CN113158302B - Method for evaluating earthquake vulnerability of base shock isolation system based on component reliability index - Google Patents
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Abstract
The invention discloses a basic shock isolation system earthquake vulnerability assessment method based on a component reliability index, which comprises the following steps: step 1: dividing a basic shock isolation system to form a component; step 2: calculating the reliability index of each component under the action of earthquakes with different intensities; step 3: analyzing the failure probability of the whole structure based on the component reliability indexes under the action of earthquakes with different intensities; step 4: and forming a base shock isolation system vulnerability curve according to failure probabilities of the components and the integral structure under the action of different intensity earthquakes. Compared with the prior art, the method for evaluating the earthquake vulnerability of the base shock isolation system based on the component reliability index can evaluate the failure probability of the structural system under the action of different levels of earthquakes in a multi-scale manner, and can more comprehensively understand the earthquake resistance of the structural system.
Description
Technical Field
The invention relates to the field of building earthquake resistance evaluation methods, in particular to a basic earthquake isolation system earthquake vulnerability evaluation method based on a component reliability index.
Background
In recent decades, destructive earthquake frequently occurs worldwide, but China is one of countries with serious earthquake disasters, and a large number of building structures are destroyed and collapsed by the earthquake to bring great harm to national economy and people property safety, so that the structural earthquake resistance evaluation becomes a key subject of engineering field research. However, due to the uncertainty influence of actual earthquake excitation, the structural earthquake resistance has stronger randomness, so that the vulnerability evaluation method based on probability theory can evaluate the earthquake resistance of the structural system more comprehensively and reasonably, and has better guiding significance for further disaster prevention measure formulation and structural system optimization.
In the existing building system, the foundation vibration isolation structure is widely applied due to the good vibration resistance. The basic shock insulation structure is a complex system formed by a plurality of components (such as a shock insulation layer, a main body structure and the like) which are mutually connected and have different performances, and the prior vulnerability analysis method is biased to the vulnerability research of a single component or an integral structure. However, research shows that the single component is used for replacing the whole structure to analyze, so that the anti-seismic performance of the structural system is easy to overestimate, and on the contrary, only the vulnerability of the whole structure is concerned, and the system is unfavorable for optimizing the weak links of the system, so that the anti-seismic performance of the whole structure is improved.
Disclosure of Invention
The invention aims to provide a method for evaluating the earthquake vulnerability of a base shock isolation system based on a component reliability index, which evaluates the earthquake resistance of the base shock isolation system from multiple scales so as to solve the limitations and the defects in the prior art when evaluating the earthquake resistance of a structural system from a single scale (local or whole).
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
the method for evaluating the earthquake vulnerability of the base shock isolation system based on the component reliability index is characterized by comprising the following steps:
step 1: dividing all components from a base shock isolation system;
step 2: calculating the reliability indexes of each component obtained by dividing in the step 1 under the action of earthquakes with different intensities;
step 3: analyzing the failure probability of the integral structure of the base shock isolation system based on the reliable indexes of each component under the action of the earthquakes with different intensities obtained in the step (2);
step 4: and (3) drawing a component vulnerability curve, and simultaneously obtaining a base shock isolation system integral structure vulnerability curve according to the failure probability of the base shock isolation system integral structure obtained in the step (3), wherein the base shock isolation system vulnerability curve is obtained based on the component vulnerability curves and the base shock isolation system integral structure vulnerability curve and is used for multi-scale evaluation of the base shock isolation system seismic vulnerability.
The method for evaluating the earthquake vulnerability of the base shock isolation system based on the component reliability index is characterized in that in the step 1, the base shock isolation system is divided into an upper structure and a shock isolation layer.
The method for evaluating the earthquake vulnerability of the basic shock isolation system based on the component reliability index is characterized in that in the step 2, the calculation process of the reliability index of each component is as follows:
step 2-1: n pieces of representative earthquake motion are selected, S pieces of intensity level earthquake motion intensity indexes IM, IM= { IM are determined 1 ,im 2 ,…,im i ,…,im s N.gtoreq.20, S.gtoreq.10, im i Vibration intensity index value for the i-th intensity level, i=1, 2, … S;
step 2-2: establishing a finite element model of a basic shock isolation system, and determining a component seismic demand parameter D and a corresponding capacity parameter C, wherein D= { D 1 ,d 2 }，C＝{c 1 ,c 2 }，d 1 、d 2 Respectively the earthquake requirement parameters of each component, c 1 、c 2 The corresponding capability parameters of the components are respectively;
step 2-3: calculating a component earthquake demand parameter D and a correlation coefficient omega under the earthquake action of different intensity grades by adopting an incremental dynamic analysis method, wherein the component earthquake demand parameter D comprises the following components:
the correlation coefficient Ω is:
Ω＝[ω 1 ,ω 2 ,…,ω i ,…,ω S ] (3)，
in the formulas (1) and (2), x ij 、y ij The parameters are respectively the earthquake requirement parameters of the assembly under the action of the jth earthquake of the ith intensity level, j=1, 2 and … N; in the formula (3), ω i The correlation coefficients of the earthquake demand parameters of different components under the earthquake action of the ith intensity level are obtained;
step 2-4: the probabilistic seismic demand model for fitting the assembly using linear regression is as follows:
in the formulas (4) and (5),the median value and the +.A. of the earthquake demand parameters of the component under the earthquake action of different intensity levels are respectively shown> Component seismic demand parameters [ x ] under the action of N representative earthquakes of ith intensity level respectively i1 ,x i2 ,…,x ij ,…,x iN ]、[y i1 ,y i2 ,…,y ij ,…,y iN ]Is a median value of (2); a, a 1 、a 2 、b 1 、b 2 Fitting parameters;
step 2-5: calculating the reliability index B of each component under the earthquake action of different intensity levels 1 And B 2 Wherein B is 1 ＝[β 11 ,β 12 ,…,β 1i ,…,β 1S ]，B 2 ＝[β 21 ,β 22 ,…,β 2i ,…,β 2S ]，β 1i 、β 2i The reliable indexes under the earthquake action of the ith intensity level of the component are respectively as follows:
the method for evaluating the earthquake vulnerability of the base shock isolation system based on the component reliability index is characterized in that the IPCM method is adopted to analyze the failure probability P of the integral structure of the base shock isolation system under the earthquake action of different intensity grades in the step 3 f ，P f ＝{p f1 ,p f2 ,…,p fi ,…,p fS Probability of failure p of the overall structure under the action of earthquake of the ith intensity level fi ：
p fi ＝1-Φ(α)Φ(β 1i ) (8)，
Alpha in the formula (8) is a conditional normal quantile, and is calculated according to the following formula:
in formula (9):
Φ(-β 2i ，-β 1i ；ω i )＝Φ(ε 2 )Φ(-β 1i ) (10)，
ε 1 ＝φ(-β 1i )/Φ(-β 1i ) (11)，
phi (·) is a standard normal distribution probability density function and phi (·) is a standard normal distribution function.
The method for evaluating the earthquake vulnerability of the base shock isolation system based on the component reliability index is characterized in that a component vulnerability curve in the step 4 is drawn according to the following formula:
P 1 、P 2 the component failure probabilities, respectively.
The method for evaluating the earthquake vulnerability of the base shock isolation system based on the component reliability index is characterized in that in the step 4, a vulnerability curve of the integral structure of the base shock isolation system is fitted by a least square method to obtain failure probability P of the integral structure under the action of S intensity level earthquakes f ＝{p f1 ,p f2 ,…,p fi ,…,p fS Obtained.
The invention provides a method for evaluating the earthquake vulnerability of a base shock isolation system based on a component reliability index. Compared with the traditional analysis method, the method is based on probability theory, the seismic performance of the seismic isolation structure is characterized in multiple scales from the local assembly to the whole structure, the connection between the seismic intensity and the structural system and the connection between the whole structure and the local assembly are deeply described, the method has the advantages of simple and efficient calculation, and a foundation is laid for further improvement and optimization of the structural system performance.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a schematic diagram of the partitioning components of the base shock isolation system of the present invention.
Detailed Description
The invention will be further described with reference to the drawings and examples.
The invention provides a basic shock isolation system earthquake vulnerability assessment method based on a component reliability index, which is shown in a figure 1, and specifically comprises the following steps:
step 1: as shown in fig. 2, the basic shock insulation system on the ground 3 is divided into 2 components connected in series with each other, i.e. comprising the component 1 shock insulation layer and the component 2 superstructure.
Step 2: the reliable indexes of 2 assemblies under the earthquake action of different intensity levels are calculated, and the process is as follows:
step 2-1: according to the site condition of the structure, 20 representative earthquake motions are selected as earthquake excitation, the ground peak acceleration PGA is selected as the earthquake motion intensity index IM, and the 10 intensity level earthquake motion intensity index values are determined to be {0.05g,0.1g,0.2g,0.3g,0.35g,0.4g,0.45g,0.5g,0.55g,0.6g }, wherein g is gravity acceleration;
step 2-2: establishing a finite element model of a basic shock isolation system, and respectively selecting the maximum shear strain d of a shock isolation support 1 And the superstructure maximum interlayer displacement angle d 2 As the seismic demand parameters of the assemblies 1 and 2, the corresponding capacity parameters {200%,1/100} are determined in combination with the relevant research results and specification. The main structure common earthquake demand parameters are structure top displacement, interlayer displacement angle, various damage indexes of the structure and the like, and the earthquake isolation layers are interlayer displacement, interlayer displacement angle, earthquake isolation support shear strain, various earthquake isolation support damage indexes and the like.
Step 2-3: the embodiment adopts an incremental dynamic analysis method (incremental dynamic analysis, IDA) to calculate the maximum shear strain d of the shock insulation support under the action of the earthquakes with different intensity grades 1 Maximum layer displacement angle d of upper structure 2 And a correlation coefficient Ω, wherein:
Ω＝[ω 1 ,ω 2 ,…,ω i ,…,ω S ]，
in the above, ω i Maximum shear strain [ x ] of component 1 shock-insulating support under action of ith intensity level earthquake i1 ,x i2 ,…,x i20 ]And maximum layer displacement angle of the upper structure of the assembly 2 [ y ] i1 ,y i2 ,…,y i20 ]I=1, 2,...
Step 2-4: fitting the component probabilistic seismic demand model (probabilistic seismic demand model, PSDM) using linear regression:
wherein,,for the median value of the maximum shear strain of the shock insulation support and the maximum interlayer displacement angle of the upper structure of the component under the earthquake action of different intensity levels, +.> Maximum shear strain [ x ] of the shock insulation support under the action of earthquake with the ith intensity level i1 ,x i2 ,…,x i20 ]And the superstructure maximum interlayer displacement angle [ y ] i1 ,y i2 ,…,y i20 ]Is a median value of (2); a, a 1 、a 2 、b 1 、b 2 Is a fitting parameter.
Step 2-5: computing componentsReliable index B under earthquake action of different intensity levels 1 And B 2 Wherein B is 1 ＝[β 11 ,β 12 ,…,β 1i ,…,β 110 ]，B 2 ＝[β 21 ,β 22 ,…,β 2i ,…,β 210 ]，β 1i 、β 2i The reliable index under the earthquake action of the ith intensity level of the component is as follows:
step 3: based on the component reliability index, the IPCM method (improved product of conditional marginal method) is adopted to analyze the failure probability P of the integral structure under the action of earthquake with different intensities f ，P f ＝{p f1 ,p f2 ,…,p fi ,…,p f10 Probability of failure p of the overall structure under the action of earthquake of the ith intensity level fi The method comprises the following steps:
p fi ＝1-Φ(α)Φ(β 1i )，
wherein alpha is a conditional normal quantile calculated as follows
In the above formula:
Φ(-β 2i ，-β 1i ；ω i )＝Φ(ε 2 )Φ(-β 1i )，
ε 1 ＝φ(-β 1i )/Φ(-β 1i )，
phi (·) is a standard normal distribution probability density function and phi (·) is a standard normal distribution function.
Step 4: the component vulnerability curve is plotted according to the following formula:
P 1 、P 2 the component failure probabilities, respectively.
The vulnerability curve of the integral structure of the basic shock isolation system adopts a least square method to fit the failure probability P of the integral structure under the action of 10 intensity level earthquakes f ＝{p f1 ,p f2 ,…,p f10 Obtained.
And finally, forming a base shock isolation system vulnerability curve based on the assembly and the base shock isolation system integral structure vulnerability curve.
The embodiments of the present invention are merely described in terms of preferred embodiments of the present invention, and are not intended to limit the spirit and scope of the present invention, and various modifications and improvements made by those skilled in the art to the technical solutions of the present invention should fall within the protection scope of the present invention, and the technical content of the present invention as claimed is fully described in the claims.
Claims (4)
1. The method for evaluating the earthquake vulnerability of the base shock isolation system based on the component reliability index is characterized by comprising the following steps:
step 1: dividing all components from a base shock isolation system;
step 2: calculating the reliability indexes of each component obtained by dividing in the step 1 under the action of earthquakes with different intensities;
step 3: analyzing the failure probability of the integral structure of the base shock isolation system based on the reliable indexes of each component under the action of the earthquakes with different intensities obtained in the step (2);
step 4: drawing a component vulnerability curve, and simultaneously obtaining a base shock isolation system integral structure vulnerability curve according to the failure probability of the base shock isolation system integral structure obtained in the step 3, wherein the base shock isolation system vulnerability curve is obtained based on the component vulnerability curves and the base shock isolation system integral structure vulnerability curve and is used for multi-scale evaluation of the base shock isolation system seismic vulnerability;
in step 2, the reliability index calculation process of each component is as follows:
step 2-1: n pieces of representative earthquake motion are selected, S pieces of intensity level earthquake motion intensity indexes IM, IM= { IM are determined 1 ,im 2 ,…,im i ,…,im s N.gtoreq.20, S.gtoreq.10, im i Vibration intensity index value for the i-th intensity level, i=1, 2, … S;
step 2-2: establishing a finite element model of a basic shock isolation system, and determining a component seismic demand parameter D and a corresponding capacity parameter C, wherein D= { D 1 ,d 2 }，C＝{c 1 ,c 2 D1 and d2 are respectively the earthquake requirement parameters of each component, and c1 and c2 are respectively the corresponding capacity parameters of each component;
step 2-3: calculating a component earthquake demand parameter D and a correlation coefficient omega under the earthquake action of different intensity grades by adopting an incremental dynamic analysis method, wherein the component earthquake demand parameter D comprises the following components:
the correlation coefficient Ω is:
Ω＝[ω 1 ,ω 2 ,…,ω i ,…,ω S ] (3)，
in the formulas (1) and (2), x ij 、y ij The parameters are respectively the earthquake requirement parameters of the assembly under the action of the jth earthquake of the ith intensity level, j=1, 2 and … N; male (Male)In the formula (3), ω i The correlation coefficients of the earthquake demand parameters of different components under the earthquake action of the ith intensity level are obtained;
step 2-4: the probabilistic seismic demand model for fitting the assembly using linear regression is as follows:
in the formulas (4) and (5),the median value and the +.A. of the earthquake demand parameters of the component under the earthquake action of different intensity levels are respectively shown> Component seismic demand parameters [ x ] under the action of N representative earthquakes of ith intensity level respectively i1 ,x i2 ,…,x ij ,…,x iN ]、[y i1 ,y i2 ,…,y ij ,…,y iN ]Is a median value of (2); a, a 1 、a 2 、b 1 、b 2 Fitting parameters;
step 2-5: calculating the reliability index B of each component under the earthquake action of different intensity levels 1 And B 2 Wherein B is 1 ＝[β 11 ,β 12 ,…，β 1i ,…,β 1S ]，B 2 ＝[β 21 ,β 22 ,…,β 2i ,…,β 2S ]，β 1i 、β 2i The reliable indexes under the earthquake action of the ith intensity level of the component are respectively as follows:
in the step 3, the IPCM method is adopted to analyze the failure probability P of the integral structure of the base shock isolation system under the action of earthquakes with different intensity grades f ，P f ＝{p f1 ,p f2 ,…,p fi ,…,p fS Probability of failure p of the overall structure under the action of earthquake of the ith intensity level fi ：
p fi ＝1-Φ(α)Φ(β 1i ) (8)，
Alpha in the formula (8) is a conditional normal quantile, and is calculated according to the following formula:
in formula (9):
Φ(-β 2i ，-β 1i ；ω i )＝Φ(ε 2 )Φ(-β 1i ) (10)，
ε 1 ＝φ(-β 1i )/Φ(-β 1i ) (11)，
phi (·) is a standard normal distribution probability density function and phi (·) is a standard normal distribution function.
2. The method for evaluating the seismic vulnerability of a base shock isolation system based on component reliability indexes according to claim 1, wherein in step 1, the base shock isolation system is divided into two components of a superstructure and a shock isolation layer.
3. The method for evaluating the seismic vulnerability of a base seismic isolation system based on a component reliability index according to claim 1, wherein the component vulnerability curve in the step 4 is drawn according to the following formula:
P 1 、P 2 the component failure probabilities, respectively.
4. The method for evaluating the vulnerability of a base shock isolation system based on a component reliability index according to claim 1, wherein in step 4, a vulnerability curve of the integral structure of the base shock isolation system is fitted by a least square method to the failure probability P of the integral structure under the action of S intensity level earthquakes f ＝{p f1 ,p f2 ,…,p fi ,…,p fS Obtained.
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