Multi-dimensional seismic risk assessment method based on seismic oscillation space-time distribution

Abstract

The invention relates to a multi-dimensional seismic risk assessment method based on seismic oscillation space-time distribution. The method comprises the following steps: S1, selecting IM indexes; s2, key structure parameters are extracted; s3, recording an engineering demand parameter EDP; s4, selecting an optimal IM index; s5, establishing an agent model of structural seismic response; s6, establishing an earthquake prediction equation; s7, establishing an aftershock risk analysis model; s8, obtaining aftershock intensity samples of the positions of the target structures; s9, obtaining an aftershock vulnerability curve; and S10, determining repair time and repair cost according to the repair of the structure and the repair of the structure function so as to finally determine the total repair cost of the structure of the regional line and the anti-seismic capacity after repair. Compared with the prior art, the method has the advantages of improving the accuracy of earthquake risk estimation and the like.

Description

Technical Field

[0001] The present invention relates to the field of earthquake engineering, and in particular to a multi-dimensional earthquake risk assessment method based on the temporal and spatial distribution of earthquake motion. Background Art

[0002] The spatial effect of earthquake motion is mainly caused by three factors: 1) decoherence effect, which is the property of earthquake waves losing correlation as the distance increases; 2) traveling wave effect, which is caused by the time difference between earthquake waves reaching different excitation points; 3) site effect, due to the different dynamic characteristics of different soil layers, the intensity and spectrum of earthquake waves when they are transmitted from rock through soil layers to the surface are different. The above three factors are the main considerations when analyzing the impact of the spatial effect of earthquake motion on single structures. For large-scale assessment objects such as road networks, the spatial distribution of earthquake motion intensity is also an important manifestation of the spatial effect of earthquake motion.

[0003] Since aftershocks may occur for a long time after the main shock, structural damage will continue to accumulate in the main shock-aftershock sequence. Therefore, repairs should be carried out continuously in the interval between the main shock and aftershocks. Depending on whether the structure is repaired in time after the main shock, the impact of the main shock-aftershock sequence on the structure has three forms: 1) no repair measures are taken during the aftershock period; 2) timely repairs are carried out during the aftershock period and completed before the next aftershock; 3) repair measures are taken during the aftershock period but interrupted by the subsequent aftershock.

[0004] If no repair measures are taken during the aftershock period, structural damage will continue to accumulate, and structural damage may change from minor damage to serious damage or even collapse, making the cost of post-disaster repair and reconstruction higher and longer, increasing direct and indirect economic losses. When timely repairs are carried out during the aftershock period and completed before the next aftershock, the seismic capacity of the repaired structure is improved, the probability of causing serious damage is also reduced, the repair time is shortened, and the indirect economic losses are reduced. However, the cost of post-earthquake repair is lower than the cost of repair during the earthquake period, so whether the direct repair cost is reduced needs further study. In the case where repair measures are taken during the aftershock period but are interrupted by subsequent aftershocks, the increase or decrease in the seismic capacity of the structure, direct economic losses, and indirect economic losses depends on the completion of the repair work.

[0005] The performance-based seismic design framework proposed by the Pacific Earthquake Engineering Research Center (PEER) has been widely used in seismic design and retrofitting of structures. This method takes into account the uncertainty of ground motion characteristics, structural geometry and material parameters, physical damage, and direct and indirect economic losses after an earthquake. From a probabilistic perspective, it establishes the relationship between ground motion input and structural performance indicators (such as economic losses, repair time, and casualties), so as to conduct seismic design and performance evaluation of structures more comprehensively and reliably. The performance-based structural seismic design framework mainly consists of four parts: seismic hazard analysis, structural probabilistic seismic demand analysis, structural seismic vulnerability analysis, and structural seismic disaster loss assessment. Seismic hazard analysis is to establish the relationship between seismic intensity indicators and annual exceedance probability under given site and design conditions based on the analysis of earthquake recurrence period, ground motion attenuation relationship, fault mechanism, site conditions and their uncertainties. Structural probabilistic seismic demand analysis is to obtain the probabilistic seismic demand model and annual exceedance probability of each engineering demand parameter through structural seismic response analysis. Vulnerability analysis is to conduct a probabilistic assessment of the damage state corresponding to the EDP based on the response analysis results and capabilities of the EDP of interest. Structural earthquake loss analysis mainly combines the results of vulnerability analysis to calculate decision variables that describe the performance of the structural system, including the cost of post-earthquake structural repair, repair time, and number of casualties.

[0006] In current research, earthquake risk assessment of structures usually does not consider the spatial effect of ground motion and the impact of the main shock-aftershock sequence. However, for the earthquake risk assessment of regional structural systems, the spatial effect of ground motion causes different structures in the structural system to be subjected to different ground motion intensities, different structural damage states after the earthquake, and different repair difficulties. The impact of the main shock-aftershock sequence on the regional structural system is reflected in the different repair strategies for individual structures in the region and the different indirect economic losses caused by the connectivity or interruption of the route.

[0007] The existing assessment methods do not take into account the spatial effects of seismic motion and the impact of the mainshock-aftershock sequence, resulting in the assessment results being unable to be applied to all regions. Ignoring aftershocks also means that the risks caused by aftershocks within the entire earthquake cycle are not calculated in the overall earthquake risk, and the risk estimate is not accurate enough. Summary of the invention

[0008] The purpose of the present invention is to provide a multi-dimensional earthquake risk assessment method in order to improve the accuracy of earthquake risk estimation.

[0009] The purpose of the present invention can be achieved by the following technical solutions:

[0010] A multi-dimensional earthquake risk assessment method based on the temporal and spatial distribution of ground motion, the method comprising the following steps:

[0011] S1, select N ground motions and calculate the IM index corresponding to each ground motion;

[0012] S2. Establish a simplified bar model of the regional structural system and extract key structural parameters that affect the seismic response of the structure;

[0013] S3, input N earthquake motions into the simplified bar model of the regional structural system for nonlinear time history analysis, and record the engineering demand parameter EDP;

[0014] S4, selecting the optimal IM indicator among the IM indicators;

[0015] S5. Establish a proxy model of structural seismic response, take the optimal IM index and key structural parameters as input of the proxy model, and take the parameter EDP as output of the proxy model;

[0016] S6. Establishing an earthquake prediction equation of the optimal IM index based on the spatial distribution relationship of the optimal IM index and taking into account the spatial variability of ground motion;

[0017] S7. Establish an aftershock hazard analysis model;

[0018] S8. Monte Carlo sampling is performed according to the aftershock hazard analysis model and combined with the earthquake prediction equation to obtain aftershock sequence intensity samples at the locations of each target structure;

[0019] S9. According to the seismic intensity at each target structure location and the established proxy model of structural seismic response, the Monte Carlo-based time-varying aftershock vulnerability analysis method is used to calculate the structural vulnerability and obtain the aftershock vulnerability curve;

[0020] S10. Determine the repair time and repair cost based on the repair of the structure itself and the repair of the structural function determined by the aftershock vulnerability curve, so as to finally determine the total structural repair cost of the regional line and the seismic resistance of the seismic resistance after the repair.

[0021] Furthermore, the IM index includes the seismic peak acceleration PGA, peak velocity PGV, peak displacement PGD, and the spectral acceleration Sa(T1), spectral velocity Sv(T1) and spectral displacement Sd(T1) corresponding to the first-order period of the structure.

[0022] Furthermore, the key structural parameters are [H, m, T, R], where the pier height is H, the main beam weight is m, the first-order period of the structure is T, and the friction pendulum bearing radius is R.

[0023] Furthermore, the parameter EDP is the relative displacement of the pier and beam and the curvature of the pier.

[0024] Furthermore, the earthquake prediction equation is:

[0025]

[0026] in, is the estimated value of the IM index for earthquake event i record j, f mag is the magnitude term, f dis is the distance term, f site is the site term, f atn is the inelastic attenuation term.

[0027] Furthermore, the establishment of the aftershock hazard analysis model is specifically as follows:

[0028] According to Omori's law and Gutenberg-Richter's law, the probability of aftershock occurrence and time t and the magnitude m of the main shock are established. m , and the relationship between the aftershock magnitude m, and based on the relationship, a non-homogeneous Poisson process is used to represent the random process of aftershock occurrence, forming an aftershock hazard analysis model.

[0029] Furthermore, the aftershock risk analysis model is a model for aftershocks with a magnitude of m m In any period of time [t, t+f] after the main shock, an earthquake with a magnitude of [m l , m m The average number of aftershocks in the range μ*(t, T; m m )for:

[0030]

[0031] Where T is the time period, and the upper limit of the aftershock magnitude m considered is the corresponding mainshock magnitude m m , the lower limit is the minimum earthquake magnitude m that may cause damage l , a, b, c and p represent the parameters adopted for the aftershock sequence.

[0032] Furthermore, the specific steps of S8 are:

[0033] A1. Determine the key parameters of the main shock; obtain the probability distribution of aftershocks according to the aftershock hazard analysis model, and obtain the probability of aftershocks within a time period based on the probability distribution;

[0034] A2: Based on the Monte Carlo method, Monte Carlo sampling is performed according to the probability of aftershocks occurring in the time period as the expectation of the 0-1 distribution. If the sampling result is that no aftershocks occur, the intensity of aftershocks in this time period is 0; if they occur, A3 is executed;

[0035] A3. Sampling of aftershock magnitudes. The sampling range of aftershock magnitudes is from the main shock magnitude m m The magnitude of the aftershocks of concern is m l Determine, according to the interval [m l ,m m] is sampled from a truncated exponential distribution;

[0036] A4. Assuming that the distribution of aftershocks on the fault is uniform, sample the locations where aftershocks occur, and determine the fault distance of each target structure based on the sampling results;

[0037] A5. Combining the aftershock magnitude sampled in A3 and the fault distance and site conditions obtained in A4, the IM index of each target structure location is sampled according to the earthquake prediction equation;

[0038] A6. Repeat the above steps to obtain a large number of aftershock sequence intensity samples;

[0039] The probability of aftershocks occurring within the time period is:

[0040]

[0041] Among them, P(N AS =1) is the probability of aftershocks, P(N AS =0) is the probability that no aftershocks will occur.

[0042] Furthermore, the specific steps of S9 are:

[0043] B1. Determine the initial conditions of the main shock;

[0044] B2. Sampling the intensity of the main shock at each target structure location according to the earthquake prediction equation to determine the main shock intensity im0 at each target structure location;

[0045] B3, sampling is performed according to the aftershock intensity of each interval in the aftershock sequence intensity sample, and the sampled aftershock sequence intensity sample and the main shock intensity obtained in B2 form a mainshock-aftershock sequence intensity sample;

[0046] B4. Calculate the transfer matrix T of the damage state probability when the kth aftershock has an earthquake intensity of im k (im), assuming that the probability of structural damage i after the k-1th aftershock is P k-1 (DS = i), where DS represents the i-th damage state of the structure. The probability P of the structure being in a damaged state after the k-th aftershock with intensity im is determined according to the Markov transformation. k , the main shock intensity is im0, and the kth aftershock intensity is im k The probability P of the structure being in each damage state after the action of any sequence wave consisting of the main shock and n aftershocks is n , based on the probability P n The aftershock vulnerability P corresponding to the jth limit state of the structure after an aftershock of any intensity im is obtained. f , and obtain the aftershock vulnerability curve.

[0047] Furthermore, the transfer matrix T k (im) is:

[0048]

[0049] Among them, P ij (im) is the probability that the structure originally in the i-th damage state will change to the j-th damage state after an aftershock with intensity im occurs. When i>j, P ij When (im)=0, i<j, P ij (im)=P(EDP>edp j |DS0=i, IM=im)-P(EDP>edp j+1 |DS0=i,IM=im)

[0050] Among them, DS0 is the initial damage state of the structure, DS0 = 1, 2, 3, 4, edp j represents the structural engineering requirement parameter corresponding to the jth limit state,

[0051] The probability P of the structure being in a damaged state after the kth aftershock with intensity im k for:

[0052]

[0053] The probability of each damage state P n for:

[0054]

[0055] Aftershock vulnerability P corresponding to the jth limit state f for:

[0056]

[0057] Among them, V j =(0…01…1) T , where V j The first j-1 elements of V are 0, and the remaining elements are 1. j It indicates the structural damage state when the structure is hit by aftershocks again.

[0058] Compared with the prior art, the present invention has the following beneficial effects:

[0059] The present invention uses an aftershock hazard analysis model to perform Monte Carlo sampling and combines it with an earthquake prediction equation to obtain aftershock sequence intensity samples at each target structure location. According to the seismic intensity at each target structure location and an established proxy model of structural seismic response, a Monte Carlo-based time-varying aftershock vulnerability analysis method is used to calculate structural vulnerability, and an aftershock vulnerability curve is obtained. The regional structural damage after the action of any sequence wave consisting of a main shock and n aftershocks is then analyzed, and the risk caused by aftershocks is included in the risk estimation, thereby accurately estimating the risk brought by the overall earthquake. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a schematic diagram of the process of the present invention.

[0061] Figure 2 It is a basic flow chart of aftershock hazard analysis;

[0062] Figure 3 It is a schematic diagram of the relationship between economic loss and injury status;

[0063] Figure 4 It is a schematic diagram of the railway line considering the spatial distribution of ground motion;

[0064] Figure 5 It is the 241 selected ground motions;

[0065] Figure 6 It is a seismic isolation railway bridge bar system model;

[0066] Figure 7 is the change in the probability of aftershocks occurring over time after the main shock;

[0067] Figure 8 is the aftershock vulnerability curve under each mainshock damage state;

[0068] Fig. 9 is the time-varying aftershock vulnerability curve of the structure;

[0069] Fig.10 Direct economic losses;

[0070] Fig.11 Indirect economic losses. DETAILED DESCRIPTION

[0071] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0072] The present invention provides a multi-dimensional earthquake risk assessment method based on the spatial distribution dimension of earthquake motion and the time series dimension of main and aftershocks. The main analysis object of the present invention is the railway simply supported beam bridge of the railway bridge line. In order to achieve the above purpose, the present invention adopts the following technical scheme, the main process is shown in Figure 1 :

[0073] S1, select N ground motions and calculate the IM index corresponding to each ground motion;

[0074] S2. Establish a simplified bar model of the regional structural system and extract key structural parameters that affect the seismic response of the structure;

[0075] S3, input N earthquake motions into the simplified bar model of the regional structural system for nonlinear time history analysis, and record the engineering demand parameter EDP;

[0076] S4, selecting the optimal IM indicator among the IM indicators;

[0077] S5. Establish a proxy model of structural seismic response, take the optimal IM index and key structural parameters as input of the proxy model, and take the parameter EDP as output of the proxy model;

[0078] S6. Establishing an earthquake prediction equation of the optimal IM index based on the spatial distribution relationship of the optimal IM index and taking into account the spatial variability of ground motion;

[0079] S7. Establish an aftershock hazard analysis model;

[0080] S8. Monte Carlo sampling is performed according to the aftershock hazard analysis model and combined with the earthquake prediction equation to obtain aftershock sequence intensity samples at the locations of each target structure;

[0081] S9. According to the seismic intensity at each target structure location and the established proxy model of structural seismic response, the Monte Carlo-based time-varying aftershock vulnerability analysis method is used to calculate the structural vulnerability and obtain the aftershock vulnerability curve;

[0082] S10. Determine the repair time and repair cost based on the repair of the structure itself and the repair of the structural function determined by the aftershock vulnerability curve, so as to finally determine the total structural repair cost of the regional line and the seismic resistance of the seismic resistance after the repair.

[0083] Taking a railway line composed of railway simply supported beam bridges as an example, a multi-dimensional earthquake risk assessment considering the spatial distribution dimension of ground motion and the time sequence dimension of main shocks and aftershocks is carried out. Figure 4 Shown

[0084] In S1, N seismic motions: The seismic motions are selected based on the site where the structure is located and the design method of the structure. According to the research results of structural vulnerability analysis, the number of selected seismic motions is preferably greater than 80.

[0085] Based on the characteristics of the project site, select N ground motions that meet the requirements, and calculate the possible ground motion intensity index (IM index) corresponding to each ground motion according to the needs;

[0086] The number of selected ground motions is 241, including 120 non-pulse ground motions and 121 pulse ground motions. Figure 5 . Statistically select the IM indicators of seismic motion. Commonly used IM indicators include seismic peak acceleration PGA, peak velocity PGV, peak displacement PGD, spectral acceleration Sa(T1), spectral velocity Sv(T1), spectral displacement Sd(T1) corresponding to the first-order period of the structure, etc.

[0087] In S2, the same type of structures in the region have the same structural form, but the parameter selection is different. For example, railway beam bridges within a certain area all use simply supported beams, but the span of the main beam, the height of the pier, the support model, and the pile foundation form are different. These parameters directly related to the seismic response of the structure are recorded, and the location and series-parallel relationship of the target structures considered in each area are determined and recorded to determine the impact of the failure of each structure on the entire line.

[0088] Establish a simplified model of the regional structural system: Establish a simplified bar system model of the main analysis structure within the regional scope, and extract the key structural parameters [x1, x2, ..., x n ], and determine the position and series-parallel relationship of each target structure;

[0089] OpenSEES is used to perform parametric modeling of the structure, such as Figure 6 As shown in the figure, for the seismic isolation railway simply supported beam, there are four key parameters of the structure, including the pier height H, the main beam weight m, the first-order period of the structure T, and the radius R of the friction pendulum support. They can form a vector [H, m, T, R] and are sampled according to the value range of the key parameters to obtain a certain number of structural parameter groups.

[0090] In S3, the selected engineering demand parameter EDP should have a significant correlation with the damage of the structure and the decline of the structural function. Taking the railway beam bridge as an example, the relative displacement of the pier and the beam and the curvature of the pier are generally used as the main EDP.

[0091] Nonlinear time history analysis: Input N earthquake motions into the structure, perform nonlinear time history analysis on a selected series of structures, and record the selected m engineering demand parameters EDP;

[0092] The finite element model set obtained by the above sampling is matched with the ground motion, the ground motion is input, and the selected EDP includes the curvature of the bridge pier The relative displacement of the pier and beam is δ, and the two EDPs are recorded, which form the output vector

[0093] In S4, when selecting the optimal IM index, in addition to efficiency, practicality, proficiency, and sufficiency, disaster computability represents the computational consumption required to determine the earthquake hazard curve associated with the selected IM. Therefore, when selecting IM indicators, IM indicators with relatively mature earthquake prediction equations, such as PGA and PGV, should be given priority.

[0094] Select the best IM indicators: Select appropriate IM indicators based on their efficiency, practicality, proficiency, adequacy and disaster computability;

[0095] By comparing the efficiency, practicality, proficiency, adequacy and disaster calculability of the alternative IM indicators, PGV was finally selected as the optimal IM indicator. For near-field seismic isolation bridges, PGV can show good efficiency, practicality and proficiency. At the same time, a large number of studies have proposed the attenuation relationship of PGV under various site conditions, which has good disaster calculability.

[0096] In S5, the proxy model recommendation uses multiple machine learning models for comparison, and finally selects the model with the best prediction effect to establish the final proxy model. The input of the model is x = [x1, x2, ..., x p , IM], where x1, x2, ..., x p The output of the model is y = [y1, y2, ..., y k ], where y1, y2, ..., y k is the EDP selected in step 3), thus, a probabilistic proxy model is obtained which can quickly calculate the EDP based on the main structural parameters and seismic parameters.

[0097] Establish a proxy model for structural seismic response: select a suitable machine learning model, take the optimal IM index and key structural parameters as the input of the model, and train the corresponding EDP as the output of the model to obtain the most reasonable proxy model, that is, [EDP1, …, EDP m ]=f([x1,x2,…,x n ,IM]) to quickly obtain the seismic response of the structure in the seismic analysis of the structure within the regional scope;

[0098] Select XGBoost (distributed gradient boosting library) to build a proxy model, and use [H, m, T, R, PGV] as the model input. As the model output, training the model can get better training results. 2 It reaches 0.89, which can be used to quickly determine the structural earthquake response based on the structural and ground motion parameters.

[0099] In S6, the earthquake prediction equation is used to determine the earthquake intensity of the site where the target structure is located. Currently, a large number of studies have proposed earthquake prediction equations for different regions and different earthquake intensity indicators. The main function form is

[0100]

[0101] in, is the estimated value of the IM index for earthquake event i record j, f mag is the magnitude term, f dis is the distance term, f site is the site term, f atn is the inelastic attenuation term.

[0102] The distance term that can be used to correlate magnitude can generally be expressed as:

[0103]

[0104] The magnitude term is expressed by a piecewise linear function (Campbell and Bozorgnia), as shown in formula (3).

[0105]

[0106] The site effect includes linear site effect and nonlinear site response model, as shown in equation (4).

[0107]

[0108] Inelastic attenuation of ground motion in M S >6.5、R rup >80km, it shows an inelastic attenuation phenomenon, while near the source (R rup There is no obvious inelastic attenuation effect on the ground motion parameters with a depth of ≤80km, and the inelastic attenuation term is as shown in formula (5).

[0109]

[0110] 1) Establishing earthquake prediction equation: Based on the spatial distribution relationship of the selected optimal IM index and considering the spatial variability of ground motion, an earthquake prediction equation of the optimal IM index is established to take into account the spatial effect of ground motion;

[0111] Search the literature to find a suitable earthquake prediction equation for PGV, such as c0=1.1599, c1=0.5607, c2=0.0682, c3=0.0842, c4=-1.6915, c5=0.0871, c6=3.6, c7=2.0565, c8=0.0050 in the explanation of step 6).

[0112] In S7, Omori's law states that the probability of aftershocks decreases exponentially, which can be expressed as (t+c)p, where t is the time from the main shock, and c and p are parameters of the specific site. Gutenberg-Richter's law states that the magnitude of aftershocks is correlated with the magnitude of the main shock. Based on the above two laws, the average daily probability of aftershocks γ(t, m; m m ) is shown in the following formula;

[0113]

[0114] Among them, m m is the main shock magnitude, m is the aftershock magnitude, α=ln10·(a+bm m ), β = b·ln10. Taking California as an example, the parameters used in the common aftershock sequence are: a = -1.67, b = 0.91, p = 1.08, c = 0.05.

[0115] Taking partial differential of formula (6), we get:

[0116]

[0117] Therefore, μ(t; m m ) is an aftershock with a magnitude of m m The daily average occurrence rate at time t after the main shock occurs, f M (m) is the probability density function of the exponential distribution of aftershock magnitude.

[0118] The magnitude can be calculated as m m In any period of time [t, t+T] after the main shock, an earthquake with a magnitude of [m l , m m The average number of aftershocks in the range μ*(t, T; m m ) as formula (8):

[0119]

[0120] Establish an aftershock hazard analysis model: According to the Omori law and Gutenberg-Richter law, establish the probability of aftershock occurrence and time (t), main shock magnitude (M), aftershock magnitude (M m), and based on this, the non-homogeneous Poisson process is used to represent the random process of aftershock occurrence;

[0121] Establish an aftershock hazard analysis model based on the specific contents described in step 7).

[0122] In S8, based on the occurrence of an earthquake with a magnitude of [m l , m M The average number of aftershocks in the range μ*(t, T; m m ), and the occurrence of aftershocks in [t, t+T] follows the Poisson distribution, so the probability distribution of aftershocks is as follows:

[0123]

[0124] When the time interval T is small enough, at most one aftershock will occur within any period [t, t+T], and P(N AS ≥2)=0, so the probability of aftershocks occurring in this time period is as shown in formula (10).

[0125]

[0126] The analysis process of aftershock intensity determination based on Monte Carlo method is shown in Figure 2 , the specific steps are as follows:

[0127] (1) Determine the key parameters of the main shock (magnitude, epicenter distance, and fault length).

[0128] (2) Sampling whether aftershocks occur: According to formula (10), the probability P(N) of aftershocks occurring in the time period [t0, t0+T] is calculated. AS =1), P(M AS =1) as the expectation of 0-1 distribution for Monte Carlo sampling. If the sampling result is no aftershock, the aftershock intensity in this period is 0. If it occurs, execute step (3).

[0129] (3) Sampling of aftershock magnitudes: The sampling range of aftershock magnitudes is from the main shock magnitude m m The magnitude of the aftershocks of concern is m l Determine, for [m l ,m m ] and samples are drawn from a truncated exponential distribution within this interval.

[0130] (4) Sampling the spatial locations of aftershocks: Assuming that the distribution of aftershocks on the fault is uniform, the locations where aftershocks occur are sampled, and the fault distance of each target structure is determined based on the sampling results.

[0131] (5) Sampling the seismic intensity IM at each target structure location: Combining the aftershock magnitude obtained by sampling, the fault distance of each target object and the site conditions, the IM at each target structure location is sampled according to the earthquake prediction equation determined in step 4).

[0132] (6) Repeat the above steps for each time period [t, t+T] within the total time considered to obtain a large number of samples.

[0133] Generate aftershock intensity at each target structure location: N m Monte Carlo sampling and combined with earthquake prediction equation, we get N m The aftershock intensity samples at each target structure location are collected.

[0134] The lower limit of the earthquake intensity considered for the main shock and aftershocks is 5, and it is assumed that the time interval T is one day, and aftershocks occur at most once a day, and the total time considered is 1 year. The probability of aftershocks after the main shock is as follows: Figure 7 As shown, Monte Carlo sampling is performed based on the aftershock hazard analysis model established in step 7).

[0135] In S9, the time-varying aftershock vulnerability analysis method is essentially an aftershock vulnerability analysis method that considers time correlation. This method uses the Markov process to describe the changes in the damage state of a structure under multiple aftershocks, that is, the damage state of the structure after the kth aftershock is only related to the damage state of the structure after the k-1th aftershock. This probability conversion from the damage state after the k-1th aftershock to the damage state after the kth aftershock can be achieved through the Markov probability transfer matrix. Each row of the Markov probability transfer matrix is ​​a mutually exclusive complete event group, and the sum of the elements in each row is 1. The structure is divided into r damage states, and the transfer matrix T of the damage state probability when the kth aftershock with seismic intensity im occurs is k (im):

[0136]

[0137] Among them, P ij (im) is the probability that the structure originally in the i-th damage state will change to the j-th damage state after an aftershock with intensity im occurs. At the same time, since the aftershock damage state can only go from low to high, therefore, when i>j, P ij When (im)=0, i<j, P ij (im) As shown in formula (12). Each row of the transfer matrix is ​​a complete time group. When the structural damage state is i, the sum of the probabilities of being in the i-th to r-th damage states after the aftershock is 1.

[0138] P ij (im)=P(EDP>edp j|DS0=i,IM=im) (12) -P(EDP>edp j+1 |DS0=i,IM=im)

[0139] Among them, P(EDP>edp j |DS0=i,IM=im) is the aftershock vulnerability corresponding to the limit state j when the structure is in the i-th damage state and an aftershock with intensity im occurs. DS0 is the initial damage state of the structure, DS0=1, 2, 3, 4.

[0140] After the transfer matrix is ​​determined, the probability that the structural damage is i after the k-1th aftershock is P k-1 (DS=i), then according to Markov transformation, the probability that the structure is in a damaged state after the kth aftershock with intensity im is P k , as shown in formula (13):

[0141]

[0142] Therefore, when the main shock intensity is im0 and the kth aftershock intensity is im k In the case of , the probability P of the structure being in each damage state after the action of any sequence wave consisting of the main shock and n aftershocks n As shown in formula (14).

[0143]

[0144] In order to measure the seismic performance of the structure after the main shock and n aftershocks, it is necessary to calculate the aftershock vulnerability P of the current structure when an aftershock occurs again. f , at this time the structural damage state is V j =(0…01…1) T , where V j The first j-1 elements of are 0, and the remaining elements are 1. Then the aftershock vulnerability P corresponding to the jth limit state of the current structure after an aftershock of any intensity im is f As shown in formula (15).

[0145]

[0146] The specific steps of the time-varying aftershock vulnerability method based on the Monte Carlo method are:

[0147] (1) Determine the initial conditions of the main shock (magnitude, epicenter distance, and fault length).

[0148] (2) According to the earthquake prediction equation (attenuation relationship), the intensity of the main shock at each target structure location is sampled to determine the main shock intensity im0 at each target structure location.

[0149] (3) Generate aftershock sequence samples according to the Monte Carlo method based aftershock hazard analysis method in step 8), and calculate the probability of aftershock sequence samples for each interval (t m , t m +Δt) aftershock intensity is sampled, and if it does not occur, the intensity is recorded as 0.

[0150] (4) After determining the strength sample of the mainshock-aftershock sequence, the time-varying aftershock vulnerability analysis method described in equations (11) to (15) is used to analyze the mainshock-aftershock sequence sample to determine the probability of the structure being in each damage state within any time interval.

[0151] (5) Repeat the above 4 steps for each group of main shock and aftershock sequences generated to obtain the structure at (t m , t m +Δt) samples of the probability of being in each damage state in each time period, and using time as the unit, according to the Monte Carlo theory, calculate the probability of each (t m , t m +Δt), as the probability P(t m , im0).

[0152] According to formula (15), calculate any time t m The aftershock vulnerability curve P corresponding to the jth limit state of the structure under an aftershock of arbitrary intensity im is f (t).

[0153] Conduct time-varying aftershock vulnerability analysis: According to the earthquake intensity of each structure site and the established proxy model of structural seismic response, the Monte Carlo-based time-varying aftershock vulnerability analysis method is used to calculate the structural vulnerability.

[0154] According to the specific contents of step 9), a time-varying aftershock vulnerability analysis model is developed. According to the aforementioned aftershock time-intensity sampling method, 10,000 main-aftershock sequence samples are sampled. The time-varying aftershock vulnerability analysis is repeated for each target structure. The average value of all samples is taken for the probability of each damage state at each moment. According to the Monte Carlo theory, the average value is used as the time-varying probability of each damage state of the structure. The aftershock vulnerability curves under each mainshock damage state are as follows: Figure 8 As shown in Figure 2, the time-varying aftershock vulnerability of the structure within one year is as follows: Fig. 9 shown.

[0155] In S10, the direct economic loss of the structure can be estimated by the proportional factor method. In this model, the demolition and reconstruction costs are considered to be the sum of the costs of bridge reconstruction, debris removal and establishment of temporary branches, where each cost is proportional to the bridge deck area. At the same time, a proportional factor related to the degree of damage to the bridge is set for the bridge reconstruction cost, which is related to the damage state of the structure. The indirect economic loss comes from the loss of train operation costs and time costs caused by the closure of the route. For a bridge under given conditions, the indirect economic loss is directly determined by the functionality of the structure, which is related to the damage state of the structure, the repair strategy and the corresponding recovery function. The specific relationship is as follows: Figure 3 shown.

[0156] Calculate regional economic losses: Determine the repair time and cost based on the repair of the structure itself and the repair of the structural function, so as to finally determine the total structural repair cost of the regional line and the seismic resistance of the seismic capacity after repair.

[0157] According to the existing economic loss assessment model, the direct economic losses caused by the cost of repairing the damaged structure and the indirect economic losses caused by line interruption are calculated. The direct economic losses are as follows: Fig.10 As shown in the figure, indirect economic losses are Fig.11 As shown, the two parts are superimposed to obtain the final economic loss.

[0158] Compared with the prior art, the present invention has the following beneficial effects:

[0159] 1. The present invention solves the problem of taking the effect of aftershocks into account in the loss assessment of railway beam bridges and lines, and realizes the loss assessment of the entire earthquake cycle.

[0160] 2. The present invention takes into account the spatial variability of earthquake motion in the loss and risk assessment of railway lines in high-intensity areas during earthquake cycles, and the results are more in line with the actual situation.

[0161] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A multi-dimensional earthquake risk assessment method based on the temporal and spatial distribution of ground motion, characterized in that: The method comprises the following steps: S1, select N ground motions and calculate the IM index corresponding to each ground motion; S2. Establish a simplified bar model of the regional structural system and extract key structural parameters that affect the seismic response of the structure; S3, input N earthquake motions into the simplified bar model of the regional structural system for nonlinear time history analysis, and record the engineering demand parameter EDP; S4, selecting the optimal IM indicator among the IM indicators; S5. Establish a proxy model of structural seismic response, take the optimal IM index and key structural parameters as input of the proxy model, and take the parameter EDP as output of the proxy model; S6. Establishing an earthquake prediction equation of the optimal IM index based on the spatial distribution relationship of the optimal IM index and taking into account the spatial variability of ground motion; S7. Establish an aftershock hazard analysis model; S8. Monte Carlo sampling is performed according to the aftershock hazard analysis model and combined with the earthquake prediction equation to obtain aftershock sequence intensity samples at the locations of each target structure; S9. According to the seismic intensity at each target structure location and the established proxy model of structural seismic response, the Monte Carlo-based time-varying aftershock vulnerability analysis method is used to calculate the structural vulnerability and obtain the aftershock vulnerability curve; S10. Determine the repair time and repair cost based on the repair of the structure itself and the repair of the structural function determined by the aftershock vulnerability curve, so as to finally determine the total structural repair cost of the regional line and the seismic resistance of the seismic resistance after the repair.

2. A multi-dimensional earthquake risk assessment method based on the temporal and spatial distribution of ground motion according to claim 1, characterized in that: The IM indicators include the seismic peak acceleration PGA, peak velocity PGV, peak displacement PGD, and the spectral acceleration Sa(T1), spectral velocity Sv(T1) and spectral displacement Sd(T1) corresponding to the first-order period of the structure.

3. A multi-dimensional earthquake risk assessment method according to claim 2, characterized in that: The key structural parameters are [H, m, T, R], where the pier height is H, the main beam weight is m, the first-order period of the structure is T, and the friction pendulum bearing radius is R.

4. A multi-dimensional earthquake risk assessment method according to claim 1, characterized in that: The parameter EDP is the relative displacement of the pier and beam and the curvature of the pier.

5. The multi-dimensional earthquake risk assessment method based on the temporal and spatial distribution of ground motion according to claim 1, characterized in that: The earthquake prediction equation is: in, is the estimated value of the IM index for earthquake event i record j, f mag is the magnitude term, f dis is the distance term, f site is the site term, f atn is the inelastic attenuation term.

6. The multi-dimensional earthquake risk assessment method based on the temporal and spatial distribution of ground motion according to claim 1, characterized in that: The establishment of the aftershock hazard analysis model is specifically as follows: According to Omori's law and Gutenberg-Richter's law, the probability of aftershock occurrence and time t and the magnitude m of the main shock are established. m , and the relationship between the aftershock magnitude m, and based on the relationship, a non-homogeneous Poisson process is used to represent the random process of aftershock occurrence, forming an aftershock hazard analysis model.

7. The multi-dimensional earthquake risk assessment method based on the temporal and spatial distribution of ground motion according to claim 6, characterized in that: The aftershock hazard analysis model is based on a magnitude of m m In any period of time [t, t+T] after the main shock, an earthquake with a magnitude of [m l ,m m The average number of aftershocks in the range μ * (t,T;m m )for: Where T is the time period, and the upper limit of the aftershock magnitude m considered is the corresponding mainshock magnitude m m , the lower limit is the minimum earthquake magnitude m that may cause damage l , a, b, c and p represent the parameters adopted for the aftershock sequence.

8. The multi-dimensional earthquake risk assessment method based on the temporal and spatial distribution of ground motion according to claim 7, characterized in that: The specific steps of S8 are: A1. Determine the key parameters of the main shock; obtain the probability distribution of aftershocks according to the aftershock hazard analysis model, and obtain the probability of aftershocks within a time period based on the probability distribution; A2: Based on the Monte Carlo method, Monte Carlo sampling is performed according to the probability of aftershocks occurring in the time period as the expectation of the 0-1 distribution. If the sampling result is that no aftershocks occur, the intensity of aftershocks in this time period is 0; if they occur, A3 is executed; A3. Sampling of aftershock magnitudes. The sampling range of aftershock magnitudes is from the main shock magnitude m m The magnitude of the aftershocks of concern is m l Determine, according to the interval [m l ,m m ] is sampled from a truncated exponential distribution; A4. Assuming that the distribution of aftershocks on the fault is uniform, sample the locations where aftershocks occur, and determine the fault distance of each target structure based on the sampling results; A5. Combining the aftershock magnitude sampled in A3 and the fault distance and site conditions obtained in A4, the IM index of each target structure location is sampled according to the earthquake prediction equation; A6. Repeat the above steps to obtain a large number of aftershock sequence intensity samples; The probability of aftershocks occurring within the time period is: Among them, P(N AS =1) is the probability of aftershocks, P(N AS =0) is the probability that no aftershocks will occur.

9. A multi-dimensional earthquake risk assessment method based on the temporal and spatial distribution of ground motion according to claim 8, characterized in that: The specific steps of S9 are: B1. Determine the initial conditions of the main shock; B2. Sampling the intensity of the main shock at each target structure location according to the earthquake prediction equation to determine the main shock intensity im0 at each target structure location; B3, sampling is performed according to the aftershock intensity of each interval in the aftershock sequence intensity sample, and the sampled aftershock sequence intensity sample and the main shock intensity obtained in B2 form a mainshock-aftershock sequence intensity sample; B4. Calculate the transfer matrix T of the damage state probability when the kth aftershock has an earthquake intensity of im k (im), assuming that the probability of structural damage i after the k-1th aftershock is P k-1 (DS = i), where DS represents the i-th damage state of the structure. The probability P of the structure being in a damaged state after the k-th aftershock with intensity im is determined according to the Markov transformation. k , the main shock intensity is im0, and the kth aftershock intensity is im k The probability P of the structure being in each damage state after the action of any sequence wave consisting of the main shock and n aftershocks is n , based on the probability P n The aftershock vulnerability P corresponding to the jth limit state of the structure after an aftershock of any intensity im is obtained. f , and obtain the aftershock vulnerability curve.

10. A multi-dimensional earthquake risk assessment method according to claim 9, characterized in that: Transfer matrix T k (im) is: Among them, P ij (im) is the probability that the structure originally in the i-th damage state will change to the j-th damage state after an aftershock with intensity im occurs. When i>j, P ij When (im)=0, i<j, P ij (im)=P(EDP>edp j |DS0=i,IM=im)-P(EDP>edp j +1|DS0=i,IM=im) Among them, DS0 is the initial damage state of the structure, DS0 = 1, 2, 3, 4, edp j represents the structural engineering requirement parameter corresponding to the jth limit state, The probability P of the structure being in a damaged state after the kth aftershock with intensity im k for: The probability of each damage state P n for: Aftershock vulnerability P corresponding to the jth limit state f for: Among them, V j =(0…0 1…1) T , where V j The first j-1 elements of V are 0, and the remaining elements are 1. j It indicates the structural damage state when the structure is hit by aftershock again.

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