Method for Evaluating Seismic Loss Probability of Building Complexes Based on Simulation of Ground Motion Intensity Random Field

Abstract

The present invention provides a method for evaluating the seismic loss probability of a building complex based on the simulation of ground motion intensity random field, belonging to the technical field of seismic loss assessment. The method provided by the present invention first uses the ground motion intensity random field simulation technology to simulate the ground motion of the region, obtains the spatial distribution of ground motion intensity at different sites, and then estimates the loss probability distribution of each building by using the building seismic performance model and the building vulnerability database. This method can more quickly and accurately evaluate the occurrence probability of extreme seismic losses of large-scale building complexes, provide important support for seismic risk assessment and post-disaster emergency decision-making, thereby enhancing the disaster resistance and recovery ability of cities and improving the overall resilience of cities.

Description

Technical Field

[0001] The present invention belongs to the technical field of seismic loss assessment, and particularly relates to a method for assessing the seismic loss probability of a building complex based on the simulation of ground motion intensity random field. Background Art

[0002] As a major natural disaster, earthquakes cause serious damage to high-density building complexes and pose huge challenges to urban development. Therefore, how to accurately assess the losses of building complexes under earthquakes, especially extreme seismic losses, and provide a basis for urban seismic planning has become an urgent problem to be solved.

[0003] In the assessment of the seismic loss probability of a building complex, it is necessary to first predict the ground motion intensity. However, in the prior art, the influence of terrain and geological conditions on the ground motion intensity is usually ignored, resulting in a lack of certain accuracy in the prediction of ground motion intensity and affecting the assessment of the final seismic loss probability distribution of the building complex.

[0004] Therefore, it is necessary to provide a method for assessing the seismic loss probability of a building complex based on the simulation of ground motion intensity random field to solve the above problems. Summary of the Invention

[0005] The present invention provides a method for assessing the seismic loss probability of a building complex based on the simulation of ground motion intensity random field. Considering the influence of terrain and geological conditions, through the ground motion intensity random field simulation technology, the loss probability of each building is evaluated by using the building seismic performance model and the vulnerability curve, and the total loss probability of the entire building complex is calculated in combination with the basic information of the building. This method can calculate the occurrence probability of the seismic loss of the building complex more quickly and accurately, provide important support for seismic risk assessment and post-disaster emergency decision-making, and can effectively solve at least one problem mentioned in the background art.

[0006] In order to solve the above technical problems, the present invention is implemented as follows:

[0007] A method for assessing the seismic loss probability of a building complex based on the simulation of ground motion intensity random field includes the following steps:

[0008] Step S1, collect the basic information of all buildings in the area to be evaluated, establish a simplified multi-degree-of-freedom mechanical model for each building, and summarize the simplified multi-degree-of-freedom mechanical models of all buildings to form a building complex structure model database; collect the terrain and geological condition data of the area to be evaluated, and establish a geological terrain grid data model;

[0009] Step S2: Based on historical earthquake data, perform cluster analysis on the seismic responses and repair costs of different types of buildings under seismic waves. Construct a building vulnerability database using the seismic responses of buildings in a certain damage state under different combinations of seismic design levels and structural types; construct a building loss ratio database using the percentages of different repair costs to the replacement cost of the building in a certain damage state under different combinations of building repair cost categories and usage categories.

[0010] Step S3: After amplitude - modulating the historical seismic waves, input them into the building complex structure model database. Based on the incremental dynamic analysis method, conduct vulnerability analysis on the buildings to obtain the distribution of engineering demand parameters and construct a building seismic performance evaluation model.

[0011] Step S4: Considering the terrain and geological conditions of the area to be evaluated, introduce terrain - related terms into the Campbell2014 ground motion prediction equation and correct the geological - condition - related terms based on the terrain and geological conditions to obtain a corrected Campbell2014 ground motion prediction equation. After an earthquake occurs, through pre - earthquake analysis, using the building complex structure model database and the regional geological terrain grid data model, based on the Monte Carlo simulation method, use the corrected Campbell2014 ground motion prediction equation to predict the ground motion intensity.

[0012] Step S5: Input the predicted ground motion intensity into the building seismic performance evaluation model. Obtain the corresponding seismic response through numerical simulation, and then input it into the building vulnerability database to obtain the probability that the building is in or exceeds a certain damage state. Finally, based on the building loss ratio database, use the building complex earthquake loss probability assessment method to calculate the repair cost and time - consumption cost of the building complex.

[0013] As a preferred improvement, the establishment process of the simplified multi - degree - of - freedom mechanical model of each building includes the following steps:

[0014] Use the basic information of the building to establish a simplified finite - element model. Adopt the lumped - mass method to model each floor in the building as a lumped mass block. Each mass block has only mass and no elastic stiffness, and the mass blocks are connected by shear springs. Each shear spring has only elastic stiffness and no mass, and the dynamic response of the shear spring is specified by the bearing capacity curve and hysteretic rules of the building.

[0015] As a preferred improvement, the structural parameters of each building model include the mass m of the mass block and the elastic stiffness k of the shear spring. Assume that the mass of each mass block is equal and the elastic stiffness of each shear spring is also equal. Through modal calculation, derive the elastic stiffness k of the shear spring from the mass m of the mass block and the fundamental period T of the building. The derivation process is expressed as:

[0016]

[0017] Among them, the basic period T of the building is calculated based on the typical period T0 and the typical number of floors N0 of this type of building, and the calculation process is expressed as:

[0018]

[0019] As a preferred improvement, the bearing capacity curve of the building is generated based on the Hazus database, and the generation process is as follows:

[0020] The bearing capacity curve of the t-th floor of the building is defined by the yield shear force V y，t , the yield displacement D y , the ultimate shear force V u，t , the ultimate displacement D u , and the complete damage displacement D c . Among them: the yield displacement D y and the complete damage displacement D c are provided by the Hazus database;

[0021] The yield shear force V y，t is expressed as:

[0022] V y，t = γC s mgNΓ t ;

[0023] The ultimate shear force V y，t is expressed as:

[0024] V u，t = βV y，t ;

[0025] The ultimate displacement D u is expressed as:

[0026] D u = μD y ;

[0027] Γ i The calculation process is:

[0028]

[0029] In the formula, γ represents the ratio of the yield strength to the design strength; C s represents the design strength coefficient; mgN represents the total weight of the target building; Γ t represents the ratio of V y，t and V y，1 ; β represents the overstrength coefficient related to the ultimate strength and the yield strength; μ represents the ductility coefficient; N represents the total number of floors of the building; γ, C s, the values of β and μ are provided by the Hazus database, and the value sizes depend on the building's structural type and seismic design level;

[0030] The hysteretic rules of the building are set as follows:

[0031] The flexural steel frame S1 and the light steel frame S3 have good energy dissipation capacity and adopt the elastic-perfectly plastic model; other structural types are modeled using hysteretic materials in Opensees.

[0032] As a preferred improvement, the seismic design levels are divided into four types, namely high code, medium code, low code, and pre-code seismic design levels; the damage states are divided into mild damage state, moderate damage state, extensive damage state, and complete damage state; the building usage categories include residential, commercial, public facilities, and industrial; the engineering demand parameters include, for example, the maximum inter-story drift ratio, peak floor acceleration, and residual inter-story drift.

[0033] As a preferred improvement, the modified Campbell2014 ground motion prediction equation is used to estimate the median μ of the ground motion intensity lnIM and the standard deviation σ, where:

[0034] lnIM = μ lnIM + δB + δW;

[0035]

[0036] In the formula, lnIM represents the logarithm of the ground motion intensity; δB and δW are the between-event residual and within-event residual respectively, and the two are independently and identically distributed, both following a normal distribution with a mean of 0 and variances of β and ω respectively;

[0037] μ lnIM = f mag + f dis + f flt + f hng + f hyp + f dip + f atn + f topo + f site ;

[0038] In the formula, f mag represents the magnitude-related term; f dis represents the geometric attenuation-related term; f flt represents the fault type-related term; f hng represents the hanging wall effect-related term; f hyp represents the focal depth-related term; f dip represents the fault dip-related term; f atn represents the rupture distance-related term; f topoIndicates items related to topographic conditions; f site Indicates items related to geological conditions;

[0039]

[0040]

[0041] f site = f site，G + S C f site，C ;

[0042]

[0043]

[0044] In the formula, c 21 , c 22 , c 23 , c 24 Indicates coefficients, with values of -0.0048, 0.0056, 0.0063, 0.0049 respectively; e represents the absolute elevation of the site; z represents the source distance elevation of the site; f site，G Indicates the shallow soil response term; S C Indicates the regional site effect index; f site，C Indicates the deep soil response term; θ1, θ2 represent coefficients, with values of 1.03, 1.05 respectively; k1 represents the threshold related to V S30 and is used to distinguish different soil types; V s30 represents the average shear wave velocity within 30 meters of the site depth; k2 represents the model coefficient related to the structural period; n represents the model coefficient independent of the structural period, taking 1.18; c 11 represents the model coefficient related to the structural period; c represents the model coefficient independent of the structural period, taking 1.88; A 1100 represents V S30 and is the median estimated value of the ground peak acceleration on the rock layer with V = 1100 m / s.

[0045] As a preferred improvement, the probability that the building is in or exceeds a certain damage state is expressed as:

[0046]

[0047] In the formula, Φ represents the standard normal distribution function; P[ds|S d represents the probability of being in or exceeding a certain damage state; ds represents the building damage state; S d represents the structural seismic response value; represents the median of the structural seismic response when the building reaches the threshold of a certain damage state; β dsRepresents the standard deviation of the natural logarithm of the structural seismic response under a certain damage state.

[0048] As a preferred improvement, the maintenance cost includes structural maintenance cost, acceleration-sensitive non-structural maintenance cost, and displacement-sensitive non-structural maintenance cost; the time consumption cost is divided into maintenance time cost, recovery time cost, and function loss time cost.

[0049] As a preferred improvement, the structural maintenance cost CS i Is expressed as:

[0050]

[0051]

[0052]

[0053] The acceleration-sensitive non-structural maintenance cost CNSA i Is expressed as:

[0054]

[0055] CNSA ds，i = BRC i * PONSA ds，i * λ (N) RCA ds，i ;

[0056] The displacement-sensitive non-structural maintenance cost CNSD i Is expressed as:

[0057]

[0058] CNSD ds，i = BRC i * PONSD ds，i * λ (N) RCD ds，i ;

[0059] In the formula, CS ds，i Represents the structural maintenance cost of a building of usage category i in damage state ds, BRC i Represents the replacement cost of a building of usage category i; PMBTSTR ds，i Represents the probability that a building of usage category i is in a structural damage state ds; λ (N) Represents the correction coefficient related to the number of floors N; RCS ds，i Represents the percentage of the structural maintenance cost of a building of usage category i in damage state ds to the building replacement cost; CNSA ds，iDenote the acceleration-sensitive non-structural repair cost of a building of usage category i in damage state ds; PONSA ds，i Denote the probability that a building of usage category i is in an acceleration-sensitive non-structural damage state ds; RCA ds，i Denote the percentage of the acceleration-sensitive non-structural repair cost of a building of usage category i in damage state ds to the replacement cost of the building; CNSD ds，i Denote the displacement-sensitive non-structural repair cost of a building of usage category i in damage state ds; PONSD ds，i Denote the probability that a building of usage category i is in a displacement-sensitive non-structural damage state ds; RCD ds，i Denote the percentage of the displacement-sensitive non-structural repair cost of a building of usage category i in damage state ds to the replacement cost of the building;

[0060] Then the non-structural repair cost CNS i Is expressed as: CNSi = CNSA i + CNSD i ;

[0061] The repair cost CBD of a building of usage category i i Is expressed as: CBD i = μ j (CS i + CNS i );

[0062] In the formula, μ j Denote the correction coefficient related to urban classification j, j = 1, 2, 3, 4, 5. When the urban classification is the first, second, third, fourth, and fifth levels, μ j The values are 1.2, 1.1, 1.0, 0.95, and 0.9 in sequence;

[0063] The total repair cost CBD is expressed as:

[0064] As a preferred improvement, the repair time cost is expressed as:

[0065]

[0066]

[0067] The recovery time cost is expressed as:

[0068]

[0069]

[0070] The function loss time cost is expressed as:

[0071]

[0072] In the formula, M represents the number of standard maintenance teams; N ds，i represents the number of buildings with usage category i and in the damaged state ds; RPT ds，i represents the maintenance time cost of buildings with usage category i in the damaged state ds; TRP ds，i represents the maintenance time cost of a single building with usage category i in the damaged state ds; RCT ds，i represents the recovery time cost of buildings with usage category i in the damaged state ds; TRC ds，i represents the recovery time cost of a single building with usage category i in the damaged state ds; FLT ds，i represents the maintenance time cost of buildings with usage category i in the damaged state ds; FLT i represents the building function loss time cost of buildings with usage category i; TFL ds，i represents the recovery time cost of buildings with usage category i in the damaged state ds.

[0073] The beneficial effects of the present invention are as follows:

[0074] (1) The present invention uses the Monte Carlo method to simulate the ground motion intensity random field, which can more accurately reflect the spatial correlation and uncertainty of ground motion, is closer to the actual situation compared with a single average value or simple interpolation method, and takes into account the influence of terrain and geological conditions on the propagation of seismic waves, improving the accuracy of the ground motion intensity random field simulation and laying a good foundation for subsequent building loss assessment;

[0075] (2) For areas with a large number of complex terrains such as mountains and hills, the present invention introduces a terrain condition-related term into the ground motion prediction equation and corrects it. Compared with the ground motion prediction equation that does not consider terrain conditions, the prediction accuracy can be greatly improved;

[0076] (3) Compared with means such as on-site exploration, satellite / UAV, Internet of Things, and image recognition, the use of the ground motion intensity random field simulation technology to predict the seismic losses of building groups through seismic performance models, building vulnerability databases, and building loss ratio databases has the advantages of low technical cost, fast calculation speed, strong timeliness, and wide coverage; it can quickly predict the seismic losses of building groups after an earthquake, timely understand the actual disaster situation in each area after the earthquake, and provide first-hand data for accurately assessing seismic risks; it helps to timely discover potential high-risk areas, provide decision-making basis for subsequent disaster prevention and mitigation work; provide guidance for the emergency repair and reinforcement of vulnerable buildings and infrastructure; guide the rational allocation of rescue forces, improve the emergency response efficiency; optimize the utilization of rescue resources, and improve the scientificity and effectiveness of emergency decision-making. Description of the Drawings

[0077] Figure 1 A flowchart showing the method for evaluating the seismic loss probability of a building group based on the ground motion intensity random field simulation;

[0078] Figure 2 A schematic diagram showing the building group structure model database;

[0079] Figure 3 A schematic diagram showing the multi-degree-of-freedom mechanical model of a building;

[0080] Figure 4 A schematic diagram showing the geological terrain grid data model;

[0081] Figure 5 A schematic diagram showing the seismic performance evaluation model;

[0082] Figure 6 A schematic diagram showing the distribution of ground motion intensity in the area to be evaluated;

[0083] Figure 7 A schematic diagram showing the building vulnerability database;

[0084] Figure 8 A schematic diagram showing the probability distribution of the repair cost of the building group;

[0085] Figure 9 A schematic diagram showing the probability distribution of the time-consuming cost of the building group. Detailed Implementation Manner

[0086] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0087] Please refer to Figures 1-9 , the present invention provides a method for evaluating the seismic loss probability of a building complex based on the simulation of the seismic ground motion intensity random field, including the following steps:

[0088] Step S1, collect the basic information of all buildings in the area to be evaluated, establish a simplified multi-degree-of-freedom mechanical model for each building, and summarize the simplified multi-degree-of-freedom mechanical models of all buildings to form a building complex structure model database; collect the terrain and geological condition data of the area to be evaluated, and establish a geological terrain grid data model.

[0089] The basic information of the building includes the building age, structural type, usage category, building height, number of floors, building area, longitude and latitude of the building location, and construction cost.

[0090] The establishment process of the simplified multi-degree-of-freedom mechanical model of each building includes the following steps:

[0091] Use the basic information of the building to establish a simplified finite element model. The lumped mass method is used to model each floor in the building as a lumped mass block. Each mass block has only mass and no elastic stiffness. The mass blocks are connected by shear springs. Each shear spring has only elasticity and no mass. The dynamic response of the shear spring is specified by the bearing capacity curve and hysteresis rule of the building. Then the structural parameters of each building model include the mass m of the mass block and the elastic stiffness k of the shear spring.

[0092] By using the lumped mass method, the complex structure of the building is simplified into a system composed of several mass blocks with only mass and no elastic stiffness and some shear springs with only elasticity and no mass. In this way, a discretized, intuitive and simple finite-degree-of-freedom system is formed. Only partial damping needs to be considered in this system, which can greatly simplify the calculation amount and make the calculation easier to solve.

[0093] Assume that the mass of each mass block is equal and the elastic stiffness of each shear spring is also equal. Then, through modal calculation, the elastic stiffness k of the shear spring can be easily derived from the mass m of the mass block and the fundamental period T of the structure. The derivation process is expressed as:

[0094]

[0095] Among them, the fundamental period T of the building is calculated according to the typical period T0 and typical number of floors N0 of this type of building. The calculation process is expressed as:

[0096]

[0097] According to Hazus (multi-hazard loss assessment software), the period T of the corresponding target building is calculated based on the typical period T0 and typical number of floors N0 of a building of a certain structural type:

[0098]

[0099] The bearing capacity curve of the building is generated based on the Hazus database, and the generation process is as follows:

[0100] The bearing capacity curve of the t-th floor of the building is defined by the yield shear force V y，t , yield displacement D y , ultimate shear force V u，t , ultimate displacement D u , and complete damage displacement D c . Among them: the yield displacement D y and the complete damage displacement D c are provided by the Hazus database;

[0101] The yield shear force V y，i is expressed as:

[0102] V y，t = γC s mgNΓ t ;

[0103] The ultimate shear force V u，i is expressed as:

[0104] V u，t = βV y，t ;

[0105] The ultimate displacement D u is expressed as:

[0106] D u = μD y ;

[0107] Γ i The calculation process is:

[0108]

[0109] In the formula, γ represents the ratio of the yield strength to the design strength; C s represents the design strength coefficient; mgN represents the total weight of the target building; Γ t represents the ratio of V y，t and V y，1 ; β represents the overstrength coefficient related to the ultimate strength and the yield strength; μ represents the ductility coefficient; N represents the total number of floors of the building; the values of γ, C s , β, μ are provided by Hazus, and the value depends on the structural type of the building and the seismic design level.

[0110] The yield shear force V y，t , yield displacement D y , ultimate shear force V u，t, ultimate displacement D u and complete damage displacement D c Once determined, the bearing capacity curve of the building can be obtained.

[0111] After determining the bearing capacity curve, the hysteretic rules for different structural types should also be determined. The moment-resisting steel frame S1 and the light steel frame S3 have good energy dissipation capacity, so the elastic-perfectly plastic model is adopted. Other structural types are modeled using hysteretic materials in Opensees.

[0112] Step S2: Conduct a cluster analysis on the seismic responses and repair costs of different types of buildings under seismic waves based on historical earthquake data. Construct a building vulnerability database with the seismic responses of buildings in a certain damage state under different seismic design levels and different structural type combinations; construct a building loss ratio database with the percentages of different repair costs to the replacement cost of the building in a certain damage state under different building repair cost categories and different usage categories combinations.

[0113] Specifically, the building vulnerability database includes the median and lognormal standard deviation of the seismic responses of buildings in a certain damage state under different seismic design levels and different structural type combinations. Among them, the seismic design levels are divided into four types, namely high-code, moderate-code, low-code, and pre-code seismic design levels. The damage states are divided into slight damage states, moderate damage states, extensive damage states, and complete damage states.

[0114] The building loss ratio database includes the percentages of different repair costs to the replacement cost of the building in a certain damage state under different building repair cost categories and different usage categories combinations, that is, the percentage RCS of the structural repair cost to the replacement cost of the building of building type i in damage state ds in the subsequent steps ds，i , the percentage RCA of the acceleration-sensitive non-structural repair cost to the replacement cost of the building of building type i in damage state ds ds，i and the percentage RCD of the displacement-sensitive non-structural repair cost to the replacement cost of the building of building type i in damage state ds ds，i .

[0115] Usage categories include residential, commercial, public facilities, industrial, etc.

[0116] Step S3: After amplitude - modulating the historical seismic waves, input them into the building complex structure model database, conduct vulnerability analysis on the buildings based on the incremental dynamic analysis method, obtain the distribution of engineering demand parameters, and construct a building seismic performance evaluation model.

[0117] The engineering demand parameters include, for example, the maximum inter - story drift ratio (IDR), peak floor acceleration (PFA), residual inter - story drift, etc.

[0118] During the input process of the historical seismic waves, at least 7 seismic wave data are selected and at least 8 amplitude - modulation operations are performed to ensure the reliability of the evaluation model.

[0119] Step S4: Considering the topographic and geological conditions of the area to be evaluated, introduce the topographic - condition - related term into the Campbell2014 ground - motion prediction equation, and correct the geological - condition - related term based on the topographic and geological conditions to obtain the corrected Campbell2014 ground - motion prediction equation; after an earthquake occurs, through pre - earthquake analysis, use the building complex structure model database and the regional geological and topographic grid data model, and based on the Monte Carlo simulation method, use the corrected Campbell2014 ground - motion prediction equation to predict the ground - motion intensity.

[0120] The geological - condition data includes the average shear - wave velocity Vs within 30 meters of the site 30 and the depth Z at which the horizontal shear - wave velocity is 1.0 km / s 1.0 and the depth Z at which the horizontal shear - wave velocity is 2.5 km / s. 2.5 The topographic data includes the absolute elevation of the site (with the sea - level as the reference) and the source - distance elevation (with the horizontal plane where the earthquake source is located as the reference).

[0121] The inter - event residual δB indicates that for a given period building in a single simulation, it is constant in space, but the ground - motion intensity residuals of buildings with different periods are correlated; the intra - event residual δW indicates that under a given simulation, the ground - motion intensities at different sites are correlated. Therefore, the inter - event and intra - event correlations need to be considered.

[0122] The corrected Campbell2014 ground - motion prediction equation is used to estimate the median μ lnIM and the standard deviation σ of the ground - motion intensity, where:

[0123] lnIM = μl n I M + 6B + δW;

[0124]

[0125] Where, lnIM represents the logarithm of ground motion intensity; δB and δW are the inter-event residual and intra-event residual respectively, and the two are independently and identically distributed, both following a normal distribution with a mean of 0 and variances of β and ω respectively;

[0126] μ lnIM = f mag + f dis + f flt + f hng + f hyp + f dip + f atn + f topo + f site ;

[0127] Where, f mag represents the magnitude-related term; f dis represents the geometric attenuation-related term; f flt represents the fault type-related term; f hng represents the hanging wall effect-related term; f hyp represents the focal depth-related term; f dip represents the fault dip-related term; f atn represents the rupture distance-related term; f topo represents the topographic condition-related term; f site represents the geological condition-related term;

[0128]

[0129]

[0130] f site = f site，G + S C f site，C ;

[0131]

[0132]

[0133] Where, c 21 , c 22 , c 23 , c 24 represent coefficients, with values of -0.0048, 0.0056, 0.0063, 0.0049 respectively; e represents the absolute elevation of the site; z represents the elevation of the source distance of the site; f site，G represents the shallow soil response term; S C represents the regional site effect index; f site，C represents the deep soil response term; θ1, θ2 represent coefficients, with values of 1.03, 1.05 respectively; k1 represents related to V S30Relevant thresholds for differentiating different soil types; V s30 represents the average shear wave velocity within 30 meters of the site depth; k2 represents a model coefficient related to the structural period; n represents a model coefficient independent of the structural period, taking 1.18; c 11 represents a model coefficient related to the structural period; c represents a model coefficient independent of the structural period, taking 1.88; A 1100 represents V S30 is the median estimated value of the peak ground acceleration on the 1100 m / s rock stratum surface.

[0134] Step S5: Input the predicted ground motion intensity into the building seismic performance evaluation model, obtain the corresponding seismic response through numerical simulation, then input it into the building vulnerability database to obtain the probability that the building is in or exceeds a certain damage state; finally, based on the building loss ratio database, use the seismic loss probability assessment method for building groups to calculate the repair cost and time consumption cost of the building group.

[0135] Probability that the building is in or exceeds a certain damage state:

[0136]

[0137] In the formula, Φ represents the standard normal distribution function; P[ds|S d represents the probability of being in or exceeding a certain damage state; ds represents the building damage state; S d represents the structural seismic response value; represents the median of the structural seismic response when the building reaches the threshold of a certain damage state; β ds represents the standard deviation of the natural logarithm of the structural seismic response under a certain damage state.

[0138] Based on the probability P[ds|S d that the building is in or exceeds a certain damage state, calculate the probability of being in a specific damage state, that is, the subsequent PMBTSTR ds，i , PONSA ds，i , PONSD ds，i Calculation formula for the probability of being in a specific damage state:

[0139] P(PMBTSTR ds，i , PONSA ds，i , PONSD ds，i ) = P[ds2|S d - P[ds1|S d .

[0140] The maintenance cost includes the structural maintenance cost, the acceleration-sensitive non-structural maintenance cost, and the displacement-sensitive non-structural maintenance cost; the time consumption cost includes the maintenance time cost, the recovery time cost, and the function loss time cost.

[0141] Structural maintenance cost CS i Is expressed as:

[0142]

[0143]

[0144]

[0145] Acceleration-sensitive non-structural maintenance cost CNSA i Is expressed as:

[0146]

[0147] CNSA ds，i = BRC i * PONSA ds，i * λ (N) RCA ds，i ;

[0148] Displacement-sensitive non-structural maintenance cost CNSD i Is expressed as:

[0149]

[0150] CNSD ds，i = BRC i * PONSD ds，i * λ (N) RCD ds，i ;

[0151] In the formula, CS ds，i Represents the structural maintenance cost when the building of usage category i is in the damage state ds, BRC i Represents the replacement cost of the building of usage category i; PMBTSTR ds，i Represents the probability that the building of usage category i is in the structural damage state ds; λ (N) Represents the correction coefficient related to the number of floors N; RCS ds，i Represents the percentage of the structural maintenance cost to the replacement cost of the building of usage category i when the building is in the damage state ds; CNSA ds，i Represents the acceleration-sensitive non-structural maintenance cost when the building of usage category i is in the damage state ds; PONSA ds，iDenotes the probability that a building of usage category i is in the acceleration-sensitive non-structural damage state ds; RCA ds，i Denotes the percentage of the acceleration-sensitive non-structural repair cost of a building of usage category i in damage state ds to the replacement cost of the building; CNSD ds，i Denotes the displacement-sensitive non-structural repair cost of a building of usage category i in damage state ds; PONSD ds，i Denotes the probability that a building of usage category i is in the displacement-sensitive non-structural damage state ds; RCD ds，i Denotes the percentage of the displacement-sensitive non-structural repair cost of a building of usage category i in damage state ds to the replacement cost of the building.

[0152] Then the non-structural repair cost CNS i Is expressed as: CNS i = CNSA i + CNSD i ;

[0153] The repair cost CBD of a building of usage category i i Is expressed as: CBD i = μ j (CS i + CNS i );

[0154] In the formula, μ j Denotes the correction coefficient related to urban classification j, where j = 1, 2, 3, 4, 5. When the urban classification is the first, second, third, fourth, and fifth levels, the values of μ j Are 1.2, 1.1, 1.0, 0.95, and 0.9 in sequence.

[0155] It can be understood that for different urban classifications, there are certain differences in corresponding material costs, labor costs, management costs, etc. The higher the urban classification (the smaller the value of j), the higher the corresponding repair cost. The introduction of the correction coefficient μ j Fully considers the differences between different levels of cities, making the calculation of repair costs closer to the actual situation.

[0156] The total repair cost CBD is expressed as:

[0157] The repair time cost is expressed as:

[0158]

[0159]

[0160] The recovery time cost is expressed as:

[0161]

[0162]

[0163] The time cost of function loss is expressed as:

[0164]

[0165] In the formula, M represents the number of standard maintenance teams; N ds，i represents the number of buildings with usage category i and in the damaged state ds; RPT ds，i represents the maintenance time cost of buildings with usage category i in the damaged state ds; TRP ds，i represents the maintenance time cost of a single building with usage category i in the damaged state ds; RCT ds，i represents the recovery time cost of buildings with usage category i in the damaged state ds; TRC ds，i represents the recovery time cost of a single building with usage category i in the damaged state ds; FLT ds，i represents the maintenance time cost of buildings with usage category i in the damaged state ds; FLT i represents the time cost of function loss of buildings with usage category i; TFL ds，i represents the recovery time cost of buildings with usage category i in the damaged state ds.

[0166] The maintenance cost of a single building includes structural maintenance cost, acceleration-sensitive non-structural maintenance cost, and displacement-sensitive non-structural maintenance cost. The time consumption cost is divided into maintenance time cost, recovery time cost, and time cost of function loss. After an earthquake, the spatial distribution of ground motion intensity and the probability distribution of earthquake losses of the building group can be quickly and intuitively displayed.

[0167] The solution provided by the present invention can quickly and intuitively display the spatial distribution of ground motion intensity and the probability distribution of earthquake losses of the building group, providing important support for earthquake risk assessment and post-disaster emergency decision-making, thereby enhancing the disaster resistance and recovery ability of the city.

[0168] The embodiments of the present invention have been described above in conjunction with the accompanying drawings. However, the present invention is not limited to the above specific embodiments. The above specific embodiments are merely illustrative and not restrictive. Under the inspiration of the present invention, those of ordinary skill in the art can also make many forms without departing from the purpose of the present invention and the scope protected by the claims, and all of them belong to the protection scope of the present invention.

Claims

1. A method for assessing the probability of earthquake losses of a building complex based on random field simulation of earthquake intensity, characterized in that: The steps include: Step S1, collecting basic information of all buildings in the area to be evaluated, establishing a simplified multi-degree-of-freedom mechanical model of each building, and aggregating the simplified multi-degree-of-freedom mechanical models of all buildings to form a building complex structural model database; Collect terrain and geological condition data of the area to be evaluated and establish a geological and topographic raster data model; Step S2, based on historical earthquake data, cluster analysis is performed on the seismic responses and maintenance costs of different types of buildings under the action of seismic waves, and a building vulnerability database is constructed based on the seismic responses of buildings in a certain damage state under different seismic design levels and different structural type combinations; a building loss proportion database is constructed based on the percentage of different maintenance costs of buildings in a certain damage state under different building maintenance cost categories and different usage category combinations to the replacement cost of the building; Step S3, inputting the amplitude modulated historical seismic waves into the building complex structure model database, performing vulnerability analysis on the building based on the incremental dynamic analysis method, obtaining the distribution of engineering demand parameters, and constructing a building seismic performance evaluation model; Step S4, considering the topography and geological conditions of the area to be evaluated, introducing the terrain condition related terms into the Campbell2014 earthquake motion prediction equation, and correcting the geological condition related terms based on the topography and geological conditions to obtain a corrected Campbell2014 earthquake motion prediction equation; After an earthquake occurs, the building complex structure model database and the regional geological terrain grid data model are used for pre-earthquake analysis, and the seismic intensity is predicted using the modified Campbell 2014 seismic motion prediction equation based on the Monte Carlo simulation method; the modified Campbell 2014 seismic motion prediction equation is used to estimate the median value μ of the seismic intensity. lnIM and standard deviation σ, where: lnIM=μ lnIM +δB+δW; Where, lnIM represents the logarithm of the ground motion intensity; δB and δW are the inter-event residual and intra-event residual, respectively. Both are independent and identically distributed and obey the normal distribution with mean 0 and variance β and ω, respectively. μ lnIM =f mag +f dis +f flt +f hng +f hyp +f dip +f atn +f topo +f site ; In the formula, f mag represents the magnitude-related term; f dis represents the geometric attenuation related term; f flt represents the fault type related item; f hng represents the hanging plate effect related term; f hyp represents the focal depth related term; f dip represents the fault dip related term; f atn represents the rupture distance related term; f topo represents the terrain condition related item; f site Indicates items related to geological conditions; In the formula, c 21 , c 22 , c 23 , c 24 represents the coefficient, and its values ​​are -0.0048, 0.0056, 0.0063, and 0.0049 respectively; e represents the absolute elevation of the station; z represents the source distance elevation of the station; f site，G represents the shallow soil response term; S C represents the regional site effect index; f site，C represents the deep soil response term; θ1, θ2 represent coefficients, with values ​​of 1.03 and 1.05 respectively; k1 represents the coefficient with V S30 Related thresholds are used to distinguish different soil types; V s30 represents the average shear wave velocity within the 30-meter depth range of the site; k2 represents the model coefficient related to the structural period; n represents the model coefficient unrelated to the structural period, which is taken as 1.18; c 11 represents the model coefficient related to the structural period; c represents the model coefficient independent of the structural period, which is 1.88; A 1100 Indicates V S30 is the median estimate of the peak ground acceleration on the rock layer of 1100 m / s; Step S5, input the predicted earthquake motion intensity into the building seismic performance assessment model, obtain the corresponding earthquake response through numerical simulation, and then input it into the building vulnerability database to obtain the probability that the building is in or exceeds a certain damage state; finally, based on the building loss ratio database, the building complex earthquake loss probability assessment method is adopted to calculate the maintenance cost and time consumption cost of the building complex.

2. The method for assessing the probability of earthquake loss of a building complex by simulating a random field of earthquake intensity according to claim 1 is characterized in that: The process of establishing a simplified multi-degree-of-freedom mechanical model for each building includes the following steps: A simplified finite element model is established using the basic information of the building. The concentrated mass method is used to model each floor in the building as a concentrated mass block. Each mass block has only mass but no elastic stiffness. The mass blocks are connected by shear springs. Each shear spring has only elastic stiffness but no mass. The dynamic response of the shear spring is specified by the bearing capacity curve and hysteresis rule of the building.

3. The method for assessing the probability of earthquake loss of a building complex by simulating a random field of earthquake intensity according to claim 2, characterized in that: The structural parameters of each building model include the mass m of the mass block and the elastic stiffness k of the shear spring. Assuming that the mass of each mass block is equal, the elastic stiffness of each shear spring is also equal. The elastic stiffness k of the shear spring is derived from the mass m of the mass block and the basic period T of the building through modal calculation. The derivation process is expressed as: The basic period T of the building is calculated based on the typical period T0 and typical number of floors N0 of this type of building. The calculation process is expressed as:

4. The method for assessing the probability of earthquake loss of a building complex by simulating a random field of earthquake intensity according to claim 2, characterized in that: The building's bearing capacity curve is generated based on the Hazus database. The generation process is as follows: The bearing capacity curve of the tth floor of the building is given by the yield shear force V y，t , yield displacement D y , Ultimate shear force V u，t 、Limit displacement D u , Complete damage displacement D c is defined as follows: y and the complete damage displacement D c Provided by Hazus database; Yield shear stress V y，t It is expressed as: V y，t =γC s mgNΓ t ; Ultimate shear force V y，t It is expressed as: V u，t =βV y，t ; Limit displacement D u It is expressed as: D u =μD y ; Γ i The calculation process is: In the formula, γ represents the ratio of yield strength to design strength; C s represents the design strength coefficient; mgN represents the total weight of the target building; Γ t Indicates V y，t and V y，1 ratio; β represents the super strength coefficient related to the ultimate strength and yield strength; μ represents the ductility coefficient; N represents the total number of floors of the building; γ, C s , β, μ are provided by the Hazus database, and their values ​​depend on the structural type and seismic design level of the building; The hysteresis rules for buildings are set as follows: The moment-resisting steel frame S1 and the light steel frame S3 have good energy dissipation capacity and adopt the elastic perfect plastic model; other structural types are modeled using hysteretic materials in Opensees.

5. The method for assessing the probability of earthquake loss of a building complex by simulating a random field of earthquake intensity according to claim 1, characterized in that: There are four types of seismic design levels, namely high standard, medium standard, low standard and pre-standard seismic design levels; the damage states are divided into slight damage state, moderate damage state, extensive damage state and complete damage state; the building use categories include residential, commercial, public facilities and industrial; the engineering demand parameters include maximum inter-story displacement angle, peak floor acceleration and residual inter-story displacement.

6. The method for assessing the probability of earthquake losses of buildings using random field simulation of earthquake intensity according to claim 1 is characterized in that: The probability that a building is in or exceeds a certain damage state is expressed as: Where Φ represents the standard normal distribution function; P[ds|S d ] represents the probability of being in or exceeding a certain damage state; ds represents the building damage state; S d Represents the structural seismic response value; It represents the median value of the structural seismic response when the building reaches a certain damage state threshold; β ds It represents the standard deviation of the natural logarithm of the seismic response of the structure under a certain damage state.

7. The method for assessing the probability of earthquake losses of buildings using random field simulation of earthquake intensity according to claim 1 is characterized in that: Maintenance costs include structural maintenance costs, acceleration-sensitive non-structural maintenance costs and displacement-sensitive non-structural maintenance costs; time consumption costs are divided into maintenance time costs, recovery time costs and function loss time costs.

8. The method for assessing the probability of earthquake losses of buildings using random field simulation of earthquake intensity according to claim 7 is characterized in that: Structural repair costs CS i It is expressed as: Acceleration-sensitive non-structural repair costs CNSA i It is expressed as: CNSA ds，i =BRC i *PONSA ds，i *λ(N)RCA ds，i ; Displacement-sensitive non-structural repair costs (CNSD) i It is expressed as: CNSD ds，i =BRC i *PONSD ds，i *l (N) RCD ds，i ; In the formula, CS ds，i It represents the structural repair cost of a building with use category i in the damaged state ds, BRC i represents the replacement cost of a building with use category i; PMBTSTR ds，i represents the probability that a building with usage category i is in a structural damage state ds; λ (N) Indicates the correction factor related to the number of floors N; RCS ds，i It represents the percentage of the structural repair cost of a building with use category i in the damaged state ds to the replacement cost of the building; CNSA ds，i PONSA represents the acceleration-sensitive non-structural repair cost of a building with utilization category i in damage state ds; ds，i RCA represents the probability that a building with utilization category i is in an acceleration-sensitive non-structural damage state ds; ds，i CNSD is the percentage of the acceleration-sensitive non-structural repair cost of a building in use category i in damage state ds to the replacement cost of the building; ds，i PONSD is the displacement-sensitive non-structural repair cost of a building with usage category i in damage state ds; ds，i RCD represents the probability that a building with utilization category i is in a displacement-sensitive non-structural damage state ds; ds，i represents the percentage of displacement-sensitive non-structural repair costs of a building in use category i in damaged state ds to the replacement cost of the building; The non-structural maintenance cost CNS i Expressed as: CNS i =CNSA i +CNSD i ; Building maintenance cost CBD for category i i Expressed as: CBD i =μ j (CS i +CNS i ); In the formula, μ j represents the correction coefficient related to the city classification j, j = 1, 2, 3, 4, 5, when the city classification is level 1, level 2, level 3, level 4 and level 5, μ j The values ​​are 1.2, 1.1, 1.0, 0.95, and 0.9; The total maintenance cost CBD is expressed as:

9. The method for assessing the probability of earthquake losses of buildings using random field simulation of earthquake intensity according to claim 7 is characterized in that: The maintenance time cost is expressed as: The recovery time cost is expressed as: The time cost of loss of function is expressed as: Where M represents the number of standard maintenance teams; N ds，i represents the number of buildings with use category i and in damage state ds; RPT ds，i TRP represents the repair time cost of a building with usage category i in the damaged state ds; ds，i represents the repair time cost of a single building with usage category i in the damaged state ds; RCT ds，i TRC represents the time cost of restoration of a building with usage category i in damaged state ds; ds，i FLT represents the recovery time cost of a single building with usage category i in damaged state ds; ds，i FLT represents the repair time cost of a building with usage category i in the damaged state ds; i TFL represents the time cost of loss of building function for use category i; ds，i It represents the recovery time cost of a building with usage category i in the damaged state ds.

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