CN113191056B - Earthquake slippage and swing risk assessment method for showcase display floating cultural relics in museum - Google Patents

Earthquake slippage and swing risk assessment method for showcase display floating cultural relics in museum Download PDF

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CN113191056B
CN113191056B CN202110494868.1A CN202110494868A CN113191056B CN 113191056 B CN113191056 B CN 113191056B CN 202110494868 A CN202110494868 A CN 202110494868A CN 113191056 B CN113191056 B CN 113191056B
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刘佩
杨维国
葛家琪
邹晓光
王萌
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Beijing Jiaotong University
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Abstract

The invention discloses a seismic slippage and swing risk assessment method for a museum showcase for displaying floating cultural relics. According to the method, the influence of structural collapse and showcase overturning risks is considered, a seismic slip and sway risk assessment method for the floating cultural relics is provided, a nonlinear finite element model of a cultural relic-showcase-museum system is firstly established, then the seismic slip and sway vulnerability of the floating cultural relics, the seismic overturning vulnerability of a showcase and the seismic collapse vulnerability of a structure are assessed, then the seismic slip and sway risk of the floating cultural relics, the seismic overturning risk of the showcase and the seismic collapse risk of the structure are assessed, further probability estimation values of the seismic slip and sway risk of the floating cultural relics considering three risk factors are calculated, and finally the seismic slip and sway risk of the floating cultural relics are rated; the invention provides scientific basis for judging the seismic safety of the floating cultural relics, and is used for guiding scientific implementation of the shock-proof preventive protection of the floating cultural relics.

Description

Earthquake slippage and swing risk assessment method for showcase display floating cultural relics in museum
Technical Field
The invention relates to the technical field of antique earthquake preventive protection, in particular to a floating relic earthquake slippage and swing risk assessment method based on a relic-showcase-museum system.
Background
Cultural relics are valuable cultural heritage of human society and are carriers of historical cultural information. Based on statistics, about 1.08 hundred million mobile cultural relics are mainly stored in 5300 museums, wherein more than 70% of primary and secondary museums are located in high-intensity areas of 7 degrees and above for seismic fortification. Because of the display requirements of cultural relics, a large number of cultural relics float on the surface of a display cabinet; in addition, although many cultural relics are fixed by means of a fixture through clamping, gluing, binding and the like, the cultural relic-fixture combination still floats on the surface of the showcase; on the other hand, showcases located in the middle of a showroom often float on the floor due to variations in the theme of the showcase.
Investigation of strong shock damage at home and abroad shows main shock damage causes of cultural relics such as 'structural collapse of a museum', 'structural non-collapse but display cabinet overturning', 'falling or collision damage caused by overlarge slippage of a cultural relic without display cabinet', 'collision or overturning damage caused by overlarge swing angle of a cultural relic without display cabinet'.
The earthquake-proof preventive protection of the cultural relics in the collection is developed, and the problem of 'how to scientifically evaluate the earthquake safety of the cultural relics in the collection' is faced at present.
In the framework of performance-based seismic engineering, the risk of a seismic event refers to the likelihood of a subject developing some type of damage under various possible earthquakes over a specified period of time. The reasonable consideration of the earthquake risk is helpful for accurately grasping the safety level of the study object, and the earthquake risk assessment result has important significance for developing scientific disaster prevention and reduction planning. The demand of carrying out earthquake risk assessment on projects with higher importance level is particularly urgent, and related researches on nuclear power plants, ancient architectures, major geotechnical engineering, dams and the like are carried out in the early stage. However, no seismic risk assessment research on the cultural relics in the floating collection has been developed at present, and the basis for scientifically assessing the seismic risk level of the cultural relics in the floating collection and adopting reasonable shockproof measures is lacking.
More importantly, the earthquake waves are transmitted to the cultural relics through the museums and showcases, and the security of the cultural relics is endangered when earthquake damage occurs in any link, so that the influence of multiple risk factors must be considered in developing the earthquake risk assessment of the floating cultural relics. Aiming at two damage modes of floating cultural relics, namely the earthquake slippage and the overrun of the swing angle, the cultural relics earthquake slippage and swing risk assessment method considering the influence of structural collapse and showcase overturning risks is blank.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention provides a floating cultural relic earthquake slippage and swing risk assessment method based on a cultural relic-showcase-museum system.
The invention relates to a seismic slippage and sway risk assessment method for floating cultural relics, which comprises the following steps of:
1) Establishing a nonlinear finite element model of a cultural relic-showcase-museum system;
2) Evaluating the seismic slip and sway vulnerability of the floating cultural relics, the seismic toppling vulnerability of the showcase and the seismic collapse vulnerability of the museum structure:
i. respectively taking the maximum slippage and the maximum swing angle of the floating cultural relics as engineering demand parameters, respectively dividing the earthquake slippage failure and the earthquake swing failure of the floating cultural relics into three layers, defining performance targets of the three layers of the earthquake slippage failure and the earthquake swing failure of the floating cultural relics, and defining limit states of the earthquake slippage failure and the earthquake swing failure of the floating cultural relics corresponding to the three layers;
selecting a plurality of seismic waves as input excitation of a museum structure according to the place condition of the museum, and ensuring that the average reaction spectrum of each seismic wave accords with the design reaction spectrum of the place;
based on a nonlinear finite element model of the cultural relic-showcase-museum system, taking peak ground acceleration as a seismic intensity index, respectively taking the maximum slip quantity and the maximum swing angle of the floating cultural relic as engineering demand parameters, carrying out incremental power analysis, and establishing a seismic slip incremental power analysis curve and a seismic swing incremental power analysis curve of the floating cultural relic;
iv, setting the maximum slippage of the floating cultural relics to follow log normal distribution, and establishing a seismic slippage vulnerability function of the floating cultural relics; determining the median and standard deviation of the earthquake slippage vulnerability function by a linear regression method based on the earthquake slippage incremental dynamic analysis curve of the floating cultural relics, and respectively establishing earthquake slippage vulnerability curves of the floating cultural relics corresponding to three layers of performance targets;
v, setting the maximum swing angle of the floating cultural relics to follow the lognormal distribution, and establishing a seismic swing vulnerability function of the floating cultural relics; based on the earthquake swing incremental dynamic analysis curve of the floating cultural relics, determining the median value and standard deviation of the earthquake swing vulnerability function by a nonlinear regression method, and respectively establishing the earthquake swing vulnerability curves of the floating cultural relics corresponding to the performance targets of three layers;
if the showcase floats, taking peak ground acceleration as an earthquake intensity index, taking the maximum swing angle of the floating showcase as an engineering demand parameter, carrying out incremental power analysis, and establishing an earthquake swing incremental power analysis curve of the showcase; determining the median and standard deviation of the earthquake swing vulnerability function by a nonlinear regression method, and establishing an earthquake overturning vulnerability curve of the showcase; if the showcase is fixed, the vulnerability of the showcase to earthquake overturning is not considered;
performing incremental dynamic analysis by taking peak ground acceleration as a seismic intensity index and taking the maximum interlayer displacement angle of the museum structure as an engineering demand parameter, and establishing an incremental dynamic analysis curve of the museum structure; setting the maximum interlayer displacement angle of the museum structure to obey the lognormal distribution, and establishing an earthquake collapse vulnerability function of the museum structure; based on an incremental dynamic analysis curve of the museum structure, determining the median value and standard deviation of the earthquake collapse vulnerability function through a linear regression technology, and establishing an earthquake collapse vulnerability curve of the museum structure;
3) Assessing the risk of seismic slippage and sway of the floating cultural relics taking into account three types of risk factors:
i. three types of risk factors affecting the risk probability estimates of seismic slip and sway of the floating cultural relics are defined:
setting three types of risk factors, wherein the first risk factor represents the earthquake collapse risk of the museum structure, the second risk factor represents the earthquake collapse risk of the showcase, the third risk factor comprises the earthquake slippage risk of the floating cultural relics and the earthquake swing risk of the floating cultural relics, the earthquake slippage risk of the floating cultural relics represents the earthquake slippage risk of the floating cultural relics in the case that the museum structure is not collapsed and the showcase is not tilted, and the earthquake swing risk of the floating cultural relics represents the earthquake swing risk of the floating cultural relics in the case that the museum structure is not collapsed and the showcase is not tilted;
calculating probability estimates for the first and second risk factors:
according to the place conditions of the museum and the Chinese earthquake motion zone parameter diagram, obtaining the annual average overrun probability of different intensity earthquakes of the place of the museum, namely a place danger curve;
the annual average failure probability P of the first risk factor is obtained by convolving the site danger curve with the earthquake collapse vulnerability curve of the museum structure 1 Further obtain the probability estimated value P of the earthquake collapse risk of the museum structure in the service life of the museum structure design SC ：
P SC ＝1-exp(-P 1 ×tL)
Wherein tL is the structural design service life;
if the showcase floats, the site danger curve and the earthquake capsizing vulnerability curve of the showcase are convolved to obtain the annual average failure probability P of the second risk factor 2 Further obtain the probability estimated value P of the earthquake toppling risk of the showcase under the condition that the museum structure does not have earthquake collapse within the service life of the museum structure design SO ：
P SO ＝(1-P SC )×[1-exp(-P 2 ×tL)]；
If the showcase is fixed, probability estimation value P of earthquake toppling risk of showcase SO ＝0；
Calculating a probability estimate of the third risk factor:
aiming at the three-level performance targets, the sliding annual average failure probability of the third risk factors is calculated respectively by convolving the site danger curves with the seismic sliding vulnerability curves of the floating cultural relics of the three-level performance targets respectivelyAnd->Further, the probability estimation value of the earthquake slippage risk of the floating cultural relics corresponding to the performance targets of three layers is obtained under the conditions that the museum structure does not collapse and the showcase does not topple within the service life of the museum structure design:
wherein,and->Probability estimation values of seismic slippage risks of the floating cultural relics corresponding to the three levels of performance targets are respectively obtained;
aiming at the three-level performance targets, the earthquake swing vulnerability curves of the floating cultural relics of the three-level performance targets are respectively convolved with the site hazard curves, and the swing annual average failure probability of the third risk factors is respectively calculatedAnd->Further, the probability estimated value of the earthquake swing risk of the floating cultural relics corresponding to the performance targets of three layers is obtained under the conditions that the museum structure does not collapse and the showcase does not topple within the service life of the museum structure design:
wherein,and->Probability estimation values of earthquake swing risks of the floating cultural relics corresponding to the three levels of performance targets respectively;
calculating probability estimation values of earthquake slippage and sway risks of the floating cultural relics considering three risk factors:
aiming at three levels of performance targets, calculating the seismic slip risk estimation values of the floating cultural relics considering three types of risk factors respectively:
wherein,and->The method comprises the steps of respectively estimating the earthquake slippage risk probability of the floating cultural relics which correspond to three levels of performance targets and consider three types of risk factors;
aiming at three levels of performance targets, calculating floating cultural relic earthquake swing risk probability estimation values considering three types of risk factors respectively:
wherein,and->The seismic sway risk probability estimation values of the floating cultural relics which respectively correspond to three levels of performance targets and consider three types of risk factors;
4) The risk of seismic slippage and sway of the floating relics is rated.
In step 1, a nonlinear finite element model of an cultural relic-showcase-museum system is established, which comprises the following steps: firstly, building a nonlinear finite element model of a museum structure according to a structural design drawing of the museum; on the basis, friction, sliding, swinging and collision characteristics of floating interfaces between the cultural relics and the showcase and between the showcase and the floor slab are simulated, and a showcase equivalent to a three-dimensional rectangular rigid body and a floating cultural relic model in the showcase are added, so that a nonlinear finite element model of a cultural relic-showcase-museum system is built.
In step i) of step 2), the definition includes the following:
a) The three layers of earthquake slippage failure and earthquake swing failure of the floating cultural relics are a first layer, a second layer and a third layer respectively;
b) The performance targets of the first to third layers of earthquake slip failure of the floating cultural relics are respectively as follows: non-slip, limited slip and maximum slip, the corresponding limit states are respectively: the slipping occurs, the slipping quantity exceeds a set limit value, and the slipping quantity exceeds the distance between the cultural relics and the edge of the exhibition stand or the distance between the cultural relics and the neighboring cultural relics;
c) The performance targets of the first to third layers of earthquake swing failure of the floating cultural relics are respectively as follows: the non-swing, limited swing and maximum swing are overturning, and the corresponding limit states are respectively as follows: swing occurs, the swing angle exceeds a set limit and the swing angle exceeds the static overturning angle.
In step ii) of 2), 10-20 seismic waves are selected as input excitation of the museum structure.
In iii) of step 3), the probability estimate for the third risk factor comprises a calculation for three hierarchical performance targets.
In step iv) of step 3), the floating cultural relic seismic risk probability estimation values taking into account the three types of risk factors comprise calculation results for three hierarchical performance targets.
In step 4), the risk of seismic slippage and sway of the floating relic is rated, comprising the steps of:
a) Setting multi-level risk thresholds according to the sequence from small to large aiming at three levels of performance targets respectively;
b) If the estimated value of the earthquake slippage risk of the floating cultural relics and the estimated value of the earthquake swing risk of the floating cultural relics are smaller than the first-level risk threshold value, risk is ignored;
c) If the estimated value of the earthquake slippage risk of the floating cultural relics and the estimated value of the earthquake swing risk probability of the floating cultural relics are smaller than the threshold value of the second-stage risk, the risk is acceptable;
d) If the estimated value of the earthquake slippage risk of the floating cultural relics and the estimated value of the earthquake swing risk of the floating cultural relics are smaller than the third-level risk threshold, the risk is tolerable;
e) Otherwise, to be intolerable, cultural relic anti-shock measures must be taken.
The invention has the advantages that:
the invention provides the earthquake slippage and swing risk assessment method for the floating cultural relics by considering the influence of the structural collapse and the showcase overturning risk, provides a scientific basis for judging the earthquake safety of the floating cultural relics, and can be used for guiding scientific implementation of earthquake-proof preventive protection of the floating cultural relics.
Drawings
FIG. 1 is a flow chart of a method for seismic glide and sway risk assessment of a floating relic of the present invention;
FIG. 2 is a graph of a seismic slip delta kinetic analysis of a floating relic obtained in accordance with an embodiment one of the seismic slip and sway risk assessment method of the floating relic of the present invention;
FIG. 3 is a graph of vulnerability to seismic migration of a floating relic obtained in accordance with an embodiment one of the seismic migration and sway risk assessment method of the floating relic of the present invention;
FIG. 4 is a graph of incremental dynamic analysis of museum structure obtained from embodiments one and two of the seismic slip and sway risk assessment method for a floating relic in accordance with the present invention;
FIG. 5 is a graph of vulnerability to earthquake collapse of a museum structure obtained in accordance with embodiments one and two of the seismic glide and sway risk assessment method of a floating relic of the present invention;
FIG. 6 is a graph of a seismic sway delta power analysis of a floating relic obtained in accordance with embodiment two of the seismic slip and sway risk assessment method of the floating relic of the present invention;
fig. 7 is a graph of seismic sway vulnerability of a floating relic obtained by embodiment two of the seismic slip and sway risk assessment method of the floating relic according to the present invention.
Detailed Description
The invention will be further elucidated by means of specific embodiments in conjunction with the accompanying drawings.
Example 1
The embodiment evaluates the risk of earthquake slippage of the floating cultural relics.
The seismic slip risk assessment method for the floating cultural relics in the embodiment, as shown in fig. 1, comprises the following steps:
1) Building a nonlinear finite element model of the cultural relic-showcase-museum system:
firstly, building a nonlinear finite element model of a museum structure according to a structural design drawing of the museum; on the basis, simulating friction and sliding characteristics of a floating interface between the cultural relics and the showcase, and adding a showcase equivalent to a three-dimensional rectangular rigid body and a floating cultural relic model in the showcase, so as to establish a nonlinear finite element model of a cultural relic-showcase-museum system;
in the embodiment, the museum is a four-layer reinforced concrete frame structure, the earthquake fortification intensity is 8 degrees, the field type is II type, the plane size of the museum structure is 13.5m multiplied by 12.9m, the layer height is 3.3m, the section size of a column is 400mm multiplied by 400mm, the section size of a beam is 250mm multiplied by 500mm, the thickness of a floor slab is 100mm, the strength grade of concrete is C30, and the strength grade of reinforcing steel bars is HRB335; in the finite element analysis software OpenSees, a material constitutive model of concrete and steel bars is arranged, a beam column unit based on a compliance method is utilized to simulate a beam column member of a frame structure, a fiber section is utilized to arrange a section restoring force model of the beam column member, and a floor slab is simulated by adopting a rigid partition plate; a maximum layer displacement angle of the museum structure exceeding 1/50 is considered to collapse; aiming at floating cultural relics with the size of 30cm multiplied by 5cm on a second layer, wherein the friction coefficient of the cultural relics and a showcase surface is 0.2, the showcase is fixed on a floor, and the showcase and the cultural relics are simulated by utilizing a beam column unit with infinite rigidity and based on a compliance method; because the aspect ratio of the cultural relics is 6, only pure sliding motion occurs under the earthquake action along the short axial direction of the structure, and friction and sliding characteristics of a floating interface are simulated by using the flat sliding support unit.
2) Evaluating the seismic slip vulnerability of the floating cultural relics, the seismic toppling vulnerability of the showcase and the seismic collapse vulnerability of the museum structure:
i. respectively taking the slippage of the floating relics as engineering demand parameters, respectively dividing the earthquake slippage failure of the floating relics into three layers, defining performance targets of the three layers of the earthquake slippage failure of the floating relics, and defining limit states of the earthquake slippage failure of the floating relics corresponding to the three layers;
in the embodiment, the slippage limit value of the cultural relics is 150mm, and the slippage limit value corresponds to the second level;
according to the place condition of the museum, 14 earthquake waves are selected as input excitation of the museum structure, and the average response spectrum of each earthquake wave is ensured to be consistent with the design response spectrum of the place; the 14 seismic waves are E1 to E14 respectively;
based on a nonlinear finite element model of the cultural relic-showcase-museum system, carrying out incremental power analysis by taking peak ground acceleration as a seismic vibration intensity index and taking the maximum slippage of the floating cultural relic as an engineering demand parameter, and establishing a seismic slippage incremental power analysis curve of the floating cultural relic, as shown in figure 2;
iv, setting the maximum slippage of the floating cultural relics to follow log normal distribution, and establishing a seismic slippage vulnerability function of the floating cultural relics; determining the median value and standard deviation of the seismic slip vulnerability function by a linear regression method based on the seismic slip incremental dynamic analysis curve of the floating cultural relics, and establishing the seismic slip vulnerability curve of the floating cultural relics, as shown in fig. 3;
in the embodiment, the vulnerability of the showcase to earthquake overturning is not considered because the showcase is fixed;
taking peak ground acceleration as a seismic intensity index, taking the maximum interlayer displacement angle of the museum structure as an engineering demand parameter, carrying out incremental power analysis, and establishing an incremental power analysis curve of the museum structure, as shown in fig. 4; setting the maximum interlayer displacement angle of the museum structure to obey the lognormal distribution, and establishing an earthquake collapse vulnerability function of the museum structure; based on the incremental dynamic analysis curve of the museum structure, the median value and standard deviation of the earthquake collapse vulnerability function are determined through a linear regression technology, and the earthquake collapse vulnerability curve of the museum structure is established, as shown in fig. 5.
3) Assessing the risk of seismic slip of the floating cultural relics taking into account three risk factors:
i. three types of risk factors affecting the seismic slip risk estimation of the floating cultural relics are defined:
setting three types of risk factors, wherein the first risk factor represents the earthquake collapse risk of the museum structure, the second risk factor represents the earthquake collapse risk of the showcase, the third risk factor comprises the earthquake slippage risk of the floating cultural relics, and the earthquake slippage risk of the floating cultural relics represents the earthquake slippage risk of the floating cultural relics under the condition that the museum structure is not collapsed and the showcase is not collapsed;
calculating probability estimates for the first and second risk factors:
according to the place conditions of the museum and the Chinese earthquake motion zone parameter diagram, obtaining the annual average overrun probability of different intensity earthquakes of the place of the museum, namely a place danger curve;
the annual average failure probability P of the first risk factor is obtained by convolving the site danger curve with the earthquake collapse vulnerability curve of the museum structure 1 Further obtain the probability estimated value P of the earthquake collapse risk of the museum structure in the service life of the museum structure design SC ：
P SC ＝1-exp(-P 1 ×tL)
Wherein tL is the structural design service life;
in this embodiment, tl=50, and the estimated value P of the risk probability of earthquake collapse of the museum structure is calculated SC ＝0.002；
In this embodiment, since the showcase is fixed, the estimated value P of the probability of risk of earthquake toppling of the showcase SO ＝0；
Calculating a probability estimate of the third risk factor:
aiming at the three-level performance targets, the sliding annual average failure probability of the third risk factors is calculated respectively by convolving the site danger curves with the seismic sliding vulnerability curves of the floating cultural relics of the three-level performance targets respectivelyAnd->Further, the probability estimation value of the earthquake slippage risk of the floating cultural relics corresponding to the performance targets of three layers is obtained under the conditions that the museum structure does not collapse and the showcase does not topple within the service life of the museum structure design:
wherein,and->Probability estimation values of seismic slippage risks of the floating cultural relics corresponding to the three levels of performance targets are respectively obtained;
in the embodiment, the slip limit value is 150mm, and the seismic slip risk probability estimated value of the cultural relics is calculated corresponding to the second level
Calculating probability estimation values of earthquake slip risks of floating cultural relics considering three risk factors:
aiming at three levels of performance targets, calculating the seismic slip risk estimation values of the floating cultural relics considering three types of risk factors respectively:
wherein,and->The method comprises the steps of respectively estimating the earthquake slippage risk probability of the floating cultural relics which correspond to three levels of performance targets and consider three types of risk factors;
in the embodiment, the slip limit value is 150mm, and the seismic slip risk probability estimated value of the cultural relics considering the three risk factors is calculated and obtained corresponding to the second level
4) Rating the earthquake slippage risk of the floating cultural relics:
in this embodiment, the second-stage risk threshold is set to 0.01, and the first-stage risk threshold is set to 0.0001;greater than the first level risk threshold and less than the second level risk threshold, and therefore the risk of seismic slip of the assessed cultural relics is rated as an acceptable risk.
Example two
The embodiment evaluates the earthquake swing risk of the floating cultural relics.
The earthquake swing risk assessment method for the floating cultural relics comprises the following steps:
1) Building a nonlinear finite element model of the cultural relic-showcase-museum system:
firstly, building a nonlinear finite element model of a museum structure according to a structural design drawing of the museum; on the basis, the swinging and collision characteristics of a floating interface between the cultural relics and the showcase are simulated, and a showcase equivalent to a three-dimensional rectangular rigid body and a floating cultural relic model in the showcase are added, so that a nonlinear finite element model of a cultural relic-showcase-museum system is built;
in the embodiment, the museum is a four-layer reinforced concrete frame structure, the earthquake fortification intensity is 8 degrees, the field type is II type, the plane size of the museum structure is 13.5m multiplied by 12.9m, the layer height is 3.3m, the section size of a column is 400mm multiplied by 400mm, the section size of a beam is 250mm multiplied by 500mm, the thickness of a floor slab is 100mm, the strength grade of concrete is C30, and the strength grade of reinforcing steel bars is HRB335; in the finite element analysis software OpenSees, a material constitutive model of concrete and steel bars is arranged, a beam column unit based on a compliance method is utilized to simulate a beam column member of a frame structure, a fiber section is utilized to arrange a section restoring force model of the beam column member, and a floor slab is simulated by adopting a rigid partition plate; maximum layer displacement angles of the museum structure exceeding 1/50 are shown as collapsing; aiming at floating cultural relics with the dimensions of 10cm multiplied by 30cm, wherein the friction coefficient of the cultural relics and a showcase surface is 0.7, the showcase is fixed on a floor slab, and the beam column units with infinite rigidity and based on a compliance method are used for simulating the showcase and the cultural relics; because the aspect ratio of the cultural relics is 3 and the friction coefficient is large enough, only pure swinging motion occurs under the earthquake action along the short axial direction of the structure, and swinging and collision characteristics of a floating interface are simulated by using the rotary spring parallel viscous damper.
2) Evaluating the seismic swing vulnerability of the floating cultural relics, the seismic overturning vulnerability of the showcase and the seismic collapse vulnerability of the museum structure:
i. respectively taking the swing angle of the floating cultural relics as engineering demand parameters, respectively dividing the earthquake swing failure of the floating cultural relics into three layers, defining performance targets of the three layers of the earthquake swing failure of the floating cultural relics, and defining limit states corresponding to the earthquake swing failure of the floating cultural relics under the three layers;
in this embodiment, the third level is considered, that is, when the maximum swing angle of the cultural relic is greater than the static swing angle of 18 °, the cultural relic is turned over, and the seismic swing risk of the cultural relic is the seismic swing risk of the cultural relic.
According to the place condition of the museum, 14 earthquake waves are selected as input excitation of the museum structure, and the average response spectrum of each earthquake wave is ensured to be consistent with the design response spectrum of the place; the 14 seismic waves are E1 to E14 respectively;
based on a nonlinear finite element model of the cultural relic-showcase-museum system, carrying out incremental power analysis by taking peak ground acceleration as a seismic vibration intensity index and taking the maximum swing angle of the floating cultural relic as an engineering demand parameter, and establishing a seismic swing incremental power analysis curve of the floating cultural relic, as shown in fig. 6;
setting the earthquake swing angle of the floating cultural relics to follow the lognormal distribution, establishing an earthquake swing vulnerability function of the floating cultural relics, determining the median value and standard deviation of the earthquake swing vulnerability function based on an earthquake swing incremental dynamic analysis curve of the floating cultural relics through a nonlinear regression method, and establishing an earthquake overturning vulnerability curve of the floating cultural relics, wherein the earthquake overturning vulnerability curve is shown in fig. 7;
in the embodiment, the vulnerability of the showcase to earthquake overturning is not considered because the showcase is fixed;
taking peak ground acceleration as a seismic intensity index, taking the maximum interlayer displacement angle of the museum structure as an engineering demand parameter, carrying out incremental power analysis, and establishing an incremental power analysis curve of the museum structure, as shown in fig. 4; setting the maximum interlayer displacement angle of the museum structure to obey the lognormal distribution, and establishing an earthquake collapse vulnerability function of the museum structure; determining the median value and standard deviation of the earthquake collapse vulnerability function based on the incremental dynamic analysis curve of the museum structure through a linear regression technology, and establishing the earthquake collapse vulnerability curve of the museum structure, as shown in fig. 5;
3) Assessing the risk of earthquake swaying of the floating cultural relics taking three types of risk factors into consideration:
defining three risk factors affecting the seismic swing risk probability estimation value of the floating cultural relics:
setting three types of risk factors, wherein the first risk factor represents the earthquake collapse risk of the museum structure, the second risk factor represents the earthquake collapse risk of the showcase, and the third risk factor comprises the earthquake swing risk of the earthquake floating cultural relics floating the cultural relics, and the earthquake swing risk of the floating cultural relics represents the earthquake swing risk of the floating cultural relics under the condition that the museum structure is not collapsed and the showcase is not tilted;
calculating probability estimates for the first and second risk factors:
according to the place conditions of the museum and the Chinese earthquake motion zone parameter diagram, obtaining the annual average overrun probability of different intensity earthquakes of the place of the museum, namely a place danger curve;
the annual average failure probability P of the first risk factor is obtained by convolving the site danger curve with the earthquake collapse vulnerability curve of the museum structure 1 Further obtain the probability estimated value P of the earthquake collapse risk of the museum structure in the service life of the museum structure design SC ：
P SC ＝1-exp(-P 1 ×tL)
Wherein tL is the structural design service life;
in this embodiment, tl=50, and the estimated value P of the risk probability of earthquake collapse of the museum structure is calculated SC ＝0.002；
In this embodiment, since the showcase is fixed, the estimated value P of the probability of risk of earthquake toppling of the showcase SO ＝0；
Calculating a probability estimate of a third risk factor:
aiming at the three-level performance targets, the earthquake swing vulnerability curves of the floating cultural relics of the three-level performance targets are respectively convolved with the site hazard curves, and the swing annual average failure probability of the third risk factors is respectively calculatedAnd->Further, the probability estimated value of the earthquake swing risk of the floating cultural relics corresponding to the performance targets of three layers is obtained under the conditions that the museum structure does not collapse and the showcase does not topple within the service life of the museum structure design:
wherein,and->Probability estimation values of earthquake swing risks of the floating cultural relics corresponding to the three levels of performance targets respectively;
in the embodiment, considering the third level, the static capsizing angle of the cultural relics is 18 degrees, and calculating to obtain the estimated value of the probability of the earthquake capsizing risk of the cultural relics
Calculating probability estimation values of earthquake swing risk of the floating cultural relics considering three risk factors:
aiming at three levels of performance targets, calculating floating cultural relic earthquake swing risk probability estimation values considering three types of risk factors respectively:
wherein,and->The seismic sway risk probability estimation values of the floating cultural relics which respectively correspond to three levels of performance targets and consider three types of risk factors;
in the embodiment, considering the third level, the static capsizing angle of the cultural relics is 18 degrees, and calculating to obtain the estimated value of the probability of earthquake capsizing risk of the cultural relics considering three types of risk factors
4) Rating the earthquake swing risk of the floating cultural relics:
in this embodiment, the third-level risk threshold is set to 0.02;and the risk threshold value of the third level is larger than the risk threshold value of the third level, so that the earthquake swing risk of the cultural relics obtained by the embodiment is rated as intolerable risk, and cultural relics shockproof measures are required to be adopted.
Finally, it should be noted that the examples are disclosed for the purpose of aiding in the further understanding of the present invention, but those skilled in the art will appreciate that: various alternatives and modifications are possible without departing from the spirit and scope of the invention and the appended claims. Therefore, the invention should not be limited to the disclosed embodiments, but rather the scope of the invention is defined by the appended claims.

Claims (7)

1. The earthquake slippage and sway risk assessment method for the floating cultural relics is characterized by comprising the following steps of:
1) Establishing a nonlinear finite element model of a cultural relic-showcase-museum system;
2) Evaluating the seismic slip and sway vulnerability of the floating cultural relics, the seismic toppling vulnerability of the showcase and the seismic collapse vulnerability of the museum structure:
i. respectively taking the maximum slippage and the maximum swing angle of the floating cultural relics as engineering demand parameters, respectively dividing the earthquake slippage failure and the earthquake swing failure of the floating cultural relics into three layers, defining performance targets of the three layers of the earthquake slippage failure and the earthquake swing failure of the floating cultural relics, and defining limit states of the earthquake slippage failure and the earthquake swing failure of the floating cultural relics corresponding to the three layers;
selecting a plurality of seismic waves as input excitation of a museum structure according to the place condition of the museum, and ensuring that the average reaction spectrum of each seismic wave accords with the design reaction spectrum of the place;
based on a nonlinear finite element model of the cultural relic-showcase-museum system, taking peak ground acceleration as a seismic intensity index, respectively taking the maximum slip quantity and the maximum swing angle of the floating cultural relic as engineering demand parameters, carrying out incremental power analysis, and establishing a seismic slip incremental power analysis curve and a seismic swing incremental power analysis curve of the floating cultural relic;
iv, setting the maximum slippage of the floating cultural relics to follow log normal distribution, and establishing a seismic slippage vulnerability function of the floating cultural relics; determining the median and standard deviation of the earthquake slippage vulnerability function by a linear regression method based on the earthquake slippage incremental dynamic analysis curve of the floating cultural relics, and respectively establishing earthquake slippage vulnerability curves of the floating cultural relics corresponding to three layers of performance targets;
v, setting the maximum swing angle of the floating cultural relics to follow the lognormal distribution, and establishing a seismic swing vulnerability function of the floating cultural relics; based on the earthquake swing incremental dynamic analysis curve of the floating cultural relics, determining the median value and standard deviation of the earthquake swing vulnerability function by a nonlinear regression method, and respectively establishing the earthquake swing vulnerability curves of the floating cultural relics corresponding to the performance targets of three layers;
if the showcase floats, taking peak ground acceleration as a seismic vibration intensity index, taking the maximum swing angle of the showcase as an engineering demand parameter, carrying out incremental power analysis, and establishing a seismic swing incremental power analysis curve of the showcase; determining the median and standard deviation of the earthquake swing vulnerability function by a nonlinear regression method, and establishing an earthquake overturning vulnerability curve of the showcase; if the showcase is fixed, the vulnerability of the showcase to earthquake overturning is not considered;
performing incremental dynamic analysis by taking peak ground acceleration as a seismic intensity index and taking the maximum interlayer displacement angle of the museum structure as an engineering demand parameter, and establishing an incremental dynamic analysis curve of the museum structure; setting the maximum interlayer displacement angle of the museum structure to obey the lognormal distribution, and establishing an earthquake collapse vulnerability function of the museum structure; based on an incremental dynamic analysis curve of the museum structure, determining the median value and standard deviation of the earthquake collapse vulnerability function through a linear regression technology, and establishing an earthquake collapse vulnerability curve of the museum structure;
3) Estimating probability estimation values of seismic slip and sway risk of the floating cultural relics considering three types of risk factors:
i. three types of risk factors affecting the risk probability estimates of seismic slip and sway of the floating cultural relics are defined:
setting three types of risk factors, wherein the first risk factor represents the earthquake collapse risk of the museum structure, the second risk factor represents the earthquake collapse risk of the showcase, the third risk factor comprises the earthquake slippage risk of the floating cultural relics and the earthquake swing risk of the floating cultural relics, the earthquake slippage risk of the floating cultural relics represents the earthquake slippage risk of the floating cultural relics in the case that the museum structure is not collapsed and the showcase is not tilted, and the earthquake swing risk of the floating cultural relics represents the earthquake swing risk of the floating cultural relics in the case that the museum structure is not collapsed and the showcase is not tilted;
calculating probability estimates for the first and second risk factors:
according to the place conditions of the museum and the Chinese earthquake motion zone parameter diagram, obtaining the annual average overrun probability of different intensity earthquakes of the place of the museum, namely a place danger curve;
the annual average failure probability P of the first risk factor is obtained by convolving the site danger curve with the earthquake collapse vulnerability curve of the museum structure 1 Thereby obtaining the earthquake fall of the museum structure within the service life of the design of the museum structureProbability estimate P of collapse risk SC ：
P SC ＝1-exp(-P 1 ×tL)
Wherein tL is the structural design service life;
if the showcase floats, the site danger curve and the earthquake capsizing vulnerability curve of the showcase are convolved to obtain the annual average failure probability P of the second risk factor 2 Further obtaining the probability estimated value P of the earthquake toppling risk of the floating showcase under the condition that the museum structure does not collapse in the service life of the museum structure design SO ：
P SO ＝(1-P SC )×[1-exp(-P 2 ×tL)]；
If the showcase is fixed, probability estimation value P of earthquake toppling risk of showcase SO ＝0；
Calculating a probability estimate of the third risk factor:
aiming at the three-level performance targets, the sliding annual average failure probability of the third risk factors is calculated respectively by convolving the site danger curves with the seismic sliding vulnerability curves of the floating cultural relics of the three-level performance targets respectivelyAnd->Further, the probability estimation value of the earthquake slippage risk of the floating cultural relics corresponding to the performance targets of three layers is obtained under the conditions that the museum structure does not collapse and the showcase does not topple within the service life of the museum structure design:
wherein,and->Probability estimation values of seismic slippage risks of the floating cultural relics corresponding to the three levels of performance targets are respectively obtained;
aiming at the three-level performance targets, the earthquake swing vulnerability curves of the floating cultural relics of the three-level performance targets are respectively convolved with the site hazard curves, and the swing annual average failure probability of the third risk factors is respectively calculatedAnd->Further, the probability estimated value of the earthquake swing risk of the floating cultural relics corresponding to the performance targets of three layers is obtained under the conditions that the museum structure does not collapse and the showcase does not topple within the service life of the museum structure design:
wherein,and->Probability estimation values of earthquake swing risks of the floating cultural relics corresponding to the three levels of performance targets respectively;
calculating the seismic risk probability estimated value of the floating cultural relics considering three risk factors:
aiming at three levels of performance targets, calculating the seismic slip risk estimation values of the floating cultural relics considering three types of risk factors respectively:
wherein,and->The method comprises the steps of respectively estimating the earthquake slippage risk probability of the floating cultural relics which correspond to three levels of performance targets and consider three types of risk factors;
aiming at three levels of performance targets, calculating floating cultural relic earthquake swing risk probability estimation values considering three types of risk factors respectively:
wherein,and->The seismic sway risk probability estimation values of the floating cultural relics which respectively correspond to three levels of performance targets and consider three types of risk factors;
4) The risk of seismic slippage and sway of the floating relics is rated.
2. The assessment method according to claim 1, wherein in step 1, a non-linear finite element model of an cultural relic-showcase-museum system is built, comprising the steps of: firstly, building a nonlinear finite element model of a museum structure according to a structural design drawing of the museum; on the basis, friction, sliding, swinging and collision characteristics of floating interfaces between the cultural relics and the showcase and between the showcase and the floor slab are simulated, and a showcase equivalent to a three-dimensional rectangular rigid body and a floating cultural relic model in the showcase are added, so that a nonlinear finite element model of a cultural relic-showcase-museum system is built.
3. The evaluation method according to claim 1, characterized in that in step i) of step 2) the definition comprises the following:
a) The three layers of earthquake slippage failure and earthquake swing failure of the floating cultural relics are a first layer, a second layer and a third layer respectively;
b) The performance targets of the first to third layers of earthquake slip failure of the floating cultural relics are respectively as follows: non-slip, limited slip and maximum slip, the corresponding limit states are respectively: the slipping occurs, the slipping quantity exceeds a set limit value, and the slipping quantity exceeds the distance between the cultural relics and the edge of the exhibition stand or the distance between the cultural relics and the neighboring cultural relics;
c) The performance targets of the first to third layers of earthquake swing failure of the floating cultural relics are respectively as follows: the non-swing, limited swing and maximum swing are overturning, and the corresponding limit states are respectively as follows: swing occurs, the swing angle exceeds a set limit and the swing angle exceeds the static overturning angle.
4. The method of evaluating according to claim 1, wherein in step ii) of step 2) 10-20 seismic waves are selected as input stimuli for the museum structure.
5. The assessment method according to claim 1, wherein in iii) of step 3) the probability estimate of the third risk factor comprises calculation results for three hierarchical performance targets.
6. The evaluation method according to claim 1, wherein in iv) of step 3), the floating cultural relic seismic risk probability estimation values considering the three types of risk factors include calculation results for three hierarchical performance targets.
7. The assessment method according to claim 1, characterized in that in step 4) the risk of seismic slip and sway of the floating relic is rated, comprising the steps of:
a) Setting multi-level risk thresholds according to the sequence from small to large aiming at three levels of performance targets respectively;
b) If the estimated value of the earthquake slippage risk of the floating cultural relics and the estimated value of the earthquake swing risk of the floating cultural relics are smaller than the first-level risk threshold value, risk is ignored;
c) If the estimated value of the earthquake slippage risk of the floating cultural relics and the estimated value of the earthquake swing risk probability of the floating cultural relics are smaller than the threshold value of the second-stage risk, the risk is acceptable;
d) If the estimated value of the earthquake slippage risk of the floating cultural relics and the estimated value of the earthquake swing risk of the floating cultural relics are smaller than the third-level risk threshold, the risk is tolerable;
e) Otherwise, to be intolerable, cultural relic anti-shock measures must be taken.
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