A simulation method of near-fault ground motion considering site effect of soil layer

Abstract

This invention provides a near-fault ground motion simulation method considering soil layer site effects. This method primarily uses regression analysis based on measured site seismic records to obtain an acceleration spectrum amplification coefficient equation that considers soil layer site amplification effects and near-fault ground motion characteristics. This establishes a probabilistic seismic hazard analysis method for the site considering soil layer site effects. This method can determine the near-fault consistent hazard response spectrum. Then, using the obtained near-fault consistent hazard response spectrum as the target spectrum, the seismic records are adjusted using a superposition wavelet method to obtain near-fault ground motions that meet the requirements. The method proposed in this invention can more accurately assess near-fault earthquake hazards and is suitable for widespread application.

Description

Technical Field

[0001] This invention relates to the field of earthquake engineering, and in particular to techniques related to seismic motion simulation methods. Specifically, it is a near-fault seismic motion simulation method that considers soil layer site effects, used to study the seismic response characteristics of near-fault sites considering soil layer site amplification effects. Background Technology

[0002] Current commonly used seismic motion simulation methods mainly rely on the standard acceleration response spectrum model. The simulation accuracy is judged by matching the mean of the simulation record to the design response spectrum. While this method can simulate conventional seismic motion scenarios, it neglects two key factors: the pulse characteristics of near-fault site effects and the nonlinear effects of soil layers. This leads to significant biases in the assessment of the impact of simulated seismic motions on structural responses. During fault rupture events, near-field seismic waves exhibit distinct velocity pulses and forward rupture directionality. These characteristics significantly enhance long-period dynamic responses, resulting in a marked amplification effect in certain period segments of the response spectrum. Therefore, selecting a reasonable near-fault seismic motion input is crucial for the seismic analysis of near-field site structures, making near-fault seismic motion simulations that consider soil layer site effects extremely important.

[0003] Currently, methods such as high-low frequency hybrid models and frequency-wavenumber domain extensions have been proposed for simulating near-fault ground motions. However, these methods remain at the level of pulse mathematical models and do not take into account the response spectrum recorded in actual site records. Song Jian et al. established a probabilistic seismic hazard analysis approach for sites that considers the directional effects of near-faults and the nonlinear influence of soil layers, calculating the seismic hazard level and consistent hazard response spectrum of near-fault sites (Song Jian et al., 2014). Existing technologies have solved the problem of hazard characterization for near-fault sites, but have not yet further realized the technology from near-fault site hazard analysis results to target design spectra and corresponding ground motion time history samples that can be used for structural seismic analysis. It should be noted that generating ground motions that can be directly used for structural seismic analysis of near-fault sites from consistent hazard response spectra is not simply a matter of directly using existing hazard analysis results. On the one hand, it is necessary to establish a continuous and stable parameter transfer relationship among multiple stages, including screening of measured near-fault records, identification of pulse characteristics, calculation of nonlinear seismic response of soil layers, regression of amplification factors and characterization of discreteness, decomposition of hazard of pulsed and non-pulsed ground motions, and determination of target spectra under different annual exceedance probabilities, which involves a large workload. On the other hand, near-fault ground motions simultaneously exhibit significant non-stationary characteristics, pulsed characteristics, and site dependence. If only numerical matching of response spectra is pursued, it is easy to destroy the non-stationary characteristics and time-frequency features of the original ground motion, and even lead to zero drift in velocity and displacement time histories after matching, making it difficult to use directly as engineering input. Therefore, how to further transform the probabilistic hazard analysis results into target spectra and ground motion samples that can be used for engineering design and structural time history analysis, while considering the near-fault site effects, is a key technical problem with high implementation difficulty in the existing technology.

[0004] The patent applications "A Near-Fault Ground Motion Fitting Method (Application No. CN114442153B)" and "A Near-Fault Ground Motion Fitting Method Based on Improved Time-Domain Superposition Method (Application No. CN114966835B)" proposed by Zhang Chao et al., although both involve spectral fitting methods for near-fault ground motion, are based on combining high-frequency random components with low-frequency pulse components generated by pulse mathematical models. However, the given site conditions and target response spectrum do not take into account the site effects of the near-fault soil layer. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a novel simulation technique combining near-fault consistent hazard response spectrum and superimposed wavelet matching. This method primarily involves performing regression analysis on measured site seismic records, then establishing a probabilistic seismic hazard analysis method for near-fault sites that considers soil layer site effects. This method determines the near-fault consistent hazard response spectrum considering soil layer site effects, transforms it into a target response spectrum with specific site conditions and exceedance probability requirements, and then combines wavelet processing technology to generate near-fault ground motions that conform to the target response spectrum considering soil layer site effects through superimposed wavelet processing of the seismic records.

[0006] The operational process of this invention and the key difficulties it overcomes include:

[0007] By selecting near-fault bedrock seismic records as input in step (1) and performing site seismic response calculation and analysis, the surface response and acceleration response spectrum amplification characteristics are obtained;

[0008] Step (2) Based on this, calculate the acceleration response spectrum amplification factor and perform regression analysis to establish an amplification factor regression equation that considers the soil layer site amplification effect and near-fault ground motion characteristics;

[0009] Based on the amplification coefficient regression equation obtained in step (2), step (3) constructs a site probabilistic seismic hazard analysis framework that serves the subsequent generation of target spectra in this invention.

[0010] Based on the site probabilistic seismic hazard analysis framework constructed in step (3), step (4) further couples the annual occurrence probability of near-fault pulse and non-pulse ground motions with the exceedance probability of the surface amplification coefficient to calculate the surface seismic hazard level considering the characteristics of the near-fault site.

[0011] Step (5) then determines the near-fault site consistent hazard response spectrum under different annual exceedance probabilities based on the above analysis results.

[0012] Through steps (1)-(5), the present invention specifically translates the near-fault site hazard analysis results into a target response spectrum that can be used for subsequent ground motion generation. The implementation difficulties overcome by the present invention using the above steps are: solving the problems of unifying the near-fault pulse effect, the nonlinear amplification effect of the soil layer, and the probabilistic hazard analysis into the same calculation framework, as well as the problems of the mutual transmission of uncertainties from different sources in the process of determining the target spectrum and the stability of the regression analysis results.

[0013] In steps (6)-(9), the response spectrum obtained in step (5) is set as the target response spectrum, and the initial record is initially amplitude-modulated to reduce the overall difference between the calculated response spectrum and the target response spectrum in advance, so as to avoid excessive correction at the beginning of subsequent iterations and thus improve the convergence efficiency. Then, in the spectrum matching process, the spectrum is segmented according to the natural period of the target response spectrum, and the coefficient matrix C of each period segment is constructed. Then, the wavelet amplitude coefficient b is solved by the spectrum error and the inverse of the C matrix, so that the spectrum correction has a clear frequency band target, reduces the coupling interference between different period segments, and implements controlled local correction of the original ground motion. Finally, the wavelet acceleration time history to be superimposed can be obtained.

[0014] The difficulties overcome by the present invention in steps (6)-(9) are: solving the problems of mutual coupling between different period segments in the target response spectrum matching process, local correction easily leading to mismatch of adjacent frequency bands, and the problem that excessive correction amplitude easily destroys the original ground motion pulse characteristics, non-stationary characteristics and causes baseline drift.

[0015] Finally, in step (10), the obtained wavelet time history is superimposed on the original acceleration time history to form a new acceleration time history. Steps (6) to (9) are repeated through an iterative process until the set number of iterations or error threshold is met, and the final near-fault ground motion time history sample is output.

[0016] The difficulties overcome by step (10) in this invention are: solving the problem that it is difficult to balance the approximation of the target response spectrum and the preservation of the original ground motion characteristics during wavelet time history superposition and iterative correction, as well as the problem that repeated iterations can easily cause error accumulation, time history distortion and insufficient convergence.

[0017] Specifically, the technical solution of the present invention is as follows:

[0018] A near-fault ground motion simulation method considering soil layer site effects includes the following steps:

[0019] S1. Select ground motion data from near-fault sites and perform site seismic response calculation and analysis;

[0020] S2. Calculate the acceleration response spectrum amplification factor and perform regression analysis to obtain the acceleration spectrum amplification factor equation that takes into account the soil layer site amplification effect and near-fault ground motion characteristics;

[0021] S3. Based on the acceleration response spectrum amplification factor equation, a probabilistic seismic hazard analysis method for the site considering the soil layer site amplification factor and near-fault characteristics is established;

[0022] S4. Based on the analysis method in step S3, establish a surface earthquake hazard assessment method that considers the characteristics of near-fault sites;

[0023] S5. Determine the consistent hazard response spectrum of near-fault sites under different annual exceedance probabilities;

[0024] S6. Set the acceleration response spectrum obtained in step S5 as the target response spectrum, perform initial amplitude modulation on the initial recorded ground motions selected from the seismic database at each period point, and calculate the error ΔS between the target response spectrum and the target response spectrum.

[0025] S7. After setting the number of iterations and the matching error for the spectral matching process, a superimposed wavelet is introduced to perform spectral matching processing on the initial recorded ground motion in step S6;

[0026] S8. In the spectral matching process of step S7, the natural period of the target response spectrum is segmented and the C matrix is ​​solved. Then, the amplitude coefficient b of the wavelet is adjusted by combining the spectral error and the inverse of the C matrix.

[0027] S9. Obtain the superimposed acceleration time history δa(t), and then add it to the acceleration time history of the initial recorded ground motion;

[0028] S10. Repeat steps S6 to S9 for iteration. Stop the iteration when the number of iterations reaches the set value or the iteration matching error ε reaches the preset value. Use the acceleration time history generated after the iteration as the near-fault ground motion time history considering the soil layer site effect.

[0029] Preferably, the equation for the acceleration spectrum amplification factor in step S2 takes the following form:

[0030]

[0031] In the formula, c0, c1, and c2 are regression coefficients with different values; Sa r Let be the bedrock input level; AF be the amplification function; assuming that under a given bedrock input level, the amplification function AF follows a log-normal distribution, the following relationship exists:

[0032]

[0033] In the formula, z / x represents the soil amplification factor AF, defined as the ratio of the surface acceleration response spectrum to the bedrock acceleration response spectrum; μ lnAF|X Given a bedrock input strength x, σ is the logarithmic median of the soil layer amplification factor AF. lnAF|X Φ is its corresponding logarithmic standard deviation, used to characterize the uncertainty of the soil layer response; Φ represents the standard normal cumulative distribution function.

[0034] Preferably, the surface seismic hazard assessment method considering near-fault site characteristics in step S4 can be expressed by the following formula:

[0035]

[0036] In the formula, represents the annual occurrence rate of acceleration response spectra exceeding level z at the Earth's surface; j is the discrete point index used for discrete summation of acceleration response spectrum values ​​at the bedrock; #Sa r P[AF] represents the total number of discrete points in the acceleration response spectrum at the bedrock. P >(z / x j )|x j ] and P[AF NP >(z / x j )|x j [Sa] r =x j The amplification factor caused by near-fault pulse and non-pulse ground motion exceeds z / x j The probability of; and Sa caused by near-fault pulse and non-pulse ground motion, respectively r =x j The probability of occurrence in a given year.

[0037] Preferably, the initial amplitude modulation and initial error calculation of the initially recorded ground motion at each period point in step S6 can be expressed by the following formula:

[0038]

[0039]

[0040]

[0041] In the formula, N is the number of period points; S A (T i ) represents the earthquake record in period T i The acceleration response spectrum value under the following conditions; S T (T i ) represents the earthquake record in period T i Acceleration response spectrum values ​​under the following conditions; period T i Discretized on a logarithmic scale, S f The adjustment coefficient is a0(t), where a0(t) is the earthquake acceleration time history and a(t) is the initially adjusted earthquake acceleration time history; ΔS i S represents the spectral error at the i-th periodic point; Ti S' is the target spectrum at the i-th period point; Ai The reaction spectrum calculated at the i-th periodic point; P i The peak response polarity of a single-degree-of-freedom system.

[0042] Preferably, the wavelets superimposed in step S7 can be represented by the following formula:

[0043]

[0044] In the formula, t is the time variable; ω' j t is the angular frequency; j This represents the time at which a single-degree-of-freedom system reaches its maximum response at the j-th frequency in the earthquake record time history; The peak time of the wavelet function and t j The time difference between them; n is the cycle number of the trigonometric function; χ j The attenuation coefficient;

[0045] The natural period of the target response spectrum is then segmented and the C matrix is ​​solved using the following formula;

[0046]

[0047]

[0048] In the formula, c ij Represents wavelet sequence f j At time t i The response of a single-degree-of-freedom system; h i β is the impulse response function of a single-degree-of-freedom system. i ω is the damping ratio; i ω' is the undamped natural circular frequency; i It is the damped natural circular frequency.

[0049] Preferably, the amplitude coefficient b of the wavelet adjusted in step S8 is calculated by the following formula:

[0050]

[0051] In the formula, C -1 is the inverse of matrix C; ΔS is the error between the calculated reaction spectrum and the target spectrum.

[0052] Preferably, the superimposed acceleration time history δa(t) in step S9 is expressed by the following formula:

[0053]

[0054] In the formula, N is the number of discrete natural periods used in the response spectrum matching process; f j (t) represents the adjusted wavelet at the j-th frequency; b j The amplitude coefficients of the wavelet are adjusted at the j-th frequency.

[0055] Preferably, in step S4, based on the site probabilistic seismic hazard analysis method established in step S3, considering the disaster results caused by near-fault pulse and non-pulse earthquakes, the seismic disaster results of the near-fault site surface are calculated by summation, that is, the corresponding results of the annual exceedance probability at different period points and the acceleration response spectrum at the current period point. On this basis, step S5 is performed to determine the target response spectrum of near-fault ground motion considering soil layer site effects.

[0056] Preferably, the iterative matching error value ε in step S10 can be preset using the following formula:

[0057]

[0058] In the formula, N is the number of discrete natural periods used in the response spectrum matching process; S T (T i ) and S A (T i The target response spectrum and the calculated acceleration response spectrum are respectively.

[0059] Compared with the prior art, the beneficial effects of the present invention include:

[0060] 1. This invention establishes a calculation path from bedrock hazard to the target response spectrum on the surface by selecting near-fault measured records, calculating soil seismic response, regressing acceleration spectrum amplification coefficient, and analyzing site probabilistic seismic hazard. This achieves simultaneous consideration of near-fault pulse effect and soil nonlinear amplification effect, thereby obtaining a target response spectrum that can be used for seismic analysis of near-fault site structures. This makes up for the shortcomings of conventional design response spectra and existing near-fault fitting methods in not fully reflecting the characteristics of near-fault sites.

[0061] 2. This invention achieves high-precision approximation of the selected seismic record to the target response spectrum through initial amplitude modulation, segmented matching of the response spectrum, C-matrix solving, and iterative error control. Compared with existing methods that only fit a given empirical target spectrum, the ground motion generated by this invention has a direct correspondence with the near-fault site hazard analysis results, thus not only improving the spectral matching accuracy but also enhancing the applicability of the generated results to specific site conditions and exceedance probability levels.

[0062] 3. This invention achieves stable convergence in the spectral matching process by employing a control mechanism that combines superimposed wavelets satisfying constraints, local correction around the peak response time of a single degree of freedom, and the average relative error with the number of iterations. This effectively avoids zero drift in the velocity and displacement time histories after matching. Therefore, this invention eliminates the need for additional manual baseline correction processing to obtain near-fault ground motion samples that possess both target spectral consistency and temporal physical rationality. This provides more reasonable input ground motions for nonlinear time history analysis, seismic performance assessment, and earthquake hazard research of near-fault site structures. Attached Figure Description

[0063] Figure 1 This is a flowchart illustrating the method implementation of an embodiment of the present invention.

[0064] Figure 2 This is a schematic diagram of the geometric parameters of different types of faults in the near-fault site according to an embodiment of the present invention. Figure 2 (a) is a top view of the strike-slip fault. Figure 2 (b) is a cross-sectional view of a non-strike-slip fault.

[0065] Figure 3 The diagram shows fault and site parameters in a calculation example of this invention.

[0066] Figure 4 This is a consistent hazard response spectrum at a 50-year exceedance probability level of 10% in an embodiment of the present invention.

[0067] Figure 5 The graphs shown are the calculated reaction spectrum and the target reaction spectrum curves after 10 iterations with an average relative error of 1% in this embodiment of the invention.

[0068] Figure 6 This is a comparison of the acceleration time histories of the original earthquake and the matched earthquake in the example.

[0069] Figure 7 The following is a time history diagram of the acceleration, velocity, and displacement of the earthquake after matching in the example. Detailed Implementation

[0070] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be described in detail below. Obviously, the described embodiments are merely some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other implementation methods obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0071] Example 1

[0072] like Figure 1As shown, this embodiment provides a near-fault ground motion simulation method considering soil layer site effects, including the following steps:

[0073] Step S1: As Figure 1 As shown, the selection of near-fault site ground motions and the calculation of ground motion response were performed. Earthquake records for near-fault sites were selected from the NGA-West2 database of the Pacific Earthquake Engineering Research Center (PEER). The selected earthquake records were chosen to be as close as possible to the rock site. Baker's method was used to identify the pulse characteristics of the ground motion velocity-time histories. The selected ground motions were then used to calculate the site ground motion response, taking into account the changes in ground motion pulse characteristics caused by soil nonlinearity.

[0074] Step S2: As Figure 1 As shown, the amplification factor of the site acceleration response spectrum caused by near-fault ground motion is calculated and regression analysis is performed. The seismic hazard level of near-fault bedrock sites considering the effects of near-fault non-pulse and pulse motions can be expressed by equations (1) and (2), respectively:

[0075] (1)

[0076] (2)

[0077] In the formula, and These are the bedrock acceleration response spectra caused by pulsed and non-pulsed seismic events, respectively. Annual occurrence rate exceeding x; i is the index of potential source faults; #faults is the total number of faults considered; υ i The annual incidence of earthquakes caused by fault i; f i (m, r, z) is the probability density function for an i-fault earthquake event (m, r, z), where m is the magnitude, r is the distance from the site to the fault, and z represents the source-site geometric parameters. It is primarily used to predict the probability of pulse occurrence. P(Sa r-P >x|m, r, z) and P(Sa r-NP >x|m, r, z) are the bedrock acceleration response spectra for given pulsed and non-pulsed seismic events, respectively. r The probability of exceeding x can be derived from equations (3) and (4).

[0078] (3)

[0079] (4)

[0080] In the formula, P(pluse|m, r, z) is the probability that a pulse ground motion will occur at a given seismic event (m, r, z), and P(Sa r>x|m, r, z, pluse) represents the bedrock acceleration response spectrum caused by a pulsed seismic event. r The probability of exceeding x; P(Sa) r >x|m, r, z, no pluse) represents the bedrock acceleration response spectrum caused by a non-pulse seismic event. r The probability of exceeding x. Logistic regression fitting is performed using information from all sites in the NGA database to establish a function of site-fault geometry parameters (for strike-slip faults, this is the vertical distance r from the site to the rupture fault; along the fault strike, it is the distance between the epicenter and the site's vertical projection point on the fault line). The angle φ between the fault strike and the direction of the line connecting the epicenter and the site; for non-strike-slip faults, it is the distance d between the hypocenter and the point perpendicularly projected onto the fault line, and the angle θ between the fault strike and the direction of the line connecting the hypocenter and the site, such as... Figure 2 As shown. In the case of strike-slip earthquakes, only r and s are statistically significant predictors; while in the case of non-strike-slip earthquakes, , d, and θ are statistically significant.

[0081] The logistic regression results in the above process are shown in equations (5) and (6):

[0082] (5)

[0083] (6)

[0084] In the formula, r is the vertical distance from the site to the ruptured fault; s is the distance along the fault strike from the epicenter to the point on the fault line where the earthquake is projected vertically; d is the distance along the fault rupture surface from the hypocenter to the point on the rupture surface where the earthquake is projected vertically; θ is the angle between the line connecting the hypocenter and the site and the direction of fault rupture propagation. P(Sa r >x|m, r, z, pluse) and P(Sa r x|m, r, z, no pluse) can be calculated by the following formula:

[0085] (7)

[0086] (8)

[0087] In the formula, and These are the median and standard deviation of the logarithmic spectrum acceleration of bedrock pulse ground motion, given by the ground motion attenuation relationship. and The median and standard deviation of the logarithmic spectral acceleration of non-pulse ground motion in bedrock are given by the ground motion attenuation relationship; Φ represents the standard normal cumulative distribution function.

[0088] Step S3: As Figure 1 As shown, based on the near-fault ground motion response spectrum amplification coefficient equation using regression analysis, a probabilistic seismic hazard analysis method considering the influence of near-fault site characteristics is established. The seismic hazard level of near-fault bedrock sites considering pulse effects can be expressed as a linear superposition of pulsed and non-pulsed seismic events, which can be represented by equation (9):

[0089] (9)

[0090] Step S4: As Figure 1 As shown, based on step S3, the impact of the pulse effect and the soil layer amplification effect are further considered. The earthquake disaster considering the influence of the near-fault site characteristics can be represented by equation (10). According to this equation, the near-fault site consistent hazard acceleration response spectrum under different annual exceedance probabilities can be determined.

[0091] (10)

[0092] In the formula, represents the annual occurrence rate of acceleration response spectra exceeding level z at the Earth's surface; j is the discrete point index used for discrete summation of acceleration response spectrum values ​​at the bedrock; #Sa r P[AF] represents the total number of discrete points in the acceleration response spectrum at the bedrock. P >(z / x j )|x j ] and P[AF NP >(z / x j )|x j [Sa] r =x j The amplification factor caused by near-fault pulse and non-pulse ground motion exceeds (z / x) j The probability of ). and Sa caused by near-fault pulse and non-pulse ground motion, respectively r =x j The annual probability of occurrence can be calculated using equations (11) and (12) respectively, since the hazard curve is usually given in the form of discrete points.

[0093] (11)

[0094] (12)

[0095] In the above formula, and The surface magnification factor AF (surface acceleration response spectrum / bedrock acceleration response spectrum) established by numerical simulation is related to the bedrock input level Sa. rThe regression relationship is derived, and the regression equation for the amplification factor takes the following form:

[0096] (13)

[0097] In the formula, c0, c1, and c2 are regression coefficients with different values; Sa r Let be the bedrock input level; AF be the amplification function; it is assumed that under a given bedrock input level, the amplification function AF follows a log-normal distribution.

[0098] Finally, based on the Poisson distribution assumption, the surface seismic hazard level can be used as a metric. The probability that Sa(T) exceeds x at least once within the time interval t is obtained, i.e., the exceedance probability:

[0099] (14)

[0100] Where λ is the annual average exceedance rate of the acceleration response spectrum at the Earth's surface exceeding x; t is the time period considered.

[0101] For a given annual exceedance rate (or return period, 50-year exceedance probability), the relationship between the acceleration response spectrum values ​​for different periods and the period constitutes the consistent hazard response spectrum. To conduct a probabilistic hazard analysis of the site considering near-fault effects and soil nonlinearity, we assume an example of a 240km-long vertical strike-slip fault as the potential seismic source, with a vertical distance of 6km from the site to the fault. Figure 3 As shown. The fault is assumed to be a straight line, and the location of the ruptured fault and the location of the earthquake source are assumed to be uniformly distributed along the fault. The minimum and maximum possible magnitudes are taken as M. wmin =5.0, M wmax =8.0. Through the above process, the regression equations for the amplification coefficients of pulse and non-pulse events in equation (13) in this example can be expressed as follows:

[0102] (15)

[0103] (16)

[0104] Step S5: As Figure 1 As shown, the surface earthquake hazard calculation method in step S4 above can be used to obtain the consistent hazard response spectrum under different annual exceedance probability levels. Figure 4 The consistent hazard response spectrum of near-fault sites is given at a 50-year exceedance probability level of 10%.

[0105] Step S6: As Figure 1As shown, the response spectrum obtained in step S5 is used as the target response spectrum. First, the initial amplitude modulation is performed on the initial recorded ground motion selected from the earthquake database. The difference between the acceleration response spectrum of the earthquake record and the target response spectrum is reduced by equations (17) and (18). Then, the spectral error is calculated by equation (19). :

[0106] (17)

[0107] (18)

[0108] In the formula, N is the number of period points; S A (T i ) represents the earthquake record in period T i The acceleration response spectrum value under the following conditions; S T (T i ) represents the earthquake record in period T i Acceleration response spectrum values ​​under the following conditions; period T i Discretized on a logarithmic scale, S f The adjustment coefficient is a0(t), which is the earthquake acceleration time history, and a(t) is the earthquake acceleration time history after initial adjustment.

[0109] (19)

[0110] In the formula The spectral error at the i-th period point; The target spectrum at the i-th period point; The reaction spectrum calculated at the i-th periodic point; P i The peak response polarity of a single-degree-of-freedom system.

[0111] Step S7: As Figure 1 As shown, after setting the number of iterations and the matching error in the spectral matching process, the initial recorded ground motion in step S6 is subjected to spectral matching processing by superimposed wavelets. The superimposed wavelet can be represented by equation (20):

[0112] (20)

[0113] Where t is a time variable; t j This represents the time at which a single-degree-of-freedom system reaches its maximum response at the j-th frequency in the earthquake record time history; The peak time of the wavelet function and t j The time difference between them; n is the cycle number of the trigonometric function. Where the attenuation coefficient χ is... j The condition of equation (21) must be met:

[0114] (twenty one)

[0115] In step S7, the target response spectrum is segmented into natural period points during the spectrum matching process. The single-free system response of each period segment can be calculated by equations (22) and (23), and then the C matrix is ​​obtained.

[0116] (twenty two)

[0117] (twenty three)

[0118] In the formula c ij Represents wavelet sequence f j At time t i The response of a single-degree-of-freedom system; h i β is the impulse response function of a single-degree-of-freedom system. i ω is the damping ratio; i ω' is the undamped natural circular frequency; i It is the damped natural circular frequency.

[0119] Step S8: As Figure 1 As shown, the C matrix obtained in step S7 is inverted and combined with the spectral error. The amplitude coefficient b of the wavelet adjustment can be calculated and can be expressed by equation (24):

[0120] (twenty four)

[0121] Step S9: As Figure 1 As shown, the superimposed wavelet acceleration time history can be obtained through equation (25). Further superimposing this onto the recorded seismic acceleration time history yields the spectral-matched acceleration time history, which can be expressed by equation (26):

[0122] (25)

[0123] (26)

[0124] In the formula, b j δa(t) represents the amplitude coefficient of the adjusted wavelet at the j-th frequency; δa(t) represents the time history of the superimposed wavelet acceleration; a k (t) represents the acceleration time history of the k-th iteration; γ is the relaxation factor, which takes values ​​between 0 and 1.

[0125] Step S10: As Figure 1 As shown, in step S9, equation (26) requires an iterative process, which involves repeating steps (6) to (9). The iteration stops when the set number of iterations k or the spectral matching error ε is met, and the output result is the simulated near-fault canyon ground motion. The spectral matching error is given by equation (27):

[0126] (27)

[0127] The meanings of the symbols in the formula are consistent with those in formula (17).

[0128] Example 2

[0129] To verify the accuracy of the simulation method in Example 1, the analysis was conducted from aspects such as the matching error with the target response spectrum, the comparison of acceleration time history, and the absence of zero drift in velocity and displacement time history. First, a seismic data was selected from the seismic database as the seismic data analyzed in Example 2. The response spectrum obtained in step S5 was used as the target response spectrum. Then, the initial amplitude adjustment process was performed using formulas (17) to (19) in step S6 to initially reduce the error between the target response spectrum and the target response spectrum. Then, the number of iterations and the matching error of the spectrum matching process were set. First, it was determined whether the error requirement was met after the initial amplitude adjustment in step S6. If it was met, the result was directly output. If not, step S7 was performed. The initial amplitude adjustment result of the seismic record in Example 2 did not meet the error requirement, so step S7 was required. In step S7, the natural period of the target response spectrum was first divided into 8 segments. The natural period points were logarithmic values ​​between 0.01 and 4s, totaling 78 points. Then, the C matrix was solved sequentially from the long period to the short period. Then, step S8 was performed to solve the amplitude coefficient b of the wavelet adjustment. The superimposed wavelet time histories and the matched acceleration time histories are obtained using formulas (25) and (26) in step S9. Finally, the iterative process in step S10 is performed to meet the spectral matching error requirements. Integrating the acceleration time histories obtained in step S10 yields the corresponding velocity and displacement time histories. The results of the entire process are shown below. Figures 5-7 As shown.

[0130] Figure 5 The calculated reaction spectrum and the target reaction spectrum curves after 10 iterations are presented. It can be seen from the figure that the calculated reaction spectrum matches the target reaction spectrum well, with an average relative error of about 1%. Figure 6 The acceleration time histories of the original earthquake and the matched earthquake show obvious non-stationary characteristics. Figure 7 The simulation of near-fault ground motion acceleration, velocity, and displacement time histories shows that there is no zero drift in the time history curves, verifying the effectiveness of the near-fault ground motion simulation method of this invention.

Claims

1. A near-fault ground motion simulation method considering soil layer site effects, characterized in that, Includes the following steps: S1. Select ground motion data from near-fault sites and perform site seismic response calculation and analysis; S2. Calculate the acceleration response spectrum amplification factor and perform regression analysis to obtain the acceleration spectrum amplification factor equation that takes into account the soil layer site amplification effect and near-fault ground motion characteristics; S3. Based on the acceleration response spectrum amplification factor equation, a probabilistic seismic hazard analysis method for the site considering the soil layer site amplification factor and near-fault characteristics is established; S4. Based on the analysis method in step S3, establish a surface earthquake hazard assessment method that considers the characteristics of near-fault sites; S5. Determine the consistent hazard response spectrum of near-fault sites under different annual exceedance probabilities; S6. Set the acceleration response spectrum obtained in step S5 as the target response spectrum, perform initial amplitude modulation on the initial recorded ground motions selected from the seismic database at each period point, and calculate the error ΔS between the target response spectrum and the target response spectrum. S7. After setting the number of iterations and the matching error for the spectral matching process, a superimposed wavelet is introduced to perform spectral matching processing on the initial recorded ground motion in step S6; S8. In the spectral matching process of step S7, the natural period of the target response spectrum is segmented and the C matrix is ​​solved. Then, the amplitude coefficient b of the wavelet is adjusted by combining the spectral error and the inverse of the C matrix. S9. Obtain the superimposed acceleration time history δa(t), and then add it to the acceleration time history of the initial recorded ground motion; S10. Repeat steps S6 to S9 for iteration. Stop the iteration when the number of iterations reaches the set value or the iteration matching error ε reaches the preset value. Use the acceleration time history generated after the iteration as the near-fault ground motion time history considering the soil layer site effect.

2. The near-fault ground motion simulation method considering soil layer site effects according to claim 1, characterized in that, The equation for the acceleration spectrum amplification factor in step S2 takes the following form: In the formula, c0, c1, c2 are regression coefficients with different values; Sa r is the bedrock input level; AF is an amplification function; it is assumed that the amplification function AF obeys a lognormal distribution under a given bedrock input level, and there is a relationship of the following formula: Where z / x represents the soil amplification factor AF, defined as the ratio of the surface acceleration response spectrum to the bedrock acceleration response spectrum; μ lnAF|X Given a bedrock input strength x, σ is the logarithmic median of the soil layer amplification factor AF. lnAF|X Φ is its corresponding logarithmic standard deviation, used to characterize the uncertainty of the soil layer response; Φ represents the standard normal cumulative distribution function.

3. The near-fault ground motion simulation method considering soil layer site effects according to claim 1, characterized in that, The surface seismic hazard assessment method considering near-fault site characteristics in step S4 can be expressed by the following formula: In the formula, is the annual occurrence rate of acceleration response spectra at the surface exceeding level z; j is the discrete point index, used for discrete summation of acceleration response spectrum values ​​at bedrock; x j #Sa represents the j-th discrete value of the acceleration response spectrum at the bedrock. r The total number of discrete points in the acceleration response spectrum at the bedrock; z / x j The soil amplification factor (AF) is defined as the sum of the surface acceleration response spectrum z and the bedrock acceleration response spectrum value x. j The ratio of; P[AF] P >(z / x j )|x j ] and P[AF NP >(z / x j )|x j [Sa] r =x j The amplification factor caused by near-fault pulse and non-pulse ground motion exceeds z / x j The probability of; and Sa caused by near-fault pulse and non-pulse ground motion, respectively r =x j The probability of occurrence in a given year.

4. The near-fault ground motion simulation method considering soil layer site effects according to claim 1, characterized in that, In step S6, the initial recorded ground motion is initially amplitude-modulated at each period point, and the initial error is calculated. This can be expressed by the following formula: In the formula, N is the number of period points; S A (T i ) represents the earthquake record in period T i The acceleration response spectrum value under the given conditions; S T (T i ) represents the earthquake record in period T i The acceleration response spectrum value under the given conditions; Period T i Discretized on a logarithmic scale, S f The adjustment coefficient is a0(t), where a0(t) is the earthquake acceleration time history and a(t) is the initially adjusted earthquake acceleration time history; ΔS i S represents the spectral error at the i-th periodic point; Ti S' is the target spectrum at the i-th period point; Ai The reaction spectrum calculated at the i-th periodic point; P i The peak response polarity of a single-degree-of-freedom system.

5. The near-fault ground motion simulation method considering soil layer site effects according to claim 1, characterized in that, The superimposed wavelets in step S7 can be represented by the following formula: In the formula, t is the time variable; ω' j t is the angular frequency; j This represents the time at which a single-degree-of-freedom system reaches its maximum response at the j-th frequency in the earthquake record time history; The peak time of the wavelet function and t j The time difference between them; n is the cycle number of the trigonometric function; χ j The attenuation coefficient; The natural period of the target response spectrum is then segmented and the C matrix is ​​solved using the following formula; In the formula, c ij Represents wavelet sequence f j At time t i The response of a single-degree-of-freedom system; h i β is the impulse response function of a single-degree-of-freedom system. i ω is the damping ratio; i ω' is the undamped natural circular frequency; i It is the damped natural circular frequency.

6. The near-fault ground motion simulation method considering soil layer site effects according to claim 1, characterized in that, In step S8, the amplitude coefficient b of the wavelet is calculated using the following formula: In the formula, C -1 is the inverse of matrix C; ΔS is the error between the calculated reaction spectrum and the target spectrum.

7. The near-fault ground motion simulation method considering soil layer site effects according to claim 1, characterized in that, In step S9, the superimposed acceleration time history δa(t) is expressed by the following formula: Where N is the number of discrete natural periods used in the response spectrum matching process; f j (t) represents the adjusted wavelet at the j-th frequency; b j The amplitude coefficients of the wavelet are adjusted at the j-th frequency.

8. The near-fault ground motion simulation method considering soil layer site effects according to claim 1, characterized in that, In step S4, based on the site probabilistic seismic hazard analysis method established in step S3, considering the disaster results caused by near-fault pulse and non-pulse earthquakes, the seismic disaster results of the near-fault site surface are calculated by summation, that is, the corresponding results of the annual exceedance probability at different period points and the acceleration response spectrum at the current period point. On this basis, step S5 is carried out to determine the target response spectrum of near-fault ground motion considering soil layer site effects.

9. The near-fault ground motion simulation method considering soil layer site effects according to claim 1, characterized in that, The iterative matching error value ε in step S10 can be preset using the following formula: In the formula, N is the number of discrete natural periods used in the response spectrum matching process; S T (T i ) and S A (T i The target response spectrum and the calculated acceleration response spectrum are respectively.

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