A seismic simulation method for existing buildings considering real damage states

Abstract

The present invention discloses a method for seismic simulation of existing buildings that takes into account the actual damage state, including: determining a quantitative component damage index based on the observed component damage state; determining the material damage index of the damaged component based on the component damage index; determining key parameters of the damaged material constitutive structure based on the material damage index; establishing a finite element model of the damaged building based on the material constitutive structure of the damaged component; and evaluating the seismic risk and seismic performance of the damaged building based on the finite element model. By assigning the constitutive structure of the damaged material to the fiber model of OpenSEES, the present invention can achieve rapid modeling of the damaged building, effectively restoring the actual damage to the existing building; combined with the seismic vulnerability analysis method, it can achieve rapid assessment of the seismic risk and seismic resistance of the existing building, providing further support for relevant departments to formulate reasonable reinforcement and renovation strategies.

Description

Technical Field

[0001] The present invention belongs to the technical field of building seismic simulation, and in particular relates to a seismic simulation method for existing buildings taking into account real damage states. Background Art

[0002] During their service life, urban buildings may experience reduced bearing capacity and reduced functionality due to natural or human factors such as earthquakes, concrete carbonization, and steel corrosion. If these buildings are to continue to be used, it is necessary to conduct residual performance assessments and, based on the results, formulate appropriate reinforcement and retrofit strategies to restore and improve their original seismic performance. In this context, numerical seismic simulation of damaged buildings, due to its remarkable efficiency, convenience, and accuracy, is being used to rapidly assess the performance of existing buildings.

[0003] The pre-damage method and the component performance reduction method are two main approaches for simulating the seismic performance of damaged buildings. Taking earthquake-damaged buildings as an example, the pre-damage method simulates structural damage by applying realistic ground motion records to a numerical model of an intact building, performing nonlinear time-history analysis to simulate the structural damage and subsequently assessing the building's seismic capacity. Commonly used methods such as sequential earthquake analysis and post-earthquake pushover analysis fall under the pre-damage method. However, the structural damage determined by the numerical results of nonlinear time-history analysis may not match the actual damage state. Existing numerical simulation results indicate that, in nonlinear time-history analysis, the plastic hinge failure mode at the column end may be inappropriately predicted as the plastic hinge failure mode at the beam end. The component performance reduction method reduces the macroscopic mechanical properties of the component based on the observed damage and then assigns these reduced mechanical properties to the simulated structural elements to achieve seismic simulation of the damaged building. However, this method is a macroscopic simulation method that fails to describe the actual material damage state and may miscalculate the seismic performance of the damaged building.

[0004] In summary, traditional numerical simulation techniques for damaged buildings fail to consider the actual damage sustained by the building at the material and component level, and therefore cannot accurately assess the seismic performance of damaged buildings. Therefore, a numerical simulation method is needed that can invert the properties of damaged materials based on observable structural damage to accurately and rapidly assess the seismic performance of existing buildings. Summary of the Invention

[0005] Purpose of the invention: In order to overcome the deficiencies in the prior art, a method for seismic simulation of existing buildings that takes into account the actual damage state is provided. This method can quickly establish a numerical model of the damaged building based on the actual observed structural and component damage, and then evaluate the earthquake risk and seismic resistance of the building, which will help relevant departments to formulate reasonable reinforcement and renovation strategies.

[0006] Technical Solution: To achieve the above-mentioned purpose, the present invention provides a method for seismic simulation of existing buildings taking into account the actual damage state, comprising the following steps:

[0007] S1: Determine the quantitative component damage index based on the observed component damage state;

[0008] S2: Determine the material damage index of the damaged component based on the component damage index;

[0009] S3: Determine the key constitutive parameters of the damaged material based on the material damage index;

[0010] S4: Establish a finite element model of the damaged building based on the material structure of the damaged components;

[0011] S5: Conduct earthquake risk and seismic performance assessment of damaged buildings based on finite element models.

[0012] Furthermore, the component damage index in step S1 is quantitatively represented by the Park-Ang damage index DI.

[0013] Furthermore, in step S2, a damage distribution model is used to determine the material damage index of the damaged component; the cross-section of the reinforced concrete component is divided into three regions: protective layer concrete, core area concrete, and steel bars. The damage distribution model is represented by a mapping relationship between the material damage indices of these three regions and the component damage index DI, thereby determining the material damage index of the damaged component.

[0014] Furthermore, the damage index D of the protective layer concrete material in step S2 is c The mapping relationship between DI and the core area concrete material damage index D cc The mapping relationship between DI and steel material damage index D s The mapping relationships between and DI are shown in formulas (1), (2), and (3).

[0015]

[0016] Furthermore, the damaged materials in step S3 include three materials: damaged protective layer concrete, damaged core area concrete and damaged steel bars.

[0017] Furthermore, the constitutive structure of the damaged protective layer concrete in step S3 is simulated using the Kent-Scott-Park model, and the skeleton curve of the model is calculated by the peak compressive strain ε cd , peak compressive stress f cd , ultimate compressive strain ε cu Three parameter definitions, the calculation formulas are

[0018]

[0019]

[0020] Among them, ε c and f c represent the peak compressive strain and peak compressive stress of the intact protective layer concrete; ε cd and f cd are the peak compressive strain and peak compressive stress of the damaged cover concrete, respectively; Z is the strain softening slope coefficient.

[0021] Furthermore, the constitutive structure of the damaged core area concrete in step S3 is simulated by the Mander model, and the skeleton curve of the model is calculated by the peak compressive strain ε ccd , peak compressive stress f ccd , ultimate compressive strain ε ccu and elastic modulus E ccd Four parameter definitions, the calculation formula is

[0022]

[0023] Among them, ε cc and f cc represent the peak compressive strain and peak compressive stress of the concrete in the intact core area respectively; ε ccd and f ccd They represent the peak compressive strain and peak compressive stress of the concrete in the intact core area respectively; r represents the shape coefficient of the skeleton curve; E c represents the elastic modulus of the concrete in the intact core area; E sec =f cc / ε cc represents the secant modulus of the undamaged core concrete at peak stress; f yv Represents the yield strength of stirrups; ε su represents the fracture strain of the stirrup; ρ v Indicates the volumetric stirrup ratio of stirrups.

[0024] Furthermore, in step S3, the constitutive structure of the damaged steel bar is simulated using a three-fold line model, and the skeleton curve of the model is determined by three data points in the positive and negative directions. The mechanical behavior of the steel bar is positively and negatively symmetrical, so the key points in the positive and negative directions have the same value. The three data points (ε1, σ1), (ε2, σ2) and (ε3, σ3) are determined as follows:

[0025] The stress σ1 and strain ε1 of the first data point are calculated as follows

[0026] σ1=0.1f y (13)

[0027]

[0028] Among them, E s and f y represent the elastic modulus and yield strength of the steel bar respectively;

[0029] The stress σ2 and strain ε2 of the second data point are calculated based on the steel bar material damage index D s OK, the calculation is as follows

[0030]

[0031] Among them, ε y and b represent the yield strain and strain hardening rate of the steel bar, respectively;

[0032] The stress σ3 and strain ε3 of the third data point are calculated as follows

[0033] σ3=f u (17)

[0034]

[0035] Among them, f u Indicates the ultimate stress of the steel bar.

[0036] Furthermore, in step S4, the OpenSEES platform is used to establish a finite element model of the damaged building: since the main damage of the frame beams and frame columns under earthquake action is concentrated in the plastic hinge section at the beam end, the plastic hinge beam-column unit based on the fiber section is used to simulate the structural components; the plastic hinge beam-column unit based on the fiber section is a force-based fiber beam-column unit, and the use of this unit requires the definition of the plastic hinge length L at both ends. p , L p Calculate according to the following formula

[0037] L p =0.08L+0.022f y d l (N,mm) (19)

[0038] Where L represents the length of the structural member equivalent to the cantilever member; d l Indicates the diameter of the steel bar;

[0039] The control section of the plastic hinge area at both ends of the beam-column unit is a fiber section composed of damaged materials, and the control section of the middle section is a fiber section composed of intact materials. The constitutive model of the damaged and intact protective layer concrete is simulated using the Concrete02 model based on the skeleton curve of the Kent-Scott-Park model. cd 、f cd and ε cu Input the call command of Concrete02 model to simulate the constitutive structure of damaged cover concrete. c 、f c and ε cuInputting the call command of Concrete02 model can simulate the constitutive structure of the intact protective layer concrete; the constitutive structure of the damaged and intact core area concrete is simulated by Concrete04 model based on the skeleton curve of Mander model. cd , ε ccd 、f ccd and ε ccu Input the call command of Concrete04 model to simulate the constitutive structure of the concrete in the damaged core area. c , ε cc 、f cc and ε ccu Inputting the call command of Concrete04 model can simulate the constitutive law of the intact core area concrete; the damaged and intact steel bars are simulated by Hysteretic and Steel02 models respectively. Inputting (ε1,σ1), (ε2,σ2) and (ε3,σ3) into the call command of Hysteretic model can simulate the constitutive law of the damaged steel bars. y 、E s and b input the call command of Steel02 model to simulate the constitutive law of intact steel bars.

[0040] Furthermore, in step S5, the earthquake vulnerability analysis method is used to evaluate the earthquake risk and seismic performance of the damaged building. Seismic vulnerability is described as the cumulative probability of a structure exceeding a certain limit state under a certain earthquake intensity IM. The probabilistic earthquake vulnerability model is specifically expressed as the convolution of the demand model and the capacity model, and the formula is as follows:

[0041]

[0042] Among them, EDP is the engineering requirement parameter of the structure; LS i Indicates the EDP threshold corresponding to a certain limit state; S d|IM and β D|IM are the median and standard deviation of the structural seismic demand under a given IM; β C Indicates the degree of discreteness of the limit state, which is taken as 0.3; β M represents the standard deviation of model uncertainty, which is taken as 0.2; Φ[·] represents the cumulative normal distribution function;

[0043] Median seismic demand S d|IM and the earthquake intensity parameter IM follow a power exponential regression relationship, which is expressed as follows

[0044] S d|IM =a(IM) b (twenty one)

[0045] Performing logarithmic transformation on formula (21), we can get

[0046] lnS d|IM =lna+blnIM (22)

[0047] Where a and b are regression coefficients; the logarithmic standard deviation of seismic demand β D|IM The calculation is as follows

[0048]

[0049] Where N is the total number of nonlinear dynamic time history analyses; i represents the i-th nonlinear dynamic time history analysis; and the data points used for regression analysis are obtained using the incremental dynamic analysis (IDA) method and the cloud plot method.

[0050] Beneficial effects: Compared with the existing technology, the present invention converts the actually observed component damage state into a quantitative material damage index for existing buildings through a damage distribution model, which can intuitively reveal the degree of material damage and is more scientific and reasonable than the existing pre-damage method and component performance reduction method. A method for determining the constitutive structure of damaged materials based on the material damage index is proposed. The constitutive structure of damaged materials is assigned to the fiber model of OpenSEES to achieve rapid modeling of damaged buildings and effectively restore the real damage of existing buildings. Combined with the seismic vulnerability analysis method, it can achieve rapid assessment of the seismic risk and seismic resistance of existing buildings, providing further support for relevant departments to formulate reasonable reinforcement and renovation strategies. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 Schematic diagram of the process of the present invention;

[0052] Figure 2 Determine a schematic diagram for the constitutive curve of the damaged material;

[0053] Figure 3 Schematic diagram of OpenSEES finite element modeling of damaged buildings;

[0054] Figure 4 Schematic diagram of the material model used for finite element modeling;

[0055] Figure 5 This is a schematic diagram of a two-dimensional 5-story 4-span reinforced concrete frame structure in this embodiment;

[0056] Figure 6 The IDA curve diagrams of the intact structure and the damaged structure in this embodiment;

[0057] Figure 7 Graph showing the relationship between engineering requirement parameters and earthquake intensity parameters for the intact structure and the damaged structure in this embodiment;

[0058] Figure 8 Graph showing the vulnerability of the intact structure and damaged structure in this embodiment. DETAILED DESCRIPTION

[0059] The present invention is further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, modifications of various equivalent forms of the present invention made by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0060] The present invention provides a method for simulating the seismic performance of existing buildings taking into account the actual damage state. Figure 1 As shown, the following steps are included:

[0061] S1: Determine the quantitative component damage index based on the observed component damage state:

[0062] The component damage index is quantitatively expressed by the Park-Ang damage index DI. Table 1 summarizes the DI range corresponding to the component damage state:

[0063] Table 1 DI range corresponding to different component damage states.

[0064]

[0065] For ease of practical use, the damage index DI of components in different damage states can be expressed as the median value of the corresponding damage index range.

[0066] S2: Determine the material damage index of the damaged component based on the component damage index:

[0067] The damage distribution model is used to determine the material damage index of the damaged component. The cross-section of the reinforced concrete component is divided into three regions: the protective layer concrete, the core area concrete, and the steel bars. The damage distribution model is expressed as a mapping relationship between the material damage index of these three regions and the component damage index DI, thereby determining the material damage index of the damaged component.

[0068] Damage index D of protective layer concrete material c The mapping relationship between DI and the core area concrete material damage index D cc The mapping relationship between DI and steel material damage index D s The mapping relationships between and DI are shown in formulas (1), (2), and (3).

[0069]

[0070] S3: Determine the key constitutive parameters of the damaged material based on the material damage index:

[0071] The damaged materials include three types of materials: damaged protective layer concrete, damaged core area concrete and damaged steel bars. The schematic diagrams for determining the constitutive curves of damaged protective layer concrete, damaged core area concrete and damaged steel bars are shown in Figure 2. Figure 2 As shown in (a), (b) and (c):

[0072] The constitutive model of the damaged cover concrete is simulated using the Kent-Scott-Park model. The skeleton curve of the model is obtained by the peak compressive strain ε cd , peak compressive stress f cd , ultimate compressive strain ε cu Three parameter definitions, the calculation formulas are

[0073]

[0074] Among them, ε c and f c represent the peak compressive strain and peak compressive stress of the intact protective layer concrete; ε cd and f cd are the peak compressive strain and peak compressive stress of the damaged cover concrete, respectively; Z is the strain softening slope coefficient.

[0075] The constitutive structure of the concrete in the damaged core area is simulated by the Mander model, and the skeleton curve of the model is expressed by the peak compressive strain ε ccd , peak compressive stress f ccd , ultimate compressive strain ε ccu and elastic modulus E ccd Four parameter definitions, the calculation formula is

[0076]

[0077] Among them, ε cc and f cc represent the peak compressive strain and peak compressive stress of the concrete in the intact core area respectively; ε ccd and f ccd They represent the peak compressive strain and peak compressive stress of the concrete in the intact core area respectively; r represents the shape coefficient of the skeleton curve; E c represents the elastic modulus of the concrete in the intact core area; E sec =f cc / ε cc represents the secant modulus of the undamaged core concrete at peak stress; f yv Represents the yield strength of stirrups; ε su represents the fracture strain of the stirrup; ρ v Indicates the volumetric stirrup ratio of stirrups.

[0078] The constitutive model of the damaged steel bar is simulated using a three-fold line model. The skeleton curve of the model is determined by three data points in the positive and negative directions. The mechanical behavior of the steel bar is positively and negatively symmetrical, so the key points in the positive and negative directions have the same values. The three data points (ε1, σ1), (ε2, σ2), and (ε3, σ3) are determined as follows:

[0079] The stress σ1 and strain ε1 of the first data point are calculated as follows

[0080] σ1=0.1f y (13)

[0081]

[0082] Among them, E s and f y represent the elastic modulus and yield strength of the steel bar respectively;

[0083] The stress σ2 and strain ε2 of the second data point are calculated based on the steel bar material damage index D s OK, the calculation is as follows

[0084]

[0085] Among them, ε y and b represent the yield strain and strain hardening rate of the steel bar, respectively;

[0086] The stress σ3 and strain ε3 of the third data point are calculated as follows

[0087] σ3=f u (17)

[0088]

[0089] Among them, f u Indicates the ultimate stress of the steel bar.

[0090] S4: Construct a finite element model of the damaged building based on the material properties of the damaged components:

[0091] like Figure 3 As shown in the figure, the finite element model of the damaged building was established using the OpenSEES platform: Since the main damage of the frame beams and frame columns under earthquake action is concentrated in the plastic hinge section at the beam end, the plastic hinge beam-column unit based on the fiber section is used to simulate the structural components; the plastic hinge beam-column unit based on the fiber section is a force-based fiber beam-column unit. Using this unit requires defining the plastic hinge length L at both ends. p , L p Calculate according to the following formula

[0092] L p =0.08L+0.022f y dl (N,mm) (19)

[0093] Where L represents the length of the structural member equivalent to the cantilever member; d l Indicates the diameter of the steel bar;

[0094] The control section of the plastic hinge area at both ends of the beam-column unit is a fiber section composed of damaged materials, and the control section of the middle section is a fiber section composed of intact materials. The constitutive model of the damaged and intact protective layer concrete is simulated using the Concrete02 model based on the skeleton curve of the Kent-Scott-Park model. cd 、f cd and ε cu Input the call command of Concrete02 model to simulate the constitutive structure of damaged cover concrete. c 、f c and ε cu Inputting the call command of Concrete02 model can simulate the constitutive structure of the intact protective layer concrete; the constitutive structure of the damaged and intact core area concrete is simulated by Concrete04 model based on the skeleton curve of Mander model. cd , ε ccd 、f ccd and ε ccu Input the call command of Concrete04 model to simulate the constitutive structure of the concrete in the damaged core area. c , ε cc 、f cc and ε ccu Inputting the call command of Concrete04 model can simulate the constitutive law of the intact core area concrete; the damaged and intact steel bars are simulated by Hysteretic and Steel02 models respectively. Inputting (ε1,σ1), (ε2,σ2) and (ε3,σ3) into the call command of Hysteretic model can simulate the constitutive law of the damaged steel bars. y 、E s The call command of Steel02 model can simulate the constitutive structure of undamaged steel bars. The corresponding material model is as follows: Figure 4 shown.

[0095] To ensure the accuracy and efficiency of the numerical model, it is recommended that the number of divided fibers for the cover concrete be 16×1 or above, and the number of divided fibers for the core concrete be 14×14 or above.

[0096] S5: Rapid assessment of earthquake risk and seismic performance of damaged buildings based on finite element models:

[0097] The seismic vulnerability analysis method is used to assess the seismic risk and seismic performance of damaged buildings. Seismic vulnerability is described as the cumulative probability of a structure exceeding a certain limit state under a specific earthquake intensity IM. The probabilistic seismic vulnerability model is specifically expressed as the convolution of the demand model and the capacity model. The formula is as follows:

[0098]

[0099] Among them, EDP is the engineering requirement parameter of the structure; LS i Indicates the EDP threshold corresponding to a certain limit state; S d|IM and β D|IM are the median and standard deviation of the structural seismic demand under a given IM; β C Indicates the degree of discreteness of the limit state, which is taken as 0.3; β M represents the standard deviation of model uncertainty, which is taken as 0.2; Φ[·] represents the cumulative normal distribution function;

[0100] Median seismic demand S d|IM and the earthquake intensity parameter IM follow a power exponential regression relationship, which is expressed as follows

[0101] S d|IM =a(IM) b (twenty one)

[0102] Performing logarithmic transformation on formula (21), we can get

[0103] lnS d|IM =lna+blnIM (22)

[0104] Where a and b are regression coefficients; the logarithmic standard deviation of seismic demand β D|IM The calculation is as follows

[0105]

[0106] Where N is the total number of nonlinear dynamic time history analyses; i represents the i-th nonlinear dynamic time history analysis; and the data points used for regression analysis are obtained using the incremental dynamic analysis (IDA) method and the cloud plot method.

[0107] In order to verify the effectiveness of the method of the present invention, the above scheme is applied as an example in this embodiment, as follows:

[0108] This embodiment provides a method for simulating the seismic resistance of existing buildings taking into account the actual damage state. Figure 1 , including the following steps:

[0109] Step 1: Determine the quantitative component damage index based on the observed component damage state

[0110] The simulation object of this embodiment is a designed two-dimensional 5-story 4-span reinforced concrete frame structure, such as Figure 5 As shown, the ground floor is 4.5m high and the other floors are 3.6m high. The cross-sectional dimensions of beams and columns are 250mm×500mm and 500mm×500mm respectively. For details on reinforcement, see Figure 5 The design uniform dead load of the floor and roof is 5.0kN / m 2 and 7.0kN / m 2 , the floor uniform live load and roof snow load are both 2.0kN / m 2 The prototype building is assumed to be located in Nanjing, China, with a seismic fortification intensity of 7 degrees. The design earthquake group is Group I, Site Type II, the design basic earthquake acceleration is 0.1g, and the equivalent shear wave velocity of the soil is between 250 and 500m / s. The concrete strength grade is C40, the longitudinal reinforcement and stirrup types are both HRB400, and the concrete cover thickness of the frame beams and frame columns is 25mm. The material parameters of the undamaged cover concrete, core concrete, and steel bars are shown in Tables 2, 3, and 4, respectively. The confinement effect of the stirrups on the core concrete is considered using the Mander model.

[0111] Table 2 Material parameters of the non-destructive protective layer concrete

[0112]

[0113]

[0114] Table 3 Concrete material parameters of the intact core area

[0115]

[0116] Table 4 Material parameters of undamaged steel bars

[0117]

[0118] The damage state of the damaged structure is medium damage, and the damage state of the component is consistent with the damage state of the structure. Referring to Table 1 of the present invention, the Park-Ang damage index DI of the damaged structural component can be taken as 0.325.

[0119] Step 2: Determine the material damage index of the damaged component based on the component damage index

[0120] Substituting DI into the formulas (1), (2) and (3) of the present invention, the fiber damage index of the protective layer concrete, core area concrete and steel bar of the damaged component is obtained as D c =0.886, D cc =0.571 and D s =0.755.

[0121] Step 3: Determine the key constitutive parameters of the damaged material based on the material damage index

[0122] D c Substituting into formulas (4) and (5), D cc Substituting into formula (8) and formula (9), D s Substituting into formulas (15) and (16), the key constitutive parameters of the damaged cover concrete, core area concrete and steel bars can be obtained, which are shown in Table 5, Table 6 and Table 7, respectively.

[0123] Table 5 Material parameters of damaged protective layer concrete

[0124]

[0125] Table 6 Concrete material parameters of damaged core area

[0126]

[0127] Table 7 Material parameters of damaged steel bars

[0128]

[0129] Step 4: Create a finite element model of the damaged building based on the material structure of the damaged components

[0130] The OpenSEES platform was used to build a numerical model of the damaged building, such as Figure 3 As shown, both the frame beam and the frame column are simulated by concentrated plastic hinge elements based on fiber sections. The plastic hinge areas at both ends of the element adopt damaged material constitutive model, and the middle section adopts non-damaged material constitutive model. The damaged and non-damaged protective layer concrete are simulated by Concrete02 model, the damaged and non-damaged core area concrete are simulated by Concrete04 model, and the damaged and non-damaged steel bars are simulated by Hysteretic and Steel02 models respectively. The damaged and non-damaged materials can be simulated by inputting the material parameters in Tables 2 to 7 into the call command of the corresponding material model. The plastic hinge length L at both ends of the element is p Refer to formula (19) for calculation, where the length of the equivalent cantilever member is determined according to the position of the inflection point of the member. The plastic hinge lengths at both ends of the frame beam and frame column are summarized in Table 8.

[0131] Table 8 Plastic hinge length of frame members

[0132]

[0133] Step 5: Conduct a rapid earthquake risk and seismic performance assessment of damaged buildings.

[0134] The vulnerability analysis of the damaged building was conducted using the IDA method and compared with the analysis results of the intact building. The input seismic motion records for the seismic vulnerability analysis were selected from the 22 far-field motions recommended by the American ATC-63 program, and the spectral acceleration S corresponding to the first-order period of the structure with a damping ratio of 5% was selected. a As the seismic intensity index IM, and the maximum inter-story displacement angle IDR as the engineering demand parameter EDP of the structure. In the IDA method, the selected IM is gradually increased from 0 at intervals of 0.05g until the structure is completely destroyed to obtain the probabilistic seismic demand of the structure. The structural limit states are divided into four limit states: normal operation (OP), immediate occupancy (IO), life safety (LS), and collapse prevention (CP) with reference to the US FEMA-356. The corresponding IDR thresholds are determined according to the US "Hazus Manual of Earthquake Simulation" (hereinafter referred to as the "Hazus Manual"). According to the provisions of the "Hazus Manual", the designed 5-story, 4-span reinforced concrete frame meets the medium code seismic design level, and the structure type belongs to C1M. The corresponding IDR thresholds are summarized in Table 9.

[0135] Table 9 IDR thresholds for four limit states

[0136]

[0137] The IDA curves of the intact structure and the damaged structure are as follows: Figure 6 As shown in (a) and (b), the 16%, 50% and 84% quantile curves are used to calculate the median value and dispersion of all IDA curves. a The quantitative results are summarized in Table 10. Taking the 50% quantile curve as an example, when the maximum interstory drift angle IDR is used as the EDP, the S of the intact structure and the damaged structure to achieve the LS performance level is a They are 0.403g and 0.169g respectively, indicating that the damage will seriously reduce the structure's ability to withstand earthquakes, which is consistent with general cognition.

[0138] Table 10 S required to achieve the four performance levels in the quantile curve a (g)

[0139]

[0140] Log-linear regression of the IDA results for intact and damaged structures was performed to establish the S a Representative relationships with IDRs, such as Figure 7 As shown, the parameters for determining structural vulnerability (lna, b and β) can be obtained. D|IM ). R for log-linear regression 2 All are greater than 0.8, indicating that the use of S aIt is very suitable to build probabilistic earthquake models as IM to evaluate the impact of damage on structures.

[0141] In order to analyze the influence of damage on the fragility of RC structures, the fragility curves and exceedance probability difference diagrams of the intact structure (USM) and the damaged structure (DSM) under four limit states are drawn respectively. Figure 8 As shown. Figure 8 In (a), the solid line represents the intact structure and the dotted line represents the damaged structure. It can be seen that damage will shift the vulnerability curve of the structure to the left, reflecting a significant increase in the probability of exceeding the same limit state. The median S of the intact structure under the OP, IO, LS and CP limit states is a The maximum exceedance probabilities of the damaged structure and the intact structure are 0.055g, 0.112g, 0.387g and 1.262g respectively, while those of the damaged structure are reduced to 0.036g, 0.063g, 0.171g and 0.445g respectively. The reduction rate increases with the increase of the limit state, which are 36%, 44%, 56% and 65% respectively. In addition, the maximum exceedance probability difference between the damaged structure and the intact structure under each limit state also shows an increasing trend with the increase of the limit state, such as Figure 8 The above phenomenon shows that damage will significantly reduce the seismic capacity of RC structures.

Claims

1. A seismic simulation method for existing buildings considering the actual damage state, characterized in that: The steps include: S1: Determine the quantitative component damage index based on the observed component damage state; S2: Determine the material damage index of the damaged component based on the component damage index; S3: Determine the key constitutive parameters of the damaged material based on the material damage index; S4: Establish a finite element model of the damaged building based on the material structure of the damaged components; S5: Conduct earthquake risk and seismic performance assessment of damaged buildings based on finite element models; In step S1, the component damage index is quantitatively expressed by the Park-Ang damage index DI; In step S2, the material damage index of the damaged component is determined using a damage distribution model. The cross section of the reinforced concrete component is divided into three regions: the cover concrete, the core concrete, and the steel bars. The damage distribution model is represented by a mapping relationship between the material damage index of these three regions and the component damage index DI, thereby determining the material damage index of the damaged component. The damage index D of the protective layer concrete material in step S2 c The mapping relationship between DI and the core area concrete material damage index D cc The mapping relationship between DI and steel material damage index D s The mapping relationships between and DI are shown in formulas (1), (2), and (3). In step S3, the damaged materials include three materials: damaged protective layer concrete, damaged core area concrete, and damaged steel bars; The constitutive model of the damaged protective layer concrete in step S3 is simulated by the Kent-Scott-Park model, and the skeleton curve of the model is calculated by the peak compressive strain ε cd , peak compressive stress f cd , ultimate compressive strain ε cu Three parameter definitions, the calculation formulas are Among them, ε c and f c represent the peak compressive strain and peak compressive stress of the intact protective layer concrete; ε cd and f cd They represent the peak compressive strain and peak compressive stress of the damaged cover concrete respectively; Z represents the strain softening slope coefficient; In step S3, the constitutive structure of the concrete in the damaged core area is simulated using the Mander model, and the skeleton curve of the model is expressed by the peak compressive strain ε ccd , peak compressive stress f ccd , ultimate compressive strain ε ccu and elastic modulus E ccd Four parameter definitions, the calculation formula is Among them, ε cc and f cc represent the peak compressive strain and peak compressive stress of the concrete in the intact core area respectively; ε ccd and f ccd They represent the peak compressive strain and peak compressive stress of the concrete in the intact core area respectively; r represents the shape coefficient of the skeleton curve; E c represents the elastic modulus of the concrete in the intact core area; E sec =f cc / ε cc represents the secant modulus of the concrete in the intact core area at the peak stress; f yv Represents the yield strength of stirrups; ε su represents the fracture strain of the stirrup; ρ v Indicates the volumetric stirrup ratio of stirrups.

2. The method for seismic simulation of existing buildings considering the actual damage state according to claim 1, characterized in that: In step S3, the constitutive model of the damaged steel bar is simulated using a three-fold line model. The skeleton curve of the model is determined by three data points in the positive and negative directions. The mechanical behavior of the steel bar is positively and negatively symmetrical, so the key points in the positive and negative directions have the same value. The three data points (ε1, σ1), (ε2, σ2) and (ε3, σ3) are determined as follows: The stress σ1 and strain ε1 of the first data point are calculated as follows Among them, E s and f y represent the elastic modulus and yield strength of the steel bar respectively; The stress σ2 and strain ε2 of the second data point are calculated based on the steel bar material damage index D s OK, the calculation is as follows Among them, ε y and b represent the yield strain and strain hardening rate of the steel bar, respectively; The stress σ3 and strain ε3 of the third data point are calculated as follows σ3=f u (17) Among them, f u Represents the ultimate stress of the steel bar.

3. The method for seismic simulation of existing buildings considering the actual damage state according to claim 1, characterized in that: In step S4, the finite element model of the damaged building is established using the OpenSEES platform: the structural components are simulated using a plastic hinge beam-column unit based on a fiber section; the plastic hinge beam-column unit based on a fiber section is a force-based fiber beam-column unit, and the use of this unit requires the definition of the plastic hinge length L at both ends. p , L p Calculate according to the following formula L p =0.08L+0.022f y d l (N,mm) (19) Where L represents the length of the structural member equivalent to the cantilever member; d l Indicates the diameter of the steel bar; The control cross-sections of the plastic hinge zones at both ends of the beam-column unit are fiber cross-sections composed of damaged materials, while the control cross-sections of the middle section are fiber cross-sections composed of intact materials. The constitutive models of the damaged and intact protective layer concrete are simulated using the Concrete02 model based on the Kent-Scott-Park model skeleton curve, and the constitutive models of the damaged and intact core area concrete are simulated using the Concrete04 model based on the Mander model skeleton curve. The damaged and intact steel bars are simulated using the Hysteretic and Steel02 models, respectively.

4. The method for seismic simulation of existing buildings considering the actual damage state according to claim 1, characterized in that: In step S5, the seismic vulnerability analysis method is used to evaluate the seismic risk and seismic performance of the damaged building. Seismic vulnerability is described as the cumulative probability of a structure exceeding a certain limit state under a certain earthquake intensity IM. The probabilistic seismic vulnerability model is specifically expressed as the convolution of the demand model and the capacity model, and the formula is as follows: Among them, EDP is the engineering requirement parameter of the structure; LS i Indicates the EDP threshold corresponding to a certain limit state; S d|IM and β D|IM are the median and standard deviation of the structural seismic demand under a given IM; β C Indicates the degree of discreteness of the limit state; β M represents the standard deviation of model uncertainty; Φ[·] represents the cumulative normal distribution function; Median seismic demand S d|IM and the earthquake intensity parameter IM follow a power exponential regression relationship, which is expressed as follows S d|IM =a(IM) b (21) Performing logarithmic transformation on formula (21), we can get lnS d|IM =lna+blnIM(22)where a and b are regression coefficients; the logarithmic standard deviation of seismic demand β D|IM The calculation is as follows Where N is the total number of nonlinear dynamic time history analyses; i represents the i-th nonlinear dynamic time history analysis; and the data points used for regression analysis are obtained using the incremental dynamic analysis (IDA) method and the cloud plot method.

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