CN107589445B - Multistage natural earthquake motion synthesis method based on set reaction spectrum - Google Patents
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Abstract
The invention relates to the technical field of civil construction engineering, in particular to a multistage natural earthquake motion synthesis method based on a set reaction spectrum, which is characterized in that a large number of natural original earthquake motion records are collected, seismic wave fragments meeting the conditions in the earthquake motion records are screened out through a specific method, a synthetic reaction spectrum closest to a target design reaction spectrum is synthesized, the synthetic method follows the principle that the earthquake motion reaction spectrum is approximately consistent with the target design reaction spectrum of a site, and the synthesized earthquake kinetic energy keeps the frequency domain non-stable characteristic of the natural earthquake motion records, so that the method is suitable for earthquake resistance analysis of all structural forms with the same fortification intensity and site condition.
Description
Technical Field
The invention relates to the technical field of civil construction engineering, in particular to a multistage natural earthquake motion synthesis method based on a set reaction spectrum.
Background
The time-course analysis method is the most accurate anti-seismic analysis method at present, the accuracy of analysis results is greatly dependent on the selection of input earthquake motions, and the reasonable selection of earthquake motions for time-course analysis is important. It is most desirable if there is an actual seismic record available on the site being constructed, but the desired seismic record is not typically obtained on the site being constructed. Although the number of actual earthquake motions recorded in the world has been greatly increased, some typical strong earthquake motion records can be used as input earthquake motions, but the earthquake motion records in China are relatively lacking compared with other developed countries, and the place conditions of the earthquake motion records are greatly different from those of the site conditions of the construction project, so that the existing earthquake motion records can not meet the requirement of earthquake-resistance analysis, and therefore, in the actual calculation of the engineering, the earthquake-resistance analysis needs to be supplemented by using artificial simulated earthquake motions. At present, the artificial earthquake motion is synthesized by using a computer numerical simulation, and the common simulation method only considers the response spectrum which is in good conformity with the earthquake-proof standard design (amplitude-frequency characteristic), but neglects the frequency domain non-stable characteristic of the natural earthquake motion, and the simulated earthquake motion has larger difference with the actual natural earthquake motion record.
The earthquake-proof standard of each country is used for selecting earthquake-proof, the characteristics of earthquake-proof environment are required to be considered, the consistency of the earthquake-proof standard of China and the structural substrate shear response statistical rule is also required to be considered, and the earthquake-proof standard relates to factors such as fortification intensity, site characteristics, structural period and the like. The selection of a seismic vibration which meets the set reaction spectrum characteristics and site environment characteristics and has natural seismic vibration frequency domain non-stationary characteristics is a worldwide problem.
Disclosure of Invention
The invention aims to provide a multistage natural earthquake motion synthesis method based on a set reaction spectrum, which follows the principle that the earthquake motion reaction spectrum is approximately consistent with a site target design reaction spectrum, and the synthesized earthquake motion energy keeps the frequency domain non-stationary characteristic of natural earthquake motion record, and is suitable for earthquake-resistant analysis of all structural forms with the same fortification intensity and site condition.
In order to achieve the above purpose, the present invention adopts the following technical scheme: a multistage natural earthquake motion synthesis method based on a set reaction spectrum comprises the following steps,
S1, collecting a large number of natural original seismic records;
S2, determining the maximum acceleration value in all original earthquake motion records, unifying all original earthquake motion records according to the maximum acceleration value amplitude modulation, determining an acceleration response spectrum of each original earthquake motion record after amplitude modulation, and recording the acceleration response spectrum as an earthquake motion record acceleration response spectrum;
S3, determining a target design acceleration response spectrum according to building earthquake-resistant design specifications;
S4, dividing the target design acceleration response spectrum and the earthquake motion record acceleration response spectrum into a plurality of continuous intervals according to the whole period, solving the root mean square of the difference value of the earthquake motion record acceleration response spectrum and the target design acceleration response spectrum in each period interval, finding out one earthquake motion record with the minimum root mean square of the difference value in each period interval, and recording the earthquake motion record as the minimum earthquake motion record;
S5, determining the shortest main control section of the minimum earthquake motion record by adopting a successive approximation method, so that the root mean square of the difference value of the acceleration response spectrum of the shortest main control section of the minimum earthquake motion record and the original earthquake motion record is minimum in a specified period interval;
s6, calculating the average relative difference value of the shortest main control section recorded by each minimum earthquake motion and the set acceleration response spectrum in a specified period interval
T m and T n are respectively a starting point and an ending point of a specified period, sa part(Ti) is a spectrum value of the shortest main control section recorded by the minimum earthquake motion at a period point T i, sa set(Ti) is a spectrum value of a set acceleration response spectrum at a period point T i, a set precision value is smaller than or equal to the set precision value, if delta is not satisfied with the set precision requirement, the average relative difference value between the next shortest main control section recorded by the minimum earthquake motion and the set acceleration response spectrum is calculated, and the method is repeated until the time interval of the acceleration response spectrum recorded by the minimum earthquake motion meeting the precision is selected;
S7, recording acceleration response spectrum time courses of the minimum earthquake motion meeting the accuracy selected in the step S6, sequentially connecting the reaction spectrum time courses according to the cycle interval sequence of the response spectrum, and combining the reaction spectrum time courses into a multi-section natural earthquake motion based on the target setting response spectrum.
Further, the predetermined period may be a full period interval of the reaction spectrum, or may be a segment period interval of the reaction spectrum.
Further, the set acceleration response spectrum in step S6 may be the target design acceleration response spectrum or the original earthquake motion acceleration response spectrum in the full period section, or may be the target design acceleration response spectrum or the original earthquake motion acceleration response spectrum in the segment period section.
Further, the specific steps of the step S4 are as follows:
S41, dividing a target design acceleration response spectrum and a seismic vibration recording acceleration response spectrum into a plurality of continuous intervals according to a full period: dividing the field characteristic period into a platform section [0.1s, T g ] and a plurality of non-platform sections [Tg,TA)、[TA,TB)、[TB,TC)、[TC,TD)、[TD,TE)、……, by taking the field characteristic period as a demarcation point, wherein T A、TB、TC、TD、TE is a period point;
s42, respectively calculating the root mean square of the difference value of the target design acceleration response spectrum and the earthquake motion record acceleration response spectrum in each specified period interval
T i∈[Tm,Tn],Tm、Tn is the starting point and the ending point of a specified period interval, namely, the values of T m and T n are T g、TA、TB、TC、TD、TE … …, i is a positive integer, sa record(Ti) is the spectrum value of the earthquake motion record acceleration response spectrum at the period point T i, sa target(Ti) is the spectrum value of the target design acceleration response spectrum at the period point T i, and one earthquake motion record with the minimum root mean square difference value on each specified period interval is found and recorded as the minimum earthquake motion record.
Further, the specific steps of the step S5 are as follows:
S51, determining peak points of each minimum vibration record acceleration;
s52, determining approximation step length delta T Left side 、ΔT Right side at the left side and the right side of a peak point;
S53, carrying out the following treatment on each minimum earthquake motion record, shortening DeltaT Left side and DeltaT Right side respectively from two ends of the earthquake motion record each time, calculating the difference root mean square of the acceleration response spectrum time interval of each shortened minimum earthquake motion record and the acceleration response spectrum of the original earthquake motion record, arranging the obtained difference root mean square in sequence, and determining the minimum earthquake motion record acceleration response spectrum time interval corresponding to one difference root mean square when the value of the difference root mean square is obviously increased compared with the previous difference root mean square, wherein the difference root mean square is the primary selected main control section of each minimum earthquake motion record;
S53, intercepting the time course from the [ main control section- (delta T Left side +ΔT Right side ) ] to the [ main control section+ (delta T Left side +ΔT Right side ) ] from each minimum earthquake motion record, respectively shrinking m% delta T Left side and m% delta T Right side from the two ends of the earthquake motion record each time, wherein m is a positive integer, the value range is 1-100, calculating the root mean square of the difference value between the time course of the minimum earthquake motion record acceleration response spectrum after each time shortening and the time course of the original earthquake motion record acceleration response spectrum, selecting the time course of the minimum earthquake motion record acceleration response spectrum after shortening corresponding to the root mean square of the minimum difference value, and taking the time course of adding delta T Left side and delta T Right side from the two ends of the shortest main control section as the next shortest main control section, and so on.
The multistage natural earthquake motion synthesis method based on the set reaction spectrum, disclosed by the invention, follows the principle that the earthquake motion reaction spectrum is approximately consistent with the field target design reaction spectrum, and the synthesized earthquake kinetic energy keeps the frequency domain non-stationary characteristic of the natural earthquake motion record, so that the method is suitable for earthquake-resistant analysis of all structural forms with the same fortification intensity and field condition.
Drawings
FIG. 1 is a graph of the design acceleration response spectrum and the recorded acceleration response spectrum for a seismic event for a target;
FIG. 2 is a graph showing the periodic partitioning of a target design response spectrum;
FIG. 3 is a graph of acceleration time course for a synthetic multi-segment natural vibration;
FIG. 4 is a comparison of a synthetic multi-segment natural seismic acceleration response spectrum with a target design acceleration response spectrum.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
The master control section is the shortest master control section for intercepting the minimum earthquake motion record meeting the precision in a specified period interval, and the root mean square of the difference between the earthquake motion acceleration response spectrum and the target set acceleration response spectrum is minimum. The predetermined period interval may be a full period interval of the reaction spectrum or a segment period interval of the reaction spectrum. The set response spectrum may be a target design acceleration response spectrum or a natural earthquake motion acceleration response spectrum in a full period section, or may be a target design acceleration response spectrum or a natural earthquake motion acceleration response spectrum in a segment period section. In this embodiment, the predetermined period interval is a segmented period interval of the reaction spectrum, and the target design acceleration reaction spectrum of the segmented period interval of the reaction spectrum is set.
The invention establishes a multistage natural earthquake motion synthesis method based on a set reaction spectrum by sequentially connecting earthquake motion recording time courses of all main control sections meeting the precision by adopting the principle that the earthquake motion acceleration reaction spectrum time course selected in a specified period interval is consistent with the set acceleration reaction spectrum based on the shortest main control section of the minimum earthquake motion record. The earthquake motion synthesized by the method not only contains the frequency domain non-stationary characteristic of natural earthquake records, but also accords with the specification of the current building earthquake-proof design specification, and can be used for earthquake-proof analysis of all structural forms with the same fortification intensity and site characteristics. The multistage natural earthquake motion synthesis method based on the set reaction spectrum comprises the following steps:
A multistage natural earthquake motion synthesis method based on a set reaction spectrum is characterized by comprising the following steps,
S1, collecting a large number of natural original earthquake records.
S2, determining the maximum acceleration value in all original earthquake motion records, unifying all original earthquake motion records according to the maximum acceleration value amplitude modulation, determining an acceleration response spectrum of each original earthquake motion record after amplitude modulation, and recording the acceleration response spectrum as an earthquake motion record acceleration response spectrum;
S3, determining a target design acceleration response spectrum according to building earthquake-resistant design specifications. The acceleration response spectrum of a certain target design is shown in fig. 1, and the acceleration response spectrum of the earthquake motion record is shown, wherein the curve with dark and thick color is the acceleration response spectrum of a certain target design.
S4, dividing the target design acceleration response spectrum and the earthquake motion record acceleration response spectrum into a plurality of continuous intervals according to the whole period, solving the root mean square of the difference value of the earthquake motion record acceleration response spectrum and the target design acceleration response spectrum in each period interval, finding out one earthquake motion record with the minimum root mean square of the difference value in each period interval, and recording the earthquake motion record as the minimum earthquake motion record. Wherein the full cycle is defined in the building earthquake-proof design specification to be a period of 1-6 s.
The specific steps of the step S4 are as follows:
S41, dividing a target design acceleration response spectrum and a seismic vibration recording acceleration response spectrum into a plurality of continuous intervals according to a full period: dividing the field characteristic period into a platform section [0.1s, T g ] and a plurality of non-platform sections [Tg,TA)、[TA,TB)、[TB,TC)、[TC,TD)、[TD,TE)、……, by taking the field characteristic period as a demarcation point, wherein T A、TB、TC、TD、TE is a period point; as shown in fig. 2.
S42, respectively calculating the root mean square of the difference value of the target design acceleration response spectrum and the earthquake motion record acceleration response spectrum in each specified period interval
T i∈[Tm,Tn],Tm、Tn is the starting point and the ending point of a specified period interval, namely, the values of T m and T n are T g、TA、TB、TC、TD、TE … …, i is a positive integer, sa record(Ti) is the spectrum value of the earthquake motion record acceleration response spectrum at the period point T i, sa target(Ti) is the spectrum value of the target design acceleration response spectrum at the period point T i, and one earthquake motion record with the minimum root mean square difference value on each specified period interval is found and recorded as the minimum earthquake motion record.
S5, determining the shortest main control section of the minimum earthquake motion record by adopting a successive approximation method, so that the root mean square of the difference value of the acceleration response spectrum of the shortest main control section of the minimum earthquake motion record and the original earthquake motion record is minimum in a specified period interval;
that is, in the specified period, the root mean square of the difference between the shortest main control section recorded by the minimum earthquake motion and the original earthquake motion acceleration response spectrum is intercepted
At minimum, T i ε [0,6s ], wherein Sa part(Ti) is the spectrum value of the shortest main control section recorded by intercepting the minimum earthquake motion at the periodic point T i, sa record(Ti) is the spectrum value of the original earthquake motion acceleration response spectrum at the periodic point T i.
The specific steps of the step S5 are as follows:
s51, determining peak points of each minimum vibration recording acceleration.
S52, determining approximation steps delta T Left side 、ΔT Right side ,ΔT Left side and delta T Right side on the left and right sides of the peak point can be selected empirically, for example, one tenth of the seismic records on the two sides of the peak point can be set as delta T Left side and delta T Right side .
S53, carrying out the following treatment on each minimum earthquake motion record, shortening DeltaT Left side and DeltaT Right side respectively from two ends of the earthquake motion record each time, calculating the difference root mean square of the acceleration response spectrum of each shortened minimum earthquake motion record and the acceleration response spectrum of the original earthquake motion record, arranging the obtained difference root mean square in sequence, and determining the minimum earthquake motion record acceleration response spectrum time corresponding to one difference root mean square as a primary main control section of each minimum earthquake motion record when the value of the difference root mean square is obviously increased or reduced compared with the previous difference root mean square, for example, 20% is increased or reduced;
S53, intercepting the time course from the [ main control section- (delta T Left side +ΔT Right side ) ] to the [ main control section+ (delta T Left side +ΔT Right side ) ] from each minimum earthquake motion record, respectively shrinking m% delta T Left side and m% delta T Right side from the two ends of the earthquake motion record each time, wherein m is a positive integer, the value range is 1-100, calculating the root mean square of the difference value between the time course of the minimum earthquake motion record acceleration response spectrum after each time shortening and the time course of the original earthquake motion record acceleration response spectrum, selecting the time course of the minimum earthquake motion record acceleration response spectrum after shortening corresponding to the root mean square of the minimum difference value, and taking the time course of adding delta T Left side and delta T Right side from the two ends of the shortest main control section as the next shortest main control section, and so on.
S6, calculating the average relative difference value between the shortest main control section of each minimum earthquake motion record and the minimum earthquake motion record in a specified period interval
T i∈[Tm,Tn],Tm and T n are respectively a starting point and an ending point of a specified period, sa part(Ti) is a spectrum value of the shortest main control section recorded by the minimum earthquake motion at a period point Ti, sa set(Ti) is a spectrum value of the acceleration response spectrum recorded by the minimum earthquake motion at a period point T i, a precision value is set (delta is controlled within a certain percentage, such as 15-20%), delta is required to be less than or equal to a set precision requirement, if delta does not meet the set precision requirement, an average relative difference value between the next shortest main control section recorded by the minimum earthquake motion and the acceleration response spectrum recorded by the minimum earthquake motion is calculated, and the method is repeated until a minimum earthquake motion record acceleration response spectrum time course meeting the precision is selected;
S7, recording acceleration response spectrum time courses of the minimum earthquake motion meeting the accuracy selected in the step S6, sequentially connecting the reaction spectrum time courses according to the cycle interval sequence of the response spectrum, and combining the reaction spectrum time courses into a multi-section natural earthquake motion based on the target setting response spectrum.
It will be understood that modifications and variations will be apparent to those skilled in the art from the foregoing description, and it is intended that all such modifications and variations be included within the scope of the following claims.
Claims (1)
1. A multistage natural earthquake motion synthesis method based on a set reaction spectrum is characterized by comprising the following steps,
S1, collecting a large number of natural original seismic records;
S2, determining the maximum acceleration value in all original earthquake motion records, unifying all original earthquake motion records according to the maximum acceleration value amplitude modulation, determining an acceleration response spectrum of each original earthquake motion record after amplitude modulation, and recording the acceleration response spectrum as an earthquake motion record acceleration response spectrum;
S3, determining a target design acceleration response spectrum according to building earthquake-resistant design specifications;
S4, dividing the target design acceleration response spectrum and the earthquake motion record acceleration response spectrum into a plurality of continuous intervals according to the whole period, calculating the root mean square of the difference between the earthquake motion record acceleration response spectrum and the target design acceleration response spectrum in each specified period interval, and finding out one earthquake motion record with the minimum root mean square of the difference in each specified period interval, and recording the earthquake motion record as the minimum earthquake motion record, wherein the concrete steps are as follows:
S41, dividing a target design acceleration response spectrum and a seismic vibration recording acceleration response spectrum into a plurality of continuous intervals according to a full period: dividing the field characteristic period into a platform section [0.1s, T g ] and a plurality of non-platform sections [Tg,TA)、[TA,TB)、[TB,TC)、[TC,TD)、[TD,TE)、……, by taking the field characteristic period as a demarcation point, wherein T A、TB、TC、TD、TE is a period point;
s42, respectively calculating the root mean square of the difference value of the target design acceleration response spectrum and the earthquake motion record acceleration response spectrum in each specified period interval
T i∈[Tm,Tn],Tm、Tn is a starting point and an ending point of a specified period interval, namely, the values of T m and T n are T g、TA、TB、TC、TD、TE and … …, i is a positive integer, sa record(Ti) is a spectrum value of a seismic record acceleration response spectrum at the period point T i, sa target(Ti) is a spectrum value of a target design acceleration response spectrum at the period point T i, and one seismic record with the minimum root mean square of differences in each specified period interval is found and recorded as the minimum seismic record;
S5, determining the shortest main control section recorded by the minimum earthquake motion by adopting a successive approximation method, so that the root mean square of the difference value of the acceleration response spectrum of the shortest main control section recorded by the minimum earthquake motion and the original earthquake motion record is minimum in a specified period interval, and specifically comprising the following steps:
S51, determining peak points of each minimum vibration record acceleration;
s52, determining approximation step length delta T Left side 、ΔT Right side at the left side and the right side of a peak point;
S53, carrying out the following treatment on each minimum earthquake motion record, shortening DeltaT Left side and DeltaT Right side respectively from two ends of the earthquake motion record each time, calculating the difference root mean square of the acceleration response spectrum time interval of each shortened minimum earthquake motion record and the acceleration response spectrum of the original earthquake motion record, sequentially arranging the obtained difference root mean square, and determining the minimum earthquake motion record acceleration response spectrum time interval corresponding to one difference root mean square as a primary selected main control section of each minimum earthquake motion record when the value of the difference root mean square is obviously increased or reduced compared with the previous difference root mean square;
S54, intercepting the time course from the [ initial main control section- (delta T Left side +ΔT Right side ) ] to the [ initial main control section+ (delta T Left side +ΔT Right side ) ] from each minimum vibration record, respectively shrinking m% delta T Left side and m% delta T Right side from the two ends of the minimum vibration record each time, wherein m is a positive integer, the value range is 1-100, calculating the root mean square of the difference value between the time course of the minimum vibration record acceleration response spectrum after each time shortening and the time course of the acceleration response spectrum of the original vibration record, selecting the time course of the minimum vibration record acceleration response spectrum after shortening corresponding to the minimum difference value, taking the time course of adding delta T Left side and delta T Right side from the two ends of the shortest main control section as the next shortest main control section, and so on;
s6, calculating the average relative difference value of the shortest main control section recorded by each minimum earthquake motion and the set acceleration response spectrum in a specified period interval
T i∈[Tm,Tn],Tm and T n are respectively a starting point and an ending point of a specified period, sa part(Ti) is a spectrum value of the shortest main control section recorded by the minimum earthquake motion at a period point T i, sa set(Ti) is a spectrum value of a set acceleration response spectrum at a period point T i, a set precision value is set, delta is smaller than or equal to the set precision value, if delta is not satisfied, the average relative difference value between the next shortest main control section recorded by the minimum earthquake motion and the set acceleration response spectrum is calculated, and the method is repeated until the time course of the acceleration response spectrum recorded by the minimum earthquake motion meeting the precision is selected;
S7, recording acceleration response spectrum time courses of the minimum earthquake motion meeting the accuracy selected in the step S6, sequentially connecting the reaction spectrum time courses according to the cycle interval sequence of the response spectrum, and combining the reaction spectrum time courses into a multi-section natural earthquake motion based on the target setting response spectrum.
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