A group building earthquake risk assessment method and device and a storage medium

Abstract

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

Description

Technical Field

[0001] This invention relates to the fields of seismic resistance and disaster prevention of building structures and earthquake catastrophe insurance, and in particular to a method, device and storage medium for assessing the seismic risk of a group of buildings based on probability density evolution theory. Background Technology

[0002] In recent years, driven by the two engines of industrialization and urbanization, my country's economy has maintained rapid growth. This rapid economic growth has spurred rapid urban construction and a surge in urban population. In this process, to meet the housing, living, and production needs of the large influx of people into cities, local governments have constructed numerous residential buildings, apartments, factories, and public facilities. Given my country's frequent and active earthquakes and rapid urbanization, it is foreseeable that my country's earthquake risk will exhibit urbanized characteristics in the future. Therefore, conducting earthquake risk assessments of urban building complexes is urgently needed.

[0003] Seismic hazard risk assessment for urban building complexes includes two parts: seismic hazard analysis and structural seismic vulnerability analysis. However, current seismic risk assessment methods for urban building complexes mainly suffer from the following problems:

[0004] (1) Current earthquake risk assessments mostly separate the earthquake hazard analysis and earthquake vulnerability analysis processes. This artificial separation has resulted in problems such as difficulty in wave selection, lack of standards, and difficulty in considering the spatial variability and correlation of earthquake input to a group of buildings.

[0005] (2) Current seismic vulnerability analysis mainly focuses on individual buildings, using detailed nonlinear finite element simulations to obtain seismic vulnerability curves for several representative buildings. When applied to seismic vulnerability analysis of building groups, this method suffers from several drawbacks. First, the selection of representative buildings lacks a unified standard. Second, the seismic vulnerability curves of buildings of the same type located in different areas are identical, thus failing to reflect real-world earthquake damage scenarios. Third, if detailed nonlinear finite element simulations are conducted for each building, it becomes difficult to obtain detailed component dimensions and reinforcement parameters for building groups, making it impossible to establish detailed nonlinear finite element models.

[0006] (3) Most current seismic vulnerability analyses obtain a limited number of seismic motion time history samples based on different selection or seismic wave generation strategies, and then use the log-normal distribution assumption to obtain the seismic vulnerability curve of the building structure. Therefore, they cannot fully characterize the randomness of seismic motion. If the Monte Carlo simulation method is used to fully characterize the randomness of seismic motion, there are problems of computation time consumption and low efficiency when facing a group of buildings, and there may even be a phenomenon that the calculation cannot be completed. Summary of the Invention

[0007] The purpose of this invention is to provide a method, device, and storage medium for seismic risk assessment of building groups based on probability density evolution theory, which combines seismic hazard analysis with seismic vulnerability analysis to improve the computational efficiency of the assessment process and the accuracy of the assessment results.

[0008] The objective of this invention can be achieved through the following technical solutions:

[0009] A method for seismic risk assessment of building clusters based on probability density evolution theory includes probabilistic seismic hazard analysis and seismic vulnerability analysis of building clusters.

[0010] The probabilistic seismic hazard analysis includes the following steps:

[0011] Step 1-1) Obtain the historical earthquake catalog database for the target area and calculate the average annual earthquake occurrence rate for each seismically active zone in the target area;

[0012] Steps 1-2) Divide the potential source areas within each seismic activity zone and determine the upper and lower magnitude limits for each potential source area;

[0013] Steps 1-3) Establish the spatial probability distribution function using magnitude grading;

[0014] Steps 1-4) Based on the spatial probability distribution function, the upper and lower limits of magnitude in the seismic activity zone, determine the annual average earthquake occurrence rate of the magnitude range centered on the j-th magnitude in the i-th potential source area of ​​each seismic activity zone;

[0015] Steps 1-5) Rasterize the target area, determine the attenuation relationship of the ground motion acceleration response spectrum parameters, and increase the natural vibration period of the building structure in each grid from 0 seconds to the upper limit of the natural vibration period of the building structure according to the pre-configured natural vibration period variation interval. Based on the annual average earthquake occurrence rate of the magnitude range centered on the j-th magnitude of the i-th potential source area in each seismic active zone, calculate the annual average exceedance probability of the acceleration response spectrum parameters of each grid center exceeding the pre-configured parameter threshold, and generate the seismic hazard curve under different building structure natural vibration periods at each grid center.

[0016] Steps 1-6) Based on the pre-configured earthquake return period and the corresponding annual average exceedance probability, determine the spectral acceleration under the natural vibration period of different building structures at the center of each grid, and obtain the consistent hazard spectrum for different earthquake return periods.

[0017] Steps 1-7) Based on the consistent hazard spectrum of different earthquake return periods for each grid center, a physical random ground motion model is used to generate random artificial ground motion time history sample curves for different earthquake return periods for each grid center.

[0018] The seismic vulnerability analysis of the building complex includes the following steps:

[0019] Step 2-1) Obtain the database of group buildings and classify them according to basic attributes. The basic attributes of group buildings include: building age, building height, structural type, usage type, and floor area.

[0020] Step 2-2) For each building, the deformation characteristics of each floor are represented by an elastic bending beam and a nonlinear shear spring to establish a multi-degree-of-freedom bending-shear type floor model.

[0021] Steps 2-3) Based on the basic attributes of the building complex and the pre-configured parameter calibration rules, determine the parameters of the multi-degree-of-freedom bending-shear layer model;

[0022] Steps 2-4) Input the random artificial ground motion time history sample curves of different earthquake return periods at the grid center of each building. Use the central difference method to determine the maximum inter-story drift angle of each building. The random artificial ground motion time history sample curves of different earthquake return periods at the grid center are determined based on steps 1-1) to 1-7).

[0023] Steps 2-5) Based on the generalized probability density evolution equation, determine the probability density distribution function of the maximum inter-story drift angle for each building;

[0024] Steps 2-6) Based on the basic attributes of each building, determine the maximum inter-story drift angle threshold for the building under different damage states, and determine the probability of each building under different damage states based on the probability density distribution function of the maximum inter-story drift angle and the maximum inter-story drift angle threshold.

[0025] Steps 2-7) Change the earthquake return period and repeat steps 2-4)-2-7) to generate an earthquake vulnerability curve for each building based on the earthquake return period.

[0026] The annual average exceedance probability is:

[0027]

[0028] In the formula, m k r k and θ k These represent the magnitude, epicentral distance, and azimuth of the k-th earthquake, respectively. N represents the annual average earthquake occurrence rate centered on the j-th magnitude range within the i-th potential source region of each seismic activity zone; p N represents the number of potential seismic source regions. m N represents the number of magnitude intervals; e The number of earthquakes occurring in each magnitude range for each potential seismic source region.

[0029] Steps 1-7) include the following steps:

[0030] Step 1-7-1) Using the consistent hazard spectrum of each grid center under different earthquake return periods as the target response spectrum, and based on the approximate relationship between the target response spectrum and the power spectrum, the consistent hazard spectrum is converted into a bedrock power spectrum:

[0031]

[0032] In the formula, S0 represents the consistent hazard spectrum of each grid center under different earthquake return periods, S represents the bedrock power spectrum, and ω represents the bedrock power spectrum. i Let η be the i-th order frequency of the seismic wave, η be the damping ratio, P be the annual average exceedance probability of the uniform hazard spectrum, and T0 be the duration of the stationary segment of the random artificial ground motion time history sample curve.

[0033] Step 1-7-2) Based on the bedrock power spectrum, for the target area, the randomness of artificial ground motion is described using the random Fourier spectrum:

[0034]

[0035] In the formula, F is the surface power spectrum, ω0 is the dominant frequency of the site, and ζ is the equivalent damping ratio of the site, both of which are basic random variables.

[0036] Step 1-7-3) Assuming the random artificial ground motion time history sample curve satisfies a stationary Gaussian process, convert the surface power spectrum into a Fourier amplitude spectrum:

[0037]

[0038] In the formula, Δω is the sampling interval, Δω=2π / T, and T is the basic period of the building structure;

[0039] Step 1-7-4) Decompose the phase angle of the random artificial ground motion time history sample curve into the initial phase angle. With the fundamental phase difference spectrum

[0040]

[0041] Wherein, the initial phase angle The fundamental random variable is the fundamental phase difference spectrum. for:

[0042]

[0043] In the formula, A is the exponential parameter;

[0044] Step 1-7-5) Convert the basic phase difference spectrum into a sequence following a log-normal distribution. After normalizing the sequence, compare it with the initial phase angle. Adding them together yields the phase angle of the random artificial ground motion time history sample curve.

[0045] Step 1-7-6) Employs the ball-cutting point selection method, based on the field's dominant frequency ω0, the field's equivalent damping ratio ζ, and the initial phase angle. Three basic random variables are used to generate random samples;

[0046] Step 1-7-7) Using the spectral representation method, each random sample is synthesized into a random artificial ground motion time history sample curve:

[0047]

[0048] In the formula, Let I be the phase angle of the time history sample curve of random artificial ground motion, and let I be the deterministic intensity envelope function.

[0049]

[0050] In the formula, T1, T2 and T are the amplitude rise time, amplitude fall start time and total duration of the random artificial ground motion time history sample curve, respectively, and c is the attenuation coefficient of the peak ground acceleration.

[0051] The parameters of the multi-degree-of-freedom bending-shear type layer model include: equivalent layer mass m, moment of inertia J, building height L, structural layer height H, bending stiffness EI, and shear stiffness k. s Shear yield angle ε and degradation parameter τ.

[0052] The motion control differential equations of the multi-degree-of-freedom bending-shear layer model are as follows:

[0053]

[0054]

[0055] In the formula, C is the damping matrix of the structure. The input is a random artificial ground motion time history sample curve, where u is the displacement response, θ is the rotation response, and N is the number of stories in the structure, determined by the building height L and the story height H; f si The restoring force of the nonlinear shear spring in the i-th layer of the structure is given by the shear stiffness k. s Determining the shear yield rotation angle ε and the degradation parameter τ; k ii Let the stiffness matrix of the i-th layer of the bending elastic beam be expressed as:

[0056]

[0057] In the formula, EI is the bending stiffness of the bending elastic beam.

[0058] Steps 2-3) specifically refer to:

[0059] Assuming the mass of the building structure is uniformly distributed along the floor height, the equivalent floor mass m is determined based on the floor area.

[0060] Assuming each floor of the building structure is a cuboid, determine the moment of inertia J based on the floor area and the equivalent floor mass m;

[0061] Determine the structural floor height H based on the building type;

[0062] The bending stiffness EI is determined based on the mass density of the structure along the height direction, the modal characteristic parameters of the structure, the bending-shear stiffness ratio, and the story height of the structure.

[0063] The shear stiffness k is determined based on the bending stiffness, the bending-shear stiffness ratio, and the structural story height. s ;

[0064] The shear yield rotation angle ε is determined based on shear bearing capacity, shear stiffness, and structural story height.

[0065] The degradation parameter τ is determined based on the structural type and the building age.

[0066] Steps 2-5) include the following steps:

[0067] Step 2-5-1) Based on the generalized probability density evolution equation, a virtual stochastic process is introduced to determine the probability density distribution of the maximum inter-story drift angle:

[0068]

[0069] In the formula, X is the maximum inter-story drift angle; Θ is a random vector space, including three basic random variables: the site dominant frequency ω0, the site equivalent damping ratio ζ, and the initial phase angle. p is the evolution rate of the maximum inter-story drift angle. XΘ It is a joint probability density distribution;

[0070] Step 2-5-2) Solve the generalized probability density evolution equation using a finite difference scheme, and integrate over Θ to obtain the probability density distribution function of the maximum inter-story drift angle:

[0071]

[0072] The influencing factors of the maximum inter-story drift angle threshold include structural type, building height, and seismic fortification level.

[0073] A group building seismic risk assessment device based on probability density evolution theory includes a memory, a processor, and a program stored in the memory. When the processor executes the program, it implements the method described above.

[0074] A storage medium having a program stored thereon, which, when executed, implements the method described above.

[0075] Compared with the prior art, the present invention has the following beneficial effects:

[0076] (1) This invention combines the probabilistic seismic hazard analysis step and the seismic vulnerability analysis step. Based on the probabilistic seismic hazard analysis, it obtains the consistent hazard spectrum under different earthquake return periods at different grid centers within the target site. Then, it uses a physical random ground motion model to generate random artificial ground motion time history sample curves. This solves the problems of lack of wave selection difficulty, lack of standards, and difficulty in reflecting the spatial variability of ground motion input in group buildings in traditional seismic vulnerability analysis, making the seismic risk assessment results of group buildings more complete.

[0077] (2) This invention simplifies each building into a 7-parameter multi-degree-of-freedom bending-shear layer model, and proposes a rule for calibrating 7 model parameters based on 5 basic attributes of group buildings. This solves the problems of numerous parameters, difficult calibration, time-consuming calculation, and difficulty in applying to the inelastic seismic dynamic response analysis of group buildings in the current simplified calculation model of building structure, making the seismic risk assessment of group buildings more efficient.

[0078] (3) This invention introduces the generalized probability density evolution equation into the seismic vulnerability analysis of building groups, calculates the probability density distribution of the maximum inter-story drift angle, abandons the log-normal distribution assumption used in traditional seismic vulnerability analysis, and makes the seismic risk assessment results of building groups more reasonable.

[0079] (4) This invention uses earthquake return period to represent the seismic vulnerability curve of a group of buildings, which solves the problem that traditional indicators such as peak ground acceleration, spectral acceleration and seismic damage are not applicable to the seismic vulnerability analysis of group of buildings, making the seismic risk assessment results of group of buildings more practical. Attached Figure Description

[0080] Figure 1 This is a flowchart of the method of the present invention;

[0081] Figure 2 A schematic diagram showing the distribution of historical earthquake events in the target area;

[0082] Figure 3 For embodiments of the present invention, the Gutenberg-Richter relation is used to calculate the average annual earthquake occurrence rate v for each seismically active zone. m The estimated results are shown in the diagram, where (a) is the North Region and (b) is the Central Region;

[0083] Figure 4 This invention defines the potential seismic source region for the target area in an embodiment of the invention.

[0084] Figure 5 The attenuation relationship of the seismic acceleration response spectrum parameters in an embodiment of the present invention;

[0085] Figure 6 These are the seismic hazard curves for grid A and grid B in an embodiment of the present invention;

[0086] Figure 7 The present invention provides a consistent hazard spectrum for grid A and grid B, wherein (a) is the consistent hazard spectrum of grid A and (b) is the consistent hazard spectrum of grid B.

[0087] Figure 8 The following are sample curves of random artificial ground motion time history in an embodiment of the present invention, wherein (a) represents a 50-year return period, (b) represents a 100-year return period, (c) represents a 475-year return period, (d) represents a 949-year return period, (e) represents a 1600-year return period, and (f) represents a 4950-year return period.

[0088] Figure 9 This is the distribution of the group of buildings at grid A in an embodiment of the present invention;

[0089] Figure 10 This is a schematic diagram of a multi-degree-of-freedom bending-shear layered model structure.

[0090] Figure 11 This is a probability density distribution diagram of the maximum inter-story drift angle of a certain building.

[0091] Figure 12 This is the seismic vulnerability curve of a certain building. Detailed Implementation

[0092] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0093] A method for assessing the seismic risk of buildings in a cluster based on probability density evolution theory, such as Figure 1 As shown, it includes two parts: probabilistic seismic hazard analysis and seismic vulnerability analysis of building groups. Among them,

[0094] The probabilistic seismic hazard analysis includes the following steps:

[0095] Step 1-1) Obtain the historical earthquake catalog database for the target area, and use the classic Gutenberg-Richter relation (GR) to estimate the average annual earthquake occurrence rate v for each seismically active zone. m Its calculation expression is as follows:

[0096] lgv m =ab·M

[0097] In the formula, M is the magnitude, and a and b are empirical fitted values.

[0098] Steps 1-2) Divide the potential source areas within each seismic activity zone and determine the upper and lower magnitude limits for each potential source area;

[0099] Steps 1-3) Establish the spatial probability distribution function using magnitude grading;

[0100] Steps 1-4) Based on the spatial probability distribution function and the upper and lower limits of magnitude in seismically active zones, determine the annual average occurrence rate of earthquakes in the magnitude range centered on the j-th magnitude in the i-th potential source area of ​​each seismically active zone.

[0101]

[0102] In the formula, M u M0 and M0 are the upper and lower limits of magnitude for each seismic activity zone, respectively; β = b × ln10, where b is the empirically fitted value in step 1-1); ΔM is the magnitude interval, generally taken as 0.5; sh is a hyperbolic sine function; The spatial probability distribution function for magnitude classification can be simply estimated using the area ratio of potential source areas within each seismic activity zone, satisfying the following:

[0103] The average annual occurrence rate of earthquakes is Figure 1 The seismic activity parameters described in [the document].

[0104] Steps 1-5) Rasterize the target area, determine the attenuation relationship of the ground motion acceleration response spectrum parameters, and increase the natural vibration period of the building structure in each grid from 0 seconds to the upper limit of the natural vibration period of the building structure according to the pre-configured natural vibration period variation interval. Based on the annual average earthquake occurrence rate ν of the magnitude range centered on the j-th magnitude of the i-th potential source area in each seismic active zone. i,Mj Calculate the annual average exceedance probability of the acceleration response spectrum parameters of each grid center exceeding the pre-configured parameter threshold, and generate seismic hazard curves for each grid center under different building structure natural vibration periods.

[0105] The decay relationship of the seismic ground motion acceleration response spectrum parameters is described by an elliptic function, and the expressions for its major and minor axes are as follows:

[0106] logS a = e1 + e2M + e3log[R + e4exp(e5M)]

[0107] In the formula, S ais the ground motion response spectrum acceleration; R is the distance from the center of each grid to the location of the earthquake; e1 to e5 are empirical regression coefficients.

[0108] The annual average exceedance probability is:

[0109]

[0110] In the formula, m k r k and θ k These represent the magnitude, epicentral distance, and azimuth of the k-th earthquake, respectively. N represents the annual average earthquake occurrence rate centered on the j-th magnitude range within the i-th potential source region of each seismic activity zone; p N represents the number of potential seismic source regions. m N represents the number of magnitude intervals; e The number of earthquakes occurring in each magnitude range for each potential seismic source region.

[0111] Steps 1-6) Based on the pre-configured earthquake return period and the corresponding annual average exceedance probability, determine the spectral acceleration under the natural vibration period of different building structures at the center of each grid, and obtain the consistent hazard spectrum for different earthquake return periods.

[0112] The earthquake return period RP and the annual average exceedance probability satisfy the following relationship:

[0113]

[0114] Steps 1-7) Based on the consistent hazard spectrum of different earthquake return periods for each grid center, a physical random ground motion model is used to generate random artificial ground motion time history sample curves for different earthquake return periods for each grid center.

[0115] Step 1-7-1) Using the consistent hazard spectrum of each grid center under different earthquake return periods as the target response spectrum, and based on the approximate relationship between the target response spectrum and the power spectrum, the consistent hazard spectrum is converted into a bedrock power spectrum:

[0116]

[0117] In the formula, S0 represents the consistent hazard spectrum of each grid center under different earthquake return periods, S represents the bedrock power spectrum, and ω represents the bedrock power spectrum. i η is the i-th order frequency of the seismic wave, η is the damping ratio, which can be taken as 0.05 unless there are special circumstances, P is the annual average exceedance probability of the consistent hazard spectrum, and T0 is the duration of the stationary segment of the random artificial ground motion time history sample curve.

[0118] Step 1-7-2) Based on the bedrock power spectrum, for the target area, the randomness of artificial ground motion is described using the random Fourier spectrum:

[0119]

[0120] In the formula, F is the surface power spectrum; ω0 is the dominant frequency of the site, which can be regarded as a basic random variable; ζ is the equivalent damping ratio of the site, which can be regarded as a basic random variable.

[0121] Step 1-7-3) Assuming the random artificial ground motion time history curve sample satisfies a stationary Gaussian process, convert the surface power spectrum into a Fourier amplitude spectrum:

[0122]

[0123] In the formula, Δω is the sampling interval, Δω=2π / T, and T is the basic period of the building structure;

[0124] Step 1-7-4) Decompose the phase angle of the random artificial ground motion time history sample curve into the initial phase angle. With the fundamental phase difference spectrum

[0125]

[0126] Wherein, the initial phase angle The fundamental random variable is the fundamental phase difference spectrum. for:

[0127]

[0128] In the formula, A is a relatively small value, which can be 0.01; A is an exponential parameter. By adjusting this value, the obtained basic phase difference spectrum can be made to follow a log-normal distribution, which can generally be taken as 3.

[0129] Step 1-7-5) Convert the basic phase difference spectrum into a sequence following a log-normal distribution. After normalizing the sequence, compare it with the initial phase angle. Adding them together yields the phase angle of the random artificial ground motion time history sample curve. Specifically, this involves: taking the sequence generated in step 1-7-1). Taking the remainder and then the negative, and normalizing it to the interval [0, -2π], the resulting sequence follows a uniform distribution. Further, using the method of generating log-normal random numbers from uniformly distributed random numbers, the standard phase difference spectrum is transformed into a sequence following a log-normal distribution;

[0130]

[0131] The obtained u and v are independent random numbers that follow a standard normal distribution. Then, u and v are transformed into a sequence following a log-normal distribution. The mean of the log-normal distribution is π, and the standard deviation is 0.8π. Finally, the generated sequence is normalized to the interval [0, -2π] by taking the negative and then the remainder. This generated sequence is then compared with the initial phase angle. By adding them together, the phase angle of the random artificial ground motion time history sample curve can be obtained.

[0132] Step 1-7-6) Employs the ball-cutting point selection method, based on the field's dominant frequency ω0, the field's equivalent damping ratio ζ, and the initial phase angle. Three basic random variables are used to generate random samples;

[0133] Step 1-7-7) Using the spectral representation method, each random sample is synthesized into a random artificial ground motion time history sample curve:

[0134]

[0135] In the formula, Let be the phase angle of the random artificial ground motion time history sample curve, and I be the deterministic intensity envelope function to reflect the non-stationarity of the ground motion amplitude, which can be taken as follows:

[0136]

[0137] In the formula, T1, T2 and T are the amplitude rise time, amplitude fall start time and total duration of the random artificial ground motion time history sample curve, respectively, and c is the attenuation coefficient of the peak ground acceleration.

[0138] In the probabilistic seismic hazard analysis process, steps 1-1) to 1-5) are to complete the seismic hazard analysis and generate seismic hazard curves; steps 1-6) to 1-7) are to generate random artificial ground motion time history sample curves to provide parameters for the seismic vulnerability analysis of building groups.

[0139] The seismic vulnerability analysis of the building complex includes the following steps:

[0140] Step 2-1) Obtain the database of the group of buildings and classify them according to their basic attributes. The basic attributes of the group of buildings include: building age, building height, structural type, usage type, and floor area.

[0141] The basic attribute classification rules for building groups are as follows:

[0142] ① Construction period

[0143] The building's construction date is a specific numerical value, which can be further divided into four categories: no fortification (before 1989), low fortification (1990-2000), medium fortification (2001-2010), and high fortification (after 2010).

[0144] ② Building height

[0145] Building height is a specific numerical value, which can be further divided into three categories: low-rise (less than 9 meters), mid-rise (9 to 21 meters), and high-rise (more than 21 meters).

[0146] ③Structure type

[0147] The structural types are divided into five categories: masonry structures, reinforced concrete frame structures, reinforced concrete frame-shear wall structures, steel structures, and other structures.

[0148] ④ Usage type

[0149] The usage types are divided into five categories: residential buildings, commercial buildings, industrial buildings, public utilities, and other types.

[0150] ⑤ Floor area

[0151] The floor area is a specific numerical value, which can be further divided into: small buildings (less than 150m²) 2 ), medium-sized buildings (150m) 2 ~600m 2 ), large buildings (600m) 2 ~3000m 2 ) and super-large buildings (greater than 3000m) 2 There are 4 categories.

[0152] Step 2-2) For each building, the deformation characteristics of each floor are represented by an elastic bending beam and a nonlinear shear spring, establishing a multi-degree-of-freedom bending-shear floor model, such as... Figure 10 As shown;

[0153] The parameters of the multi-degree-of-freedom bending-shear type layer model include: equivalent layer mass m, moment of inertia J, building height L, structural layer height H, bending stiffness EI, and shear stiffness k. s Shear yield angle ε and degradation parameter τ.

[0154] The motion control differential equations of the multi-degree-of-freedom bending-shear layer model are as follows:

[0155]

[0156]

[0157] In the formula, C is the damping matrix of the structure. The input is a random artificial ground motion time history sample curve, where u is the displacement response, θ is the rotation response, and N is the number of stories in the structure, determined by the building height L and the story height H; f si The restoring force of the nonlinear shear spring in the i-th layer of the structure is given by the shear stiffness k. s Determining the shear yield rotation angle ε and the degradation parameter τ; k ii Let the stiffness matrix of the i-th layer of the bending elastic beam be expressed as:

[0158]

[0159] In the formula, EI is the bending stiffness of the bending elastic beam.

[0160] Steps 2-3) Based on the basic attributes of the building complex and the pre-configured parameter calibration rules, determine the parameters of the multi-degree-of-freedom bending-shear layer model;

[0161] The parameter calibration rules are as follows:

[0162] ① Equivalent layer quality m

[0163] Assuming the mass of the building structure is uniformly distributed along the floor height, estimate the equivalent floor mass m based on the floor area:

[0164] m=ρ×S

[0165] In the formula, S is the floor area and ρ is the mass density per unit area, which is related to the structural type and building height. The following values ​​can be used as the basis for estimation: (1) Masonry structure: 17kN / m 2 (2) Reinforced concrete frame structure: 11~16kN / m 2 (3) Reinforced concrete frame-shear wall structure: 13~16kN / m 2 (4) Steel structure: 8kN / m 2 (5) Other structures: 12kN / m 2 Among them, the upper limit value is used when the number of stories of reinforced concrete frame structures and reinforced concrete frame-shear wall structures is greater than 20, and the lower limit value is used when the number of stories is less than 5.

[0166] ②Moment of inertia J

[0167] Assuming each floor of the building structure is a cuboid, estimate the moment of inertia J based on the floor area and the equivalent floor mass m:

[0168]

[0169] In the formula, B is the side length of the cuboid, which can be estimated based on the floor area S; h0 is the floor thickness, which can be taken as 1 meter.

[0170] ③Structural layer height H

[0171] The structural floor height H is related to the type of use and is estimated according to the following values: (1) Residential buildings: 3m; (2) Commercial buildings: 2.8m; (3) Industrial buildings: 4m; (4) Public facilities and other types: 3.5m.

[0172] ④ Bending stiffness EI

[0173]

[0174] Where κ is the mass density of the structure along the height direction, which can be obtained from... Estimate; α0 is the bending-shear stiffness ratio:

[0175]

[0176] Where γ1 and γ2 are characteristic parameters related to the i-th mode of the structure, which can be calculated by the following formula:

[0177]

[0178] T1 is the first natural period of the building structure, which is related to the structural type and building height. For reinforced concrete frame structures, reinforced concrete frame-shear wall structures, and steel structures, the following empirical formula can be used to estimate it:

[0179] T1=C1H x

[0180] Among them, (1) reinforced concrete frame structure: C1 = 0.0466, x = 0.9; (2) reinforced concrete frame-shear wall structure: C1 = 0.0731, x = 0.75; (3) steel structure: C1 = 0.0724, x = 0.8. For masonry structures and other structures, the following empirical formulas can be used for estimation:

[0181] T1 = 0.221 + 0.225 × N

[0182] T2 is the second natural period of the building structure, which can be estimated using the following empirical formula:

[0183] T2 = 0.27T1

[0184] ⑤ Shear stiffness k s

[0185]

[0186] ⑥ Shear yield angle ε

[0187] The shear yield angle ε can be calculated using the following formula:

[0188]

[0189] In the formula, V y To determine the yield capacity of a nonlinear shear spring, the design bearing capacity V of each story in the structure can be calculated first. d Then multiply by the super-strength coefficient Ω to obtain the design load-bearing capacity V of each floor of the structure. d This can be determined through the following steps:

[0190] 1) Based on the stiffness matrix K and mass matrix M of the building structure, the modal decomposition response spectrum method is used to calculate the natural periods T of the structure at each order. n And mode vector

[0191] 2) Based on the construction date of the building structure, determine the seismic design code to be adopted, and in conjunction with site information, obtain the design response spectrum S of the building structure. a ;

[0192] 3) The design response spectrum S of the structure a Converted to displacement response spectrum S d Meanwhile, based on the natural vibration periods T of the structure... n Obtain the spectral displacement D corresponding to each mode shape. n :

[0193]

[0194] 4) Based on the mode shape vectors of each order Spectral shift D n Calculate the inter-story displacement u corresponding to each mode of vibration of the structure. n Based on this, and based on the inter-story displacement u n Calculate the peak bearing capacity corresponding to each mode shape by taking the difference:

[0195]

[0196] 5) The peak bearing capacity of each vibration mode is combined using the SRSS method to obtain the total peak bearing capacity of each story of the structure:

[0197]

[0198] 6) Considering that the bearing capacity of each floor is not less than 20% of the total shear force at the bottom, the peak bearing capacity of each floor of the structure is adjusted accordingly:

[0199] V d =max[V a 0.2V b ]

[0200] Among them, V b It is the total shear force at the base;

[0201] 7) The peak bearing capacity V of each layer of the structure d Multiply by the peak overstrength coefficient Ω of the structure to obtain the yield strength of the structure:

[0202] V y =ΩV d

[0203] The estimation basis for the peak super-strength coefficient Ω is as follows: (1) Masonry structure: Ω = 2; (2) Reinforced concrete frame structure: Ω = 3; (3) Reinforced concrete frame-shear wall structure: Ω = 2.5; (4) Steel structure: Ω = 3; (5) Other structures: Ω = 2.

[0204] ⑦ Degeneration parameter τ

[0205] The degradation parameter τ is related to factors such as structural type and building age, and can be estimated using the following values:

[0206] 1) Masonry structures: 0.6 (after 2010), 0.4 (2001 to 2010), 0.3 (1990 to 2001), 0.2 (before 1990);

[0207] 2) Reinforced concrete frame structures and frame-shear wall structures: 0.7 (after 2010), 0.6 (from 2001 to 2010), 0.5 (from 1990 to 2001), 0.4 (before 1990);

[0208] 3) Steel structure: 0.9 (before 1990), 0.8 (2001-2010), 0.7 (1990-2001), 0.6 (before 1990);

[0209] 4) Other structures: 0.5 (after 2010), 0.3 (from 2001 to 2010), 0.2 (from 1990 to 2001), 0.1 (before 1990).

[0210] Steps 2-4) Input random artificial ground motion time history samples of different earthquake return periods at the grid center of each building, and use the central difference method to determine the maximum inter-story drift angle of each building. The random artificial ground motion time history sample curves of different earthquake return periods at the grid center are determined based on steps 1-1) to 1-7).

[0211] Steps 2-5) Based on the generalized probability density evolution equation, a virtual stochastic process is introduced to determine the probability density distribution function of the maximum inter-story drift angle for each building;

[0212] Step 2-5-1) Based on the generalized probability density evolution equation, a virtual stochastic process is introduced to determine the probability density distribution of the maximum inter-story drift angle:

[0213]

[0214] In the formula, X is the maximum inter-story drift angle; Θ is a random vector space, including three random variables: the site dominant frequency ω0, the site equivalent damping ratio ζ, and the initial phase angle. p is the evolution rate of the maximum inter-story drift angle. XΘ It is a joint probability density distribution;

[0215] Step 2-5-2) Solve the generalized probability density evolution equation using a finite difference scheme, and integrate over Θ to obtain the probability density distribution function of the maximum inter-story drift angle:

[0216]

[0217] Steps 2-6) Based on the basic attributes of each building, determine the maximum inter-story drift angle threshold for the building under different damage states, and determine the probability of each building under different damage states based on the probability density distribution function of the maximum inter-story drift angle and the maximum inter-story drift angle threshold.

[0218] The influencing factors of the maximum inter-story drift angle threshold include structural type, building height, and seismic fortification level. Specifically, the maximum inter-story drift angle threshold for mid-rise and high-rise buildings can be taken as 2 / 3 and 1 / 2 of the corresponding low-rise building thresholds, respectively.

[0219] The damage states include minor damage, moderate damage, severe damage, and complete destruction.

[0220] Steps 2-7) Change the earthquake return period and repeat steps 2-4)-2-7) to generate an earthquake vulnerability curve for each building based on the earthquake return period.

[0221] This embodiment uses the method described above to conduct an earthquake risk assessment on a group of buildings in a target area, for further detailed explanation.

[0222] The target area is located on the eastern coast of China, on the western shore of the Pacific Ocean, along the eastern edge of the Asian continent, and at the forefront of the Yangtze River Delta. This region is part of the Yangtze River Delta alluvial plain, with an average elevation of approximately 2 meters. The vast majority of the urban area is covered by layers of silt and sand deposited by rivers and the ocean over the past 3 million years. Since the 1990s, the rapid urbanization and land-use planning in the target area have resulted in a coexistence of skyscrapers and old buildings. In recent years, the target area has been affected by several distant-field moderate-to-strong earthquakes, causing noticeable tremors in some high-rise buildings.

[0223] (I) Probabilistic Seismic Hazard Analysis:

[0224] Collect and organize historical earthquake catalog data of magnitude 4.0 and above in the target area from 1500 to 2020, and their distribution is as follows: Figure 2 As shown, since 1500 AD, a total of 100 earthquakes of magnitude 4.0 or above have occurred in the target area. Among them, there were 29 earthquakes of magnitude 4.0 to 4.9, 48 earthquakes of magnitude 5.0 to 5.9, 22 earthquakes of magnitude 6.0 to 6.9, and 1 earthquake of magnitude 7 or above.

[0225] Given that the target area is located in the Lower Yangtze-Southern Yellow Sea Seismic Belt (Lower Yangtze-Southern Yellow Sea Seismic Belt) within the North China Seismic Zone, this seismic belt can be divided into three seismic activity statistical zones from north to south based on geological structure and neotectonic movements: the northern Jiangsu-Southern Yellow Sea seismic activity zone (hereinafter referred to as the Northern Zone), the central southern Jiangsu-Northern Zhejiang-Northern East China Sea seismic activity zone (hereinafter referred to as the Central Zone), and the southern Zhejiang seismic activity zone bounded by 29.8°N latitude (hereinafter referred to as the Southern Zone). Since the southern Zhejiang seismic zone has a relatively low level of seismic activity and weak intensity compared to the Northern and Central Zones, it is not statistically significant. Therefore, the classic Gutenberg-Richter relation (GR) is used to estimate only the annual average earthquake occurrence rate v of the Northern and Central Zones. m ,like Figure 3 As shown in the figure, the a and b values ​​for the North region are 4.8913 and 0.6398, respectively, while the a and b values ​​for the Central region are 4.6001 and 0.6764, respectively.

[0226] The northern and southern regions can be divided into a total of 24 potential seismic source areas, such as... Figure 4 As shown in the table below, the northern region includes 8 potential seismic source areas, and the central region includes 16 potential seismic source areas. The upper limit of the magnitude for each potential seismic source area is estimated. Simultaneously, a magnitude grading method is adopted, and a spatial probability distribution function is established based on the area ratio of the potential seismic source areas to obtain the annual average earthquake occurrence rate of the magnitude grading centered on the j-th magnitude in the i-th potential seismic source area of ​​each seismically active zone, as shown in the table below.

[0227]

[0228]

[0229] The attenuation relationship of the ground motion acceleration response spectrum parameters in the target area is described using elliptic function form, such as... Figure 5 As shown.

[0230] The entire study area was divided into 30×30 grids with a grid spacing of 2.5 kilometers. Using the Monte Carlo simulation method, the natural vibration period of the building structures within each grid was gradually varied from 0 seconds to 6 seconds at 0.05-second intervals. The exceedance probability of the acceleration response spectrum parameter at the center of each grid exceeding a certain value was calculated, generating the corresponding seismic hazard curve. Figure 6 As shown.

[0231] The exceedance probabilities of grids A and B within 50 and 100 years are set to 63.2%, 10%, and 2%, respectively. The 50-year exceedance probabilities of 63.2%, 10%, and 2% correspond to the most frequent earthquakes (50-year return period), the design earthquakes (475-year return period), and the rare earthquakes (1600-year return period) in my country's seismic design code for building structures, respectively. The 100-year exceedance probabilities of 63.2%, 10%, and 2% correspond to the 100-year, 949-year, and 4950-year return periods, respectively. The spectral accelerations at different building structure natural periods at the centers of grids A and B are calculated to generate consistent hazard spectra for grids A and B with different earthquake return periods. Figure 7 As shown.

[0232] Based on the consistent hazard spectrum of grid A under different earthquake return periods, a physical random ground motion model is used to generate time history samples of artificial ground motions under different earthquake return periods, such as... Figure 8 As shown.

[0233] (II) Seismic Vulnerability Analysis of Building Complexes:

[0234] Collect and organize the group building data within grid A, such as Figure 9 As shown, there are a total of 21,115 buildings within the target area. The earliest building was constructed in 1981, and the latest in 2019, spanning nearly 40 years. The majority of the buildings on the target site were constructed between 1990 and 2010, with the largest proportion built around 2000. There are 14,482 low-rise buildings, accounting for nearly 70%; 2,051 high-rise buildings exceeding 8 stories; and 148 super high-rise buildings exceeding 100 meters in height. In terms of usage, there are 13,153 residential buildings, accounting for approximately 65%, with the remainder including 1,465 commercial buildings and 5,509 public facilities. Structurally, the vast majority of buildings on the target site are masonry structures and reinforced concrete frame structures. Among them, 15,762 are reinforced concrete frame structures, accounting for approximately 75%. The total building area is approximately 150 square meters. 2 There are 12,525 small buildings within this area, accounting for more than half; 3,000m 2 There are 102 such super-large buildings. Therefore, the buildings in this area have obvious differences in construction age, building height, structural type and building area, and can well represent the structural characteristics of urban building clusters under the background of my country's rapid urbanization.

[0235] For each building, the deformation characteristics of each floor are represented by an elastic bending beam and a nonlinear shear spring, establishing a multi-degree-of-freedom bending-shear floor model, such as... Figure 10 As shown.

[0236] Based on the given building attribute classification and pre-configured parameter calibration rules, the values ​​of 7 parameters for the multi-degree-of-freedom bending-shear layer model are determined. For example, if a building on the target site is a residential building with a reinforced concrete frame structure, 17 stories, built in 2000, with a floor area of ​​526 square meters and a structural height of 51 meters, the equivalent floor mass of the multi-degree-of-freedom bending-shear layer model can be estimated as m = 8.051 × 10⁻⁶. 5 kg; Moment of inertia J = 3.5357 × 10⁷ kg * m 2 Structural floor height H = 51m; Bending stiffness EI = 1.854 × 10⁻⁶ m 12 N*m 2 Shear stiffness k s =1.14×10 10 N;V y The values ​​are not equal across layers, starting from 9.83 × 10 5 N to 6.3 × 10 6 N; degradation parameter τ = 0.45. Simultaneously, the maximum inter-story drift angle thresholds for the building under slight damage, moderate damage, severe damage, and complete destruction states can be estimated to be 0.0025, 0.004, 0.010, and 0.025, respectively.

[0237] Input random artificial ground motion time history sample curves for different earthquake return periods in the grid where the building is located. Using the central difference method, the maximum inter-story drift angle of the building is calculated. Then, using the generalized probability density evolution equation and introducing a virtual stochastic process, the probability density distribution of the maximum inter-story drift angle of the building is calculated, such as... Figure 11 As shown, the mean of the maximum inter-story drift angle increases with the increase of the earthquake recurrence period. Under the design earthquake action (50-year exceedance probability 10%), the probability of the building remaining in a basically intact state is 99%, meeting the current seismic design code requirements of "no damage in minor earthquakes, repairable in moderate earthquakes, and no collapse in major earthquakes". Under rare earthquake action (50-year exceedance probability 2%), the probability of the building remaining in an intact state is 79%.

[0238] The earthquake return period of the raster where the change occurs is used to generate the corresponding artificial ground motion time history sample curve. Steps 2-4) to 2-7) are repeated to obtain the seismic vulnerability curve of the building based on the earthquake return period, such as... Figure 12 As shown, when the earthquake recurrence interval is once in 10,000 years, the probability of the building experiencing minor and moderate damage is 80% and 39%, respectively.

[0239] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes: USB flash drives, portable hard drives, online cloud storage, read-only memory (ROM), random access memory (RAM), magnetic disks, optical disks, and other media capable of storing program code.

[0240] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for assessing the seismic risk of a group of buildings based on probability density evolution theory, characterized in that, This includes probabilistic seismic hazard analysis and seismic vulnerability analysis of building groups, among which, The probabilistic seismic hazard analysis includes the following steps: Step 1-1) Obtain the historical earthquake catalog database for the target area and calculate the average annual earthquake occurrence rate for each seismically active zone in the target area; Steps 1-2) Divide the potential source areas within each seismic activity zone and determine the upper and lower magnitude limits for each potential source area; Steps 1-3) Establish a spatial probability distribution function using magnitude grading; Steps 1-4) Determine the magnitude of each earthquake in the active seismic zone based on the spatial probability distribution function, the upper and lower limits of the magnitude in the active seismic zone. i The potential seismic source region is the first j The average annual occurrence rate of earthquakes centered on a magnitude range; Steps 1-5) Rasterize the target area, determine the attenuation relationship of the seismic ground acceleration response spectrum parameters, and increase the natural vibration period of the building structure in each grid from 0 seconds to the upper limit of the pre-configured natural vibration period according to the pre-configured natural vibration period variation interval. Based on the first... i The potential seismic source region is the first j The annual average occurrence rate of earthquakes at each magnitude level is calculated, the annual average exceedance probability of the acceleration response spectrum parameters of each grid center exceeding the pre-configured parameter threshold is calculated, and the seismic hazard curves of each grid center under different building structure natural vibration periods are generated. Steps 1-6) Based on the pre-configured earthquake return period and the corresponding annual average exceedance probability, determine the spectral acceleration under the natural vibration period of different building structures at the center of each grid, and obtain the consistent hazard spectrum for different earthquake return periods. Steps 1-7) Based on the consistent hazard spectrum of different earthquake return periods for each grid center, a physical random ground motion model is used to generate random artificial ground motion time history sample curves for different earthquake return periods for each grid center. The seismic vulnerability analysis of the building complex includes the following steps: Step 2-1) Obtain the database of group buildings and classify them according to basic attributes. The basic attributes of group buildings include: building age, building height, structural type, usage type, and floor area. Step 2-2) For each building, the deformation characteristics of each floor are represented by an elastic bending beam and a nonlinear shear spring to establish a multi-degree-of-freedom bending-shear floor model. Steps 2-3) Based on the basic attributes of the building complex and the pre-configured parameter calibration rules, determine the parameters of the multi-degree-of-freedom bending-shear layer model; Steps 2-4) Input the random artificial ground motion time history sample curves of different earthquake return periods at the grid center of each building. Use the central difference method to determine the maximum inter-story drift angle of each building. The random artificial ground motion time history sample curves of different earthquake return periods at the grid center are determined based on steps 1-1) to 1-7). Steps 2-5) Based on the generalized probability density evolution equation, determine the probability density distribution function of the maximum inter-story drift angle for each building; Steps 2-6) Based on the basic attributes of each building, determine the maximum inter-story drift angle threshold for the building under different damage states, and determine the probability of each building under different damage states based on the probability density distribution function of the maximum inter-story drift angle and the maximum inter-story drift angle threshold. Steps 2-7) Change the earthquake return period, repeat steps 2-4)-2-6) to generate an earthquake vulnerability curve for each building based on the earthquake return period.

2. The method for assessing the seismic risk of a group of buildings based on probability density evolution theory according to claim 1, characterized in that, The annual average exceedance probability is: In the formula, m k , r k and θ k The first k The magnitude, epicentral distance, and azimuth of the earthquake; For each seismically active zone i The potential seismic source region is the first j The average annual occurrence rate of earthquakes centered on a magnitude range; N p The number of potential seismic source areas; N m This represents the number of intervals within the magnitude range; N e The number of earthquakes occurring in each magnitude range for each potential seismic source region.

3. The method for assessing the seismic risk of a group of buildings based on probability density evolution theory according to claim 1, characterized in that, Steps 1-7) include the following steps: Step 1-7-1) Using the consistent hazard spectrum of each grid center under different earthquake return periods as the target response spectrum, and based on the approximate relationship between the target response spectrum and the power spectrum, the consistent hazard spectrum is converted into a bedrock power spectrum: In the formula, S 0 represents the consistent hazard spectrum for each grid center under different earthquake return periods. S The power spectrum of bedrock. For the first seismic wave i First frequency, η For the damping ratio, P The annual average exceedance probability of the consistent hazard spectrum. T 0 represents the duration of the stationary segment of the random artificial ground motion time history sample curve; Step 1-7-2) Based on the bedrock power spectrum, for the target area, the randomness of artificial ground motion is described using the random Fourier spectrum: In the formula, F The surface power spectrum, ω 0 represents the dominant frequency of the site, and ζ represents the equivalent damping ratio of the site; both are basic random variables. Step 1-7-3) Assuming the random artificial ground motion time history sample curve satisfies a stationary Gaussian process, convert the surface power spectrum into a Fourier amplitude spectrum: In the formula, The sampling interval is... , T The basic cycle of a building structure; Step 1-7-4) Decompose the phase angle of the random artificial ground motion time history sample curve into the initial phase angle. φ 0 With the fundamental phase difference spectrum Δ φ : Wherein, the initial phase angle φ 0 Let Δ be the basic random variable and the basic phase difference spectrum. φ for: In the formula, A For exponential parameters; Step 1-7-5) Convert the basic phase difference spectrum into a sequence following a log-normal distribution. After normalizing the sequence, compare it with the initial phase angle. φ Adding 0s together yields the phase angle of the random artificial ground motion time history sample curve. φ ; Step 1-7-6) Employ the ball-cutting point selection method, based on the field's superior frequency. ω 0. Site equivalent damping ratio ζ and initial phase angle φ 0. Three basic random variables are used to generate random samples; Step 1-7-7) Using the spectral representation method, each random sample is synthesized into a random artificial ground motion time history sample curve: In the formula, φ The phase angle of the time history sample curve of random artificial ground motion. I For deterministic intensity envelope function: In the formula, T 1. T 2 and T These represent the amplitude rise time, amplitude fall start time, and total duration of the random artificial ground motion time history sample curve, respectively. c It is the attenuation coefficient of peak ground acceleration.

4. The method for assessing the seismic risk of a group of buildings based on probability density evolution theory according to claim 1, characterized in that, The parameters of the multi-degree-of-freedom bending-shear layer model include: equivalent layer mass. m Moment of inertia J Building height L、 Structural layer height H Bending stiffness EI Shear stiffness k s Shear yield angle ε and degradation parameter τ.

5. The method for assessing the seismic risk of a group of buildings based on probability density evolution theory according to claim 4, characterized in that, The motion control differential equations of the multi-degree-of-freedom bending-shear layer model are as follows: In the formula, C Here is the damping matrix of the structure. The input is a random artificial ground motion time history sample curve. u For displacement response, θ For corner response, N The number of stories in the structure, determined by the building height. L With structural layer height H Sure; For the structure of the first i The restoring force of a layered nonlinear shear spring is determined by its shear stiffness. k s The shear yield rotation angle ε and the degradation parameter τ are determined. k ii For the structure of the first i The stiffness matrix of a layered bending elastic beam is expressed as: In the formula, EI This refers to the bending stiffness of a bending elastic beam.

6. The method for assessing the seismic risk of a group of buildings based on probability density evolution theory according to claim 4, characterized in that, Steps 2-3) specifically refer to: Assuming the mass of the building structure is uniformly distributed along the floor height, the equivalent floor mass is determined based on the floor area. m ; Assuming each floor of the building structure is a cuboid, based on the floor area and equivalent floor mass... m Determine the moment of inertia J ; Determine the structural floor height based on building type H ; The bending stiffness is determined based on the mass density of the structure along its height, structural modal characteristic parameters, bending-shear stiffness ratio, and story height. EI ; Shear stiffness is determined based on bending stiffness, bending-shear stiffness ratio, and structural story height. k s ; The shear yield rotation angle ε is determined based on shear bearing capacity, shear stiffness, and structural story height. The degradation parameter τ is determined based on the structural type and the building age.

7. The method for assessing the seismic risk of a group of buildings based on probability density evolution theory according to claim 1, characterized in that, Steps 2-5) include the following steps: Step 2-5-1) Based on the generalized probability density evolution equation, a virtual stochastic process is introduced to determine the probability density distribution of the maximum inter-story drift angle: In the formula, X is the maximum inter-story drift angle; Θ is a random vector space, including three basic random variables: site dominant frequency ω0, site equivalent damping ratio ζ, and initial phase angle φ0. The evolution rate of the maximum inter-story drift angle. p XΘ It is a joint probability density distribution; Step 2-5-2) Solve the generalized probability density evolution equation using a finite difference scheme, and integrate over Θ to obtain the probability density distribution function of the maximum inter-story drift angle: 。 8. The method for assessing the seismic risk of a group of buildings based on probability density evolution theory according to claim 1, characterized in that, The influencing factors of the maximum inter-story drift angle threshold include structural type, building height, and seismic fortification level.

9. A group building seismic risk assessment device based on probability density evolution theory, comprising a memory, a processor, and a program stored in the memory, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1-8.

10. A storage medium having a program stored thereon, characterized in that, When the program is executed, it implements the method as described in any one of claims 1-8.

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