Structural vulnerability analysis method under combined action of post-earthquake fire

Abstract

The invention discloses a method for analyzing the vulnerability of a structure under the combined action of a post-earthquake fire, and the method comprises the steps: firstly obtaining design parameters which affect the performance of the structure as random variables, building a numerical model, selecting a plurality of seismic oscillation records, and combining the seismic oscillation records with a plurality of fire loads to form a post-earthquake fire condition; and engineering demand parameters representing earthquake and fire damage are obtained through numerical analysis. And constructing a sample vector containing disaster intensity and engineering requirements, and obtaining a mapping sample value by utilizing probability integral transformation. On the basis of the Copula theory and a vine type connection function, a joint probability model between different disaster intensities and engineering demand parameters is established, and a parameterized analytical expression of a conditional probability density function is derived; and finally, calculating a vulnerability curve of the structure under the combined action of the post-earthquake fire by inputting different earthquake and fire intensity measurements. According to the method, the failure probability of the structure under the combined action of multiple disasters can be evaluated more accurately, and the accuracy and reliability of vulnerability analysis are improved.

Description

Technical Field

[0001] This invention relates to the field of structural vulnerability technology, specifically to a method for analyzing structural vulnerability under the combined effects of earthquake and fire. Background Technology

[0002] Existing structural vulnerability analysis methods are mostly based on single-hazard scenarios. Post-earthquake fires are typical multi-hazard scenarios, and the cumulative damage to a structure after an earthquake impact may lead to more severe damage during secondary disasters. Therefore, using existing single-hazard vulnerability analysis methods may not yield accurate assessment results. Current post-earthquake fire vulnerability analyses often use only one EDP to describe structural damage, but the resistance mechanisms of structures differ significantly under earthquake and fire conditions. Earthquake deformation is primarily lateral deformation of vertical members, while fire deformation is primarily vertical deformation of lateral members. Therefore, using a single EDP for post-earthquake fire vulnerability analysis is unreasonable. Furthermore, existing vulnerability analysis methods still have some shortcomings. On the one hand, the widely used incremental dynamic analysis (IDA) method typically requires extensive nonlinear analysis to obtain the structural response under different hazard intensities, thereby constructing a structural vulnerability surface, which is computationally expensive. On the other hand, current structural vulnerability analysis methods are mostly based on linear correlation approximations and log-normal empirical assumptions, which, due to oversimplification, may lead to significant analytical errors. In fact, there is a significant nonlinear and stochastic correlation between earthquakes and fires, and disaster intensity and structural damage also have complex coupling characteristics. Traditional vulnerability methods cannot effectively quantify these characteristics. Summary of the Invention

[0003] Purpose of the invention: The purpose of this invention is to provide a structural vulnerability analysis method under the combined effects of earthquake and fire. It combines the unique failure modes of structures under earthquake and fire conditions, and uses the Vine-copula method to consider the strong nonlinear relationship between disaster intensity and structural damage to calculate the structural exceedance probability under different limit states, so as to solve the problems existing in the background technology.

[0004] Technical solution: The present invention provides a structural vulnerability analysis method under the combined effects of earthquake and fire, comprising the following steps:

[0005] (1) Obtain the design parameters that affect the structural performance as random variables and establish a numerical model;

[0006] (2) Select multiple ground motion records and various fire loads to form a post-earthquake fire condition;

[0007] (3) Post-earthquake fire analysis was performed on the numerical model. The maximum inter-story drift angle and the maximum residual vertical deflection of the transverse members were selected as engineering requirement parameters to characterize the structural damage under earthquake and fire.

[0008] (4) Construct a sample vector containing disaster intensity measurement and engineering demand parameters, and set the engineering demand parameters as the main variable and the disaster intensity measurement as the secondary variable;

[0009] (5) Perform probability integral transformation on the sample vector to obtain the mapped sample value;

[0010] (6) Based on the mapped sample values, the optimal two-dimensional Copula connection function between different secondary variables and the main variable is determined by maximum likelihood estimation and the Akaike information criterion;

[0011] (7) Based on the optimal two-dimensional Copula connection function, further determine the optimal three-dimensional conditional Copula connection function;

[0012] (8) Using the three-dimensional vine-like connection function theory, derive the parameterized analytical expression of the conditional probability density function with engineering demand parameters as the main variables;

[0013] (9) Based on the conditional probability density function, input different earthquake and fire intensity measures to calculate the vulnerability of the structure under the combined action of earthquake and fire.

[0014] Furthermore, in step (1), a sample set of design parameters is generated using the Latin hypercube sampling method.

[0015] Furthermore, in step (2), the ground motion record includes near-fault records and near-fault pulse-type ground motion, and the fire load is represented by a parametric fire curve.

[0016] Furthermore, in step (3), the maximum inter-story drift angle and the maximum residual vertical deflection correspond to different failure modes of the structure under earthquake and fire conditions, respectively.

[0017] Furthermore, in step (6), the optimal connection function is selected from various Copula function forms to accurately describe the nonlinear dependencies between variables.

[0018] Furthermore, in step (7), a joint dependency structure among three-dimensional variables is constructed using the conditional Copula function.

[0019] Furthermore, in step (9), the failure probability of the structure under the combined action of earthquake and fire is calculated based on the two-parameter damage model, as shown in the following formula: ; Where D1 and D2 represent the requirements corresponding to earthquakes and fires, respectively; C1 and C2 represent the performance corresponding to earthquakes and fires under given extreme conditions, respectively; ∨ represents the OR gate; IM (Intensity measure) represents the intensity index; and IM1 and IM2 represent the intensity indices corresponding to the primary disaster and the secondary disaster, respectively.

[0020] The structural vulnerability analysis system under the combined effects of earthquake and fire as described in this invention includes:

[0021] The model building module is used to build structural numerical models that include stochastic design parameters.

[0022] The disaster scenario generation module is used to combine earthquake and fire load conditions;

[0023] The damage simulation module is used to obtain the engineering requirements parameters of the structure under the action of post-earthquake fire.

[0024] The sample vector construction module is used to organize sample data on disaster intensity and structural response;

[0025] The probability transformation module is used to perform probability integral transformations;

[0026] The Copula function optimization module is used to determine the optimal two-dimensional and three-dimensional Copula connection functions;

[0027] The conditional probability density analysis module is used to derive the analytical expression of the conditional probability density function;

[0028] The vulnerability calculation module is used to output the vulnerability results of a structure under a given disaster intensity.

[0029] The present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any of the methods described herein.

[0030] An electronic device according to the present invention includes a memory and a processor, wherein the memory stores a computer program, and when the program is executed by the processor, it implements any of the methods described herein.

[0031] Beneficial Effects: Compared with existing technologies, this invention has the following significant advantages: By integrating two EDPs reflecting structural seismic damage and fire damage into a single post-earthquake fire scenario DM, a joint failure model of the structure under post-earthquake fire action is considered. Furthermore, a vulnerability analysis method for structures under the combined action of post-earthquake fire is proposed using Vine-copula theory. This invention overcomes the limitations of traditional vulnerability analysis, which uses a single parameter to quantify structural damage and cannot consider the strong nonlinear relationship between disaster intensity and structural damage, thus obtaining more accurate post-earthquake fire vulnerability assessment results. Attached Figure Description

[0032] Figure 1 This is a flowchart of the present invention; Figure 2 This is a schematic diagram of the structural prototype of the present invention, wherein... Figure 2 (a) is a three-dimensional diagram of the structure; Figure 2 (b) shows the structural plan and reinforcement details of the components; Figure 3 These are the AIC values ​​corresponding to different types of Copula link functions for the earthquake vector and fire vector of this invention; wherein... Figure 3 In the table, (a) represents the AIC values ​​corresponding to different types of Copula link functions for the earthquake vectors; Figure 3 In the table, (b) represents the AIC value corresponding to different types of Copula link functions for the fire vector; Figure 4 The vulnerable surface calculated using the present invention is the vulnerable surface obtained by the present invention; wherein, Figure 4 (a) represents the normal operation (NO) limit state. Figure 4 (b) represents the Immediate Occupancy (IO) limit state. Figure 4 (c) represents the life safety limit state (LS). Figure 4 (d) represents the complete collapse prevention (CP) limit state. Figure 5 The present invention is a vulnerable surface calculated using existing technology; wherein, Figure 5 (a) represents the normal operation (NO) limit state. Figure 5 In the middle (b), the immediate occupancy (IO) limit state is represented. Figure 5 (c) represents the life safety limit state (LS). Figure 5 (d) represents the complete collapse prevention (CP) limit state. Figure 6 The present invention provides structural vulnerability curves at different seismic risk levels obtained from the cross-section of the vulnerability surface derived from the present invention; wherein, Figure 6 (a) represents the normal operation (NO) limit state. Figure 6 In the middle (b), the immediate occupancy (IO) limit state is represented. Figure 6(c) represents the life safety limit state (LS). Figure 6 (d) represents the complete collapse prevention (CP) limit state. Detailed Implementation

[0033] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0034] like Figure 1 As shown, this embodiment of the invention provides a method for analyzing structural vulnerability under the combined effects of earthquake and fire, including the following steps:

[0035] Step 1: Obtain the design parameters affecting structural performance as random variables, denoted as Y=(Y1,Y2,…,Y…). m ) T Where m is the number of random variables, the corresponding sampling to generate the sub-model design parameter sample set is carried out using Latin hypercube sampling, and the sample size is 320; where the mean of each random variable is the initial design value, the corresponding coefficient of variation, and the distribution assumptions they follow will be given later.

[0036] Step 2: Select 160 ground motions from the ground motion database, including 120 near-fault records and 40 near-fault pulse-type ground motions. The amplitude of all ground motions is scaled by 2.0. Fire events are represented using ISO 834 standard temperature rise curves. 320 fire temperature rise curves are obtained by sampling the highest temperature during the fire. Peak ground acceleration (PGA) and the highest temperature (T) during the fire are used as the corresponding instantaneous intensity (IM) for the earthquake and fire, respectively.

[0037] Step 3, select the maximum inter-story drift angle θ max and the maximum residual vertical deflection ζ of the transverse component r,max As engineering requirement parameters, they correspond to the failure modes of the structure under earthquake and fire conditions, respectively.

[0038] Step 4: Sample vectors corresponding to earthquakes and fires were established, respectively, as (PGA, T, θ) max ) T and (PGA,T,ζ) r,max ) T All are recorded as We will use x3 as the main variable and x1 and x2 as secondary variables.

[0039] Step 5, define random variables U1, U2, U3, which are uniformly distributed on the interval [0,1] and satisfy:

[0040] (1);

[0041] Based on the sample observations The marginal empirical probability distribution functions of X1, X2, and X3 can be used to obtain the mapped sample values ​​of U1, U2, and U3, i.e.

[0042] (2);

[0043] in For variable X s The marginal empirical probability distribution function can be obtained from sample observations, that is:

[0044] (3);

[0045] Step 6: Utilize maximum likelihood estimation and, based on the mapped sample values... Determine the optimal connection parameters for different Copula functions The optimal Copula connection form is determined using the Akaike information criterion. Among them, binary variables Mapped to There are 6 Copula functions as candidate Copula functions. Therefore, the form of each candidate Copula function k=1,⋯,6 will be given later.

[0046] Further solution using the following formula : (4);

[0047] The AIC value corresponding to different alternative Copula functions is calculated using the following formula:

[0048] (5);

[0049] Where k is the number of correlation parameters of the Copula function.

[0050] The AIC value reflects the goodness of fit; a smaller AIC value indicates that the corresponding Copula function is considered to better describe the correlation between variables, and this Copula function is thus considered the optimal Copula function for that data set. Based on the above, the optimal two-dimensional Copula function C can be determined. 12 (·), C 13 (·)

[0051] Step 7, Assumptions:

[0052] (6);

[0053] Furthermore, the above formula also follows a uniform distribution on the interval [0,1].

[0054] Using maximum likelihood estimation, and based on the mapped sample values and the two-dimensional optimal Copula function C obtained in step (6) 12 (·) and C 13 (·) The Copula density functions of X2 and X3 under condition X1 can be calculated. First, find the optimal two-dimensional Copula function C. 12 (·) and C 13 (·) corresponds to the Copula conditional join function C 1|2 (u|v) and C 1|3 (u|v), the corresponding expression will be given later. Then, substituting the corresponding optimal connection parameter θ, we can obtain W. 2|1 and W 3|1 Corresponding mapped sample values:

[0055] (7);

[0056] The obtained mapping sample values In the execution and step (6) C 12 (·) and C 13 (·) Optimal Copula Functions: Using the same analysis procedure, determine the optimal connection parameters for different Copula functions. And determine the optimal Copula conditional connection function using the AIC criterion. .

[0057] Step 8, assuming the marginal empirical probability distribution functions of random variables X1, X2, and X3 are denoted as F1(x1), F2(x2), and F3(x3) respectively, and their marginal probability density functions are denoted as p1(x1), p2(x2), and p3(x3), then the joint probability density function can be expressed as:

[0058] (8);

[0059] in, It is the conditional probability density of X2 under the condition X1=x1; It is the conditional probability density function of X3 under the conditions X1=x1 and X2=x2.

[0060] According to Sklar's theorem It can be represented as:

[0061] (9);

[0062] in, Let X1 and X2 be the connection density functions.

[0063] further, It can be represented as:

[0064] (10);

[0065] Among them, with similar, It can be represented as:

[0066] (11);

[0067] Substituting the above equation into equation (10), we get:

[0068] (12);

[0069] Step 9, based on step (8), we obtained This is the parametric expression of the conditional probability density function of X3 under the conditions X1=x1 and X2=x2. According to step (4), θ was used for earthquake damage and fire damage respectively. max and ζ r,max Therefore, it is necessary to determine whether the structure will collapse under a given limit state based on the desired threshold. Thus, under a given limit state, the vulnerability of the structure under the combined effects of an earthquake and fire can be calculated using the following formula:

[0070] (13);

[0071] Where D1 and D2 represent the requirements corresponding to earthquakes and fires, respectively; C1 and C2 represent the performance corresponding to earthquakes and fires under given extreme conditions; and ∨ is a logic gate OR, meaning that as long as θ max and ζ r,max If one of the values ​​exceeds the corresponding threshold, the structure fails.

[0072] In fact, equation (13) is equivalent to the combined probability of structural failure due to earthquake or fire, and therefore can be written as:

[0073] (14);

[0074] Assuming that the earthquake and fire events are independent of each other, then equation (14) can be written as:

[0075] (15);

[0076] in, (16); (17);

[0077] The result obtained from step (8) Substituting the parameter analysis into equations (16) and (17) allows us to calculate the vulnerability of the structure under the combined effects of earthquakes and fires.

[0078] Taking a three-dimensional, four-story RC frame structure with floor slabs as an example, the structural prototype and reinforcement details are as follows: Figure 2 As shown. Assume that after the earthquake, only the corner rooms on the ground floor experienced fires, specifically as shown... Figure 2 As shown in (b) of the diagram. First, the main parameters affecting the progressive collapse resistance of the structure were selected, including 13 random parameters related to geometric dimensions and material properties. Assuming that the random variables are independent, Latin hypercube sampling was conducted, and corresponding numerical simulations were performed. During the sampling process, the mean of each variable was taken as the structural design value. The coefficients of variation and the distribution functions of each random variable were determined by referring to relevant classical studies, and detailed information is shown in Table 1.

[0079] Table 1. Random parameter distribution of a 4-story RC frame structure with floor slabs ;

[0080] For a four-story RC frame structure with floor slabs, corresponding numerical models were established based on the sample set defined in Table 2. Nonlinear time history analysis (NLTHA) and nonlinear static analysis (NLSA) were performed on 320 numerical models. Using Monte Carlo simulation principles, 320 earthquake-fire load cases were randomly assigned to 320 sub-models for post-earthquake fire analysis, and the corresponding maximum inter-story drift angle θ was recorded. max and the maximum residual vertical deflection ζ of the floor slab r,max Four extreme states were considered: Normal Operation (NO) indicating negligible structural damage; Immediate Use (IO) corresponding to minor damage and intact function; Life Safe (LS) representing severe but repairable post-disaster damage; and Complete Collapse (CP) describing severe damage leading to loss of structural integrity. θ max and ζ r,max The corresponding thresholds are shown in Table 2.

[0081] Table 2 θ under different limiting states max and ζ r,max threshold ;

[0082] Figure 3 The seismic vector (PGA, T, θ) is shown. max ) T And the fire vector (PGA, T, ξ) r,max ) TThe AIC values ​​calculated using different forms of Copula connection functions are shown in Tables 3 and 4. Alternative Copula density functions and expressions for Copula conditional connection functions are also presented.

[0083] Table 3. Six alternative Copula density functions

[0084] in, for Function, i.e. .

[0085] Table 4. Six alternative Copula conditional join functions ; Where a is the standard t distribution function with degrees of freedom v. ; ; It is the Pochhammer notation, i.e. .

[0086] The results show that, for the seismic vector, C 12 (·), C 13 (·) and C 23|1 The minimum AIC values ​​for (·) are 0.46, -382.97, and -3.62, respectively, and their corresponding optimal Copula connection functions are Gumbel-Hougaard, Frank, and Gumbel-Hougaard, respectively. The C corresponding to the fire vector... 12 (·), C 13 (·) and C 23|1 The minimum AIC values ​​of (·) are 0.46, 0.58 and -983.01, respectively, and their corresponding optimal Copula connection functions are Gumbel-Hougaard, Gumbel-Hougaard and Frank.

[0087] Based on the determined optimal Copula connection form, the post-earthquake fire vulnerability surface of the structure can be further calculated. Simultaneously, existing techniques (cloud mapping method) were used to calculate the corresponding vulnerability surfaces and conduct comparative analysis. Figure 4 and Figure 5 The vulnerability surfaces of a four-story reinforced concrete frame structure with floor slabs, calculated using both the present invention and existing techniques, are presented under different extreme states. The results show that, under the same disaster intensity, the structural vulnerability calculated using the present invention is generally greater than that calculated using existing techniques. This indicates that using existing techniques for post-earthquake fire vulnerability analysis will overestimate the structure's post-earthquake fire resistance.

[0088] based on Figure 4 The vulnerability surface in the image shows orthogonal slices of vulnerability at different seismic hazard levels, i.e., vulnerability curves, such as... Figure 6 As shown in the figure, the seismic risk level is represented by PGA, with PGA values ​​of 0.07g, 0.2g, 0.4g, and 1.0 considered. The results indicate that the fire vulnerability of the structure increases with the seismic risk level. Stronger earthquakes will result in higher initial fire vulnerability. Furthermore, fire vulnerability remains relatively consistent in the initial stage, but increases sharply after exceeding a certain temperature. This suggests that in the early stages of a fire, structural vulnerability is primarily influenced by the seismic risk level, but when the fire reaches high temperatures, structural vulnerability is mainly affected by the fire intensity.

Claims

1. A method for analyzing structural vulnerability under the combined effects of earthquake and fire, characterized in that, Includes the following steps: (1) Obtain the design parameters that affect the structural performance as random variables and establish a numerical model; (2) Select multiple ground motion records and various fire loads to form a post-earthquake fire condition; (3) Post-earthquake fire analysis was performed on the numerical model. The maximum inter-story drift angle and the maximum residual vertical deflection of the transverse members were selected as engineering requirement parameters to characterize the structural damage under earthquake and fire. (4) Construct a sample vector containing disaster intensity measurement and engineering demand parameters, and set the engineering demand parameters as the main variable and the disaster intensity measurement as the secondary variable; (5) Perform probability integral transformation on the sample vector to obtain the mapped sample value; (6) Based on the mapped sample values, the optimal two-dimensional Copula connection function between different secondary variables and the main variable is determined by maximum likelihood estimation and the Akaike information criterion; (7) Based on the optimal two-dimensional Copula connection function, further determine the optimal three-dimensional conditional Copula connection function; (8) Using the three-dimensional vine-like connection function theory, derive the parameterized analytical expression of the conditional probability density function with engineering demand parameters as the main variables; (9) Based on the conditional probability density function, input different earthquake and fire intensity measures to calculate the vulnerability of the structure under the combined action of earthquake and fire.

2. The structural vulnerability analysis method under the combined effects of earthquake and fire as described in claim 1, characterized in that, In step (1), the Latin hypercube sampling method is used to generate a sample set of design parameters.

3. The structural vulnerability analysis method under the combined effects of earthquake and fire as described in claim 1, characterized in that, In step (2), the ground motion record includes near-fault record and near-fault pulse ground motion, and the fire load is represented by a parametric fire curve.

4. The structural vulnerability analysis method under the combined effects of earthquake and fire as described in claim 1, characterized in that, In step (3), the maximum inter-story drift angle and the maximum residual vertical deflection correspond to different failure modes of the structure under earthquake and fire conditions, respectively.

5. The structural vulnerability analysis method under the combined effects of earthquake and fire as described in claim 1, characterized in that, In step (6), the optimal connection function is selected from various Copula function forms to accurately describe the nonlinear dependencies between variables.

6. The structural vulnerability analysis method under the combined effects of earthquake and fire as described in claim 1, characterized in that, In step (7), a joint dependency structure among three-dimensional variables is constructed using the conditional Copula function.

7. The structural vulnerability analysis method under the combined effects of earthquake and fire as described in claim 1, characterized in that, In step (9), the failure probability of the structure under the combined action of earthquake and fire is calculated based on the two-parameter damage model, as shown in the following formula: ； Where D1 and D2 represent the requirements corresponding to earthquakes and fires, respectively; C1 and C2 represent the performance corresponding to earthquakes and fires under given extreme conditions, respectively; ∨ represents the OR gate; IM (Intensity measure) represents the intensity index; and IM1 and IM2 represent the intensity indices corresponding to the primary disaster and the secondary disaster, respectively.

8. A structural vulnerability analysis system under the combined effects of earthquake and fire, characterized in that, include: The model building module is used to build structural numerical models that include stochastic design parameters. The disaster scenario generation module is used to combine earthquake and fire load conditions; The damage simulation module is used to obtain the engineering requirements parameters of the structure under the action of post-earthquake fire. The sample vector construction module is used to organize sample data on disaster intensity and structural response; The probability transformation module is used to perform probability integral transformations; The Copula function optimization module is used to determine the optimal two-dimensional and three-dimensional Copula connection functions; The conditional probability density analysis module is used to derive the analytical expression of the conditional probability density function; The vulnerability calculation module is used to output the vulnerability results of a structure under a given disaster intensity.

9. A computer-readable storage medium, characterized in that, It stores a computer program that, when executed by a processor, implements the method as described in any one of claims 1-7.

10. An electronic device, characterized in that, It includes a memory and a processor, the memory storing a computer program that, when executed by the processor, implements the method as described in any one of claims 1-7.

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