A method for evaluating the progressive collapse vulnerability of structures by combining static and dynamic probabilistic analyses

Abstract

The present invention discloses a method for evaluating the progressive collapse vulnerability of structures by combining static and dynamic probabilistic analyses, comprising the following steps: (1) obtaining the design parameters affecting the progressive collapse resistance of the structure; a sample set of design parameters; (2) constructing corresponding static and dynamic progressive collapse deterministic numerical models; establishing corresponding sub-models according to the sample set; (3) performing Pushdown analysis; (4) performing non-linear displacement time history analysis under different load intensities; (5) fitting to obtain the probability density function of the progressive collapse resistance of the structure and calculating the corresponding mean value and standard deviation; (6) fitting to obtain the probability density function of the progressive collapse load effect of the structure and calculating the corresponding mean value and standard deviation; (7) obtaining the scatter points of the progressive collapse vulnerability of the structure; (8) obtaining the progressive collapse vulnerability curve of the structure; the present invention obtains accurate vulnerability assessment results.

Description

Technical Field

[0001] The present invention relates to the technical field of structural uncertainty quantification, and particularly to a method for evaluating the progressive collapse vulnerability of structures by combining static and dynamic probabilistic analyses. Background Art

[0002] Alternative load path analysis is the main method for evaluating the progressive collapse resistance of structures. This method first removes key structural members to simulate local failures in the system, and then predicts the structural response through nonlinear static or dynamic analysis to determine whether the structure is damaged. However, only understanding the catastrophic behavior of structures through deterministic conditions cannot explain the uncertainties in structural systems and external loads. At the same time, existing methods for evaluating the progressive collapse vulnerability of structures from the perspective of uncertainty are mostly based on the static column removal condition. There are also methods using incremental dynamic analysis (IDA) based on dynamic instantaneous analysis to conduct vulnerability analysis of structures under dynamic column removal conditions. This method has been widely used in the uncertainty analysis of structural dynamic progressive collapse, but existing techniques for evaluating the progressive collapse vulnerability of structures mostly use the results of structural performance analysis under deterministic analysis as thresholds. Currently, there are still some deficiencies in the evaluation methods applicable to the progressive collapse vulnerability of structures. On the one hand, according to the theory of structural random reliability, the failure probability of a structure depends on the uncertainties of both resistance and load effects. However, current vulnerability analysis methods are mostly based on static or dynamic analysis and can only reflect one of the random effects of resistance or load effects. On the other hand, the thresholds for different limit states in existing dynamic vulnerability analysis of progressive collapse are mostly determined values given in codes, but the discreteness of the progressive collapse resistance of structures at different development stages will seriously affect the thresholds, and directly using the thresholds in codes may greatly underestimate the possibility of structural damage. Summary of the Invention

[0003] Object of the Invention: The object of the present invention is to provide a method for evaluating the progressive collapse vulnerability of structures by combining static and dynamic probabilistic analyses, which combines the probabilistic analyses of the progressive collapse resistance and load effects of structures, and evaluates the probability of exceedance of structures under different limit states through the convolution integral method to solve the problems existing in the background art.

[0004] Technical Solution: A method for evaluating the progressive collapse vulnerability of structures by combining static and dynamic probabilistic analyses according to the present invention includes the following steps:

[0005] (1) Obtain the design parameters affecting the progressive collapse resistance of the structure as random variables, denoted as X = ( X 1 , X 2 , …, X n )T , where n is the number of random variables; the design parameter sample set;

[0006] (2) Construct the corresponding static and dynamic progressive collapse deterministic numerical models; establish the corresponding sub-models according to the sample set;

[0007] Based on the models constructed in step (2), perform Pushdown analysis;

[0008] Based on the models constructed in step (2), perform non-linear displacement time-history analysis under different load intensities;

[0009] (5) Based on the normal distribution assumption, fit to obtain the probability density function of the progressive collapse resistance of the structure; calculate the corresponding mean value and standard deviation, and determine the thresholds of the structure at different performance levels considering static uncertainty;

[0010] Based on the lognormal distribution assumption, fit to obtain the probability density function of the progressive collapse load effect of the structure; calculate the corresponding mean value and standard deviation, and determine the probability load effect of the structure at different performance levels considering dynamic uncertainty;

[0011] (7) Obtain the scatter points of the progressive collapse vulnerability of the structure;

[0012] (8) Based on the lognormal distribution assumption, fit the scatter points of the exceedance probability corresponding to each load coefficient obtained in step (7) through regression analysis to obtain the progressive collapse vulnerability curve of the structure.

[0013] Furthermore, in step (1), use Latin hypercube sampling to carry out the corresponding sampling to generate the sub-model design parameter sample set, and the sample size is 1000; among them, the mean value of each random variable is the initial design value.

[0014] Furthermore, step (3) is specifically as follows: The entire process of Pushdown analysis is controlled by the incremental gravity load applied to the structure until the structure collapses; the vertical displacement Δ is applied proportionally to the beam-column joints, and the change in the gravity load of the damaged span is recorded to obtain the corresponding Pushdown curve; the displacements corresponding to different limit states are determined through the Pushdown curve, denoted as Δ R .

[0015] Furthermore, step (4) is specifically as follows: Take the gravity load applied to the structure as the strength index, and take the vertical displacement of the beam-column joint at the top of the removed column as the damage index; by changing the load coefficient α , gradually increase the gravity load applied to the damaged span, and record the vertical displacement of the beam-column joint at the top of the removed column corresponding to different limit states, denoted as Δ S .

[0016] Furthermore, the formula for the progressive collapse vulnerability of the structure in step (7) is as follows:

[0017] (1);

[0018] Wherein, S is the structural load effect, R is the progressive collapse resistance corresponding to a certain limit state of the structure; IM is the strength index; formula (1) is rewritten as:

[0019] (2);

[0020] Wherein, F RS ( r , s ) and f RS ( r , s ) are the joint cumulative density function and the joint probability density function of R and S respectively;

[0021] For simplified calculation, assume that R and S are independent of each other; the final progressive collapse vulnerability of the structure can be calculated by the following formula:

[0022] (3);

[0023] Substitute the mean value μ R of the probability density function of the progressive collapse resistance of the structure obtained in steps (5) and (6), the standard deviation σ R of the probability density function of the progressive collapse resistance of the structure, the mean value μ S of the probability density function of the progressive collapse load effect of the structure, and the standard deviation σ S of the probability density function of the progressive collapse load effect of the structure into formula (3), and the probability that the structure exceeds a certain limit state under a certain load factor, that is, the scatter points of the progressive collapse vulnerability of the structure, can be obtained through the convolution integral method.

[0024] A structural progressive collapse vulnerability assessment system combining static and dynamic probability analysis according to the present invention includes:

[0025] An acquisition module: used to acquire the design parameters affecting the progressive collapse resistance of the structure as random variables, denoted as X = ( X 1 , X 2 ,…,X n ) T , where n is the number of random variables; the design parameter sample set;

[0026] Progressive collapse deterministic numerical model module: used to construct the corresponding static and dynamic progressive collapse deterministic numerical models; establish the corresponding sub-models according to the sample set;

[0027] Pushdown module: used to perform Pushdown analysis based on the models constructed in the progressive collapse deterministic numerical model module;

[0028] Nonlinear displacement time history analysis module: used to perform nonlinear displacement time history analysis under different load intensities based on the models constructed in the progressive collapse deterministic numerical model module;

[0029] Structural progressive collapse resistance probability density function module: used to fit the structural progressive collapse resistance probability density function based on the normal distribution hypothesis; calculate the corresponding mean and standard deviation, and determine the thresholds of the structure at different performance levels considering static uncertainty;

[0030] Structural progressive collapse load effect probability density function module: used to fit the structural progressive collapse load effect probability density function based on the lognormal distribution hypothesis; calculate the corresponding mean and standard deviation, and determine the probabilistic load effects of the structure at different performance levels considering dynamic uncertainty;

[0031] Progressive collapse vulnerability scatter point module: used to obtain the progressive collapse vulnerability scatter points of the structure;

[0032] Progressive collapse vulnerability curve module: used to obtain the progressive collapse vulnerability curve of the structure by regression analysis based on the scatter points of the exceedance probability corresponding to each load coefficient fitted based on the lognormal distribution hypothesis.

[0033] Furthermore, in the acquisition module, the Latin hypercube sampling is used to carry out the corresponding sampling to generate the sub-model design parameter sample set, and the sample size is 1000; among them, the mean of each random variable is the initial design value.

[0034] Furthermore, in the Pushdown module, specifically as follows: The entire process of Pushdown analysis is controlled by the incremental gravity load applied to the structure until the structure collapses; the vertical displacement Δ is applied proportionally to the beam-column joints, and the change in the gravity load of the damaged span is recorded to obtain the corresponding Pushdown curve; the displacements corresponding to different limit states are determined through the Pushdown curve, denoted as Δ R .

[0035] Furthermore, in the non-linear displacement time history analysis module, specifically as follows: The gravity load applied to the structure is used as the strength index, and the vertical displacement of the beam-column joint at the top of the demolished column is used as the damage index; by changing the load factor α , gradually increase the gravity load applied to the damaged span, and record the vertical displacement of the beam-column joint at the top of the demolished column corresponding to different limit states, denoted as Δ S .

[0036] Furthermore, in the progressive collapse vulnerability scatter point module, the progressive collapse vulnerability formula of the structure is as follows:

[0037] (1);

[0038] Among them, S is the structural load effect, R is the progressive collapse resistance corresponding to a certain limit state of the structure; IM is the strength index; Formula (1) is rewritten as:

[0039] (2);

[0040] Among them, F RS ( r , s ) and f RS ( r , s ) are the joint cumulative density function and joint probability density function of R and S respectively;

[0041] For simplified calculation, assume that R and S are independent of each other; finally, the progressive collapse vulnerability of the structure can be calculated by the following formula:

[0042] (3);

[0043] Substitute the mean value μ R of the structural progressive collapse resistance probability density function, the standard deviation σ R of the structural progressive collapse resistance probability density function, the mean value μ S of the structural progressive collapse load effect probability density function, and the standard deviation σ S of the structural progressive collapse load effect probability density function into Formula (3), and the probability of the structure exceeding a certain limit state under a certain load factor, that is, the progressive collapse vulnerability scatter point of the structure, can be obtained through the convolution integral method.

[0044] Advantages: Compared with the prior art, the present invention has the following remarkable advantages: By using Latin Hypercube Sampling to characterize the inherent variability of the structure and the randomness of external loads, and by using Pushdown analysis and IDA to respectively consider the progressive collapse resistance of the structure at different performance levels and the uncertainty effects of load effects, it further provides guidance for the probabilistic assessment of the progressive collapse performance of the structure. The present invention overcomes the limitation of the traditional progressive collapse vulnerability analysis method that cannot simultaneously consider the uncertainty of structural performance and demand, and integrates the probabilistic behaviors of structural resistance and load effects into the vulnerability analysis framework through the convolution integral method, and can obtain more accurate assessment results of the progressive collapse vulnerability of the structure. Brief Description of the Drawings

[0045] Figure 1 is a schematic flowchart of the present invention;

[0046] Figure 2 is a schematic diagram of the structural prototype of the present invention;

[0047] Figure 3 is a Pushdown curve graph of the present invention; wherein, Figure 3 in (a) is the working condition of removing column A; Figure 3 in (b) is the working condition of removing column B;

[0048] Figure 4 is a histogram and a probability density function PDF curve of ΔR of the present invention; wherein, Figure 4 in (a) is the normal operation condition of the working condition of removing column A; Figure 4 in (b) is the anti-collapse condition of the working condition of removing column A; Figure 4 in (c) is the normal operation condition of the working condition of removing column B; Figure 4 in (d) is the anti-collapse condition of the working condition of removing column B;

[0049] Figure 5 is a histogram and a PDF curve of Δ corresponding to different load coefficients of the present invention; S wherein, Figure 5 in (a) is the working condition of removing column A; Figure 5 in (b) is the working condition of removing column B;

[0050] Figure 6 shows the vulnerability curves obtained by the present invention and the prior art; wherein Figure 6 in (a) is based on the Pushdown method; Figure 6 in (b) is based on the IDA method. Detailed Embodiment

[0051] The technical solution of the present invention will be further described below with reference to the drawings.

[0052] AsFigure 1 As shown, an embodiment of the present invention provides as follows Figure 1 As shown, a method for evaluating the progressive collapse vulnerability of a structure by combining static and dynamic probabilistic analysis, comprising the following steps:

[0053] Step 1, select the design parameters affecting the progressive collapse resistance of the structure as random variables, denoted as X = ( X 1 , X 2 , …, X n ), T where n is the number of random variables. Subsequently, Latin Hypercube Sampling is used to carry out the corresponding sampling to generate a sample set of sub-model design parameters, with a sample size of 1000. Among them, the mean value of each random variable is the initial design value, and the corresponding coefficient of variation and the assumed distribution will be given later.

[0054] Step 2, select a certain column removal condition and establish the corresponding static and dynamic progressive collapse deterministic numerical models. Establish the corresponding sub-models according to the sample set.

[0055] Step 3, based on all static progressive collapse sub-models, carry out Pushdown analysis. The entire process of Pushdown analysis is controlled by the incremental gravity load applied to the structure until the structure collapses. However, only the gravity load on the beam adjacent to the removed column will increase, and the loads on the remaining beams remain unchanged at the initial design loads. The vertical displacement Δ is applied proportionally to the beam-column joints, and the change in the gravity load of the damaged span is recorded to obtain the corresponding Pushdown curve. Determine the displacements corresponding to different limit states through the Pushdown curve, denoted as Δ R .

[0056] Step 4, based on all dynamic progressive collapse sub-models, carry out non-linear displacement time-history analysis under different load intensities. Take the gravity load applied to the structure as the intensity index and the vertical displacement of the beam-column joint at the top of the removed column as the damage index. By changing the load factor α , gradually increase the gravity load applied to the damaged span, and record the vertical displacements of the beam-column joints at the top of the removed column corresponding to different limit states, denoted as Δ S .

[0057] Step 5, based on the normal distribution assumption, fit the probability density function of the progressive collapse resistance of the structure according to the recorded Δ R , and calculate the corresponding mean value μ R and standard deviation σ R , and determine the thresholds of the structure under different performance levels considering static uncertainty.

[0058] Step 6, based on the lognormal distribution assumption, according to the recorded Δ S fit to obtain the probability density function of the structural progressive collapse load effect, and calculate the corresponding mean value μ S and standard deviation σ S , and determine the probability load effect of the structure at different performance levels considering dynamic uncertainty.

[0059] Step 7, the vulnerability of structural progressive collapse can be expressed as:

[0060] (1);

[0061] where, S is the structural load effect, R is the progressive collapse resistance corresponding to a certain limit state of the structure; IM is the strength index; formula (1) is rewritten as:

[0062] (2);

[0063] where, F RS ( r , s ) and f RS ( r , s ) are the joint cumulative density function and joint probability density function of R and S respectively;

[0064] For simplified calculation, assume that R and S are independent of each other; finally, the vulnerability of structural progressive collapse can be calculated by the following formula:

[0065] (3);

[0066] Substitute the mean value μ R of the probability density function of the structural progressive collapse resistance, the standard deviation σ R of the probability density function of the structural progressive collapse resistance, the mean value μ S of the probability density function of the structural progressive collapse load effect, and the standard deviation σ S of the probability density function of the structural progressive collapse load effect obtained in steps (5) and (6) into formula (3), and the probability of the structure exceeding a certain limit state under a certain load factor, that is, the scatter points of the vulnerability of structural progressive collapse, can be obtained through the convolution integral method.

[0067] Step 8: Based on the lognormal distribution assumption, the continuous collapse vulnerability curve of the structure is obtained by fitting the scatter plot of the exceedance probability corresponding to each load coefficient obtained in step (7) through regression analysis.

[0068] Taking a two-dimensional 10-story 5-span RC frame structure as an example, considering the failure of the corner columns and side columns at the bottom layer, denoted as column A and column B respectively, the prototype and reinforcement details of the structure are as Figure 2 shown. First, the main parameters affecting the continuous collapse resistance of the structure are selected, including 13 random parameters related to geometric dimensions, material properties, and load effects. Assuming that the random variables are independent of each other, Latin hypercube sampling is carried out and the corresponding numerical simulation work is carried out. During the sampling process, the mean value of each variable is taken as the structural design value, and the coefficient of variation of the variable and the distribution function followed by each random variable refer to relevant classical studies. The detailed information is shown in Table 1. Among them, the shape coefficients α and β of the β distribution are 3.2 and 4.28 respectively. At the same time, since there are many types of structural beam / column reinforcement design values, the specific mean values are not given.

[0069] Table 1 Random parameter distribution of 10-story RC frame structure

[0070]

[0071] Figure 3 shows the random Pushdown curves of the structure, where Figure 3 (a) and Figure 3 (b) are the cases of removing column A and column B respectively. Figure 4 shows the histogram and probability density function (PDF) curve of Δ R , where Figure 4 (a) and Figure 4 (b) are the NO and CP limit states of the case of removing column A respectively; Figure 4 (c) and Figure 4 (d) correspond to the NO and CP limit states of the case of removing column B respectively. It can be seen from Figure 3 and Figure 4 that in the catenary arch stage, σ R changes little, while when the structure enters the catenary stage, σ C changes rapidly. In both cases of removing column A and column B, σ R in the NO limit state is less than σ R in the CP limit state. After removing column A, σ RThey are 0.009 and 0.081 respectively, and the latter is 9 times the former. In the case of removing the B column, NO ( σ R = 0.007) and CP ( σ R = 0.082) at the ultimate state σ R differ greatly. The σ R at the CP ultimate state is 11.7 times that at the NO ultimate state. The above results show the significant influence of uncertainty on the progressive collapse capacity of the structure, especially in the catenary action stage. Therefore, it is necessary to determine the thresholds at different ultimate states of the structure through stochastic analysis under the condition of statically removing columns.

[0072] Figure 5 shows the histograms and PDF curves of Δ S corresponding to different load factors, where Figure 5 (a) and Figure 5 (b) are the cases of removing column A and column B respectively. It can be seen from Figure 5 that as the load factor increases, the PDF curve shows a more obvious tendency to tilt to the left and greater discreteness. This is because most sub-models can maintain balance without failure under the action of a smaller load factor. When the structure is subjected to a larger gravity load, although the PDF peak still appears in a smaller displacement range, due to the increase in the proportion of collapsed structures, the frequency of large deformations increases, so an asymmetric trend appears.

[0073] Figure 6 shows the vulnerability curves obtained by the present invention and existing methods (based on the Pushdown method and IDA method), where Figure 6 (a) and Figure 6 (b) are the cases of removing column A and column B respectively. Table 2 statistics the load factors corresponding to a failure probability of 50%. The results show that: the vulnerability curve of the NO ultimate state calculated by the present invention is between the vulnerability curves obtained based on IDA and the Pushdown method, while the curve of the CP ultimate state shifts to the left. In the scenarios of removing column A and column B, the S values of the NO ultimate state calculated by the present invention are 0.921 and 0.887 respectively. The difference in S values between the vulnerability curve calculated by the present invention and the curve obtained based on the Pushdown method is much greater than the difference between the curves obtained based on the IDA method, reaching 30.29% and 33.26% respectively. For the CP ultimate state, in the scenarios of removing column A and column B, the SThe values are 1.343 and 1.359 respectively. Compared with the corresponding vulnerability curves based on Pushdown and IDA, S the average changes are -10.92% and -8.64% respectively, which indicates that under the action of the same load intensity, the failure probability of the structure is higher when considering both performance and demand uncertainties. Compared with the present invention, the results obtained by using the existing method for vulnerability analysis of progressive collapse structures in static and dynamic column removal scenarios are more conservative. The significant differences in the vulnerability curves also prove the necessity of considering both capacity and demand uncertainties in the progressive collapse analysis of structures.

[0074] Table 2 S

[0075]

[0076] An embodiment of the present invention also provides a progressive collapse vulnerability assessment system for structures combining static and dynamic probability analysis, including:

[0077] An acquisition module: used to acquire design parameters affecting the progressive collapse resistance of the structure as random variables, denoted as X = ( X 1 , X 2 , …, X n ), T where n is the number of random variables; a design parameter sample set; wherein, the corresponding sampling is carried out by Latin hypercube sampling to generate a sub-model design parameter sample set, and the sample size is 1000; wherein, the mean value of each random variable is the initial design value.

[0078] A progressive collapse deterministic numerical model module: used to construct corresponding static and dynamic progressive collapse deterministic numerical models; establish corresponding sub-models according to the sample set;

[0079] A Pushdown module: used to perform Pushdown analysis based on the model constructed in the progressive collapse deterministic numerical model module; specifically as follows: The entire process of Pushdown analysis is controlled by the incremental gravity load applied to the structure until the structure collapses; the vertical displacement Δ is applied proportionally to the beam-column joints, and the change in the gravity load of the damaged span is recorded to obtain the corresponding Pushdown curve; the displacements corresponding to different limit states are determined through the Pushdown curve, denoted as Δ R .

[0080] Nonlinear displacement time history analysis module: It is used to perform nonlinear displacement time history analysis under different load intensities based on the model constructed in the continuous collapse deterministic numerical module. Specifically, the gravity load applied to the structure is used as the intensity index, and the vertical displacement of the beam-column joint at the top of the demolished column is used as the damage index. By changing the load coefficient α , the gravity load applied to the damaged span is gradually increased, and the vertical displacement of the beam-column joint at the top of the demolished column corresponding to different limit states is recorded and denoted as Δ S .

[0081] Structural continuous collapse resistance probability density function module: It is used to fit the structural continuous collapse resistance probability density function based on the normal distribution hypothesis, calculate the corresponding mean and standard deviation, and determine the thresholds of the structure at different performance levels considering static uncertainty.

[0082] Structural continuous collapse load effect probability density function module: It is used to fit the structural continuous collapse load effect probability density function based on the lognormal distribution hypothesis, calculate the corresponding mean and standard deviation, and determine the probabilistic load effect of the structure at different performance levels considering dynamic uncertainty.

[0083] Continuous collapse vulnerability scatter point module: It is used to obtain the continuous collapse vulnerability scatter points of the structure. The formula for the continuous collapse vulnerability of the structure is as follows:

[0084] (1);

[0085] Where, S is the structural load effect, R is the continuous collapse resistance corresponding to a certain limit state of the structure; IM is the intensity index. The formula (1) is rewritten as:

[0086] (2);

[0087] Where, F RS ( r , s ) and f RS ( r , s ) are the joint cumulative density function and joint probability density function of R and S respectively;

[0088] For simplified calculation, assume that R and S are independent of each other. Finally, the continuous collapse vulnerability of the structure can be calculated by the following formula:

[0089] (3);

[0090] The mean value of the probability density function of the progressive collapse resistance of the obtained structure μ R , the standard deviation of the probability density function of the progressive collapse resistance of the structure σ R , the mean value of the probability density function of the progressive collapse load effect of the structure μ S and the standard deviation of the probability density function of the progressive collapse load effect of the structure σ S Substitute them into formula (3), and the probability of the structure exceeding a certain limit state under a certain load factor can be obtained through the convolution integral method, that is, the scatter points of the progressive collapse vulnerability of the structure.

[0091] Progressive collapse vulnerability curve module: used to obtain the progressive collapse vulnerability curve of the structure based on the scatter points of the exceeding probability corresponding to each load factor obtained by regression analysis under the assumption of lognormal distribution.

Claims

1. A structural progressive collapse vulnerability assessment method combining static and dynamic probabilistic analysis, characterized in that: The following steps are involved: (1) The design parameters that affect the progressive collapse resistance of the structure are obtained as random variables, denoted as X = ( X 1, X 2,…, X n ) T ,in, n is the number of random variables; design parameter sample set; (2) Construct the corresponding static and dynamic progressive collapse deterministic numerical models; establish the corresponding sub-models based on the sample set; (3) Based on the model constructed in step (2), perform pushdown analysis; (4) Based on the model constructed in step (2), nonlinear displacement time history analysis under different load intensities is performed; (5) Based on the normal distribution assumption, the probability density function of the structure's progressive collapse resistance is fitted; the corresponding mean and standard deviation are calculated to determine the thresholds of the structure at different performance levels after considering static uncertainty; (6) Based on the log-normal distribution assumption, the probability density function of the load effect of the structural continuous collapse is fitted; the corresponding mean and standard deviation are calculated to determine the probabilistic load effect of the structure at different performance levels after considering the dynamic uncertainty; (7) The scatter points of the structural progressive collapse vulnerability are obtained; the formula for the structural progressive collapse vulnerability is as follows: (1)； in, S is the structural load effect, R is the continuous collapse resistance corresponding to a certain limit state of the structure; IM is the strength index; formula (1) is rewritten as: （2）； in, F RS ( r , s )and f RS ( r , s ) are respectively R and S The joint cumulative density function and joint probability density function of; To simplify the calculation, assume R and S Independent of each other; the final structural progressive collapse vulnerability is calculated by the following formula: （3）； The mean of the probability density function of the structural progressive collapse resistance obtained in steps (5) and (6) is μ R , Standard deviation of probability density function of structural progressive collapse resistance σ R , mean value of probability density function of load effect of structural progressive collapse μ S and standard deviation of the probability density function of the load effect of structural progressive collapse σ S Substituting into formula (3), the probability of the structure exceeding a certain limit state under a certain load coefficient can be obtained through the convolution integral method, that is, the scatter point of the structural continuous collapse vulnerability; (8) Based on the log-normal distribution assumption, the exceedance probability scatter points corresponding to each load factor obtained in step (7) are fitted by regression analysis to obtain the progressive collapse fragility curve of the structure.

2. The structural progressive collapse vulnerability assessment method combining static and dynamic probabilistic analysis according to claim 1 is characterized in that: In step (1), Latin hypercube sampling is used to carry out corresponding sampling to generate a sub-model design parameter sample set with a sample size of 1000; among which, the mean of each random variable is the initial design value.

3. The structural progressive collapse vulnerability assessment method combining static and dynamic probabilistic analysis according to claim 1 is characterized in that: Step (3) is as follows: The entire process of Pushdown analysis is controlled by the incremental gravity load applied to the structure until the structure collapses; the vertical displacement Δ is applied proportionally to the beam-column joints, and the change in gravity load of the damaged span is recorded to obtain the corresponding Pushdown curve; the displacement corresponding to different limit states is determined by the Pushdown curve, which is recorded as Δ R .

4. The structural progressive collapse vulnerability assessment method combining static and dynamic probabilistic analysis according to claim 1 is characterized in that: Step (4) is as follows: the gravity load applied to the structure is used as the strength index, and the vertical displacement of the beam-column node at the top of the demolished column is used as the damage index; by changing the load coefficient α , gradually increase the gravity load applied to the damaged span, and record the vertical displacement of the beam-column node at the top of the demolished column corresponding to different limit states, denoted as Δ S .

5. A structural progressive collapse vulnerability assessment system combining static and dynamic probability analysis, characterized in that: include: Acquisition module: used to obtain the design parameters that affect the progressive collapse resistance of the structure as random variables, denoted as X=( X 1, X 2,…, X n ) T ,in, n is the number of random variables; design parameter sample set; Progressive collapse deterministic numerical model module: used to construct corresponding static and dynamic progressive collapse deterministic numerical models; establish corresponding sub-models based on sample sets; Pushdown module: used to perform pushdown analysis based on the model constructed in the progressive collapse deterministic numerical model module; Nonlinear displacement time history analysis module: used to perform nonlinear displacement time history analysis under different load intensities based on the model constructed in the progressive collapse deterministic numerical model module; Structural progressive collapse resistance probability density function module: used to fit the structural progressive collapse resistance probability density function based on the normal distribution assumption; and calculate the corresponding mean and standard deviation to determine the threshold of the structure at different performance levels after considering static uncertainty; Structural progressive collapse load effect probability density function module: used to fit the structural progressive collapse load effect probability density function based on the log-normal distribution assumption; and calculate the corresponding mean and standard deviation to determine the probabilistic load effect of the structure at different performance levels after considering dynamic uncertainty; Progressive collapse vulnerability scatter point module: used to obtain the structural progressive collapse vulnerability scatter points; the structural progressive collapse vulnerability formula is as follows: (1)； in, S is the structural load effect, R is the continuous collapse resistance corresponding to a certain limit state of the structure; IM is the strength index; formula (1) is rewritten as: （2）； in, F RS ( r , s )and f RS ( r , s ) are respectively R and S The joint cumulative density function and joint probability density function of; To simplify the calculation, assume R and S Independent of each other; the final structural progressive collapse vulnerability is calculated by the following formula: （3）； The mean probability density function of the structural continuous collapse resistance is obtained μ R , Standard deviation of probability density function of structural progressive collapse resistance σ R , mean value of probability density function of load effect of structural progressive collapse μ S and standard deviation of the probability density function of the load effect of structural progressive collapse σ S Substituting into formula (3), the probability of the structure exceeding a certain limit state under a certain load coefficient can be obtained through the convolution integral method, that is, the scatter point of the structural continuous collapse vulnerability; Progressive collapse fragility curve module: It is used to obtain the progressive collapse fragility curve of the structure based on the log-normal distribution assumption and the exceedance probability scatter points corresponding to each load coefficient obtained by regression analysis fitting.

6. A structural progressive collapse vulnerability assessment system combining static and dynamic probabilistic analysis according to claim 5, characterized in that: In the acquisition module, Latin hypercube sampling is used to carry out corresponding sampling to generate a sub-model design parameter sample set with a sample size of 1000; among them, the mean of each random variable is the initial design value.

7. The structural progressive collapse vulnerability assessment system combining static and dynamic probabilistic analysis according to claim 5, characterized in that: In the Pushdown module, the details are as follows: The entire Pushdown analysis process is controlled by the incremental gravity load applied to the structure until the structure collapses; the vertical displacement Δ is applied proportionally to the beam-column node, and the gravity load change of the damaged span is recorded to obtain the corresponding Pushdown curve; the displacement corresponding to different limit states is determined by the Pushdown curve, which is recorded as Δ R .

8. The structural progressive collapse vulnerability assessment system combining static and dynamic probabilistic analysis according to claim 5, characterized in that: In the nonlinear displacement time-history analysis module, the gravity load applied to the structure is used as the strength index, and the vertical displacement of the beam-column node at the top of the demolished column is used as the damage index; by changing the load coefficient α , gradually increase the gravity load applied to the damaged span, and record the vertical displacement of the beam-column node at the top of the demolished column corresponding to different limit states, denoted as Δ S .

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