

[0010] wherein,

[0011] The high-frequency ground motion in step S2 uses Harichandran-Vanmarcke coherence model to construct spectral covariance matrix, and performs frequency domain superposition through Cholesky decomposition and phase spectrum.

[0012] As a further preferred technical solution of the application, the step S2 further includes power spectral density (PSD) conversion: the target acceleration response spectrum (PSA) is converted into power spectral density (PSD) by using the following formula:

[0013]

[0014] In the formula:

[0015] S(ω): power spectral density;

[0016] PSA 2 (ω): square of the acceleration response spectrum;

[0017] ω: angular frequency;

[0018] ξ: damping ratio;

[0019] T: duration of seismic record;

[0020] p: probability coefficient, generally 0.85.

[0021] As a further preferred technical solution of the present application, on the basis of the power spectrum density matrix constructed in step 2, the SRM method is used for frequency domain superposition by Cholesky decomposition and introduction of independent random phase spectrum, and a multi-point seismic motion record with non-stationary characteristics and spatial coherence is generated by inverse Fourier transform;

[0022]

[0023] In the formula:

[0024] x j (t): the synthetic seismic motion acceleration of the jth observation point at time t;

[0025] j and m: reference station number in the frequency domain spectrum covariance matrix;

[0026] ω l : the angular frequency corresponding to the lth frequency step;

[0027] Δω: frequency sampling interval;

[0028] S jm (ω l , t): power spectrum density;

[0029] β jm (ω l ): amplitude;

[0030] θ jm (ω l ): phase;

[0031] φ ml : random phase.

[0032] As a further preferred technical solution of the present application, in step S2, the high-frequency random seismic motion is decomposed into fault slip normal (FN, Fault-Normal) and fault slip parallel (FP, Fault-Parallel) according to the fault strike angle and slip angle, to obtain high-frequency fault normal component (HF-FP) and high-frequency fault parallel component (HF-FN).

[0033] As a further preferred technical solution of the present application, the seismic motion record of the ith iteration is subjected to fast Fourier transform to obtain its amplitude spectrum; the spectral ratio factor is calculated and the amplitude spectrum is updated; the original phase spectrum is retained, combined with the updated amplitude spectrum to construct a new complex frequency spectrum, and then subjected to inverse Fourier transform to obtain a new seismic motion time history, and the spectral ratio factor calculation formula is as follows:

[0034]

[0035] In the formula:

[0036] Fourier amplitude of ground motion at the jth observation point at the i+1th iteration;

[0037] Fourier amplitude of ground motion at the jth observation point at the i+1th iteration;

[0038] Target acceleration response spectrum of ground motion at the jth observation point;

[0039] Acceleration response spectrum of ground motion at the jth observation point at the i+1th iteration.

[0040] As a further preferred technical solution of the present application, the LF-FS component in step S3 adopts the empirical prediction model of the slide-off parameter proposed by Kamai et al.;

[0041] Estimating the average slip D by the magnitude fault , calculating the D of ground motion on both sides of the fault site , the expression is as follows:

[0042] ln(D fault ) = 1.15M w - 3.28

[0043]

[0044] In the formula: D site : amplitude of permanent displacement (cm);

[0045] D fault : average slip on the fault surface (cm);

[0046] M w : magnitude of seismic moment;

[0047] R rup : fault distance between the station and the fault (km);

[0048] R x : projection distance of the station along the fault normal, distinguishing the lower plate (R x <0) and the upper plate (R x >0);

[0049] a0: normalized amplitude of permanent displacement at R rup =0;

[0050] a2 and a3: parameters controlling the distance attenuation rate and curvature;

[0051] a4: additional displacement of the upper plate compared with the lower plate.

[0052] As a further preferred technical solution of the present application, in step S4, the LF-FD velocity pulse amplitude is predicted.

[0053] According to the set earthquake parameters and station position parameters, the LF-FD parameter empirical prediction model proposed by Mukhopadhyay and Gupta et al. is called to calculate the velocity pulse amplitude V of the ground motion on both sides of the fault p , and the expression is as follows:

[0054]

[0055] In the formula:

[0056] V p : directional velocity pulse amplitude (cm / s);

[0057] M w : seismic moment magnitude;

[0058] R rup : fault distance (km);

[0059] X, θ: strike-slip fault strike-to-forward rupture ratio and azimuth angle;

[0060] Y, φ: dip-slip fault dip-to-forward rupture ratio and zenith angle;

[0061] f1=1, f2=0: for strike-slip fault; f1=0, f2=1: for dip-slip fault;

[0062] Xcosθ, Ycosφ: represent the directional parameters related to the fault geometry;

[0063] c1-c7: regression coefficients.

[0064] As a further preferred technical solution of the present application, in step S5, a Butterworth filter is used to perform high-pass filtering on the HF component, and the stitching frequency is taken from the cross-over frequency corresponding to the period of LF-FS and LF-FD respectively;

[0065] The cross-over frequency is calculated as follows:

[0066] According to the slip-chase period T f of LF-FS and the pulse period T p of LF-FD, the cross-over frequency f fc of LF-FS and HF and the cross-over frequency f pc of LF-FD and HF are determined respectively by the following formulas:

[0067]

[0068] S502: HF high-pass filtering

[0069] The fourth-order Butterworth high-pass filter is performed on the HF-FN and HF-FP components, and the cut-off frequencies are f fc and f pc , respectively, to ensure that the frequency bands do not overlap when the HF and LF components are superimposed.

[0070] As a further preferred technical solution of the present application, in step S5, the Fourier transform is superimposed in the frequency domain:

[0071] The Fourier transform is performed on the HF-FP, HF-FN, LF-FS and LF-FD components to obtain their amplitude spectrum (FAS) and phase spectrum (FPS); the FP component is superimposed with the HF-FP and LF-FS components, the FN component is superimposed with the HF-FN and LF-FD components, and the complete complex spectrum expression is obtained by piecewise splicing and superimposing at the cross frequency according to the following formula.

[0072] FAS syn = FAS low + FAS high

[0073]

[0074] In the formula:

[0075] FAS syn : Fourier amplitude spectrum of the wide-band seismic motion of the FP or FN component;

[0076] FAS low : Fourier amplitude spectrum of the LF-FS or LF-FD seismic motion component;

[0077] FAS high : Fourier amplitude spectrum of the HF-FP or HF-FN seismic motion component;

[0078] FPS syn : Fourier phase spectrum of the wide-band seismic motion of the FP or FN component;

[0079] FPS low : Fourier phase spectrum of the LF-FS or LF-FD seismic motion component;

[0080] FPS high : Fourier phase of the HF-FP or HF-FN seismic motion component.

[0081] As a further preferred technical solution of the present application, the finally synthesized seismic motion record includes a velocity pulse component in the FN direction and a permanent displacement component in the FP direction, the FN component has consistent pulse characteristics on both sides of the fault, the FP component shows symmetrical and opposite displacement in the strike-slip fault, and shows displacement amplitude difference between the hanging wall and the footwall in the dip-slip fault.

[0082] Beneficial effects

[0083] 1. The cross-fault multi-point input capability of the present application: the generated ground motion has the difference of the two sides of the fault and the spatial coherence of multiple points, which is suitable for the seismic response analysis of cross-fault linear engineering such as bridge and tunnel.

[0084] 2. The physical mechanism of the present application is clear: the three types of ground motion components of HF, LF-FS and LF-FD have clear physical basis and parameter model support, which can adapt to different magnitude, fault type and site condition.

[0085] 3. The spectrum structure of the present application is continuous: through reasonable cross-frequency division and frequency domain splicing, the natural transition of the frequency spectrum distribution of the ground motion is ensured, and there is no unreasonable jump.

[0086] 4. The present application has strong engineering adaptability: it is suitable for setting earthquake situation, completing missing record, simulating ground motion scene and other tasks, and can be connected with structural platforms such as OpenSees and ABAQUS.

[0087] 5. The present application has good scalability: the three types of components of HF, LF-FS and LF-FD can be upgraded independently, which is convenient for subsequent integration of more complex source-path-site models. BRIEF DESCRIPTION OF DRAWINGS

[0088] The technical solutions of the present application will be described in detail below in combination with the accompanying Figure 1 - the accompanying Figure 9 and implementation cases, but it should be known that these drawings are designed only for explanatory purposes, and therefore do not limit the scope of the present application. In addition, unless specifically indicated, these drawings are only intended to conceptually illustrate the structural configuration described herein, and do not necessarily be drawn in proportion.

[0089] the accompanying Figure 1 is a technical route diagram of the present application application;

[0090] the accompanying Figure 2 is a schematic diagram of the upper wall FP component of the synthesized ground motion on both sides of the strike-slip fault provided by the embodiment of the present application;

[0091] the accompanying Figure 3 is a schematic diagram of the lower wall FP component of the synthesized ground motion on both sides of the strike-slip fault provided by the embodiment of the present application;

[0092] the accompanying Figure 4 is a schematic diagram of the upper wall FN component of the synthesized ground motion on both sides of the strike-slip fault provided by the embodiment of the present application;

[0093] the accompanying Figure 5 is a schematic diagram of the lower wall FN component of the synthesized ground motion on both sides of the strike-slip fault provided by the embodiment of the present application;

[0094] the accompanyingFigure 6 A schematic diagram of the upper FP component of the synthetic dip-slip fault two-side ground motion provided by the embodiment of the present application is shown in the figure;

[0095] Figure 1 shows a schematic diagram of the upper FP component of the synthetic dip-slip fault two-side ground motion provided by the embodiment of the present application; Figure 7 A schematic diagram of the lower FP component of the synthetic dip-slip fault two-side ground motion provided by the embodiment of the present application is shown in the figure;

[0096] Figure 2 shows a schematic diagram of the lower FP component of the synthetic dip-slip fault two-side ground motion provided by the embodiment of the present application; Figure 8 Figure 3 shows a schematic diagram of the upper FN component of the synthetic dip-slip fault two-side ground motion provided by the embodiment of the present application;

[0097] Figure 9 Figure 4 shows a schematic diagram of the lower FN component of the synthetic dip-slip fault two-side ground motion provided by the embodiment of the present application. DETAILED DESCRIPTION

[0098] It should be noted that the technical solutions of the present application will be described in detail below by way of examples, including the cross-fault ground motion synthesis process, the simulation strategy of three types of ground motion components, and typical synthesis results. It should be understood that the described embodiments are only used to better illustrate the structure and process of the present application, and should not be regarded as limiting the scope of protection of the present application.

[0099] In the present specification and its accompanying drawings, the terms not explicitly defined (such as "synthesis", "simulation", "setting", "decomposition", etc.) should be understood broadly, including but not limited to software calculation, data mapping or parameter model, etc. For those skilled in the art, the constituent steps can be adapted, combined and equivalently replaced without deviating from the core idea of the present application.

[0100] In addition, in order to simplify the expression of the drawings, the same or similar processing steps, data structures or model calls are not repeated in the drawings, but do not affect the integrity of the present application. Figure 1 to the accompanying drawings Figure 9 The flowchart and result diagram shown are functional description diagrams, not physical structure limitation diagrams.

[0101] The following will be described in detail with reference to the accompanying Figure 1 to the accompanying drawings Figure 9 ,

[0102] The method should consider various influencing factors such as the spatial coherence of high-frequency ground motion, the velocity pulse caused by the directional effect in the low-frequency component, and the permanent displacement caused by the slip-off effect, to construct a wide-band ground motion synthesis process with time-frequency consistency and physical interpretability. Such a method not only helps to improve the physical reasonableness and engineering applicability of the input ground motion, but also provides key theoretical support and technical tools for the seismic performance evaluation, safety design and specification of cross-fault engineering;

[0103] Two preferred embodiments of the present application will be described in detail;​

[0104] Embodiment 1, a broadband ground motion artificial synthesis method for cross-fault linear engineering is adopted, and for a set strike-slip fault type earthquake scenario, broadband ground motion records on both sides of the cross-fault are synthesized, and the method includes the following steps:

[0105] S1: Setting of earthquake scenario and station parameters:

[0106] The magnitude of the target earthquake, the type of fault, the geometric parameters of the fault (such as dip angle, strike angle), the spatial position of the target station on both sides of the fault, the fault distance and the site condition (such as V s30 The parameters of the target engineering site, such as the seismic fortification intensity, the seismic influence (such as the frequently occurring earthquake, the rare earthquake) and the characteristic period of the response spectrum, are set. In this embodiment 1, the source, station and engineering site parameters of the set strike-slip earthquake scenario are shown in Table 1.

[0107] Table 1 Setting of source, station and engineering site parameters of strike-slip earthquake scenario

[0108]

[0109]

[0110] S2: High-frequency component (HF, High-Frequency) simulation;

[0111] Wavelet packet transform combined with spectral representation method (WPT-SRM) is adopted to generate high-frequency random ground motion on both sides of the cross-fault with non-stationarity and spatial coherence characteristics through spatial coherence function, and according to the fault strike angle and slip angle, it is decomposed into fault normal direction (FN, Fault-Normal) and fault parallel direction (FP, Fault-Parallel) to obtain high-frequency fault normal component (HF-FP) and high-frequency fault parallel component (HF-FN);

[0112] Further, in the embodiment, the specific steps of simulating the high-frequency component of the ground motion in step S2 can be considered as follows:

[0113] S201: Setting of target response spectrum

[0114] According to the parameters of the seismic fortification intensity of the engineering site, the site category, the seismic influence (frequently occurring earthquake, rare earthquake) and the characteristic period of the response spectrum, the target response spectrum curve is generated as the spectral shape constraint of high-frequency synthesis, combined with the design response spectrum of Chinese seismic code or other target spectrum forms.

[0115] S202: Power spectral density (PSD) conversion;

[0116] To convert the target response spectrum into frequency domain energy constraint, the empirical formula proposed by Kaul is used to convert the target acceleration response spectrum (PSA) into power spectral density (PSD).

[0117]

[0118] wherein:

[0119] S(ω): power spectral density;

[0120] PSA 2 (ω): square of acceleration response spectrum;

[0121] ω: angular frequency;

[0122] ξ: damping ratio;

[0123] T: duration of ground motion record;

[0124] p: probability coefficient, generally taken as 0.85.

[0125] S203: Seed ground motion generation

[0126] Based on the set S1, the set S1 is set up. The earthquake scenario and station parameters are used to generate a representative wideband ground motion record with non-stationary characteristics by using the 13 group wavelet packet parameter prediction model proposed by Yamamoto and Baker.

[0127] S204: Wavelet packet energy spectrum construction;

[0128] The seed ground motion record is decomposed by wavelet packet using Meyer wavelet, the WPT coefficient is extracted, and the self-power spectrum is calculated.

[0129] S205: Construction of power spectral density matrix;

[0130] The energy spectrum in S204 is used as the auto-power spectral density (Auto-EPSD) of each point, and the spectral covariance matrix is constructed by combining the Harichandran-Vanmarcke empirical coherence model.

[0131] S206: Synthesis of multi-point non-stationary ground motion by spectral representation method (SRM);

[0132] Based on the constructed power spectral density matrix, Cholesky decomposition is performed, and independent random phase spectrum is introduced. The SRM method is used for frequency domain superposition, and the inverse Fourier transform is used to generate multi-point ground motion records with non-stationary characteristics and spatial coherence.

[0133]

[0134] wherein:

[0135] x j (t) : synthetic ground motion acceleration at the jth observation point at time t;

[0136] j and m : reference station number in the frequency domain spectral covariance matrix;

[0137] ω l : angular frequency corresponding to the lth frequency step;

[0138] Δω : frequency sampling interval;

[0139] S jm (ω l , t) : power spectral density;

[0140] β jm (ω l ) : amplitude;

[0141] θ jm (ω l ) : phase;

[0142] φ ml : random phase.

[0143] S207 : response spectrum matching adjustment;

[0144] The amplitude correction method adjusts the frequency content of each synthetic ground motion record. The ground motion record of the ith iteration is subjected to a fast Fourier transform to obtain its amplitude spectrum; the spectral ratio factor is calculated with reference to equation (3) and the amplitude spectrum is updated; the original phase spectrum is retained, and a new complex frequency spectrum is constructed by combining the updated amplitude spectrum, and then subjected to an inverse Fourier transform to obtain a new time history of the ground motion. This operation is iterated, the spectral difference is evaluated and optimized at each round, and the consistency of the simulated ground motion and the target response spectrum is improved.

[0145]

[0146] In the formula:

[0147] Fourier amplitude of the jth observation point in the i+1th iteration of the ground motion;

[0148] Fourier amplitude of the jth observation point in the ith iteration of the ground motion;

[0149] Target acceleration response spectrum of the jth observation point of the ground motion;

[0150] Acceleration response spectrum of the jth observation point of the ground motion in the ith iteration.

[0151] S208 : component decomposition

[0152] Assuming that the normal component (FN) and parallel component (FP) of high-frequency ground motion at the same location are basically consistent with the components of the fault slip direction, they can be obtained by directional decomposition of a set of common high-frequency random seismic ground motion records. The specific decomposition is determined by the strike angle and slip angle of the fault to determine the direction cosine, and the random seismic ground motion record is projected to the normal (FN) and parallel (FP) directions of the fault slip direction.

[0153] S209: S-wave arrival time extraction;

[0154] Based on the normalized ground motion energy accumulation curve, the time when the normalized energy reaches 5% is defined as the S-wave initial arrival time, which provides a time anchor point for the time alignment and splicing of LF-FS and LF-FD in the subsequent process.

[0155] S3: Simulation of permanent displacement component related to slip (LF-FS, Low-Frequency Fling-Step):

[0156] According to the parameters such as magnitude, fault type, fault geometry, fault distance of the set earthquake, the amplitude, period and starting time of the permanent displacement component and other key parameters are determined by using the empirical prediction model of permanent displacement, and the permanent displacement ground motion component is generated by combining the mathematical function model of permanent displacement time course;

[0157] Further, in the embodiments, the specific steps for determining the slip-related low-frequency permanent displacement component (LF-FS) can also be considered as follows:

[0158] S301: LF-FS permanent displacement amplitude prediction;

[0159] According to the set earthquake scenario parameters (magnitude M w , fault type, fault distance R rup , etc.), the LF-FS parameter empirical prediction model proposed by Kamai et al. is called. The average slip D fault is estimated by magnitude, and the D site of ground motion on both sides of the fault is calculated, as shown in the following expressions (4) and (5):

[0160] ln(D fault )=1.15M w -3.28 (4)

[0161]

[0162] D site : amplitude of permanent displacement (cm);

[0163] D fault : average slip on the fault surface (cm);

[0164] Mw : Moment magnitude;

[0165] R rup : Fault distance between site and fault (km);

[0166] R x : Projected distance of station along fault normal, distinguishing upper plate (R x <0) and lower plate (R x >0);

[0167] a0: Normalized amplitude of permanent displacement at R rup =0;

[0168] a2 and a3: Parameters controlling distance decay rate and curvature;

[0169] a4: Additional displacement of upper plate compared to lower plate.

[0170] S302: LF-FS slip pulse period prediction;

[0171] According to the magnitude and fault type of the set earthquake, call the slip pulse empirical prediction equation proposed by Kamai et al., as follows (6) and (7), to predict the slip pulse period of LF-FS, where T fSS and T fRS are the slip pulse prediction values for strike-slip and thrust faults, respectively.

[0172] ln(T f,SS ) = 1.16M w - 6.42 (6)

[0173] ln(T f,Rev ) = 0.7M w - 3.54 (7)

[0174] S303: LF-FS starting time setting

[0175] The starting time t f0 of LF-FS is set as the S-wave arrival time in the HF record, ensuring the synchronization of LF-FS and HF in physical timing.

[0176] S304: LF-FS ground motion time history construction;

[0177] Call the LF-FS displacement time history model proposed by Burks and Baker, and substitute the D site , T f and t f0 parameter values obtained in S301-S304 to construct the displacement time history d f (t) of LF-FS, and then through first differentiation and second differentiation to obtain the velocity time history v f(t) and acceleration time history a f (t).

[0178]

[0179] wherein:

[0180] d f (t): LF-FS displacement time history;

[0181] D site : amplitude of permanent displacement (cm);

[0182] T f : slide duration (s);

[0183] t f0 : slide onset time (s).

[0184] S4: directional related velocity pulse component (LF-FD, Low-Frequency Forward-Directivity) simulation;

[0185] According to the set parameters of magnitude, fault type, fault geometry, fault distance, etc., the amplitude, period and starting time of the key parameters of the velocity pulse component are determined by using the parameter empirical prediction model of directional velocity pulse, and the velocity pulse seismic motion component is generated by combining the mathematical function model of the velocity pulse time history;

[0186] Further, in the embodiments, the specific steps for determining the directional related low-frequency velocity pulse component (LF-FD) can also be considered, which include:

[0187] S401: LF-FD velocity pulse amplitude prediction;

[0188] According to the set seismic parameters and station location parameters, the LF-FD parameter empirical prediction model proposed by Mukhopadhyay and Gupta is called to calculate the velocity pulse amplitude V p of the seismic motion on both sides of the fault, which is expressed as follows:

[0189]

[0190] wherein:

[0191] V p : directional velocity pulse amplitude (cm / s);

[0192] M w : seismic moment magnitude;

[0193] R rup : fault distance (km);

[0194] X, θ: forward rupture ratio and azimuth angle of strike-slip fault;

[0195] Y, φ: forward rupture ratio and zenith angle of dip-slip fault;

[0196] f1 = 1, f2 = 0: for strike-slip fault; f1 = 0, f2 = 1: for dip-slip fault;

[0197] Xcosθ, Ycosφ: represent the directionality parameters related to fault geometry;

[0198] c1-c7: regression coefficients.

[0199] S402: LF-FD pulse period prediction

[0200] According to the magnitude of the set earthquake, the empirical prediction equation of pulse period proposed by Mukhopadhyay and Gupta et al. is called, as shown in the following formula (10), to predict the pulse period T of LF-FD p .

[0201] lnT p = 0.9639M w -5.3948 (10)

[0202] S403: LF-FD starting time setting;

[0203] The starting time t p0 of LF-FD is set as the S-wave arrival time in the HF record, ensuring the synchronization of LF-FD and HF in physical timing.

[0204] S404: LF-FD oscillation coefficient and phase angle setting;

[0205] The oscillation coefficient γ and the normalized phase angle φ are directly set to be sampled from or statistical distribution In this embodiment, the median value in the statistical distribution is used, γ = 2,

[0206] S405: LF-FD ground motion time history construction;

[0207] The LF-FD velocity time history model proposed by Dabaghi and Kiureghian is called, as shown in the following formulas (11)-(13). Substitute the V p , T p , t p0 , γ and parameter values obtained in S401-S404 to construct the velocity time history v p (t) of LF-FD, and then through once differentiation to obtain the acceleration time history a p (t), and once integration to obtain the displacement time history d p(t).

[0208]

[0209] wherein:

[0210] v p (t): LF-FD velocity time history (cm / s);

[0211] t max : time of peak velocity in LF-FD velocity time history (s);

[0212] T p : pulse period (s);

[0213] phase angle (rad);

[0214] γ: oscillation coefficient;

[0215] D r : residual displacement correction term (cm).

[0216] S5: broadband ground motion synthesis;

[0217] The cross-over frequencies of LF-FS and HF-FP and LF-FD and HF-FP are calculated according to empirical formulas, and the HF is high-pass filtered; then the Fourier transform is performed on each component to obtain the amplitude spectrum and the phase spectrum, and the segments are spliced at the cross-over frequencies; the inverse Fourier transform is performed to obtain the broadband ground motion time history on both sides of the fault;

[0218] Further, the specific steps of synthesizing the broadband cross-fault ground motion include:

[0219] S501: cross-over frequency calculation;

[0220] According to the slide period T f of LF-FS, the pulse period T p of LF-FD, the cross-over frequencies f fc of LF-FS and HF are determined by empirical formulas (14) and (15) respectively, and the cross-over frequencies f pc of LF-FD and HF are determined by empirical formulas (14) and (15) respectively:

[0221]

[0222] S502: HF high-pass filtering;

[0223] The fourth-order Butterworth high-pass filtering is performed on the HF-FN and HF-FP components, and the cut-off frequencies are f fc and f pc respectively, to ensure that the frequency bands do not overlap.

[0224] S503: Fourier transform and frequency domain superposition;

[0225] Fourier transform the HF-FP, HF-FN, LF-FS and LF-FD components to obtain their amplitude spectrum (FAS) and phase spectrum (FPS); superimpose the FP component with HF-FP and LF-FS components, and superimpose the FN component with HF-FN and LF-FD components, and segmentally splice and superimpose at the cross frequency to obtain the complete complex spectrum expression according to the following formulas (16) and (17).

[0226] FAS syn = FAS low + FAS high (16)

[0227]

[0228] In the formula:

[0229] FAS syn : Fourier amplitude spectrum of the FP or FN component wideband ground motion;

[0230] FAS low : Fourier amplitude spectrum of the LF-FS or LF-FD ground motion component;

[0231] FAS high : Fourier amplitude spectrum of the HF-FP or HF-FN ground motion component;

[0232] FPS syn : Fourier phase spectrum of the FP or FN component wideband ground motion;

[0233] FPS low : Fourier phase spectrum of the LF-FS or LF-FD ground motion component;

[0234] FPS high : Fourier phase spectrum of the HF-FP or HF-FN ground motion component.

[0235] S504: Inverse Fourier transform;

[0236] The ground motion acceleration time history in the time domain is obtained by inverse Fourier transform, and then the velocity and displacement time histories are obtained by first integration and twice integration, respectively. Finally, the complete FN and FP component cross-fault wideband ground motion is obtained, which meets the requirements of multi-point input of structural model and has time-frequency consistency and spatial difference.

[0237] For the set strike-slip fault earthquake, the synthesized ground motion time histories on both sides of the fault are as shown in FIG. 2, and the Fourier amplitude spectrum and phase spectrum of the synthesized ground motion time histories are as shown in FIG. 3. Figures 2 to 5The acceleration time histories show good symmetry and coherence on both sides of the main vibration segment with similar amplitude and spectral distribution. The velocity time histories clearly show the directional velocity pulse characteristics, and the FN component shows consistent jump responses on both sides with almost the same pulse amplitude and duration, reflecting that the velocity pulse is mainly controlled by the modulation effect of the rupture propagation direction on the fault normal. The FP component does not contain obvious pulses in the velocity response, but shows symmetric step characteristics in the displacement time history, representing the thrust effect of strike-slip rupture. The displacement time history shows that the permanent displacement of the FP component is equal and opposite on both sides of the fault, indicating that there is obvious reverse dislocation behavior on both sides of the fault, which is consistent with the symmetry characteristics of the surface dislocation of strike-slip fault. Overall, it presents the typical dynamic-static coupling mode of "FN in phase, FP anti-symmetric", which is highly consistent with the actual near-fault strike-slip earthquake record. In addition, the high-frequency part of the synthetic ground motion is generated by the WPT-SRM method, which exhibits non-stationary evolution characteristics and strong spatial coherence, thereby maintaining the consistency and physical authenticity of high-frequency response in the wideband input. The final acceleration, velocity and displacement responses all show good spectral continuity and physical rationality, which are suitable for the input requirements of cross-fault linear engineering under the condition of strike-slip fault rupture.

[0238] Example 2, see attached Figure 1 and attached Figures 6 to 9 For a set of dip-slip fault type earthquake scenarios, the wideband ground motion records on both sides of the fault are synthesized, and the main difference from Example 1 is the set of earthquake scenarios and station parameters, and the rest of the process is consistent with Example 1. In this embodiment 2, the source, station and engineering site parameters of the set earthquake scenario are shown in Table 2.

[0239] Table 2 Source, station and engineering site parameters of the set dip-slip earthquake scenario

[0240]

[0241]

[0242] For the set of dip-slip fault earthquakes, the synthesized fault two-side ground motion time histories are shown in the attached Figures 6 to 9The acceleration time histories show similar amplitudes and consistent duration and frequency structure in the main vibration segments of the upper and lower plates, which reflects the basic consistent input characteristics driven by the co-source rupture process. In the velocity time histories, the FN component shows a sudden directional velocity pulse response in both the upper and lower plates, with similar pulse amplitudes and durations, indicating that the velocity pulse is still mainly controlled by the fault normal rupture propagation mechanism. However, the FP component does not show a significant velocity pulse, but it does show a permanent displacement in the displacement response that is significantly different in amplitude between the upper and lower plates. Specifically, the FP direction displacement is close to 100 cm in the upper plate, while it is only about 50 cm in the lower plate, showing a significant asymmetric feature between the upper and lower plates. This trend is consistent with the surface observations of thrust faults: since the upper plate is closer to the rupture surface, it bears the superposition of fault uplift and horizontal propulsion, resulting in a larger residual displacement amplitude; while the lower plate is relatively far from the rupture surface, the displacement is offset in the opposite direction and the amplitude is relatively small. Overall, the dynamic-static coupling effect is "FN in phase and FP amplitude asymmetric", which is highly consistent with the observations of near-fault dip-slip earthquakes. Similarly, the high-frequency part of the synthetic ground motion is generated by the WPT-SRM method, which maintains the spatial variability and non-stationary characteristics of the frequency distribution, further enhancing the expressiveness and physical consistency in the high-frequency band. The final wideband ground motion shows good spectral continuity and mechanical reasonableness in the acceleration, velocity, and displacement response indicators, verifying the adaptability and engineering applicability of the proposed method under the condition of dip-slip faults.

Claims

1. A method for broadband ground motion synthesis for trans-fault linear engineering projects, characterized in that, The method includes the following steps: S1: Seismic scenario and station parameter settings: Set the magnitude, fault type, geometric parameters, station location and site conditions of the target earthquake; S2: High-frequency component HF simulation: Multi-point high-frequency ground motion with non-stationarity and spatial coherence is generated by using wavelet packet transform combined with spectral representation; S3: LF-FS simulation of permanent displacement components related to slip-slip: The slip-slip parameter prediction model is called to determine the amplitude, period and start time, and mathematical functions are used to generate displacement, velocity and acceleration time histories; S4: Directional velocity pulse component LF-FD simulation: The directional parameter prediction model is called to determine the amplitude, period, oscillation coefficient, phase and start time, and the velocity, acceleration and displacement time history are generated using mathematical functions; S5: Wideband Synthesis: Based on the cross frequency, the HF and LF-FS, LF-FD components are spliced ​​in the frequency domain, and the acceleration time history on both sides of the fault is obtained by inverse Fourier transform, and the velocity and displacement time history is obtained by integration. in, In step S2, the high-frequency ground motion is constructed using the Harichandran–Vanmarcke coherence model to create a spectral covariance matrix, which is then superimposed with the phase spectrum in the frequency domain through Cholesky decomposition.

2. The method for broadband ground motion synthesis for trans-fault linear engineering projects according to claim 1, characterized in that, Step S2 also includes power spectral density conversion: the target acceleration response spectrum is converted into power spectral density using the following formula: ； In the formula: S ( ω ): Power spectral density; PSA 2 ( ω ): The square of the acceleration response spectrum; ω Angular frequency; ξ Damping ratio; T Duration of earthquake motion recording; p : Probability coefficient, usually taken as 0.

85.

3. The method for broadband ground motion synthesis for trans-fault linear engineering projects according to claim 2, characterized in that, Based on the power spectral density matrix constructed in step 2, Cholesky decomposition is performed, and independent random phase spectra are introduced. Frequency domain superposition is then carried out using the SRM method, and multi-point ground motion records with non-stationary characteristics and spatial coherence are generated through inverse Fourier transform. j Each observation point at time t The formula for calculating the combined seismic ground acceleration at a given location is: ； In the formula: x j ( t ): No. j Each observation point at time t The combined ground motion acceleration at the location; j and m Reference station number in the frequency domain spectral covariance matrix; ω l : No. l The angular frequency corresponding to each frequency step; Δ ω Frequency sampling interval; S jm ( ω l , t ): Power spectral density; β jm ( ω l ): Amplitude; θ jm ( ω l ): Phase; ml : Random phase.

4. The method for broadband ground motion synthesis for trans-fault linear engineering projects according to claim 2, characterized in that, In step S2, the high-frequency random ground motion fault is decomposed into the fault slip normal direction and the fault slip parallel direction based on the strike angle and slip angle, thus obtaining the high-frequency fault normal direction component and the high-frequency fault parallel direction component.

5. The method for broadband ground motion synthesis for trans-fault linear engineering projects according to claim 2, characterized in that, For the first i The amplitude spectrum of the seismic ground motion records obtained by the round-iteration fast Fourier transform is obtained. Calculate the spectral ratio factor and update the amplitude spectrum; Retaining the original phase spectrum, a new complex spectrum is constructed by combining it with the updated amplitude spectrum. An inverse Fourier transform is then performed to obtain the new ground motion time history. The spectral ratio factor is calculated using the following formula: ； In the formula: : No. j The observation point at the ... i+ Fourier amplitude of seismic motion in one iteration; : No. j The observation point at the ... i Fourier amplitude of seismic motion in each iteration; : No. j Target acceleration response spectrum of ground motion at each observation point; : No. j The observation point at the ... i The acceleration response spectrum of the earthquake motion during the cycle iteration.

6. The method for broadband ground motion synthesis for trans-fault linear engineering projects according to claim 1, characterized in that, In step S3, the LF-FS component adopts the empirical prediction model of the slip-strike parameter proposed by Kamai et al.; Estimating average slip using magnitude D fault Calculate the ground motion on both sides of the fault D site The expression is as follows: ； ； In the formula: D site : Amplitude of permanent displacement (cm); D fault : Average slip on the fault plane (cm); R rup : Fault distance (km) between the station and the fault. R x The projected distance of the measuring point along the fault normal, distinguishing the footwall ( R x < 0) and the upper plate ( R x > 0); a 0: Lower plate R rup = Normalized amplitude of permanent displacement at 0; a 2 and a 3: Parameters controlling the distance decay rate and curvature; a 4: The additional displacement of the upper plate relative to the lower plate.

7. The method for broadband ground motion synthesis for trans-fault linear engineering projects according to claim 1, characterized in that, In step S4: LF-FD velocity pulse amplitude prediction Based on the set seismic parameters and station location parameters, the LF-FD parameter empirical prediction model proposed by Mukhopadhyay and Gupta et al. was used to calculate the velocity pulse amplitude of ground motion on both sides of the fault. V p The expression is as follows: ； In the formula: V p : Directional velocity pulse amplitude in cm / s; M w Earthquake moment and magnitude; R rup Fault distance (km); X , θ : Strike-slip fault forward fracture ratio and azimuth; Y , : The forward fracture ratio and zenith angle of the dip-slip fault; f 1=1, f 2=0: Used for strike-slip faults; f 1=0, f 2=1: Used for dip-slip faults; X cos θ , Y cos : Represents directional parameters related to fault geometry; c 1– c 7: Regression coefficients.

8. The method for broadband ground motion synthesis for trans-fault linear engineering projects according to claim 1, characterized in that, In step S5, a Butterworth filter is used to perform high-pass filtering on the HF component, and the splicing frequencies are taken from the crossover frequencies corresponding to the periods of LF-FS and LF-FD, respectively. The crossover frequency is calculated as follows: Based on the slip stroke cycle of LF-FS T f LF-FD pulse period T p The crossover frequencies of LF-FS and HF are determined using the following formulas. f fc Crossover frequency of LF-FD and HF f pc : ； ； S502: HF High-Pass Filter Fourth-order Butterworth high-pass filtering was applied to the HF-FN and HF-FP components, with cutoff frequencies of [missing information]. f fc and f pc This ensures that the frequency bands do not overlap when the HF and LF components are superimposed.

9. The method for broadband ground motion synthesis for trans-fault linear engineering projects according to claim 1, characterized in that, In step S5, the Fourier transform and frequency domain are superimposed: Fourier transforms of the HF-FP, HF-FN, LF-FS, and LF-FD components are performed to obtain their amplitude and phase spectra. The FP components are superimposed with the HF-FP and LF-FS components, and the FN components are superimposed with the HF-FN and LF-FD components. The complete complex spectrum expression is obtained by splicing and superimposing the components in segments at the cross frequencies according to the following formula. ； ； In the formula: FAS syn Fourier amplitude spectra of broadband ground motions with FP or FN components; FAS low Fourier amplitude spectra of LF-FS or LF-FD ground motion components; FAS high Fourier amplitude spectra of HF-FP or HF-FN ground motion components; FPS syn Fourier phase spectrum of broadband ground motions with FP or FN components; FPS low Fourier phase spectra of LF-FS or LF-FD ground motion components; FPS high Fourier phase of HF-FP or HF-FN ground motion components.

10. A method for broadband ground motion synthesis for trans-fault linear engineering projects according to claim 1, characterized in that, The final synthesized ground motion record includes velocity pulse components in the FN direction and permanent displacement components in the FP direction. The FN component has consistent pulse characteristics on both sides of the fault, while the FP component exhibits symmetrical reverse displacement in strike-slip faults and shows differences in displacement amplitude between the hanging wall and footwall in dip-slip faults.

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