Structural progressive collapse vulnerability assessment method combining static and dynamic probability analysis

Abstract

The invention discloses a method for evaluating vulnerability of progressive collapse of a structure by combining static and dynamic probability analysis. The method comprises the following steps: (1) obtaining design parameters influencing progressive collapse resistance of the structure; designing a parameter sample set; (2) constructing a corresponding static and dynamic progressive collapse deterministic numerical model; establishing a corresponding sub-model according to the sample set; (3) carrying out Pushdown analysis; (4) carrying out nonlinear displacement time-history analysis under the action of different load strengths; (5) fitting to obtain a progressive collapse resistance probability density function of the structure, and calculating a corresponding mean value and a standard deviation; (6) fitting to obtain a structure progressive collapse load effect probability density function, and calculating a corresponding mean value and a standard deviation; (7) obtaining progressive collapse vulnerable scatter points of the structure; (8) obtaining a progressive collapse vulnerability curve of the structure; according to the invention, an accurate vulnerability evaluation result is obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of structural uncertainty quantification, and in particular to a structural progressive collapse vulnerability assessment method combining static and dynamic probability analysis. Background Art

[0002] Alternative load path analysis is the main method for evaluating the ability of structures to resist progressive collapse. This method first removes key structural components 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, understanding the catastrophic behavior of the structure only through deterministic conditions cannot explain the uncertainty in the structural system and external loads. At the same time, the existing structural progressive collapse vulnerability methods considered from the perspective of uncertainty are mostly based on the static removal of columns. There is also an incremental dynamic analysis (IDA) method based on dynamic transient analysis to carry out the vulnerability analysis of the structure under the dynamic removal of columns. This method has been widely used in the uncertainty analysis of structural dynamic progressive collapse, but the existing structural progressive collapse vulnerability analysis techniques mostly use the structural performance analysis results under deterministic analysis as the threshold. There are still some defects in the current assessment methods for structural progressive collapse vulnerability. On the one hand, according to the random reliability theory of structures, the failure probability of the structure depends on the uncertainty of both resistance and load effects. However, the current vulnerability analysis methods are mostly based on static or dynamic analysis, which can only reflect one of the random effects of resistance or load effects. On the other hand, the thresholds for different limit states in the existing progressive collapse dynamic fragility analysis are mostly fixed values ​​given in the specifications. However, the discreteness of the structural progressive collapse resistance at different development stages will seriously affect the thresholds. Directly using the thresholds in the specifications may greatly underestimate the possibility of structural damage. Summary of the invention

[0003] Purpose of the invention: The purpose of the present invention is to provide a method for assessing the vulnerability of structural progressive collapse by combining static and dynamic probability analysis, combining the probability analysis of structural progressive collapse resistance and load effect, and evaluating the exceedance probability of the structure under different limit states by the convolution integral method, so as to solve the problems existing in the background technology.

[0004] Technical solution: The method for evaluating the vulnerability of structural progressive collapse by combining static and dynamic probability analysis of the present invention comprises the following steps: (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, nis 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) Obtaining the scattered points of the structural progressive 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.

[0005] Furthermore, 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; wherein the mean of each random variable is the initial design value.

[0006] Furthermore, 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 proportionally applied to the beam-column joints, 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 .

[0007] Furthermore, 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 .

[0008] Furthermore, the progressive collapse fragility formula of the structure in step (7) is as follows: (1); in, S is the structural load effect, Ris 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 progressive collapse vulnerability of the structure can be 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 progressive collapse fragility.

[0009] The structural progressive collapse vulnerability assessment system combining static and dynamic probability analysis of the present invention comprises: 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 structure progressive collapse vulnerability scatter points; 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.

[0010] Furthermore, in the acquisition module, Latin hypercube sampling is used to carry out corresponding sampling to generate a 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.

[0011] Furthermore, 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 proportionally applied 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 .

[0012] Furthermore, 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 .

[0013] Furthermore, in the progressive collapse vulnerability scatter point module, 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 progressive collapse vulnerability of the structure can be 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 progressive collapse fragility.

[0014] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: Latin hypercube sampling is used to characterize the intrinsic variability of the structure and the randomness of the external load, and Pushdown analysis and IDA are used to consider the uncertainty of the progressive collapse resistance and load effect of the structure at different performance levels, respectively, to further provide guidance for the probabilistic assessment of the structural resistance to progressive collapse. The present invention overcomes the limitation that the traditional structural progressive collapse vulnerability analysis method cannot simultaneously consider the structural performance and demand uncertainty, and integrates the probabilistic behavior of structural resistance and load effect into the vulnerability analysis framework through the convolution integral method, so as to obtain a more accurate structural progressive collapse vulnerability assessment result. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a schematic diagram of the process of the present invention; Figure 2 It is a schematic diagram of the structural prototype of the present invention; Figure 3 is a Pushdown curve diagram of the present invention; wherein, Figure 3 (a) is the condition where the A-pillar is removed; Figure 3Middle (b) is the condition with the B-pillar removed; Figure 4 is the histogram and probability density function PDF curve of ΔR of the present invention; wherein, Figure 4 (a) is the normal operation condition with the A-pillar removed; Figure 4 (b) is the collapse prevention condition when the A-pillar is removed; Figure 4 (c) is the normal operation condition with the B-pillar removed; Figure 4 (d) is the collapse prevention condition when the B-pillar is removed; Figure 5 is the Δ corresponding to different load factors of the present invention S Histogram and PDF curve of ; Among them, Figure 5 (a) is the condition where the A-pillar is removed; Figure 5 Middle (b) is the condition with the B-pillar removed; Figure 6 The vulnerability curves obtained by the present invention and the prior art are shown; wherein Figure 6 (a) is based on the Pushdown method; Figure 6 (b) in is based on the IDA method. DETAILED DESCRIPTION

[0016] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0017] like Figure 1 As shown, the embodiment of the present invention provides Figure 1 As shown, a structural progressive collapse vulnerability assessment method combining static and dynamic probabilistic analysis includes the following steps: Step 1: Select 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. Latin hypercube sampling is then used to generate the sub-model design parameter sample set, with a sample size of 1000. The mean of each random variable is the initial design value, and the corresponding coefficient of variation and the distribution assumptions it obeys will be given later.

[0018] Step 2: Select a column demolition condition and establish the corresponding static and dynamic progressive collapse deterministic numerical model. Establish the corresponding sub-model based on the sample set.

[0019] Step 3: Perform a Pushdown analysis based on all static progressive collapse sub-models. The entire Pushdown analysis process is controlled by the incremental gravity load applied to the structure until the structure collapses. However, only the gravity load on the beams adjacent to the demolished columns will increase, and the loads on the remaining beams will remain unchanged from the initial design load. The vertical displacement Δ is applied proportionally to the beam-column nodes, 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 .

[0020] Step 4: Based on all dynamic progressive collapse sub-models, nonlinear displacement time history analysis is performed under different load intensities. 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 .

[0021] Step 5: Based on the normal distribution assumption, according to the recorded Δ R The probability density function of the structural continuous collapse resistance is obtained by fitting, and the corresponding mean is calculated μ R and standard deviation σ R , determine the thresholds of the structure at different performance levels after considering static uncertainty.

[0022] Step 6: Based on the log-normal distribution assumption, according to the recorded Δ S The probability density function of the load effect of structural progressive collapse is obtained by fitting, and the corresponding mean is calculated μ S and standard deviation σ S , determine the probabilistic load effects of the structure at different performance levels after considering dynamic uncertainty.

[0023] Step 7, the progressive collapse vulnerability of the structure can be expressed as: (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 )andf 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 progressive collapse vulnerability of the structure can be 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 progressive collapse fragility.

[0024] Step 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 continuous collapse fragility curve of the structure.

[0025] Taking a two-dimensional 10-story 5-span RC frame structure as an example, the failure of the bottom corner column and side column is considered, which are recorded as A column and B column respectively. The structural prototype and reinforcement details are as follows Figure 2 As shown. First, the main parameters that affect the continuous collapse resistance of the structure are selected, including 13 random parameters related to geometric dimensions, material properties, and load effects. Assuming that each random variable is independent of each other, Latin hypercube sampling is carried out and corresponding numerical simulations are performed. During the sampling process, the mean of each variable is taken as the structural design value, and the coefficient of variation of the variable and the distribution function obeyed by each random variable refer to relevant classical studies. The detailed information is shown in Table 1. The shape coefficients α and β of the β distribution are 3.2 and 4.28, respectively. At the same time, due to the large number of structural beam / column reinforcement design values, the specific mean is not given.

[0026] Table 1 Random parameter distribution of 10-story RC frame structure

[0027] Figure 3 shows the random Pushdown curve of the structure, where Figure 3 (a) and Figure 3 (b) The A-pillar and B-pillar removal conditions respectively. Figure 4 Shows Δ R The histogram and probability density function (PDF) curve of Figure 4 (a) and Figure 4 (b) NO and CP limit states of the A-pillar removal condition; Figure 4 (c) and Figure 4 (d) The NO and CP limit states correspond to the B-pillar removal condition. Figure 3 and Figure 4 It can be seen that in the arch compression stage, σ R The change is small, and when the structure enters the catenary stage, σ C The change range increases rapidly. In the two cases where the A-pillar and the B-pillar are removed, the NO limit state σ R All are less than the CP limit state σ R After removing the A-pillar, the NO and CP limit states correspond to σ R are 0.009 and 0.081 respectively, the latter being 9 times the former. σ R =0.007) and CP ( σ R =0.082) limit state σ R The difference is large, the CP limit state σ R It is 11.7 times that of the NO limit 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 of the structure under different limit states through stochastic analysis under static column removal conditions.

[0028] Figure 5 Shows the Δ corresponding to different load factors S Histogram and PDF curve of Figure 5 (a) and Figure 5 (b) The A-pillar and B-pillar removal conditions are shown in Figure 1. Figure 5 It can be seen that as the load factor increases, the PDF curve tends to tilt to the left more obviously and the discreteness is greater. This is because most sub-models can maintain balance without damage under 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, the increase in the proportion of collapsed structures leads to an increase in the frequency of large deformations, thus showing an asymmetric trend.

[0029] Figure 6 The vulnerability curves obtained by the present invention and the existing method (based on the Pushdown method and the IDA method) are shown, where Figure 6 (a) and Figure 6 (b) The A-pillar removal condition and the B-pillar removal condition are respectively. Table 2 summarizes the load factors corresponding to the failure probability of 50%. The results show that the NO limit state fragility curve calculated by the present invention is between the fragility curves based on the IDA method and the Pushdown method, while the CP limit state curve shifts to the left. In the scenario of removing the A-pillar and the B-pillar, the NO limit state fragility curve calculated by the present invention is S The values ​​are 0.921 and 0.887 respectively. The vulnerability curve calculated by the present invention is different from the curve obtained by the Pushdown method. S The difference in values ​​is much larger than that between the curves obtained based on the IDA method, reaching 30.29% and 33.26% respectively. For the CP limit state, the A-pillar and B-pillar removal scenarios obtained by the proposed framework S The values ​​are 1.343 and 1.359 respectively. Compared with the corresponding Pushdown-based and IDA-based vulnerability curves, S The average changes of are -10.92% and -8.64%, respectively, which indicates that the failure probability of the structure is higher when both performance and demand uncertainties are considered under the same load intensity. Compared with the present invention, the results of fragility analysis of progressive collapse structures under static and dynamic column removal scenarios using existing methods are more conservative. The significant difference in fragility curves also demonstrates the necessity of considering both capacity and demand uncertainties in the progressive collapse analysis of structures.

[0030] Table 2 Vulnerability curves obtained based on the present invention and the existing method S

[0031] The embodiment of the present invention further provides a structural progressive collapse vulnerability assessment system combining static and dynamic probability analysis, comprising: 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; among them, Latin hypercube sampling is used to carry out 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.

[0032] 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 built in the progressive collapse deterministic numerical model 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, recorded as Δ R .

[0033] 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 progressive collapse deterministic numerical model module. The structure 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 .

[0034] 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 progressive collapse vulnerability of the structure can be 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 progressive collapse fragility.

[0035] 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.

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) Obtaining the scattered points of the structural progressive 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. The structural progressive collapse vulnerability assessment method combining static and dynamic probabilistic analysis according to claim 1 is characterized in that: Step (7) The progressive collapse vulnerability formula of the structure 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 progressive collapse vulnerability of the structure can be 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 progressive collapse fragility.

6. A structural progressive collapse vulnerability assessment system combining static and dynamic probabilistic 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 structure progressive collapse vulnerability scatter points; 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.

7. A structural progressive collapse vulnerability assessment system combining static and dynamic probabilistic analysis according to claim 6, 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.

8. The structural progressive collapse vulnerability assessment system combining static and dynamic probabilistic analysis according to claim 6, 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 .

9. The structural progressive collapse vulnerability assessment system combining static and dynamic probabilistic analysis according to claim 6, 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 .

10. The structural progressive collapse vulnerability assessment system combining static and dynamic probabilistic analysis according to claim 6, characterized in that: In the progressive collapse vulnerability scatter point module, 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 progressive collapse vulnerability of the structure can be 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 progressive collapse fragility.

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