CN115271406A - Earthquake risk assessment method and device for group building and storage medium - Google Patents

Earthquake risk assessment method and device for group building and storage medium Download PDF

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CN115271406A
CN115271406A CN202210855684.8A CN202210855684A CN115271406A CN 115271406 A CN115271406 A CN 115271406A CN 202210855684 A CN202210855684 A CN 202210855684A CN 115271406 A CN115271406 A CN 115271406A
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宁超列
苏嘉頔
彭勇波
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Abstract

The invention relates to a probability density evolution theory-based group building earthquake risk assessment method, a device and a storage medium, wherein the method comprises probability earthquake risk analysis and group building earthquake vulnerability analysis, and specifically comprises the following steps: acquiring a historical earthquake directory database; dividing a potential seismic source region; determining the relation between earthquake activity parameters and earthquake motion attenuation; generating an earthquake risk curve; determining a consistent risk spectrum; generating a random artificial seismic motion time-course sample curve; acquiring a group building database; establishing a multi-degree-of-freedom bending shear layer model and determining parameters; determining a maximum interlayer displacement angle by adopting a center difference method based on a random artificial seismic motion time-course sample curve; determining a probability density distribution function of the maximum interlayer displacement angle; determining the probability of each building in different damage states; and changing the earthquake recurrence period to generate an earthquake vulnerability curve. Compared with the prior art, the method has the advantages of complete evaluation process, accurate evaluation result and the like.

Description

Earthquake risk assessment method and device for group building and storage medium
Technical Field
The invention relates to the field of earthquake-proof disaster prevention and earthquake-flood insurance of building structures, in particular to a method and a device for evaluating earthquake risks of group buildings based on a probability density evolution theory and a storage medium.
Background
In recent years, under the strong promotion of two engines of industrialization and urbanization, the economy of China keeps increasing at a high speed. The rapid growth of the economy has driven the rapid construction of cities and the rapid growth of urban populations. In this process, local government departments build large numbers of buildings such as houses, apartments, plants and public facilities in order to meet the residential, living and production needs of the large number of people who have come into the cities. Under the background that earthquake disasters are frequently active and the urbanization process is rapidly promoted in China, the following steps can be foreseen: the earthquake disaster risk in China will present the characteristic of urbanization in the future. Therefore, the earthquake disaster risk assessment of urban group buildings is carried out very slowly.
The earthquake disaster risk assessment of urban group buildings comprises two parts of earthquake risk analysis and building structure earthquake vulnerability analysis. However, the current urban group building earthquake risk assessment mainly has the following problems:
(1) Most of the current earthquake risk assessment breaks through earthquake risk analysis and earthquake vulnerability analysis processes. The artificial fracture causes the problems of difficult wave selection, lack of standards, difficulty in considering spatial variability and relevance of earthquake input of group buildings and the like in the current earthquake vulnerability analysis.
(2) The current seismic vulnerability analysis mainly aims at single buildings, and obtains a plurality of seismic vulnerability curves which typically represent the buildings based on fine nonlinear finite element simulation. When the method is applied to the earthquake vulnerability analysis of group buildings, the problems that the typical representative buildings are not selected according to a uniform standard, and the earthquake vulnerability curves of the same type of buildings in different areas are completely the same, so that the method is not consistent with the actual earthquake vulnerability situation exist. However, if a fine nonlinear finite element model is developed for each building, there is a problem that it is difficult for a group of buildings to obtain detailed component dimensions and reinforcement parameters, and a fine nonlinear finite element model cannot be established.
(3) Most of the current earthquake vulnerability analysis obtains a plurality of limited earthquake motion time-course samples according to different selection or earthquake wave generation strategies, and then adopts a lognormal distribution hypothesis to obtain an earthquake vulnerability curve of a building structure, so that the randomness of earthquake motion cannot be completely represented, and if a Monte Carlo simulation method is adopted to fully represent the randomness of earthquake motion, the problems of time consumption and low efficiency of calculation exist when group buildings are faced, and even the phenomenon of immobility of calculation may occur.
Disclosure of Invention
The invention aims to provide a group building earthquake risk assessment method, a device and a storage medium based on a probability density evolution theory, which combine earthquake risk analysis and earthquake vulnerability analysis to improve the calculation efficiency of an assessment process and the accuracy of an assessment result.
The purpose of the invention can be realized by the following technical scheme:
a group building earthquake risk assessment method based on probability density evolution theory comprises probability earthquake risk analysis and group building earthquake vulnerability analysis, wherein,
the probabilistic earthquake risk analysis comprises the following steps:
step 1-1) obtaining a historical earthquake catalogue database of a target area, and calculating the annual average earthquake occurrence rate of each earthquake active area of the target area;
step 1-2) dividing potential earthquake source areas in each earthquake activity area, and determining an upper earthquake magnitude limit and a lower earthquake magnitude limit of each potential earthquake source area;
step 1-3) establishing a spatial probability distribution function by adopting a seismic grading mode;
step 1-4) determining the annual average earthquake occurrence rate of the magnitude gear of the ith potential source region of each earthquake activity area by taking the jth magnitude as the center based on the spatial probability distribution function, the upper magnitude limit and the lower magnitude limit of the earthquake activity area;
step 1-5) rasterization processing is carried out on a target area, the attenuation relation of seismic dynamic acceleration response spectrum parameters is determined, the self-vibration period of a building structure in each grid is increased from 0 second to the upper limit of the pre-configured self-vibration period of the building structure at the preset self-vibration period change interval, the annual average exceeding probability that the acceleration response spectrum parameters of the center of each grid exceed the threshold value of the pre-configured parameters is calculated based on the annual average occurrence rate of earthquakes of the seismic level grade with the jth seismic level as the center in the ith potential seismic source area of each seismic activity area, and the seismic hazard curves of the center of each grid under different self-vibration periods of the building structure are generated;
step 1-6) determining the spectral acceleration of different building structure self-vibration periods at the center of each grid according to the pre-configured earthquake recurrence period and the corresponding annual average transcendence probability to obtain consistent risk spectra of different earthquake recurrence periods;
step 1-7), based on the consistent risk spectrum of each grid center in different earthquake recurrence periods, generating random artificial earthquake motion time-course sample curves of each grid center in different earthquake recurrence periods by adopting a physical random earthquake motion model;
the group building earthquake vulnerability analysis comprises the following steps:
step 2-1) obtaining a group building database and carrying out basic attribute classification, wherein the basic attributes of the group building comprise: building age, building height, structure type, use type and floor area;
step 2-2) for each building, characterizing the deformation characteristics of each layer by using an elastic bending beam and a nonlinear shearing spring, and establishing a multi-degree-of-freedom bending shearing type layer model;
step 2-3) determining parameters of the multi-degree-of-freedom bending shear layer model based on basic attributes of group buildings and pre-configured parameter calibration rules;
step 2-4) inputting random artificial earthquake motion time-course sample curves of the grid center of each building in different earthquake recurrence periods, and determining the maximum interlayer displacement angle of each building by adopting a center difference method, wherein the random artificial earthquake motion time-course sample curves of the grid center in different earthquake recurrence periods are determined based on the steps 1-1) -1-7);
step 2-5) determining a probability density distribution function of the maximum interlayer displacement angle of each building based on a generalized probability density evolution equation;
step 2-6) determining maximum interlayer displacement angle thresholds of the buildings in different damage states according to basic attributes of each building, and determining the probability of each building in different damage states based on the probability density distribution function of the maximum interlayer displacement angle and the maximum interlayer displacement angle threshold;
and 2-7) changing the earthquake recurrence period, and repeating the steps 2-4) -2-7) to generate an earthquake vulnerability curve of each building based on the earthquake recurrence period.
The annual average overrun probability is:
Figure BDA0003754454240000031
in the formula, mk、rkAnd thetakThe magnitude, the epicenter distance and the azimuth angle of the kth earthquake are respectively;
Figure BDA0003754454240000032
the annual average earthquake occurrence rate of the magnitude gear which is centered on the j magnitude for the ith potential source region of each earthquake activity region; n is a radical of hydrogenpThe number of potential seismic source regions; n is a radical ofmThe number of the vibration level interval gears is set; n is a radical of hydrogeneThe number of earthquakes occurring at each seismic interval for each potential source zone.
The steps 1-7) comprise the following steps:
step 1-7-1) taking the consistent danger spectrum of each grid center in different earthquake recurrence periods as a target reaction spectrum, and converting the consistent danger spectrum into a bedrock power spectrum according to the approximate relation between the target reaction spectrum and the power spectrum:
Figure BDA0003754454240000041
in the formula, S0For consistent risk spectrum at different seismic recurrence periods at each grid center, S isPower spectrum of bedrock, omegaiIs the ith order frequency of seismic waves, eta is the damping ratio, P is the annual average transcendental probability of the consistent risk spectrum, T0The duration of the stationary section of the random artificial seismic motion time-course sample curve is obtained;
step 1-7-2) based on a bedrock power spectrum, aiming at a target area, describing the randomness of artificial earthquake motion by adopting a random Fourier spectrum:
Figure BDA0003754454240000042
wherein F is the earth surface power spectrum, omega0The method comprises the following steps of (1) taking excellent frequency of a field, wherein zeta is equivalent damping ratio of the field, and both are basic random variables;
step 1-7-3), assuming that a random artificial earthquake motion time-course sample curve meets a stable Gaussian process, converting an earth surface power spectrum into a Fourier amplitude spectrum:
Figure BDA0003754454240000043
in the formula, Δ ω is a sampling interval, Δ ω =2 pi/T, and T is a basic period of the building structure;
step 1-7-4) decomposing the phase angle of the random artificial earthquake motion time-course sample curve into initial phase angles
Figure BDA0003754454240000044
Spectrum of phase difference from basic phase
Figure BDA0003754454240000045
Figure BDA0003754454240000046
Wherein the initial phase angle
Figure BDA0003754454240000047
As basic random variables, basic phase difference spectrum
Figure BDA0003754454240000048
Comprises the following steps:
Figure BDA0003754454240000049
wherein A is an index parameter;
step 1-7-5) converting the basic phase difference spectrum into a sequence distributed from lognormal, normalizing the sequence, and comparing the normalized sequence with an initial phase angle
Figure BDA00037544542400000410
Adding to obtain the phase angle of the random artificial earthquake motion time-course sample curve
Figure BDA00037544542400000411
Step 1-7-6) adopts a ball-cutting point-selecting method based on site excellent frequency omega0Field equivalent damping ratio ζ and initial phase angle
Figure BDA00037544542400000412
Generating a random sample by using three basic random variables;
step 1-7-7) synthesizing each random sample into a random artificial earthquake motion time-course sample curve by adopting a spectral representation method:
Figure BDA0003754454240000051
in the formula (I), the compound is shown in the specification,
Figure BDA0003754454240000052
the phase angle of a random artificial seismic motion time-course sample curve is shown, and I is a deterministic intensity envelope function:
Figure BDA0003754454240000053
in the formula, T1、T2And T is the amplitude rise time, the amplitude fall starting time and the total duration of the random artificial seismic motion time-course sample curve respectively, and c is the attenuation coefficient of the seismic motion peak acceleration.
The parameters of the multi-degree-of-freedom bending shear layer model comprise: equivalent layer mass m, moment of inertia J, building height L, structural layer height H, bending stiffness EI and shearing stiffness ksShear yield angle ε and degradation parameter τ.
The motion control differential equation of the multi-degree-of-freedom bending shear layer model is as follows:
Figure BDA0003754454240000054
Figure BDA0003754454240000055
wherein C is a damping matrix of the structure,
Figure BDA0003754454240000056
the method comprises the steps that a sample curve of an input random artificial seismic motion time course is obtained, u is a displacement response, theta is a corner response, and N is the number of structural layers and is determined by a building height L and a structural layer height H; f. ofsiTo construct the restoring force of the i-th layer nonlinear shear spring, the shear stiffness ksDetermining a shearing yield corner epsilon and a degradation parameter tau; k is a radical ofiiA stiffness matrix for a structural ith layer of flexural elastic beams is expressed as:
Figure BDA0003754454240000061
where EI is the bending stiffness of the bending spring beam.
The step 2-3) is specifically as follows:
assuming that the mass of the building structure is uniformly distributed along the floor height, determining the equivalent floor mass m according to the floor area;
assuming that each floor of the building structure is a cuboid, and determining the moment of inertia J according to the floor area and the equivalent floor mass m;
determining a structural floor height H based on the building type;
determining bending rigidity EI based on the mass density of the structure along the height direction, structural modal characteristic parameters, bending shear rigidity ratio and structural layer height;
determining shear stiffness k based on bending stiffness, bending shear stiffness ratio and structural layer heights；
Determining a shear yield corner epsilon based on shear bearing capacity, shear rigidity and structural layer height;
the degradation parameter τ is determined based on the structure type and the age of the building.
The step 2-5) comprises the following steps:
step 2-5-1) introduces a virtual random process based on a generalized probability density evolution equation, and determines the probability density distribution of the maximum interlayer displacement angle:
Figure BDA0003754454240000062
wherein X is the maximum interlayer displacement angle; Θ is a random vector space, comprising three basic random variables: site prominent frequency omega0Field equivalent damping ratio ζ and initial phase angle
Figure BDA0003754454240000063
Figure BDA0003754454240000064
Evolution speed, p, of maximum interlayer displacement angleXΘIs a joint probability density distribution;
step 2-5-2) solving a generalized probability density evolution equation by adopting a finite difference format, integrating theta to obtain a probability density distribution function of the maximum interlayer displacement angle:
Figure BDA0003754454240000065
the influence factors of the maximum interlayer displacement angle threshold value comprise the structure type, the building height and the earthquake fortification level.
A group building earthquake risk assessment device based on probability density evolution theory comprises a memory, a processor and a program stored in the memory, wherein the processor executes the program to realize the method.
A storage medium having stored thereon a program which, when executed, implements the method as described above.
Compared with the prior art, the invention has the following beneficial effects:
(1) The method combines the probabilistic earthquake risk analysis step with the earthquake vulnerability analysis step, obtains consistent risk spectrums under different earthquake recurrence periods of different grid centers in a target field based on the probabilistic earthquake risk analysis, and generates a random artificial earthquake motion time-history sample curve by adopting a physical random earthquake motion model, thereby solving the problems of wave selection difficulty and standard shortage in the traditional earthquake vulnerability analysis and difficulty in reflecting the space variability of earthquake motion input of group buildings, and ensuring that the earthquake risk evaluation result of the group buildings is more complete;
(2) According to the method, each building is simplified into a 7-parameter multi-degree-of-freedom curved shear layer model, a rule for calibrating 7 model parameters based on 5 basic attributes of the group building is provided, and the problems that the existing building structure is simplified, the model parameters are numerous, the calibration is difficult, the calculation is time-consuming, and the method is difficult to be applied to inelastic vibration force response analysis of the group building are solved, so that the earthquake risk evaluation efficiency of the group building is higher;
(3) The generalized probability density evolution equation is introduced into the earthquake vulnerability analysis of the group building, the probability density distribution of the maximum interlayer displacement angle is calculated, and the lognormal distribution assumption adopted by the traditional earthquake vulnerability analysis is abandoned, so that the earthquake risk evaluation result of the group building is more reasonable.
(4) The earthquake vulnerability curve of the group building is represented by the earthquake recurrence period, so that the problem that the traditional indexes such as earthquake peak acceleration, spectrum acceleration, earthquake damage and the like are not suitable for the earthquake vulnerability analysis of the group building is solved, and the earthquake risk evaluation result of the group building is more practical.
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FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a schematic diagram of a distribution of historical seismic events in a target area;
FIG. 3 is a graph showing the annual average incidence of earthquake v for each seismic activity area using the Gutenberg-Richirest relationship in an embodiment of the present inventionmThe estimation result of (a) is north area and (b) is middle area;
FIG. 4 illustrates a potential seismic source region partition of a target region according to an embodiment of the present invention;
FIG. 5 is a seismic dynamic acceleration response spectrum parameter attenuation relation according to the embodiment of the invention;
FIG. 6 is a seismic risk curve for grid A and grid B in accordance with an embodiment of the present invention;
FIG. 7 is a consensus risk spectrum for grid A and grid B, where (a) is the consensus risk spectrum for grid A and (B) is the consensus risk spectrum for grid B, according to an embodiment of the present invention;
FIG. 8 is a sample plot of a random artificial seismic time interval of an embodiment of the present invention, wherein (a) represents a 50-year recurrence period, (b) represents a 100-year recurrence period, (c) represents a 475-year recurrence period, (d) represents a 949-year recurrence period, (e) represents a 1600-year recurrence period, and (f) represents a 4950-year recurrence period;
FIG. 9 is a group building distribution at grid A in accordance with an embodiment of the present invention;
FIG. 10 is a schematic structural diagram of a multi-degree-of-freedom curved shear-type layer model;
FIG. 11 is a graph of probability density distribution for maximum inter-floor displacement angle for a building;
FIG. 12 is a graph of seismic vulnerability of a building.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.
A group building earthquake risk assessment method based on a probability density evolution theory is shown in figure 1 and comprises two parts of probability earthquake risk analysis and group building earthquake vulnerability analysis. Wherein, the first and the second end of the pipe are connected with each other,
the probabilistic earthquake risk analysis comprises the following steps:
step 1-1) obtaining a historical earthquake catalogue database of a target area, and estimating the annual average earthquake occurrence rate v of each earthquake activity area by adopting a classic Gutenberg-Richcet relationship (G-R)mThe calculation expression is as follows:
lgvm＝a-b·M
in the formula, M is the magnitude, and a and b are empirically fitted values.
Step 1-2) dividing potential earthquake source areas in each earthquake activity area, and determining an upper earthquake magnitude limit and a lower earthquake magnitude limit of each potential earthquake source area;
step 1-3) establishing a spatial probability distribution function by adopting a seismic grading mode;
step 1-4) determining the annual average earthquake occurrence rate of the earthquake magnitude center of the jth earthquake magnitude in the ith potential earthquake source area of each earthquake activity area based on the spatial probability distribution function and the upper and lower earthquake magnitude limits of the earthquake activity area
Figure BDA0003754454240000081
Figure BDA0003754454240000082
In the formula, MuAnd M0Respectively representing the upper limit and the lower limit of the seismic level of each seismic activity area; β = b × ln10, b being the empirically fitted value in step 1-1); Δ M is the interval of vibration level grading, generally 0.5; sh is a hyperbolic sine function;
Figure BDA0003754454240000083
for the spatial probability distribution function of seismic grade grading, simple estimation can be carried out by adopting the area ratio of potential seismic source areas in each seismic activity area, and the following conditions are met:
Figure BDA0003754454240000084
the annual average incidence of an earthquake is the seismic activity parameter described in figure 1.
Step 1-5) rasterizing a target area, determining an earthquake dynamic acceleration response spectrum parameter attenuation relation, increasing the self-vibration period of the building structure in each grid from 0 second to the upper limit of the self-vibration period of the building structure according to the change interval of the pre-configured self-vibration period, and based on the annual average earthquake occurrence rate v of an earthquake magnitude grade with the jth earthquake magnitude as the center in the ith potential earthquake source area of each earthquake activity areai,MjCalculating the annual average exceeding probability of the acceleration response spectrum parameter of each grid center exceeding a preset parameter threshold value, and generating earthquake risk curves of each grid center under different building structure self-vibration periods;
the seismic dynamic acceleration response spectrum parameter attenuation relation is described by an elliptic function, and the expressions of the major axis and the minor axis are as follows:
logSa＝e1+e2M+e3log[R+e4exp(e5M)]
in the formula, SaThe seismic oscillation response spectrum acceleration is obtained; r is the distance from the center position of each grid to the earthquake occurrence position, e1～e5Are empirical regression coefficients.
The annual average overrun probability is:
Figure BDA0003754454240000091
in the formula, mk、rkAnd thetakThe magnitude, the epicenter distance and the azimuth angle of the kth earthquake are respectively;
Figure BDA0003754454240000092
the annual average earthquake occurrence rate of the magnitude gear which is centered on the j magnitude for the ith potential source region of each earthquake activity region; n is a radical ofpThe number of potential seismic source regions; n is a radical ofmThe number of the earthquake magnitude interval gears is set; n is a radical of hydrogeneFor each potential seismic source regionThe number of earthquakes occurring in each seismic interval.
Step 1-6) determining the spectral acceleration of different building structure self-vibration periods at the center of each grid according to the pre-configured earthquake recurrence period and the corresponding annual average transcendence probability to obtain consistent risk spectra of different earthquake recurrence periods;
the earthquake recurrence period RP and the annual average transcendental probability satisfy the following relationship:
Figure BDA0003754454240000093
step 1-7), based on the consistent risk spectrum of each grid center in different earthquake recurrence periods, generating random artificial earthquake motion time-course sample curves of each grid center in different earthquake recurrence periods by adopting a physical random earthquake motion model;
step 1-7-1) taking the consistent danger spectrum of each grid center in different earthquake recurrence periods as a target reaction spectrum, and converting the consistent danger spectrum into a bedrock power spectrum according to the approximate relation between the target reaction spectrum and the power spectrum:
Figure BDA0003754454240000094
in the formula, S0For consistent risk spectrum at different seismic recurrence periods at each grid center, S is the power spectrum of the bedrock, omegaiIs the ith order frequency of the seismic wave, eta is the damping ratio, if no special condition exists, 0.05 can be taken, P is the annual average transcendental probability of the consistent risk spectrum, T0The duration of the stationary section of the random artificial seismic motion time-course sample curve is obtained;
step 1-7-2) based on a bedrock power spectrum, aiming at a target area, describing the randomness of artificial earthquake motion by adopting a random Fourier spectrum:
Figure BDA0003754454240000101
in the formula, F is a ground surface power spectrum; omega0The site dominance frequency can be regarded as a basic random variable; zeta is the equivalent damping ratio of the field and can be regarded as a basic random variable;
step 1-7-3), assuming that a random artificial seismic oscillation time-course curve sample meets a stable Gaussian process, converting a surface power spectrum into a Fourier amplitude spectrum:
Figure BDA0003754454240000102
in the formula, Δ ω is a sampling interval, Δ ω =2 pi/T, and T is a basic period of the building structure;
step 1-7-4) decomposing the phase angle of the random artificial seismic motion time-course sample curve into initial phase angles
Figure BDA00037544542400001013
Spectrum of phase difference from basic phase
Figure BDA0003754454240000103
Figure BDA0003754454240000104
Wherein the initial phase angle
Figure BDA0003754454240000105
As a substantially random variable, a substantially phase difference spectrum
Figure BDA0003754454240000106
Comprises the following steps:
Figure BDA0003754454240000107
in the formula (I), the compound is shown in the specification,
Figure BDA0003754454240000108
a smaller value, which may be 0.01; a is an exponential parameter, and the obtained basic phase difference spectrum can be subjected to logarithmic correction by adjusting the valueThe state distribution can be 3 in general.
Step 1-7-5) converting the basic phase difference spectrum into a sequence distributed from a lognormal mode, normalizing the sequence, and then comparing the normalized sequence with an initial phase angle
Figure BDA0003754454240000109
Adding to obtain the phase angle of the random artificial earthquake motion time-course sample curve
Figure BDA00037544542400001010
The method specifically comprises the following steps: subjecting the sequence generated in step 1-7-1)
Figure BDA00037544542400001011
Taking the rest, taking the rest as negative, and normalizing the rest to be [0, -2 pi ]]Interval, the sequence obtained at this time obeys a uniform distribution. Further, according to the method for generating the lognormal distribution random number by uniformly distributing the random number, the standard phase difference spectrum is converted into a sequence of numbers distributed from the lognormal distribution;
Figure BDA00037544542400001012
the obtained u and v are random numbers independent of each other and obey a standard normal distribution. Further, u and v are converted into a set of arrays that follow a lognormal distribution. The mean of the lognormal distribution is pi and the standard deviation is 0.8 pi. Finally, the generated number sequence is normalized to [0, -2 pi ] in a negative and residual mode]Interval, and comparing the generated sequence with the initial phase angle
Figure BDA0003754454240000111
And adding to obtain the phase angle of the random artificial seismic motion time-course sample curve.
Step 1-7-6) adopts a ball-cutting point-selecting method based on site excellent frequency omega0Field equivalent damping ratio ζ and initial phase angle
Figure BDA0003754454240000112
Generating a random sample by using three basic random variables;
step 1-7-7) synthesizing each random sample into a random artificial earthquake motion time-course sample curve by adopting a spectral representation method:
Figure BDA0003754454240000113
in the formula (I), the compound is shown in the specification,
Figure BDA0003754454240000114
the phase angle of a random artificial seismic motion time-course sample curve is shown, I is a deterministic intensity envelope function to reflect the non-stationarity of seismic motion amplitude, and the following form can be adopted:
Figure BDA0003754454240000115
in the formula, T1、T2And T is the amplitude rise time, the amplitude fall starting time and the total duration of the random artificial seismic motion time-course sample curve respectively, and c is the attenuation coefficient of the seismic motion peak acceleration.
In the step of probability earthquake risk analysis, the steps 1-1) -1-5) are used for completing earthquake risk analysis and generating an earthquake risk curve; step 1-6) -step 1-7) are used for generating a random artificial earthquake motion time-course sample curve and providing parameters for earthquake vulnerability analysis of group buildings.
The group building earthquake vulnerability analysis comprises the following steps:
and 2-1) acquiring a group building database and carrying out basic attribute classification. The basic attributes of the group building comprise: building age, building height, structure type, use type and floor area;
the basic attribute classification rule of the group building is as follows:
(1) construction times
The construction age is a specific numerical value and can be further divided into: non-fortification (before 1989), low fortification (1990-2000), medium fortification (2001-2010) and high fortification (after 2010).
(2) Building height
The building height is a specific numerical value and can be further divided into: 3 categories of a low layer (less than 9 meters), a middle layer (9 meters to 21 meters) and a high layer (more than 21 meters).
(3) Type of construction
The structure types are divided into: masonry structures, reinforced concrete frame-shear wall structures, steel structures, and other structures 5 categories.
(4) Type of use
The usage types are divided into: residential buildings, commercial buildings, industrial buildings, utilities, and other types 5 categories.
(5) Floor area
The floor area is a specific numerical value and can be further divided into the following steps: small-sized building (less than 150 m)2) Medium-sized building (150 m)2～600m2) Large building (600 m)2～3000m2) And very large buildings (greater than 3000 m)2) 4 categories.
Step 2-2) for each building, representing the deformation characteristics of each layer by using an elastic bending beam and a nonlinear shearing spring, and establishing a multi-degree-of-freedom bending-shearing-type layer model as shown in FIG. 10;
the parameters of the multi-degree-of-freedom bending shear layer model comprise: equivalent layer mass m, moment of inertia J, building height L, structural layer height H, bending stiffness EI and shearing stiffness ksShear yield angle ε and degradation parameter τ.
The motion control differential equation of the multi-degree-of-freedom bent shear layer model is as follows:
Figure BDA0003754454240000121
Figure BDA0003754454240000122
wherein C is a damping matrix of the structure,
Figure BDA0003754454240000123
the method comprises the steps that a sample curve of an input random artificial seismic motion time course is obtained, u is a displacement response, theta is a corner response, and N is the number of structural layers and is determined by a building height L and a structural layer height H; f. ofsiTo construct the restoring force of the i-th layer nonlinear shear spring, the shear stiffness ksDetermining a shearing yield corner epsilon and a degradation parameter tau; k is a radical of formulaiiA stiffness matrix for a structural ith layer of flexural elastic beams is expressed as:
Figure BDA0003754454240000131
where EI is the bending stiffness of the bending spring beam.
Step 2-3) determining parameters of the multi-degree-of-freedom bending shear layer model based on basic attributes of the group buildings and pre-configured parameter calibration rules;
the parameter calibration rule is as follows:
(1) mass m of equivalent layer
Assuming that the mass of the building structure is uniformly distributed along the floor height, estimating the equivalent floor mass m according to the floor area:
m＝ρ×S
where S is the floor area, ρ is the mass density per unit area, and is related to the structure type and the building height, the following values can be used as the estimation basis: (1) masonry structure: 17kN/m2(ii) a (2) a reinforced concrete frame structure: 11 to 16kN/m2(ii) a (3) a reinforced concrete frame-shear wall structure: 13 to 16kN/m2(ii) a (4) steel structure: 8kN/m2(ii) a (5) other structures: 12kN/m2. And when the number of layers of the reinforced concrete frame structure and the reinforced concrete frame-shear wall structure is greater than 20, taking the upper limit value, and when the number of layers is less than 5, taking the lower limit value.
(2) Moment of inertia J
Assuming that each floor of the building structure is a cuboid, estimating the moment of inertia J according to the floor area and the equivalent floor mass m:
Figure BDA0003754454240000132
in the formula, B is the side length of a cuboid and can be estimated according to the floor area S; h is0The thickness of the floor slab can be 1 meter.
(3) Structural layer height H
The structure layer height H is related to the type of use and is estimated as follows: (1) residential buildings: 3m; (2) commercial construction: 2.8m; (3) industrial construction: 4m; (4) utilities and other types: 3.5m.
(4) Bending stiffness EI
Figure BDA0003754454240000133
Where κ is the mass density of the structure in the height direction, and may be determined from
Figure BDA0003754454240000134
Estimating; alpha (alpha) ("alpha")0Bending shear stiffness ratio:
Figure BDA0003754454240000135
wherein, γ1And gamma2Characteristic parameters related to the ith-order mode of the structure can be calculated by the following formula:
Figure BDA0003754454240000141
T1is the first order natural vibration period of the building structure, and is related to the structure type and the building height. For the reinforced concrete frame structure, the reinforced concrete frame-shear wall structure and the steel structure type, the following empirical formula can be adopted for estimation:
T1＝C1Hx
wherein, (1) reinforced concrete frame structure: c1=0.0466, x =0.9; (2) Reinforced concrete frameFrame-shear wall structure: c1=0.0731, x =0.75; (3) steel structure: c1=0.0724, x =0.8. For masonry and other structures, the following empirical formula can be used for estimation:
T1＝0.221+0.225×N
T2for the second order natural period of the building structure, the following empirical formula can be used for estimation:
T2＝0.27T1
(5) shear stiffness ks
Figure BDA0003754454240000142
(6) Shear yield angle epsilon
The shear yield angle ε may be calculated according to the following formula:
Figure BDA0003754454240000143
in the formula, VyTo obtain the yield bearing capacity of the nonlinear shear spring, the design bearing capacity V of each layer of the structure can be first calculateddAnd then multiplied by the super power coefficient omega. Design bearing capacity V of each layer of the structuredCan be determined by the following steps:
1) Based on the rigidity matrix K and the mass matrix M of the building structure, calculating the self-vibration period T of each order of the structure by adopting a vibration mode decomposition reaction spectrum methodnSum mode vector
Figure BDA0003754454240000144
2) Determining the anti-seismic design standard adopted by the design according to the construction age of the building structure, and simultaneously combining the site information to obtain the design response spectrum S of the building structurea；
3) Design reaction spectrum S of structureaConversion into shift response spectrum Sd. At the same time, according to the self-oscillation period T of each stage of the structurenObtaining the corresponding spectral displacement D of each order vibration moden：
Figure BDA0003754454240000145
4) According to each order of vibration pattern vector
Figure BDA0003754454240000151
Sum spectral shift DnCalculating the interlayer displacement u corresponding to each order vibration mode of the structuren(ii) a Based on the interlayer displacement unCalculating the peak bearing capacity corresponding to each order vibration mode:
Figure BDA0003754454240000152
5) Combining the peak bearing capacity of each order of vibration mode by adopting an SRSS method to obtain the total peak bearing capacity of each layer of the structure:
Figure BDA0003754454240000153
6) Considering that the bearing capacity of each layer is not less than 20% of the total shearing force of the bottom, adjusting the peak bearing capacity of each layer of the structure:
Vd＝max[Va,0.2Vb]
wherein, VbIs the substrate total shear;
7) The peak bearing capacity V of each layer of the structuredAnd multiplying by the peak value superstrong coefficient omega of the structure to obtain the yield bearing capacity of the structure:
Vy＝ΩVd
the peak superstrength coefficient Ω is estimated according to the following: (1) masonry structure: Ω =2; (2) a reinforced concrete frame structure: Ω =3; (3) a reinforced concrete frame-shear wall structure: Ω =2.5; (4) steel structure: Ω =3; (5) other structures: Ω =2.
(7) Degradation parameter tau
The degradation parameter tau is related to factors such as structure type and building age, and can be estimated by adopting the following numerical values:
1) Masonry structure: 0.6 (after 2010), 0.4 (2001 to 2010), 0.3 (1990 to 2001), 0.2 (1990 ago);
2) Reinforced concrete frame structure and frame-shear wall structure: 0.7 (after 2010), 0.6 (2001 to 2010), 0.5 (1990 to 2001), 0.4 (1990 ago);
3) Steel structure: 0.9 (1990 ago), 0.8 (2001 to 2010), 0.7 (1990 to 2001), 0.6 (1990 ago);
4) Other structures: 0.5 (after 2010), 0.3 (2001 to 2010), 0.2 (1990 to 2001), 0.1 (1990 ago).
And 2-4) inputting random artificial earthquake motion time-course samples of the grid center of each building in different earthquake recurrence periods, and determining the maximum interlayer displacement angle of each building by adopting a center difference method. Determining a random artificial earthquake motion time-course sample curve of the grid center in different earthquake recurrence periods based on the steps 1-1) to 1-7);
step 2-5) introducing a virtual random process based on a generalized probability density evolution equation, and determining a probability density distribution function of the maximum interlayer displacement angle of each building;
step 2-5-1) based on the generalized probability density evolution equation, introducing a virtual random process to determine the probability density distribution of the maximum interlayer displacement angle:
Figure BDA0003754454240000161
wherein X is the maximum interlayer displacement angle; Θ is a random vector space, comprising three random variables: site prominent frequency omega0Field equivalent damping ratio ζ and initial phase angle
Figure BDA0003754454240000162
Figure BDA0003754454240000163
Evolution speed, p, of maximum interlayer displacement angleXΘIs a combined summaryA rate density distribution;
step 2-5-2) solving a generalized probability density evolution equation by adopting a finite difference format, and integrating theta to obtain a probability density distribution function of the maximum interlayer displacement angle:
Figure BDA0003754454240000164
step 2-6) determining the maximum interlayer displacement angle threshold value of the building in different damage states according to the basic attribute of each building, and determining the probability of each building in different damage states based on the probability density distribution function of the maximum interlayer displacement angle and the maximum interlayer displacement angle threshold value;
the influence factors of the maximum interlayer displacement angle threshold value comprise the structure type, the building height and the earthquake fortification level. Wherein, the maximum interlayer displacement angle threshold values of the middle-level building and the high-level building can be 2/3 and 1/2 of the corresponding low-level building.
The damage states include mild, moderate, severe and devastating states.
And 2-7) changing the earthquake recurrence period, and repeating the steps 2-4) -2-7) to generate an earthquake vulnerability curve of each building based on the earthquake recurrence period.
The present embodiment adopts the above method to perform earthquake risk assessment on group buildings in a certain target area, so as to further describe in detail.
A certain target area is located along the east coast of china, along the west coast of the pacific, along the east edge of the continental asia, at the front edge of the delta of the Yangtze river. The area belongs to a part of Yangtze river delta alluvial plain, the average altitude is about 2 meters, and most of the urban area is covered by a silt layer formed by the deposition of rivers and oceans for over 300 ten thousand years. The intense urbanization process and the rapid changing of land planning of target areas since 90 years of the 20 th century led to the appearance of the coexistence of skyscrapers and older buildings throughout the city. In recent years, a target area is subjected to strong earthquake in a far field for many times, so that the earthquake feeling of a part of high-rise building structures is obvious.
Probability earthquake danger analysis:
the historical earthquake catalogue data of the target area above level 4.0 from the year 1500 to the year 2020 of the notations are collected and collated, and the distribution is shown in fig. 2. It can be seen that over 4.0-level earthquakes occur in the target area 100 times since the year 1500 of the axiom. Wherein, the earthquake of 4.0 grade to 4.9 grade is 29 times, the earthquake of 5.0 grade to 5.9 grade is 48 times, the earthquake of 6.0 grade to 6.9 grade is 22 times, and the earthquake of 7 grade and above is 1 time.
In view of the southern yellow sea seismic zone of Yangzhou (the southern yellow sea seismic zone downstream of Yangtze river) under the seismic area of North China. According to the geologic structure and the motion of a new structure, the seismic zone can be divided into three seismic activity statistical zones from north to south, namely a northern Subei seismic activity zone, a southern Huanghai seismic activity zone (hereinafter referred to as a north zone), a middle southern Sunan seismic activity zone, a Thunbei seismic activity zone and a northeast China seismic activity zone (hereinafter referred to as a middle zone) and a Thunbei seismic activity zone (hereinafter referred to as a south zone) with north latitude of 29.8 degrees as a south. Because the earthquake activity level of the southern earthquake region of the south is low relative to that of the north region and the middle region, the earthquake activity level is weak in strength and has no statistical significance, only the average annual earthquake occurrence rate v of the north region and the middle region is estimated by adopting the classic Gutenberg-Richihite relation (G-R)mAs shown in fig. 3. Wherein the values of a and b of the north area are 4.8913 and 0.6398 respectively, and the values of a and b of the middle area are 4.6001 and 0.6764 respectively.
The north and south regions may be collectively divided into 24 potential seismic source regions, as shown in FIG. 4. Wherein, the north area comprises 8 potential seismic source areas, the middle area comprises 16 potential seismic source areas, and the upper limit of the magnitude of each potential seismic source area is estimated. Meanwhile, a seismic grade grading mode is adopted, a spatial probability distribution function is established based on the area ratio of the potential seismic source areas, and the annual average earthquake occurrence rate of seismic grade gears of the ith potential seismic source area of each seismic activity area with the jth seismic grade as the center is obtained, and is shown in the following table.
Figure BDA0003754454240000171
Figure BDA0003754454240000181
The attenuation relation of seismic dynamic acceleration response spectrum parameters of the target area is described in an elliptic function form, and is shown in figure 5.
Dividing the whole research area into 30 × 30 grids, wherein the grid interval is 2.5 km, sequentially changing the self-vibration period of the building structure in each grid from 0 second to 6 seconds at intervals of 0.05 second by adopting a Monte Carlo simulation method, calculating the transcendence probability of the central acceleration response spectrum parameter of each grid exceeding a certain value, and generating a corresponding earthquake risk curve as shown in FIG. 6.
The overrun probabilities for grid a and grid B were set to 63.2%, 10% and 2% in 50 and 100 years, respectively. Wherein, the 50-year exceeding probability of 63.2 percent, 10 percent and 2 percent respectively corresponds to a frequently encountered earthquake (50-year recurrence period), a fortifying earthquake (475-year recurrence period) and a rarely encountered earthquake (1600-year recurrence period) of the earthquake-resistant design specification of the building structure in China; the 100-year transcendence probabilities of 63.2%, 10% and 2% respectively correspond to a 100-year recurrence period, a 949-year recurrence period and a 4950-year recurrence period, spectral accelerations of different building structure natural vibration periods at the centers of the grid A and the grid B are calculated, and consistent risk spectrums of the grid A and the grid B with different earthquake recurrence periods are generated, as shown in FIG. 7.
Based on the consistent risk spectrum of the grid A in different earthquake recurrence periods, a physical random earthquake motion model is adopted to generate artificial earthquake motion time-course samples in different earthquake recurrence periods, as shown in FIG. 8.
(II) analyzing earthquake vulnerability of group buildings:
the crowd building data within grid a is collected and collated as shown in fig. 9. It can be seen that 21115 buildings are shared in the target area. Wherein, the earliest building is built in 1981, the latest building is built in 2019, and the span is nearly 40 years. The construction era in the target site has centered on 1990-2010. Wherein, the building built before and after 2000 years accounts for the largest proportion. Meanwhile, 14482 low-rise buildings account for nearly 70% of the target site; there are 2051 high-rise buildings of over 8 stories and 148 super high-rise buildings of over 100 meters high. In terms of usage type, the target site has a common residential building 13153, accounting for 65% or so, and the others include 1465 commercial buildings and 5509 utilities. In thatStructurally, the vast majority of buildings in a target site are masonry structures and reinforced concrete frame structures. Wherein, the reinforced concrete frame structure 15762 accounts for about 75%. In terms of building area, the floor area is 150m2The small buildings in the building comprise 12525 buildings, and the proportion of the small buildings is more than half; 3000m2The super large building has 102. Therefore, the group buildings in the region have obvious differences in building age, building height, structure type and building area, and can better represent the structural characteristics of urban group buildings under the severe urbanization background of China.
For each building, the deformation characteristics of each layer are represented by an elastic bending beam and a nonlinear shearing spring, and a multi-degree-of-freedom bending-shearing-layer model is established, as shown in fig. 10.
And determining 7 parameter values of the multi-degree-of-freedom bending shear layer model according to the given building attribute classification and the preconfigured parameter calibration rule. Such as: a certain building in a target site is a residential building, belongs to a reinforced concrete frame structure, has 17 floors, the construction age is 2000 years, the floor area is 526 square meters, the structure height is 51 meters, and the equivalent layer mass m =8.051 multiplied by 10 of a multi-degree-of-freedom bent shear type layer model can be estimated5kg; moment of inertia J =3.5357 × 107kg × m2(ii) a Structural layer height H =51m; bending stiffness EI =1.854 × 1012N*m2(ii) a Shear stiffness ks＝1.14×1010N；VyLayers not equal, from 9.83X 105N to 6.3X 106N; the degradation parameter τ =0.45. Meanwhile, it can be estimated that the maximum interlayer displacement angle thresholds of the building in the states of slight damage, medium damage, severe damage and damage are 0.0025, 0.004, 0.010 and 0.025, respectively.
Inputting a random artificial earthquake motion time-course sample curve of the grid of the building in different earthquake recurrence periods, and calculating to obtain the maximum interlayer displacement angle of the building by adopting a center difference method. Furthermore, a generalized probability density evolution equation is adopted, a virtual random process is introduced, and probability density distribution of the maximum interlayer displacement angle of the building is calculated and obtained, as shown in fig. 11. It can be seen that the mean value of the maximum interlayer displacement angle increases with increasing earth-quake recurrence period. Under the action of a fortification earthquake (the probability is more than 10% in 50 years), the probability that the building is in a basically intact state is 99%, and the standards of 'small earthquake damage prevention, medium earthquake repairable and large earthquake collapse' required by the current building seismic fortification standard are met. Under rare earthquakes (50 years beyond probability 2%), the probability of the building being in an intact state is 79%.
And changing the earthquake recurrence period of the grid, generating a corresponding artificial earthquake motion time-course sample curve, and repeating the steps 2-4) -2-7) to obtain an earthquake vulnerability curve of the building based on the earthquake recurrence period, as shown in fig. 12. It can be seen that when the earthquake reappearance period is one thousand years, the probability of the building being slightly damaged and the probability of being moderately damaged are respectively 80% and 39%.
The above-described functions, if implemented in the form of software functional units and sold or used as a separate product, may be stored in a computer-readable storage medium. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. The foregoing storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a cloud disk on the internet, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions that can be obtained by a person skilled in the art through logic analysis, reasoning or limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.

Claims (10)

1. A group building earthquake risk assessment method based on probability density evolution theory is characterized by comprising probability earthquake risk analysis and group building earthquake vulnerability analysis, wherein,
the probabilistic earthquake risk analysis comprises the following steps:
step 1-1) obtaining a historical earthquake catalogue database of a target area, and calculating the annual average earthquake occurrence rate of each earthquake active area of the target area;
step 1-2) dividing potential seismic source areas in each seismic activity area, and determining a seismic level upper limit and a seismic level lower limit of each potential seismic source area;
step 1-3) establishing a spatial probability distribution function by adopting a seismic grading mode;
step 1-4) determining the annual average earthquake occurrence rate of the magnitude gear of the ith potential source region of each earthquake activity area by taking the jth magnitude as the center based on the spatial probability distribution function, the upper magnitude limit and the lower magnitude limit of the earthquake activity area;
step 1-5) rasterization processing is carried out on a target area, the attenuation relation of seismic dynamic acceleration response spectrum parameters is determined, the self-vibration period of a building structure in each grid is increased from 0 second to the upper limit of the self-vibration period of the pre-configured building structure at the preset self-vibration period change interval, the annual average exceeding probability of the acceleration response spectrum parameters of the center of each grid exceeding the threshold value of the pre-configured parameters is calculated based on the annual average occurrence rate of earthquake of the seismic level grade of the ith potential seismic source area of each seismic activity area with the jth seismic level as the center, and the seismic hazard curve of each grid center under different self-vibration periods of the building structure is generated;
step 1-6) determining the spectral acceleration of different building structure self-vibration periods at the center of each grid according to the pre-configured earthquake recurrence period and the corresponding annual average transcendence probability to obtain consistent risk spectra of different earthquake recurrence periods;
step 1-7), based on the consistent risk spectrum of each grid center in different earthquake recurrence periods, generating random artificial earthquake motion time-course sample curves of each grid center in different earthquake recurrence periods by adopting a physical random earthquake motion model;
the group building earthquake vulnerability analysis comprises the following steps:
step 2-1) obtaining a group building database and carrying out basic attribute classification, wherein the basic attributes of the group building comprise: building age, building height, structure type, use type and floor area;
step 2-2) for each building, representing the deformation characteristics of each layer by using an elastic bending beam and a nonlinear shearing spring, and establishing a multi-degree-of-freedom bending-shearing layer model;
step 2-3) determining parameters of the multi-degree-of-freedom bending shear layer model based on basic attributes of the group buildings and pre-configured parameter calibration rules;
step 2-4) inputting random artificial earthquake motion time-course sample curves of the grid center of each building in different earthquake recurrence periods, and determining the maximum interlayer displacement angle of each building by adopting a center difference method, wherein the random artificial earthquake motion time-course sample curves of the grid center in different earthquake recurrence periods are determined based on the steps 1-1) -1-7);
step 2-5) determining a probability density distribution function of the maximum interlayer displacement angle of each building based on a generalized probability density evolution equation;
step 2-6) determining the maximum interlayer displacement angle threshold value of the building in different damage states according to the basic attribute of each building, and determining the probability of each building in different damage states based on the probability density distribution function of the maximum interlayer displacement angle and the maximum interlayer displacement angle threshold value;
and 2-7) changing the earthquake recurrence period, and repeating the steps 2-4) -2-7) to generate an earthquake vulnerability curve of each building based on the earthquake recurrence period.
2. The method for group building earthquake risk assessment based on probability density evolution theory as claimed in claim 1, wherein the annual average transcendental probability is:
Figure FDA0003754454230000021
in the formula, mk、rkAnd thetakThe magnitude, the epicenter distance and the azimuth angle of the kth earthquake are respectively;
Figure FDA0003754454230000022
the annual average earthquake occurrence rate of the magnitude gear which is centered on the j magnitude for the ith potential source region of each earthquake activity region; n is a radical ofpThe number of potential seismic source regions; n is a radical ofmThe number of the earthquake magnitude interval gears is set; n is a radical ofeThe number of earthquakes occurring at each seismic interval for each potential source zone.
3. The method for evaluating the earthquake risk of group buildings based on probability density evolution theory as claimed in claim 1, wherein the steps 1-7) comprise the following steps:
step 1-7-1), taking the consistent danger spectrum of each grid center in different earthquake recurrence periods as a target response spectrum, and converting the consistent danger spectrum into a bedrock power spectrum according to the approximate relation between the target response spectrum and the power spectrum:
Figure FDA0003754454230000023
in the formula, S0For consistent risk spectrum at different seismic recurrence periods at each grid center, S is the power spectrum of the bedrock, omegaiIs the ith order frequency of the seismic wave, eta is the damping ratio, P is the annual average transcendental probability of the consistent risk spectrum, T0The duration of the stationary section of the random artificial seismic motion time-course sample curve is obtained;
step 1-7-2) based on a bedrock power spectrum, aiming at a target area, describing the randomness of artificial earthquake motion by adopting a random Fourier spectrum:
Figure FDA0003754454230000031
wherein F is the earth surface power spectrum, omega0Is a fieldExcellent frequency, zeta is the equivalent damping ratio of the field, and both are basic random variables;
step 1-7-3), assuming that a random artificial earthquake motion time-course sample curve meets a stable Gaussian process, converting an earth surface power spectrum into a Fourier amplitude spectrum:
Figure FDA0003754454230000032
in the formula, delta omega is a sampling interval, delta omega =2 pi/T, and T is a basic cycle of a building structure;
step 1-7-4) decomposing the phase angle of the random artificial seismic motion time-course sample curve into initial phase angles
Figure FDA0003754454230000033
Spectrum of phase difference from basic phase
Figure FDA0003754454230000034
Figure FDA0003754454230000035
Wherein the initial phase angle
Figure FDA0003754454230000036
As a substantially random variable, a substantially phase difference spectrum
Figure FDA0003754454230000037
Comprises the following steps:
Figure FDA0003754454230000038
wherein A is an index parameter;
step 1-7-5) converting the basic phase difference spectrum into a sequence distributed from a lognormal mode, normalizing the sequence, and then comparing the normalized sequence with an initial phase angle
Figure FDA0003754454230000039
Adding to obtain the phase angle of the random artificial earthquake motion time-course sample curve
Figure FDA00037544542300000310
Step 1-7-6) adopts a ball-cutting point-selecting method based on site excellent frequency omega0Field equivalent damping ratio ζ and initial phase angle
Figure FDA00037544542300000311
Generating a random sample by using three basic random variables;
step 1-7-7) synthesizing each random sample into a random artificial earthquake motion time-course sample curve by adopting a spectral representation method:
Figure FDA00037544542300000312
in the formula (I), the compound is shown in the specification,
Figure FDA00037544542300000313
the phase angle of a random artificial seismic motion time-course sample curve is shown, and I is a deterministic intensity envelope function:
Figure FDA00037544542300000314
in the formula, T1、T2And T is the amplitude rise time, the amplitude fall starting time and the total duration of the random artificial seismic motion time-course sample curve respectively, and c is the attenuation coefficient of the seismic motion peak acceleration.
4. The method for group building earthquake risk assessment based on probability density evolution theory as claimed in claim 1, wherein the parameters of the multi-degree of freedom bending shear layer model comprise: equivalent layer massM, moment of inertia J, building height L, structural layer height H, bending stiffness EI, and shear stiffness ksShear yield angle ε and degradation parameter τ.
5. The method for group building earthquake risk assessment based on probability density evolution theory as claimed in claim 4, wherein the motion control differential equation of the multi-degree of freedom bending shear layer model is:
Figure FDA0003754454230000041
wherein C is a damping matrix of the structure,
Figure FDA0003754454230000042
the method comprises the steps that a sample curve of an input random artificial seismic motion time course is obtained, u is a displacement response, theta is a corner response, and N is the number of structural layers and is determined by a building height L and a structural layer height H; f. ofsiTo construct the restoring force of the i-th layer of nonlinear shear springs, the shear stiffness ksDetermining a shearing yield corner epsilon and a degradation parameter tau; k is a radical ofiiA stiffness matrix for a structural ith layer of flexural elastic beams is expressed as:
Figure FDA0003754454230000043
where EI is the bending stiffness of the bending spring beam.
6. The method for group building earthquake risk assessment based on probability density evolution theory as claimed in claim 4, wherein the step 2-3) is specifically:
assuming that the mass of the building structure is uniformly distributed along the floor height, determining the equivalent floor mass m according to the floor area;
assuming that each floor of the building structure is a cuboid, determining the moment of inertia J according to the floor area and the equivalent floor mass m;
determining a structural floor height H based on the building type;
determining bending rigidity EI based on the mass density of the structure along the height direction, structural modal characteristic parameters, bending shear rigidity ratio and structural layer height;
determining shear stiffness k based on bending stiffness, bending shear stiffness ratio and structural layer heights；
Determining a shear yield corner epsilon based on shear bearing capacity, shear stiffness and structural layer height;
the degradation parameter τ is determined based on the structure type and the age of the building.
7. The method for evaluating the earthquake risk of group buildings based on probability density evolution theory as claimed in claim 1, wherein the steps 2-5) comprise the following steps:
step 2-5-1) based on the generalized probability density evolution equation, introducing a virtual random process to determine the probability density distribution of the maximum interlayer displacement angle:
Figure FDA0003754454230000051
wherein X is the maximum interlayer displacement angle; Θ is a random vector space, comprising three basic random variables: site prominent frequency omega0Field equivalent damping ratio ζ and initial phase angle
Figure FDA0003754454230000052
Figure FDA0003754454230000053
Evolution speed, p, of maximum interlayer displacement angleXΘIs a joint probability density distribution;
step 2-5-2) solving a generalized probability density evolution equation by adopting a finite difference format, integrating theta to obtain a probability density distribution function of the maximum interlayer displacement angle:
Figure FDA0003754454230000054
8. the method as claimed in claim 1, wherein the influence factors of the maximum inter-storey displacement angle threshold include structure type, building height and earthquake defense level.
9. A group building earthquake risk assessment apparatus based on probability density evolution theory, comprising a memory, a processor, and a program stored in the memory, wherein the processor when executing the program implements the method of any of claims 1-8.
10. A storage medium having a program stored thereon, wherein the program when executed implements the method of any of claims 1-8.
CN202210855684.8A 2022-07-20 2022-07-20 Earthquake risk assessment method and device for group building and storage medium Pending CN115271406A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115963557A (en) * 2022-11-25 2023-04-14 哈尔滨工业大学（深圳） Earthquake hazard consistency-based earthquake motion record selection method and device
CN117744444A (en) * 2023-12-26 2024-03-22 广州大学 BSPLS-RSM-based structural seismic vulnerability curved surface prediction method

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115963557A (en) * 2022-11-25 2023-04-14 哈尔滨工业大学（深圳） Earthquake hazard consistency-based earthquake motion record selection method and device
CN115963557B (en) * 2022-11-25 2024-03-12 哈尔滨工业大学（深圳） Earthquake motion record selection method and device based on earthquake hazard consistency
CN117744444A (en) * 2023-12-26 2024-03-22 广州大学 BSPLS-RSM-based structural seismic vulnerability curved surface prediction method

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