Permanent displacement-containing near-source seismic motion synthesis method based on equivalent pulse model

Abstract

The invention discloses a permanent displacement-containing near-source seismic oscillation synthesis method based on an equivalent pulse model, and the method comprises the steps: obtaining a permanent displacement time history of a seismic oscillation low-frequency part under different earthquake magnitude conditions through employing the permanent displacement characteristics of the equivalent pulse model and combining with a formula between different earthquake magnitudes and fault displacement amounts; and finally, according to near-source seismic oscillation characteristics, synthesizing near-source seismic oscillation capable of representing permanent displacement under different seismic magnitude conditions. The seismic oscillation obtained through the synthesis method can meet the requirements for the seismic oscillation attenuation characteristic and the acceleration peak value of an engineering site area, and can also reflect permanent displacement and near-field strong vibration caused by fracture and dislocation at the same time; according to the seismic oscillation obtained by the synthesis method, the seismic oscillation duration can be adjusted, so that time and cost are saved for subsequent related calculation and analysis.

Description

Technical Field

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

[0002] As the construction of major national strategic projects advances towards the strong earthquake and tectonic areas in the west, a large number of projects cannot avoid crossing active fault zones. When active faults slip and break, they often induce strong earthquakes, which causes these projects to face the threat of disasters caused by the synergistic effects of severe co-seismic large deformation of fault break and strong near-field vibrations. In order to ensure the seismic safety of these projects, designers need to conduct seismic safety design of related projects through earthquake inputs that can simultaneously reflect the permanent displacement caused by fault break and strong near-field vibrations that meet the site characteristics. However, due to the limited measured seismic motion data, it is difficult to find measured seismic motions that meet the above goals at the same time. Therefore, it is necessary to develop corresponding near-source seismic motion artificial synthesis methods to meet the needs of engineering applications. Summary of the invention

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

[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 containing permanent displacements based on an equivalent pulse model comprises the following steps:

[0006] Step S1, setting 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 The corresponding fault displacement D is calculated n The displacement time d in step S1 is calculated based on the displacement at the end point. n (t) Amplitude modulate to D n , and the displacement time history after amplitude modulation is obtained 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, calculating the target acceleration response spectrum according to the acceleration response spectrum of the seismic design;

[0009] Step S4: Generate the initial seismic 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 seismic acceleration time history A0(t), and generate the initial seismic time history A′ containing only the high-frequency part. n (t);

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

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

[0012] Step S7: The acceleration time course after amplitude modulation in step S2 is and the earthquake time history containing only the high frequency part in step S6 By translation and superposition, we can 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] oeLh p =a1+a2M n

[0016] l V p =b1M n +b2d r +b3

[0017] Where V p is the peak value of 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 as described above, 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 as described above, 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 course after amplitude modulation. Then, by converting the displacement time The second-order differential gives the acceleration time history

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

[0023]

[0024] Where A, B, C, D, and E are all fitting constants of the earthquake motion 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 uses 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, according to 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 requirements of the seismic motion attenuation characteristics and acceleration peak value of the engineering site, but also simultaneously reflect the permanent displacement and near-field strong vibration caused by the fault dislocation;

[0031] (3) The seismic motion obtained by the synthesis method of the present invention can adjust the duration of the seismic motion, 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 requirements on the professional level of the 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 condition synthesized in Example 2 of the present invention;

[0035] FIG2( b ) is a velocity time history curve of a near-source ground motion containing permanent displacement under a magnitude 6.5 earthquake condition 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 containing permanent displacement under the conditions of a magnitude 6.5 earthquake synthesized in Example 2 of the present invention;

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

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

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

[0041] FIG4( b ) is a velocity time history curve of near-source ground motion containing 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 near-source ground motion containing 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 condition of a magnitude 8.0 earthquake synthesized in Example 2 of the present invention;

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

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

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

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

[0048] FIG6( c ) is a displacement time history curve of near-source ground motion containing 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 in conjunction with 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] Embodiment 1:

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

[0052] Step S1, setting 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] Speed ​​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] l T p =a1+a2M n (4)

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

[0059] Where, d r is the fault distance, V p is the peak value of 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, a constant of 0.1 is taken; a1, a2, b1, b2, and b3 are regression coefficients related to the seismic fault, which can be calibrated according to Table 1 and Table 2, · 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) Amplitude modulate to D n , and the displacement time history after amplitude modulation is obtained (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 course after amplitude modulation. Then, by converting the displacement time The second-order differential gives the acceleration time history

[0066] The formula between 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 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 seismic acceleration time history A0(t) by using the 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 seismic acceleration time history A0(t) by using the seismic wave processing software (SeismoSignal) to generate different magnitudes M n The initial ground motion under the condition contains only the high-frequency part of the ground motion time history A′ 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 The peak acceleration PGA after the attenuation of the ground motion under the condition n , and subtract the peak value of the 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 earthquake motion attenuation formula is:

[0073]

[0074] Among them, A, B, C, D, and E are all 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 with magnitude M n ≥6.5.

[0075] Step S6: A′ is the target peak pair n (t) Amplitude modulation is performed to adjust the magnitudes M of the different magnitudes in step S4. n The initial ground motion under the condition only contains 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 with only 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 condition and the different magnitude M of step S6 n The time history of the earthquake with only high frequency part under the condition After translation and superposition, we can finally obtain earthquakes of different magnitudes M n The time history of the 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] Embodiment 2:

[0078] The potential epicenter distance of a near-fault tunnel project in the western region is 10 km, and the adjacent fault is a strike-slip fault. The peak value of the seismic acceleration with a probability of exceeding 2% in 100 years in the project site area is 0.495g, where g is the gravitational acceleration. In this embodiment, 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 magnitudes 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 calculate the displacement time series d based on the displacement at the end point. 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 project site, including: 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, and the target acceleration response spectrum is obtained according to the acceleration response spectrum formula of seismic design;

[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 on the initial earthquake by using constant baseline calibration and Butterworth function to generate earthquakes of 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 peak accelerations after attenuation of the earthquake motion under the above conditions are 0.311g, 0.381g, 0.457g, 0.536g and 0.616g, respectively. The peak accelerations after amplitude modulation are subtracted to obtain the accelerations of different magnitudes M. n The peak accelerations of the earthquake vibrations containing only the high-frequency part 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 with only 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 After translation and superposition, we can finally obtain earthquakes of different magnitudes M n The time history of the near-source ground motion under the condition A n (t).

[0086] It should be noted that the embodiments described in the present invention are merely examples of the spirit of the present invention. Those skilled in the art may make various modifications or additions to the described embodiments or replace them in similar ways, but they will not deviate from the spirit of the present invention or exceed the scope defined by the attached 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, setting 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 The corresponding fault displacement D is calculated n The displacement time d in step S1 is calculated based on the displacement at the end point. n (t) Amplitude modulate to D n , and the displacement time history after amplitude modulation is obtained And according to the displacement time history after amplitude modulation Get the acceleration time history after amplitude modulation Then according to the acceleration time course after amplitude modulation Get the peak acceleration after amplitude modulation Step S3, calculating the target acceleration response spectrum according to the acceleration response spectrum of the seismic design; Step S4: Generate the initial seismic 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 seismic acceleration time history A0(t), and generate the initial seismic time history A′ containing only the high-frequency part. n (t); Step S5: Calculate the acceleration peak value PGA after the earthquake motion is attenuated according to the earthquake motion attenuation formula n , and subtract the peak value of the acceleration after amplitude modulation in step S2 Get the peak acceleration value of the high-frequency ground vibration only Step S6: A′ is the target peak pair n (t) Amplitude modulation is performed to convert the initial earthquake motion of step S4 into an earthquake motion time history A′ containing only the high-frequency part. n (t) is modulated to obtain the time history of the earthquake containing only the high-frequency part. Step S7: The acceleration time course after amplitude modulation in step S2 is and the earthquake time history containing only the high frequency part in step S6 By translation and superposition, we can obtain the near-source ground motion time history A n (t).

2. According to claim 1, a method for synthesizing near-source ground motions containing permanent displacements based on an equivalent pulse model, 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 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. According to claim 2, a method for synthesizing near-source ground motions containing permanent displacements based on an equivalent pulse model is 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. According to claim 3, a method for synthesizing near-source ground motions containing permanent displacements based on an equivalent pulse model is characterized in that: In step S2, the amplitude is modulated 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 course after amplitude modulation. Then, by converting the displacement time The second-order differential gives the acceleration time history 5. According to claim 4, a method for synthesizing near-source ground motions containing permanent displacements based on an equivalent pulse model is characterized in that: The earthquake attenuation formula in step S5 is: Where A, B, C, D, and E are all fitting constants of the earthquake motion attenuation formula.

6. According to claim 5, a method for synthesizing near-source ground motions containing permanent displacements based on an equivalent pulse model is characterized in that: In step S7, the near-source ground shaking time course 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 motions including permanent displacements based on an equivalent pulse model according to claim 7, characterized in that: The filtering range in step S4 is [0, 1 / T p ].

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