A method for synthesizing near-source ground motions with permanent displacement based on an equivalent pulse model

Abstract

The present invention discloses a method for synthesizing near-source seismic motions containing permanent displacements based on an equivalent pulse model. The present invention utilizes the permanent displacement characteristics of the equivalent pulse model, combined with formulas between different magnitudes and fault dislocations, to obtain the permanent displacement time history of the low-frequency part of seismic motions under different magnitude conditions. Finally, based on the near-source seismic motion characteristics, near-source seismic motions that can characterize the permanent displacements under different magnitude conditions are synthesized; the seismic motions obtained by the synthesis method of the present invention can not only meet the seismic motion attenuation characteristics and acceleration peak requirements of the engineering site area, but can also simultaneously reflect the permanent displacement and near-field strong vibrations caused by fault dislocation; the seismic motions obtained by the synthesis method of the present invention can adjust the seismic motion duration, thereby saving time and cost for subsequent related calculations and analysis.

Description

Technical Field

[0001] The present invention belongs to the technical field of earthquake engineering, and in particular relates to a method for synthesizing near-source earthquake motions containing permanent displacements based on an equivalent pulse model, which is suitable for synthesizing near-source earthquakes containing permanent displacements. Background Art

[0002] As major national strategic projects advance into the high-seismic and tectonic zones of western China, many projects inevitably cross active fault zones. Stick-slip faulting on active faults often triggers strong earthquakes, exposing these projects to the threat of severe near-source seismic motions, a synergistic effect of large co-seismic deformations from faulting and strong near-field motion. To ensure the seismic safety of these projects, designers must design them for seismic safety using earthquake inputs that meet site characteristics and simultaneously reflect both permanent displacements caused by faulting and strong near-field motion. However, due to limited measured ground motion data, finding ground motions that simultaneously meet these objectives is difficult. Therefore, it is necessary to develop methods for synthesizing near-source ground motions to meet the needs of engineering applications. Summary of the Invention

[0003] The purpose of the present invention is to address the above-mentioned problems existing in the prior art and to provide a method for synthesizing near-source ground motions containing permanent displacements based on an equivalent pulse model.

[0004] The above-mentioned purpose of the present invention is achieved by the following technical means:

[0005] A method for synthesizing near-source ground motions including permanent displacement based on an equivalent pulse model comprises the following steps:

[0006] Step S1: Set the fault distance d r , fault type, and magnitude M n , construct different magnitudes M n Velocity pulse model under conditions v n (t), and the acceleration time history a is obtained by differentiation and integration. n (t) and displacement time d n (t);

[0007] Step S2: According to the set magnitude M n Calculate the corresponding fault displacement D n The displacement time d in step S1 is calculated based on the displacement at the end point. n (t) AM to D n , get the displacement time history after amplitude modulation And according to the displacement time history after amplitude modulation Get the acceleration time history after amplitude modulation Then according to the acceleration time history after amplitude modulation Get the peak acceleration after amplitude modulation

[0008] Step S3: Calculate the target acceleration response spectrum based on the acceleration response spectrum of the seismic design;

[0009] Step S4: Generate the initial earthquake acceleration time history A0(t) according to the target acceleration response spectrum, then set the filtering range, perform baseline calibration and filtering on the initial earthquake acceleration time history A0(t), and generate the earthquake time history A′ containing only the high-frequency part of the initial earthquake. n (t);

[0010] Step S5: Calculate the acceleration peak value PGA after earthquake attenuation according to the earthquake attenuation formula n , and subtract the peak acceleration after amplitude modulation in step S2 Get the peak acceleration of the earthquake vibration containing only the high-frequency part

[0011] Step S6: The target peak pair A′ n (t) Perform amplitude modulation to convert the initial earthquake motion of step S4 into the earthquake motion time history A′ containing only the high-frequency part n (t) is amplitude modulated to obtain the earthquake time history containing only the high-frequency part

[0012] Step S7: The acceleration time after amplitude modulation in step S2 is and the earthquake time history containing only the high frequency part in step S6 Perform translation and superposition to obtain the near-source ground motion time history A n (t).

[0013] As mentioned above, the velocity pulse model v(t) in step 1 is based on the following formula:

[0014]

[0015] lnT p =a1+a2M n

[0016] ln p =b1M n +b2d r +b3

[0017] Where V p is the peak value of the pulse velocity, T p is the pulse period, ω p is the pulse frequency, ω p =2π / T p, t0 is the velocity pulse start time, Ratio is the pulse velocity peak ratio, a1, a2, b1, b2, and b3 are the regression coefficients to be calibrated.

[0018] In step S2, different magnitudes M are calculated based on the following formula: n The corresponding fault displacement D n :

[0019] M n =c1+c2 ln D n

[0020] Where ln is the natural logarithm function, c1 and c2 are regression coefficients.

[0021] In step S2, the amplitude modulation is performed in the following manner to obtain the displacement time course after amplitude modulation: and acceleration time history D n Divide by d n (t) is shifted at the end point to obtain the first amplitude modulation scaling factor, and then d n (t) is multiplied by the first amplitude modulation scaling factor to obtain the displacement time after amplitude modulation. Then, by converting the displacement time The acceleration time history is obtained by the second-order differential

[0022] The earthquake attenuation formula in step S5 is as follows:

[0023]

[0024] Where A, B, C, D, and E are the fitting constants of the earthquake attenuation formula.

[0025] As mentioned above, in step S7, the near-source ground motion time history A n The peak acceleration of (t) is equal to PGA n .

[0026] As described above, constant baseline calibration and Butterworth function filtering are used in step S4.

[0027] As mentioned above, the filtering range in step S4 is [0, 1 / T p ].

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] (1) The present invention utilizes the permanent displacement characteristics of the equivalent pulse model, combined with different magnitudes and fault dislocation formulas, to obtain the permanent displacement time history of the low-frequency part of the ground motion under different magnitude conditions. Finally, based on the characteristics of the near-source ground motion, the near-source ground motion that can characterize the permanent displacement under different magnitude conditions is synthesized;

[0030] (2) The seismic motion obtained by the synthesis method of the present invention can not only meet the seismic motion attenuation characteristics and acceleration peak requirements of the engineering site, but also simultaneously reflect the permanent displacement caused by the fault and the strong vibration in the near field;

[0031] (3) The seismic motion obtained by the synthesis method of the present invention can adjust the seismic motion duration, thereby saving time and cost for subsequent related calculation and analysis;

[0032] (4) The synthesis method of the present invention has a simple process, wide applicability, low professional level requirements for users, and can effectively improve research efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 is a flow chart of the method of the present invention;

[0034] FIG2( a ) is a graph showing the acceleration time history of near-source ground motion with permanent displacement under a magnitude 6.5 earthquake synthesized in Example 2 of the present invention;

[0035] FIG2( b ) is a velocity time history graph of a near-source ground motion with permanent displacement under the conditions of a magnitude 6.5 earthquake synthesized in Example 2 of the present invention (where Dis, Vel, Acc, and Time are displacement, velocity, acceleration, and time, respectively);

[0036] FIG2( c ) is a displacement time history curve of near-source ground motion including permanent displacement under the conditions of a magnitude 6.5 earthquake synthesized in Example 2 of the present invention;

[0037] FIG3( a ) is a graph showing the acceleration time history of near-source ground motion with permanent displacement under a magnitude 7.0 earthquake synthesized in Example 2 of the present invention;

[0038] FIG3( b ) is a velocity time history graph of near-source ground motion including permanent displacement under the conditions of a magnitude 7.0 earthquake synthesized in Example 2 of the present invention;

[0039] FIG3( c ) is a displacement time history curve of the near-source ground motion including permanent displacement under the conditions of a magnitude 7.0 earthquake synthesized in Example 2 of the present invention;

[0040] FIG4( a ) is a graph showing the acceleration time history of near-source ground motion with permanent displacement under the conditions of a magnitude 7.5 earthquake synthesized in Example 2 of the present invention;

[0041] FIG4( b ) is a velocity time history graph of the near-source ground motion including permanent displacement under the conditions of a magnitude 7.5 earthquake synthesized in Example 2 of the present invention;

[0042] FIG4( c ) is a displacement time history curve of the near-source ground motion including permanent displacement under the conditions of a magnitude 7.5 earthquake synthesized in Example 2 of the present invention;

[0043] FIG5( a ) is a graph showing the acceleration time history of near-source ground motion with permanent displacement under the conditions of a magnitude 8.0 earthquake synthesized in Example 2 of the present invention;

[0044] FIG5( b ) is a velocity time history graph of the near-source ground motion including permanent displacement under the conditions of a magnitude 8.0 earthquake synthesized in Example 2 of the present invention;

[0045] FIG5( c ) is a displacement time history curve of the near-source ground motion including permanent displacement under the conditions of a magnitude 8.0 earthquake synthesized in Example 2 of the present invention;

[0046] FIG6( a ) is a graph showing the acceleration time history of near-source ground motion with permanent displacement under the conditions of a magnitude 8.5 earthquake synthesized in Example 2 of the present invention;

[0047] FIG6( b ) is a velocity time history graph of the near-source ground motion including permanent displacement under the conditions of a magnitude 8.5 earthquake synthesized in Example 2 of the present invention;

[0048] FIG6( c ) is a displacement time history curve of the near-source ground motion including permanent displacement under the conditions of a magnitude 8.5 earthquake synthesized in Example 2 of the present invention. DETAILED DESCRIPTION

[0049] In order to facilitate those skilled in the art to understand and implement the present invention, the present invention is further described in detail below with reference to the embodiments. The embodiments described herein are only used to illustrate and explain the present invention and are not intended to limit the present invention.

[0050] Example 1:

[0051] A method for synthesizing near-source ground motions including permanent displacement based on an equivalent pulse model comprises the following steps:

[0052] Step S1: Set the fault distance d r , fault type, and magnitude M n , Based on the equivalent pulse model and its attenuation formula, construct different magnitude M n Velocity pulse model under conditions v n (t), and obtain the corresponding acceleration time history a by differentiation and integration respectively n (t) and displacement time d n (t);

[0053] Velocity Pulse Model vn (t) include:

[0054]

[0055] V p =max(|V p1 |,|V p2 |) (2)

[0056] Ratio=min(|V p1 / V p |,|V p2 / V p |) (3)

[0057] ln T p =a1+a2M n (4)

[0058] ln p =b1M n +b2d r +b3 (5)

[0059] Where, d r is the fault distance, V p is the peak value of the pulse velocity, T p is the pulse period, ω p is the pulse frequency, ω p =2π / T p , t0 is the speed pulse start time, V p1 and V p2 are the maximum positive velocity and minimum negative velocity peak values ​​of seismic motion respectively; Ratio is the pulse velocity peak ratio, and its value is the larger value of the ratio of the maximum positive velocity peak to the pulse velocity peak and the ratio of the minimum negative velocity peak to the pulse velocity peak. In this embodiment, it is taken as a constant of 0.1; a1, a2, b1, b2, and b3 are regression coefficients related to the seismic fault, which can be calibrated according to Tables 1 and 2, and · is the multiplication sign. Table 1 is a lookup table of the regression coefficient a1, regression coefficient a2 and variance σ of the same fault type; Table 2 is a lookup table of the regression coefficient b1, regression coefficient b2, regression coefficient b3 and variance σ of different fault types.

[0060] Table 1

[0061]

[0062] Table 2

[0063]

[0064] Step S2: According to the set magnitude M n Calculate different magnitudes M nThe corresponding fault displacement D n The displacement time d in step S1 is calculated based on the displacement at the end point. n (t) AM to D n , get the displacement time history after amplitude modulation (i.e. the displacement time history of the low-frequency part), and according to the displacement time history after amplitude modulation Get the acceleration time history after amplitude modulation Then according to the acceleration time history after amplitude modulation Get the peak acceleration after amplitude modulation

[0065] The displacement time history after amplitude modulation is obtained by the following method and acceleration time history D n Divide by d n (t) is shifted at the end point to obtain the first amplitude modulation scaling factor, and then d n (t) is multiplied by the first amplitude modulation scaling factor to obtain the displacement time after amplitude modulation. Then, by converting the displacement time The acceleration time history is obtained by the second-order differential

[0066] The formula between earthquake magnitude M and fault dislocation D is:

[0067] M n =c1+c2 ln D n Formula (6)

[0068] Among them, ln is the natural logarithm function, c1 and c2 are regression coefficients, which can be taken as 7.13 and 0.68 respectively.

[0069] Step S3: Obtain earthquake parameters based on the project site area. The earthquake parameters based on the project site area include the site acceleration response spectrum characteristic period T g , maximum power coefficient β max , maximum value of horizontal earthquake influence coefficient α max , damping adjustment coefficient n, earthquake acceleration peak a max , and the attenuation coefficient γ, the target acceleration response spectrum is calculated according to the acceleration response spectrum formula of seismic design;

[0070] Step S4: Generate the initial earthquake acceleration time history A0(t) by artificial earthquake simulation software (SeismoArtif) according to the target acceleration response spectrum, then set the filtering range, and perform baseline calibration and filtering (constant baseline calibration and Butterworth function filtering can be used respectively) on the initial earthquake acceleration time history A0(t) by seismic wave processing software (SeismoSignal) to generate different magnitude M n The initial ground motion contains only the high-frequency part of the ground motion time history A′ under the condition n (t), where the filtering range can be set to [0, 1 / T p ].

[0071] Step S5: Calculate the earthquake magnitudes M according to the earthquake attenuation formula of the project site. n Peak acceleration PGA after attenuation of ground motion under conditions n , and subtract the peak acceleration after amplitude modulation in step S2 Get different magnitudes M n The peak acceleration of the earthquake with only high frequency under the condition

[0072] The formula for earthquake motion attenuation is:

[0073]

[0074] Among them, A, B, C, D, and E are fitting constants of the earthquake attenuation formula, and A, B, C, D, and E can be 2.457, 0.388, -1.854, 0.612, and 0.457 respectively. The attenuation formula of this embodiment is only applicable to earthquakes of magnitude M n ≥6.5.

[0075] Step S6: The target peak pair A′ n (t) Perform amplitude modulation to adjust the magnitudes M of step S4. n The initial ground motion under the condition contains only the high-frequency part of the ground motion time history A′ n (t) is modulated to obtain different magnitudes M n The time history of the earthquake motion containing only the high-frequency part under the condition

[0076] Step S7: The different magnitudes M in step S2 are n Acceleration time history after amplitude modulation under the conditions and the different magnitude M of step S6 n The time history of the earthquake motion containing only the high-frequency part under the condition Shift and superposition are performed to obtain different magnitudes M n Time history of near-source ground motion under the condition An (t), the superimposed near-source ground motion time history A n The peak acceleration of (t) is equal to PGA n .

[0077] Example 2:

[0078] A tunnel project near a fault in western China has a potential epicenter distance of 10 km. The adjacent fault is a strike-slip fault. The peak seismic acceleration at the project site, with a 100-year probability of exceeding 2%, is 0.495 g, where g is the acceleration due to gravity. In this example, the magnitudes are set to 6.5, 7.0, 7.5, 8.0, and 8.5, respectively.

[0079] Execute step S1 in Example 1: Based on the equivalent pulse model and its attenuation formula, combined with the regional geological parameters of the project site, construct different magnitude M n Velocity pulse model under conditions v n (t), and obtain the corresponding acceleration time history a by differentiation and integration respectively n (t) and displacement time d n (t), pulse period T under different magnitude conditions p They are 2.36s, 3.96s, 6.68s, 11.24s, and 18.90s respectively;

[0080] Execute step S2 in Example 1: Calculate the fault displacements corresponding to the magnitudes M as 0.396m, 0.826m, 1.723m, 3.595m and 7.499m respectively, and use the displacement at the end time as the basis to calculate the displacement time history d. n (t) is modulated to the above fault displacement value to obtain the displacement time history after amplitude modulation and acceleration time history

[0081] Execute step S3 in embodiment 1: Based on the regional earthquake parameters of the engineering site, the site acceleration response spectrum characteristic period T g , the maximum value of the dynamic coefficient β max , the maximum value of horizontal earthquake influence coefficient α max , damping adjustment coefficient n, earthquake acceleration peak a max , attenuation coefficient γ, according to the seismic design acceleration response spectrum formula to obtain the target acceleration response spectrum;

[0082] Execute step S4 in Example 1: generate the initial earthquake acceleration time history A0(t) according to the target acceleration response spectrum, and perform baseline calibration and filtering using a constant baseline calibration and Butterworth function to generate different magnitudes M nThe time history A′ of the initial ground motion containing only the high-frequency part under the condition n (t), where the filtering range is [0, 1 / T p ].

[0083] Execute step S5 in embodiment 1: calculate different magnitudes M according to the earthquake attenuation relationship n The acceleration peaks after attenuation of the earthquake motion under these conditions are 0.311g, 0.381g, 0.457g, 0.536g and 0.616g, respectively. The acceleration peaks after amplitude modulation are subtracted to obtain the acceleration peaks of different magnitudes M. n The peak accelerations of the earthquake motions containing only high-frequency parts under the above conditions are 0.150g, 0.257g, 0.361g, 0.462g and 0.559g respectively.

[0084] Execute step S6 in embodiment 1: Based on the obtained acceleration peak value of the earthquake motion containing only the high-frequency part, convert the earthquake motion time history A′ into n (t) is modulated to obtain different magnitudes M n The time history of the earthquake motion containing only the high-frequency part under the condition

[0085] Execute step S7 in embodiment 1: convert the earthquake acceleration time history and the earthquake time history containing only the high-frequency part Shift and superposition are performed to obtain different magnitudes M n Time history of near-source ground motion under the condition A n (t).

[0086] It should be noted that the embodiments described herein are merely illustrative of the spirit of the present invention. Persons skilled in the art may make various modifications, additions, or substitutions to the described embodiments without departing from the spirit of the present invention or exceeding the scope of the appended claims.

Claims

1. A method for synthesizing near-source ground motions with permanent displacement based on an equivalent pulse model, characterized in that: The following steps are involved: Step S1: Set the fault distance d r , fault type, and magnitude M n , construct different magnitudes M n Velocity pulse model under conditions v n (t), and the acceleration time history a is obtained by differentiation and integration. n (t) and displacement time d n (t); Step S2: According to the set magnitude M n Calculate the corresponding fault displacement D n The displacement time d in step S1 is calculated based on the displacement at the end point. n (t) AM to D n , get the displacement time history after amplitude modulation And according to the displacement time history after amplitude modulation Get the acceleration time history after amplitude modulation Then according to the acceleration time history after amplitude modulation Get the peak acceleration after amplitude modulation Step S3: Calculate the target acceleration response spectrum based on the acceleration response spectrum of the seismic design; Step S4: Generate the initial earthquake acceleration time history A0(t) according to the target acceleration response spectrum, then set the filtering range, perform baseline calibration and filtering on the initial earthquake acceleration time history A0(t), and generate the earthquake time history A′ containing only the high-frequency part of the initial earthquake. n (t); Step S5: Calculate the acceleration peak value PGA after earthquake attenuation according to the earthquake attenuation formula n , and subtract the peak acceleration after amplitude modulation in step S2 Get the peak acceleration of the earthquake vibration containing only the high-frequency part Step S6: The target peak pair A′ n (t) Perform amplitude modulation to convert the initial earthquake motion of step S4 into the earthquake motion time history A′ containing only the high-frequency part n (t) is amplitude modulated to obtain the earthquake time history containing only the high-frequency part Step S7: The acceleration time after amplitude modulation in step S2 is and the earthquake time history containing only the high frequency part in step S6 Perform translation and superposition to obtain the near-source ground motion time history A n (t).

2. The method for synthesizing near-source ground motions including permanent displacements based on an equivalent pulse model according to claim 1, characterized in that: The velocity pulse model v(t) in step 1 is based on the following formula: ln T p =a1+a2M n ln V p =b1M n +b2d r +b3 Where V p is the peak value of the pulse velocity, T p is the pulse period, ω p is the pulse frequency, ω p =2π / T p , t0 is the velocity pulse start time, Ratio is the pulse velocity peak ratio, a1, a2, b1, b2, and b3 are the regression coefficients to be calibrated.

3. The method for synthesizing near-source ground motions including permanent displacements based on an equivalent pulse model according to claim 2, characterized in that: In step S2, different magnitudes M are calculated based on the following formula n The corresponding fault displacement D n : M n =c1+c2ln D n Where ln is the natural logarithm function, c1 and c2 are regression coefficients.

4. The method for synthesizing near-source ground motions including permanent displacements based on an equivalent pulse model according to claim 3 is characterized in that: In step S2, the amplitude modulation is performed in the following manner to obtain the displacement time course after amplitude modulation. and acceleration time history D n Divide by d n (t) is shifted at the end point to obtain the first amplitude modulation scaling factor, and then d n (t) is multiplied by the first amplitude modulation scaling factor to obtain the displacement time after amplitude modulation. Then, by converting the displacement time The acceleration time history is obtained by the second-order differential 5. The method for synthesizing near-source ground motions including permanent displacements based on an equivalent pulse model according to claim 4, characterized in that: The earthquake attenuation formula in step S5 is: Where A, B, C, D, and E are the fitting constants of the earthquake attenuation formula.

6. The method for synthesizing near-source ground motion including permanent displacement based on an equivalent pulse model according to claim 5, characterized in that: In step S7, the near-source ground shaking time history A n The peak acceleration of (t) is equal to PGA n .

7. The method for synthesizing near-source ground motions including permanent displacements based on an equivalent pulse model according to claim 6, characterized in that: In step S4, constant baseline calibration and Butterworth function are used for filtering.

8. The method for synthesizing near-source ground motion including permanent displacement based on an equivalent pulse model according to claim 7, characterized in that: The filtering range in step S4 is [0, 1 / T p ].

Images