Multi-dimensional seismic risk assessment method based on spatial and temporal distribution of ground motion

Abstract

The application relates to a multi-dimension seismic risk assessment method based on the space-time distribution of ground motion, and the method comprises the following steps: S1, selecting an IM index; S2, extracting a key structure parameter; S3, recording an engineering demand parameter EDP; S4, selecting an optimal IM index; S5, establishing a proxy model of structure seismic response; S6, establishing a seismic prediction equation; S7, establishing a residual earthquake hazard analysis model; S8, residual earthquake intensity samples of each target structure position; S9, obtaining a residual earthquake vulnerability curve; S10, determining repair time and repair cost according to repair of the structure itself and repair of the structure function, so as to finally determine the total repair cost of the regional line structure and the seismic capacity of the seismic capacity after repair. Compared with the prior art, the application has the advantages of improving the accuracy of seismic risk estimation.

Description

Technical Field

[0001] This invention relates to the field of earthquake engineering, and in particular to a multi-dimensional earthquake risk assessment method based on the spatiotemporal distribution of ground motion. Background Technology

[0002] The spatial effect of seismic motion is mainly caused by three factors: 1) decoherence effect, which is the characteristic of seismic waves losing correlation with increasing distance; 2) traveling wave effect, which arises from the time difference in the arrival of seismic waves at different excitation points; and 3) site effect, which is caused by the different dynamic characteristics of different soil layers, resulting in differences in the intensity and spectrum of seismic waves as they travel from rock through soil layers to the surface. These three factors are the main considerations when analyzing the impact of the spatial effect of seismic motion on individual structures. For large-scale assessment objects such as road networks, the spatial distribution of seismic motion intensity is also an important manifestation of the spatial effect of seismic motion.

[0003] Because aftershocks are likely to occur for a long period after the main shock, structural damage will accumulate continuously during the main shock-aftershock sequence. Therefore, repairs should be carried out continuously during the interval between the main shock and aftershocks. Depending on whether timely repairs are made to the structure after the main shock, the impact of the main shock-aftershock sequence on the structure can take three forms: 1) No repair measures are taken during the aftershocks; 2) Timely repairs are made during the aftershocks and completed before the next aftershock; 3) Repair measures are taken during the aftershocks but are interrupted by subsequent aftershocks.

[0004] If no repair measures are taken during the aftershocks, structural damage will continue to accumulate, potentially escalating from minor to severe damage or even collapse. This results in higher costs and longer durations for post-disaster repair and reconstruction, increasing both direct and indirect economic losses. Conversely, timely repairs during the aftershocks and completion before the next aftershock improve the structure's seismic resistance, reduce the probability of severe damage, shorten repair time, and decrease indirect economic losses. However, post-earthquake repair costs are lower than those during the earthquake itself, so whether direct repair costs are reduced requires further investigation. In cases where repair measures are taken during the aftershocks but interrupted by subsequent aftershocks, the increase or decrease in the structure's seismic resistance, direct economic losses, and indirect economic losses depends on the completeness of the repair work.

[0005] The performance-based seismic design framework proposed by the Pacific Earthquake Engineering Research Center (PEER) has been widely applied to the seismic design and retrofitting of structures. This method considers the uncertainties of seismic motion characteristics, structural geometry and material parameters, physical damage, and direct and indirect post-earthquake economic losses. It establishes a probabilistic relationship between seismic input and structural performance indicators (such as economic losses, repair time, and casualties), thus enabling more comprehensive and reliable seismic design and performance evaluation of structures. This performance-based seismic design framework mainly consists of four parts: seismic hazard analysis, probabilistic seismic demand analysis, structural seismic vulnerability analysis, and structural seismic disaster loss assessment. Seismic hazard analysis establishes the relationship between seismic intensity indicators and annual exceedance probabilities under given site and design conditions, based on the analysis of earthquake recurrence period, seismic attenuation relationships, fault mechanisms, site conditions, and their uncertainties. Probabilistic seismic demand analysis obtains probabilistic seismic demand models and their annual exceedance probabilities for various engineering demand parameters through structural seismic response analysis. Vulnerability analysis probabilistically assesses the damage state corresponding to the EDP (earthquake ground fault) based on the response analysis results and capabilities of the EDP. Structural earthquake loss analysis mainly involves calculating decision variables that describe the performance of a structural system by combining the results of vulnerability analysis, including post-earthquake repair costs, repair time, and the number of casualties.

[0006] Current research typically neglects the spatial effects of ground motion and the impact of mainshock-aftershock sequences in structural seismic risk assessments. However, for regional structural systems, the spatial effects of ground motion lead to varying intensity of ground motions experienced by different structures within the system, resulting in different post-earthquake structural damage states and varying degrees of repair difficulty. Furthermore, the impact of mainshock-aftershock sequences on regional structural systems manifests in different repair strategies for individual structures within the region and varying indirect economic losses caused by the connectivity or disruption of routes.

[0007] Existing assessment methods do not consider the spatial effects of ground motion and the impact of the mainshock-aftershock sequence, resulting in assessment results that are not applicable to all regions. Furthermore, ignoring aftershocks means that the risk caused by aftershocks throughout the entire earthquake cycle is not included in the overall earthquake risk calculation, leading to inaccurate risk estimates. Summary of the Invention

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

[0009] The objective of this invention can be achieved through the following technical solutions:

[0010] A multi-dimensional earthquake risk assessment method based on the spatiotemporal distribution of ground motion includes the following steps:

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

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

[0013] S3. Perform nonlinear time history analysis on the simplified truss model of the structural system of the N seismic input areas and record the engineering requirement parameters EDP.

[0014] S4. Select the optimal IM index from the IM indexes;

[0015] S5. Establish a surrogate model for the structural seismic response, using the optimal IM index and key structural parameters as inputs to the surrogate model, and the parameter EDP as the output of the surrogate model.

[0016] S6. Based on the spatial distribution relationship of the optimal IM index, and considering the spatial variability of ground motion, establish the earthquake prediction equation for the optimal IM index.

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

[0018] S8. Based on the aftershock hazard analysis model, Monte Carlo sampling is performed and combined with the earthquake prediction equation to obtain aftershock sequence intensity samples for each target structure location.

[0019] S9. Based on the seismic intensity at each target structure location and the established surrogate model of structural seismic response, the vulnerability of the structure is calculated using the Monte Carlo-based time-varying aftershock vulnerability analysis method, and the aftershock vulnerability curve is obtained.

[0020] S10. Based on the aftershock vulnerability curve, determine the repair time and cost for the structural repair 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 after repair.

[0021] Furthermore, the IM indices include peak ground acceleration (PGA), peak velocity (PGV), peak displacement (PGD), spectral acceleration Sa(T1), spectral velocity Sv(T1), and spectral displacement Sd(T1) corresponding to the first period of the structure.

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

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

[0024] Furthermore, the earthquake prediction equation is:

[0025]

[0026] in, It is an estimate of the IM index of record j of earthquake event i, f mag For the magnitude term, f dis f is the distance term. site For the site item, f atn This is an inelastic decay term.

[0027] Furthermore, the establishment of the aftershock hazard analysis model specifically involves:

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

[0029] Furthermore, the aftershock hazard analysis model is for a magnitude of m. m An earthquake with a magnitude between [m] occurs within any time interval [t, t+f] after the main shock. l m m The average number of aftershocks within the range μ*(t, T; m) m )for:

[0030]

[0031] Where T represents the time period, and the upper limit of the aftershock magnitude m is the corresponding main shock 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 used in the aftershock sequence.

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

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

[0034] A2. Based on the Monte Carlo method, Monte Carlo sampling is performed using the probability of aftershocks occurring within a time period as the expectation of a 0-1 distribution. If the sampling result indicates that no aftershocks occur, the intensity of the aftershocks during that time period is 0; if an aftershock occurs, then A3 is executed.

[0035] A3. Sampling of aftershock magnitudes; the sampling range for aftershock magnitudes is equal to or greater than the main shock magnitude (m). m The magnitude of the aftershocks of concern is m l Determined, based on the interval [m] l ,m mSampling is performed on the cutoff exponent distribution of ].

[0036] A4. Assuming that the aftershocks are uniformly distributed along the fault, sample the locations where the aftershocks occurred and determine the fault distance of each target structure based on the sampling results.

[0037] A5. Combining the aftershock magnitudes obtained from sampling in A3 and the fault distances and site conditions obtained in A4, the IM indexes of the locations of each target structure are obtained by sampling 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] Wherein, P(N) AS =1) is the probability of an aftershock, P(N) AS =0) represents the probability that no aftershocks will occur.

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

[0043] B1. Determine the initial conditions of the mainshock;

[0044] B2. Based on the earthquake prediction equation, sample the intensity of the mainshock at each target structure location to determine the intensity im0 of the mainshock at each target structure location.

[0045] B3. Sampling is performed based on the aftershock intensity of each interval in the aftershock sequence intensity sample. The sampled aftershock sequence intensity sample and the mainshock intensity obtained in B2 form the mainshock-aftershock sequence intensity sample.

[0046] B4. Calculate the transition matrix T for the damage state probability of an aftershock with intensity im at the k-th ground motion. k (im), let P be the probability that the structural damage is i after the (k-1)th aftershock. k-1 (DS = i), where DS represents the i-th damage state of the structure, and the probability P that the structure is in a damaged state after the k-th aftershock of intensity im is determined by Markov transformation. k The magnitude of the main shock is obtained as im0, and the magnitude of the kth aftershock is im. k The probability P of a structure being in various damage states after being subjected to any sequence of waves consisting of the main shock and n aftershocks. n Based on probability P n Obtain the aftershock vulnerability P of the structure in the j-th limit state after an aftershock of arbitrary strength im. f The aftershock vulnerability curve was obtained.

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

[0048]

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

[0050] Where DS0 represents the initial damage state of the structure, DS0 = 1, 2, 3, 4, edp j This represents the structural engineering requirement parameter corresponding to the j-th limit state.

[0051] The probability P that the structure is damaged after the k-th aftershock of intensity im is... k for:

[0052]

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

[0054]

[0055] The aftershock vulnerability P corresponding to the j-th limiting state f for:

[0056]

[0057] Among them, V j =(0…01…1) T V j The first j-1 elements are 0, and the rest are 1. V j This indicates the structural damage state when an aftershock occurs.

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

[0059] This invention uses an aftershock hazard analysis model to perform Monte Carlo sampling and combines it with earthquake prediction equations to obtain aftershock sequence intensity samples for each target structure location. Based on the ground motion intensity at each target structure location and the established surrogate model of structural seismic response, a Monte Carlo-based time-varying aftershock vulnerability analysis method is used to calculate structural vulnerability, resulting in aftershock vulnerability curves. Furthermore, it analyzes the regional structural damage after the action of any sequence wave composed of the mainshock and n aftershocks, incorporating the risk caused by aftershocks into the risk estimation, thereby accurately estimating the overall risk brought by the earthquake. Attached Figure Description

[0060] Figure 1 This is a flowchart illustrating the present invention.

[0061] Figure 2 This is a schematic diagram of the basic process for aftershock hazard analysis;

[0062] Figure 3 This is a schematic diagram illustrating the relationship between economic loss and damage status;

[0063] Figure 4 This is a schematic diagram of a railway line that takes into account the spatial distribution of seismic motion.

[0064] Figure 5 These are the 241 selected ground motions;

[0065] Figure 6 It is a model of a seismic isolation and vibration reduction railway bridge truss system;

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

[0067] Figure 8 These are the aftershock vulnerability curves under various main shock damage states;

[0068] Figure 9 The curve shows the structural vulnerability to time-varying aftershocks.

[0069] Figure 10 For direct economic losses;

[0070] Figure 11 This constitutes an indirect economic loss. Detailed Implementation

[0071] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0072] This invention provides a multi-dimensional earthquake risk assessment method based on the spatial distribution dimension of ground motion and the temporal dimension of mainshocks and aftershocks. The main analysis object of this invention is simply supported beam railway bridges. To achieve the above objectives, this invention adopts the following technical solution, the main process of which is described below. Figure 1 :

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

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

[0075] S3. Perform nonlinear time history analysis on the simplified truss model of the structural system of the N seismic input areas and record the engineering requirement parameters EDP.

[0076] S4. Select the optimal IM index from the IM indexes;

[0077] S5. Establish a surrogate model for the structural seismic response, using the optimal IM index and key structural parameters as inputs to the surrogate model, and the parameter EDP as the output of the surrogate model.

[0078] S6. Based on the spatial distribution relationship of the optimal IM index, and considering the spatial variability of ground motion, establish the earthquake prediction equation for the optimal IM index.

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

[0080] S8. Based on the aftershock hazard analysis model, Monte Carlo sampling is performed and combined with the earthquake prediction equation to obtain aftershock sequence intensity samples for each target structure location.

[0081] S9. Based on the seismic intensity at each target structure location and the established surrogate model of structural seismic response, the vulnerability of the structure is calculated using the Monte Carlo-based time-varying aftershock vulnerability analysis method, and the aftershock vulnerability curve is obtained.

[0082] S10. Based on the aftershock vulnerability curve, determine the repair time and cost for the structural repair 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 after repair.

[0083] Taking a railway line consisting of simply supported beam bridges as an example, a multi-dimensional seismic risk assessment is conducted, considering the spatial distribution dimension of ground motion and the temporal dimension of mainshocks and aftershocks. Figure 4 As shown

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

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

[0086] The number of ground motion samples selected was 241, including 120 non-pulse ground motions and 121 pulse ground motions. Figure 5 The statistical selection of IM indices for ground motion includes peak ground acceleration (PGA), peak ground velocity (PGV), peak ground displacement (PGD), spectral acceleration Sa(T1), spectral velocity Sv(T1), and spectral displacement Sd(T1) corresponding to the first period of the structure.

[0087] In S2, structures of the same type within the region have the same structural form, but differ in parameter selection. Taking railway beam bridges within a certain area as an example, they all use simply supported beams, but the span of the main beam, the height of the piers, the type of bearings, and the form of the pile foundations are different. These parameters directly related to the seismic response of the structure are recorded, and the location and series-parallel relationships of the target structures considered in each region are also recorded to determine the impact of the failure of each structure on the overall railway line.

[0088] Establish a simplified model of the regional structural system: Establish a simplified truss model of the main analytical structures within the region, and extract the key structural parameters [x1, x2, ..., x] that affect the seismic response of the structure. n [and determine the location and series / parallel relationships of each target structure;]

[0089] OpenSEES is used for parametric modeling of the structure, such as Figure 6 As shown, for a simply supported beam of a seismic isolation railway, there are four key structural parameters: pier height H, main beam weight m, first-order structural period T, and friction pendulum support radius R. These parameters can form a vector [H, m, T, R]. By sampling according to the range of values ​​of the key parameters, a certain number of structural parameter sets can be obtained.

[0090] In S3, the selected engineering requirement parameter EDP should be significantly correlated with structural damage and structural function decline. Taking railway beam bridges as an example, the relative displacement of piers and beams and the curvature of piers are generally used as the main EDPs.

[0091] Nonlinear time history analysis: Input N seismic ground motions into the structure, perform nonlinear time history analysis on the selected series of structures, and record the selected m engineering requirement parameters (EDPs).

[0092] The finite element model set obtained from the above sampling was matched with the seismic motion. The seismic motion was input, and the selected EDP included the curvature of the bridge piers. The relative displacement δ between the pier and the beam is recorded, and these two EDPs are combined to form the output vector.

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

[0094] Selecting the optimal IM metric: Choose a suitable IM metric based on its efficiency, practicality, proficiency, sufficiency, and disaster computability;

[0095] Comparing the efficiency, practicality, proficiency, adequacy, and hazard calculability of the alternative IM indices, PGV was ultimately selected as the optimal IM index. For near-field seismic isolation bridges, PGV demonstrates good efficiency, practicality, and proficiency. Furthermore, numerous studies have proposed attenuation relationships of PGV under various site conditions, indicating good hazard calculability.

[0096] In S5, the proxy model recommends comparing multiple machine learning models and ultimately selecting the model with the best prediction performance to build the final proxy model. The model's input is x = [x1, x2, ..., x...]. p [IM], where x1, x2, ..., x p For the selected structural principal parameters, the model output y = [y1, y2, ..., y3]. k ], where y1, y2, ..., y k The EDP selected in step 3) is thus obtained, which is a probabilistic surrogate model that can quickly calculate the EDP based on the main structural parameters and seismic motion parameters.

[0097] Establish a surrogate model for structural seismic response: Select a suitable machine learning model, use the optimal IM index and key structural parameters as input to the model, and use the corresponding EDP as the output to train the model, thus obtaining the most reasonable surrogate model, i.e., [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 a region;

[0098] XGBoost (a distributed gradient boosting library) was chosen to build a surrogate model, with [H, m, T, R, PGV] as the model input. Using this as model output to train the model can yield good training results, and the model's R... 2 Reaching 0.89, it can be used to quickly determine the seismic response of a structure based on its ground motion parameters.

[0099] In S6, the earthquake prediction equation is used to determine the seismic intensity of the site where the target structure is located. Numerous studies have proposed earthquake prediction equations for different regions and different seismic intensity indices, with the main functional form being...

[0100]

[0101] in, It is an estimate of the IM index of record j of earthquake event i, f mag For the magnitude term, f dis f is the distance term. site For the site item, f atn This is an inelastic decay term.

[0102] The distance term related to magnitude can generally be expressed as:

[0103]

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

[0105]

[0106] Site effects include linear site effects and nonlinear site response models, as shown in equation (4).

[0107]

[0108] Inelastic attenuation of ground motion in M S >6.5, R rup At speeds >80km, inelastic decay is observed, while near-source (R) rup The ground motion parameters of ≤80km do not show obvious inelastic attenuation effect, and the inelastic attenuation term is as shown in equation (5).

[0109]

[0110] 1) Establish earthquake prediction equation: Based on the spatial distribution relationship of the selected optimal IM index and considering the spatial variability of ground motion, establish the earthquake prediction equation of the optimal IM index to take into account the spatial effect of ground motion.

[0111] Search the literature to find a suitable earthquake prediction equation for PGV. For example, according to the research of Zhang Bin et al., in step 6), the equations c0 = 1.1599, c1 = 0.5607, c2 = 0.0682, c3 = 0.0842, c4 = -1.6915, c5 = 0.0871, c6 = 3.6, c7 = 2.0565, and c8 = 0.0050 are explained.

[0112] In S7, Omori's law states that the probability of aftershocks decreases exponentially, specifically as (t+c)p, where t is the time from the main shock, and c and p are parameters specific to the site. Gutenberg-Richter's law indicates a correlation between aftershock magnitude and main shock magnitude. Based on these two laws, the daily average probability of aftershocks is γ(t, m; m...). m As shown in the following formula;

[0113]

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

[0115] Taking the partial derivative of equation (6), we get:

[0116]

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

[0118] The magnitude can be calculated as m m An earthquake with a magnitude of [m] occurs within any time interval [t, t+T] after the main shock. l m m The average number of aftershocks within the range μ*(t, T; m) m As shown in equation (8):

[0119]

[0120] Establish an aftershock hazard analysis model: Based on Omori's law and Gutenberg-Richter's law, establish the probability and time of aftershock occurrence (t), main shock magnitude (M), and aftershock magnitude (M0). mThe relationship between these factors is established, and based on this, a non-homogeneous Poisson process is used to represent the stochastic process of aftershock occurrence.

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

[0122] In S8, based on the occurrence of an earthquake with a magnitude between [m] within any time interval [t, t+T] after the mainshock. l m M The average number of aftershocks within the range μ*(t, T; m) m Furthermore, the occurrence of aftershocks within the interval [t, t+T] follows a Poisson distribution, therefore the probability distribution of aftershock occurrence is as shown in equation (9):

[0123]

[0124] When the time interval T is sufficiently small, at most one aftershock will occur within any [t, t+T], i.e., P(N AS ≥2)=0, therefore the probability of aftershocks occurring during this period is shown in equation (10).

[0125]

[0126] The analysis procedure for determining aftershock intensity based on the Monte Carlo method is as follows: Figure 2 The specific steps are as follows:

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

[0128] (2) Sampling for aftershock occurrence: Calculate the probability P(N) of aftershock occurring within the time period [t0, t0+T] according to equation (10). AS =1), P(M) AS =1) Perform Monte Carlo sampling as the expectation of the 0-1 distribution. If the sampling result is no occurrence, the aftershock intensity for that period is 0; if it occurs, proceed to step (3).

[0129] (3) Sampling of aftershock magnitudes: The sampling range for aftershock magnitudes is from the main shock magnitude m m The magnitude of the aftershocks of concern is m l Confirmed, for [m] l ,m m Sampling is performed based on the truncation index distribution within that interval.

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

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

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

[0133] Generate aftershock intensity at each target structural location: N is calculated based on the aftershock hazard analysis model. m Sub-Monte Carlo sampling combined with earthquake prediction equations yields N m Samples of aftershock intensity at the locations of each target structure.

[0134] The lower limit of the ground motion intensity considered for both the mainshock and aftershocks is magnitude 5, and it is assumed that the time interval T is one day, and that at most one aftershock occurs per day. The total duration considered is one year. The probability of aftershocks occurring after the mainshock 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 a Markov process to describe the change in the damage state of a structure under multiple aftershocks; that is, the damage state of the structure after the k-th aftershock is only related to the damage state after the (k-1)-th aftershock. This probability transition from the damage state of the (k-1)-th aftershock to the damage state after the k-th aftershock can be achieved through a Markov probability transition matrix. Each row of the Markov probability transition matrix is ​​a mutually exclusive complete set of events, and the sum of the elements in each row is 1. Dividing the structure into r damage states, the transition matrix T represents the probability of damage state when an aftershock of intensity im occurs at the k-th earthquake. k (im):

[0136]

[0137] Among them, P ij (im) represents the probability that a structure initially in the i-th damage state will change to the j-th damage state after an aftershock of intensity im. Since the aftershock damage state can only increase from low to high, when i > j, P ij When (im) = 0 and i < j, P ij (im) as shown in equation (12). Each row of the transition matrix represents 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 state 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] Wherein, P(EDP>edp) j |DS0=i,IM=im) represents the aftershock vulnerability of the limit state j when an aftershock of intensity im occurs while the structure is in the i-th damage state. DS0 represents the initial damage state of the structure, DS0=1,2,3,4.

[0140] After the transition matrix is ​​determined, let P be the probability that the structural damage is i after the (k-1)th aftershock. k-1 If (DS=i), then according to the Markov transformation, the probability that the structure is in a damaged state after the k-th aftershock of intensity im is P. k As in equation (13):

[0141]

[0142] Therefore, with the main shock intensity being im0 and the kth aftershock intensity being im... k In the case of a sequence of waves consisting of the main shock and n aftershocks, what is the probability P that the structure will be in various damage states after being subjected to each wave sequence? n As shown in equation (14).

[0143]

[0144] To evaluate the seismic performance of a structure after the main shock and n aftershocks, it is necessary to calculate the aftershock vulnerability P of the current structure when another aftershock occurs. f At this point, the structural damage state is V. j =(0…01…1) T V j The first j-1 elements are 0, and the rest are 1. Then, the aftershock vulnerability P of the current structure in the j-th limiting state after an aftershock of arbitrary intensity im is... f As shown in equation (15).

[0145]

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

[0147] (1) Determine the initial conditions of the mainshock (magnitude, epicentral distance, fault length).

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

[0149] (3) Generate aftershock sequence samples according to the aftershock hazard analysis method based on the Monte Carlo method in step 8), and analyze each interval (t0~t) in the time period. m , t m The aftershock intensity of (+Δt) is sampled, and if no aftershock occurs, the intensity is recorded as 0.

[0150] (4) After determining the intensity sample of the main shock-aftershock sequence, the sample of the main shock-aftershock sequence is analyzed by the time-varying aftershock vulnerability analysis method described in Equations (11)-(15) 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 generated mainshock and aftershock sequence to obtain the structure in (t m , t m +Δt) samples of the probability of being in each damage state within each time period, and calculated using Monte Carlo theory in units of time, each (t) m , t m The sample mean of the probabilities of each damage state within +Δt) is used as the probability P(t) of the structure being in each damage state at any time. m ,im0).

[0152] According to formula (15), calculate t at any time. m The aftershock vulnerability curve P of the structure under an aftershock of arbitrary strength im at the j-th limit state. f (t).

[0153] Time-varying aftershock vulnerability analysis: Based on the ground motion intensity at the site of each structure and the established surrogate model of the structural seismic response, the vulnerability of the structure is calculated using the Monte Carlo-based time-varying aftershock vulnerability analysis method.

[0154] Based on the specific content described in step 9), a time-varying aftershock vulnerability analysis model was performed. Using the aforementioned aftershock time-intensity sampling method, 10,000 mainshock and aftershock sequence samples were obtained. The time-varying aftershock vulnerability analysis was repeated for each target structure. The average value of all samples was taken for the probability of each damage state at each time point. According to Monte Carlo theory, this average value was used as the time-varying probability of each damage state of the structure. The aftershock vulnerability curves for each mainshock damage state are shown below. Figure 8 As shown, the time-varying aftershock vulnerability of the structure within one year is as follows: Figure 9 As shown.

[0155] In S10, the direct economic loss of the structure can be estimated using the proportional factor method. This model considers the demolition and reconstruction cost to be the sum of the costs of bridge reconstruction, debris removal, and the establishment of temporary branch roads. Each component's cost is proportional to the bridge deck area. A proportional factor related to the degree of bridge damage is applied to the bridge reconstruction cost, relating to the structural damage state. Indirect economic losses stem from the train operation costs and time costs incurred due to route closure. For a bridge under given conditions, indirect economic losses are directly determined by the structure's functionality and are related to the structural damage state, repair strategy, and corresponding recovery function. The specific relationships are as follows: Figure 3 As shown.

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

[0157] Based on existing economic loss assessment models, the direct economic losses caused by the cost of repairing structural damage and the indirect economic losses caused by line interruption are calculated. Direct economic losses include... Figure 10 As shown, indirect economic losses are as follows Figure 11 As shown, the final economic loss is obtained by superimposing the two parts.

[0158] Compared with the prior art, the beneficial effects of the present invention are:

[0159] 1. This invention solves the problem of considering the effect of aftershocks in the loss assessment of railway beam bridges and lines, and realizes the loss assessment of the entire earthquake cycle.

[0160] 2. This invention considers the spatial variability of seismic motion in the assessment of losses and risks of railway lines in high-intensity seismic zones during earthquake cycles, resulting in results that are more consistent with actual conditions.

[0161] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A multi-dimensional earthquake risk assessment method based on the spatiotemporal distribution of ground motion, characterized in that, The method includes the following steps: S1. Select N ground motions and calculate the IM index corresponding to each ground motion; S2. Establish a simplified frame model of the regional structural system and extract key structural parameters that affect the seismic response of the structure; S3, will A simplified truss model of the structural system in the seismic input area is used for nonlinear time history analysis, and the engineering requirement parameters (EDP) are recorded. S4. Select the optimal IM index from the IM indexes; S5. Establish a surrogate model for the structural seismic response, using the optimal IM index and key structural parameters as inputs to the surrogate model, and the parameter EDP as the output of the surrogate model. S6. Based on the spatial distribution relationship of the optimal IM index, and considering the spatial variability of ground motion, establish the earthquake prediction equation for the optimal IM index. S7. Establish an aftershock hazard analysis model; S8. Based on the aftershock hazard analysis model, Monte Carlo sampling is performed and combined with the earthquake prediction equation to obtain aftershock sequence intensity samples for each target structure location. S9. Based on the seismic intensity at each target structure location and the established surrogate model of structural seismic response, the vulnerability of the structure is calculated using the Monte Carlo-based time-varying aftershock vulnerability analysis method, and the aftershock vulnerability curve is obtained. S10. Based on the aftershock vulnerability curve, determine the repair time and cost for the structural repair 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 after repair.

2. The multi-dimensional earthquake risk assessment method based on the spatiotemporal distribution of ground motion as described in claim 1, characterized in that, The IM index includes peak ground acceleration. Peak speed Peak displacement Spectral acceleration corresponding to the first-order period of the structure Spectral velocity Spectral shift .

3. The multi-dimensional earthquake risk assessment method based on the spatiotemporal distribution of ground motion as described in claim 2, characterized in that, The key structural parameters are: Among them, the height of the bridge piers Main beam weight First-order periodic structure Friction pendulum support radius .

4. The multi-dimensional earthquake risk assessment method based on the spatiotemporal distribution of ground motion as described in claim 1, characterized in that, The parameter EDP represents the relative displacement between the pier and the beam, and the curvature of the pier.

5. The multi-dimensional earthquake risk assessment method based on the spatiotemporal distribution of ground motion as described in claim 1, characterized in that, The earthquake prediction equation is: in, It is an earthquake event. Record The estimated value of the IM index, For the magnitude term, For distance, For the site item, This is an inelastic decay term.

6. The multi-dimensional earthquake risk assessment method based on the spatiotemporal distribution of ground motion according to claim 1, characterized in that, The establishment of the aftershock hazard analysis model specifically involves: Establish the probability and time of aftershock occurrence based on Omori's law and Gutenberg-Richter's law. Magnitude of the main shock Aftershock magnitude The relationship between the two is used to represent the stochastic process of aftershock occurrence using a non-homogeneous Poisson process, thus forming an aftershock hazard analysis model.

7. The multi-dimensional earthquake risk assessment method based on the spatiotemporal distribution of ground motion according to claim 6, characterized in that, The aftershock hazard analysis model is based on a magnitude of [missing information]. At any time after the main shock The magnitude of the earthquake occurred at Average number of aftershocks in the area for: Where T represents the time period and the magnitude of the aftershocks considered. The upper limit is the corresponding main shock magnitude. The lower limit is the minimum earthquake magnitude that may cause damage. a, b, c, and p represent the parameters used in the aftershock sequence.

8. The multi-dimensional earthquake risk assessment method based on the spatiotemporal distribution of ground motion according to claim 7, characterized in that, The specific steps for S8 are as follows: A1. Determine the key parameters of the main shock; obtain the probability distribution of aftershock occurrence based on the aftershock hazard analysis model, and obtain the probability of aftershock occurrence within a time period based on the probability distribution; A2. Based on the Monte Carlo method, Monte Carlo sampling is performed using the probability of aftershocks occurring within a time period as the expectation of a 0-1 distribution. If the sampling result indicates that no aftershocks occur, the intensity of the aftershocks during that time period is 0; if an aftershock occurs, then A3 is executed. A3. Sampling of aftershock magnitudes; the sampling range for aftershock magnitudes is equal to the main shock magnitude. The magnitude of the aftershocks of concern Determined, based on the interval Sampling is performed on the truncated exponential distribution; A4. Assuming that the aftershocks are uniformly distributed along the fault, sample the locations where the aftershocks occurred and determine the fault distance of each target structure based on the sampling results. A5. Combining the aftershock magnitudes obtained from sampling in A3 and the fault distances and site conditions obtained in A4, the IM indexes of the locations of each target structure are obtained by sampling 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: in, The probability of aftershocks. This represents the probability that no aftershocks will occur.

9. A multi-dimensional earthquake risk assessment method based on the spatiotemporal distribution of ground motion as described in claim 8, characterized in that, The specific steps for S9 are as follows: B1. Determine the initial conditions of the mainshock; B2. Based on the earthquake prediction equation, sample the intensity of the mainshock at each target structure location to determine the intensity of the mainshock at each target structure location. ; B3. Sampling is performed based on the aftershock intensity of each interval in the aftershock sequence intensity sample. The sampled aftershock sequence intensity sample and the mainshock intensity obtained in B2 form the mainshock-aftershock sequence intensity sample. B4. Calculate the... The intensity of the sub-earthquake was Transition matrix of damage state probability during aftershocks , set at the The damage status after the aftershock was as follows: The probability is ,in The first part representing the structure The damage state is determined based on the Markov transform. Secondary intensity is The probability that the structure is damaged after the aftershock. The intensity of the main shock was obtained as , No. The intensity of the aftershock was In the case of any structure caused by the main shock and The probability of being in various damage states after being subjected to a sequence of waves composed of secondary and aftershocks. Based on probability Obtain the structure at arbitrary strength The aftershocks Aftershock vulnerability corresponding to each extreme state The aftershock vulnerability curve was obtained.

10. A multi-dimensional earthquake risk assessment method based on the spatiotemporal distribution of ground motion according to claim 9, characterized in that, Transition matrix for: in, The structure was originally in the first position The intensity occurs under each damage state. After the aftershocks, it became the first The probability of each damage state. hour, =0, hour, in, This represents the initial damage state of the structure. , This represents the structural engineering requirement parameter corresponding to the j-th limit state. No. Secondary intensity is The probability that the structure is damaged after the aftershock. for: Probability of each damage state for: No. Aftershock vulnerability corresponding to each extreme state for: in, ,in The former One element is 0, and the rest are 1. This indicates the structural damage state when an aftershock occurs.

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