Probabilistic prediction model of post-earthquake building debris distribution range and urban road network congestion vulnerability estimation method

Abstract

The application belongs to the technical field of post-earthquake building collapse range probability prediction model and urban road network congestion vulnerability estimation, and discloses a post-earthquake building collapse range probability prediction model and a method for estimating the vulnerability of urban road network congestion. The building collapse range prediction model based on the Bayes theory considers various damage states of buildings under the action of earthquakes, including complete collapse of buildings and damage of non-structural components; the posterior probability distribution of unknown parameters of the prediction model can be obtained based on the Bayes theory, and thus the cognitive uncertainty from the model parameters is quantified in the post-earthquake road congestion vulnerability estimation. The application not only helps to improve the accuracy of post-earthquake road congestion risk assessment, but also helps to reasonably plan post-disaster rescue evacuation routes.

Description

Technical Field

[0001] This invention belongs to the technical field of probabilistic prediction model of post-earthquake building debris accumulation range and estimation method of urban road network congestion vulnerability, and relates to a probabilistic prediction model of post-earthquake building debris distribution range and a method of estimating urban road network congestion vulnerability. Background Technology

[0002] With improvements in seismic resistance measures for engineering structures, the risk of post-earthquake building collapse has significantly decreased. However, historical earthquake damage data shows that earthquakes are often accompanied by secondary disasters caused by the collapse and falling of non-structural components such as infill walls. Falling debris from earthquake-induced structures not only causes casualties, but the accumulation of rubble can also block nearby roads, hindering the implementation of post-earthquake rescue and evacuation measures. Both the US standard ASCE 7-22 and my country's "Standard for Comprehensive Disaster Prevention Planning in Urban Areas" (GB / T51327-2018) specify threshold values ​​for the fall range of external infill walls. In addition, a series of studies have been conducted on the distribution patterns of falling objects after earthquakes. Xu Hongguo, Ren You, Wang Lifang, and Lin Qingfeng revealed the generalized parabolic motion laws, including classical parabolic equations, bouncing motion, and rolling-sliding motion models, in their article "A Parabolic Motion Model of Hard Road Surface Pieces." Tian Qingyun, Ma Donghui, and Wang Wei derived the formula for calculating the safe distance under the upper floor collapse mode in their article "A Study on the Safe Distance of the Upper Floor Collapse Mode of Buildings under Seismic Action." Xie Zhaobo, Lu Xinzheng, Yang Zhebiao, Xu Zhen, and Zhang Xin calculated the distribution of falling objects after landing through projectile motion in their article "An Experimental Study on the Fall of External Enclosure Infill Walls Caused by Earthquakes and Analysis of the Range of Injury Risks." Xu Zhe, Liao Chengshuai, and Lin Feng predicted the complete distribution of rubble from the collapse of concrete frames with infill walls under earthquakes in their article "A Study on the Analysis Method of Building Collapse and Urban Secondary Disaster Chains under Earthquakes." The data required to study the distribution pattern of falling objects after an earthquake are mainly obtained through four methods: (1) physical experiments, which are reliable but expensive and usually require scaled-down experiments; (2) satellite image data after an earthquake, whose image quality is easily affected by weather, cloud cover and other factors; (3) finite element simulation, which requires solving the problem of falling elements disappearing during the calculation process; and (4) discrete element method, which requires the introduction of physical engine technology to realize the visualization of falling elements.

[0003] It should be noted that existing studies on the distribution patterns of falling debris after earthquakes mainly have the following shortcomings: (1) they focus on building collapse scenarios and lack research on the falling effects of non-structural components such as infill walls; (2) the theoretical formulas are mostly deterministic models or idealized assumptions based on rectangular distributions, which contradict the random distribution characteristics of building debris in actual earthquake damage; (3) there is a lack of theoretical models for estimating the length of building ruins. In view of this, it is necessary to develop a probabilistic prediction model that can describe the random distribution patterns of falling debris after earthquakes, and further consider the impact of the accumulation of falling debris after earthquakes, and propose a method for estimating the vulnerability of urban road network congestion. This invention not only helps to improve the accuracy of post-earthquake road congestion risk assessment, but also helps to rationally plan post-disaster rescue and evacuation routes. Summary of the Invention

[0004] This invention addresses the shortcomings of existing theoretical models by proposing a Bayesian theory-based prediction model for the distribution range of falling debris after earthquakes. The distribution range includes the maximum width and length of the debris accumulation area. Furthermore, considering the blocking effect of building rubble, a method for estimating the post-earthquake urban road network congestion vulnerability is proposed, such as… Figure 1 As shown. The main advantage of this invention is that the proposed theoretical model considers various damage states of buildings under earthquake action, including complete building collapse and damage to non-structural components; it can obtain the posterior probability distribution of unknown parameters of the model, thereby quantifying the cognitive uncertainty from the model parameters in the post-earthquake road blockage vulnerability assessment.

[0005] The technical solution of the present invention:

[0006] A probabilistic prediction model for the distribution range of post-earthquake building ruins and a method for estimating the congestion vulnerability of urban road networks, the steps of which are as follows:

[0007] Step 1: Select target ground motion records. Based on the target response spectrum curve provided in the Code for Seismic Design of Buildings (GB50011-2010), download the target ground motion records from the Pacific Earthquake Engineering Center of the United States or obtain the target ground motion records from the ground motion database recommended by the code and research report. Then, based on the relationship between the pulse period of the near-field pulse ground motion and the natural period of the structure, filter the pulse-type ground motion records from the target ground motion records.

[0008] Step 2: Based on the discrete element method, perform nonlinear dynamic time history calculations on the building structure under seismic loading to obtain the distribution data of falling objects after the earthquake; wherein, the ground motion used for the nonlinear dynamic time history calculation is obtained from Step 1, or the falling object distribution data is obtained from post-earthquake satellite image data;

[0009] Step 3: Based on the distribution data of fallen building debris determined in Step 2, a prediction model for the distribution range of fallen building debris based on Bayesian theory is proposed.

[0010] (1)

[0011] In the formula, E(x,Θ) is the prediction model for the distribution range of falling buildings after an earthquake based on Bayesian theory; IM is the seismic intensity index; d is the deterministic prediction model for the distribution range of falling buildings, which is described by the theoretical model in the "Standards and Specifications for Comprehensive Urban Disaster Prevention Planning"; γ(x,θ) is the error correction term of the prediction model for the distribution range of falling buildings after an earthquake based on Bayesian theory, where θ is the coefficient vector in the error correction term; σε is the error of the prediction model for the distribution range of falling buildings after an earthquake based on Bayesian theory, which follows a normal distribution with a mean of 0 and a standard deviation of σ; Θ=(θ,σ) represents the unknown parameters of the prediction model for the distribution range of falling buildings after an earthquake based on Bayesian theory; the error correction term of the prediction model for the distribution range of falling buildings after an earthquake based on Bayesian theory is written as:

[0012] (2)

[0013] In the formula, h i Let h1(x) represent the dimensionless explanatory function, which represents the physical quantity that may affect the random distribution of falling objects after an earthquake, and i is the i-th explanatory function. In order to capture the potential biases in the prediction model of the distribution range of falling objects after an earthquake that are independent of the variable x, let h1(x) = 1.0. The explanatory function in the error correction term is determined by the stepwise elimination method or by referring to existing literature.

[0014] Step 4, based on the Bayesian update criterion, the posterior probability density function of the unknown parameter Θ in Step 3 is expressed as:

[0015] (3)

[0016] In the formula, the proportionality coefficient k = [∫L(Θ)f(Θ)dΘ] -1 , used to ensure that the integral of f´(Θ) is 1; L(Θ) represents the likelihood function; dΘ represents the derivative with respect to the unknown parameter Θ; to reflect the objective fact of lacking prior information, the prior probability density function f(Θ) of the unknown parameter Θ is expressed as:

[0017] (4)

[0018] Step 5: Based on the posterior probability density function of the unknown model parameter Θ determined in Step 4, f´(Θ) obtains the posterior estimate samples of the unknown model parameter Θ through the MCMC sampling method; the Metropolis-Hastings algorithm is used to implement MCMC sampling, wherein the number of samples is determined by whether the samples meet the variance requirements, and the variance threshold is set at 10%~50%;

[0019] Step 6: The post-earthquake road network congestion is described by the ratio of the remaining road capacity to the pre-earthquake capacity, i.e., the congestion probability is written as:

[0020] (5)

[0021] In the formula, C post With C o These represent the road capacity before and after the earthquake, respectively; the symbol |·| represents the absolute value; λ t To define the threshold for road traffic congestion, a value of 0.45 is used; the pre-earthquake design capacity of the road network is determined based on the "Code for Design of Urban Road Engineering" (CJJ 37-2012); (IM|Θ) represents the congestion probability of IM given the unknown parameter Θ;

[0022] Therefore, the remaining traffic capacity of the urban road network after the earthquake is expressed as follows:

[0023] (6)

[0024] In the formula, C j,in To regulate the prescribed road capacity; f d This is a driver correction factor, ranging from 0.9 to 1.0. This factor is typically related to the driver's familiarity with road conditions, driving skills, and experience. c The road width reduction factor is represented by f. c =W e / W in Among them, W in W represents the pre-earthquake road width. e为 Post-earthquake building ruins will reduce the effective width of roads; N represents the number of remaining lanes on the road after the earthquake, and its calculation formula is:

[0025] (7)

[0026] In the formula, the symbol Indicates rounding down; d min The minimum width for vehicle passage is represented by 0.3; the safety margin for vehicle passage is 0.3; and the road width reduction factor is f. c Considering the impact of the length of the debris accumulation area, the post-earthquake road is divided into several sections based on the location and length of the debris accumulation area, and the reduction factor f for each section is calculated. c,k Finally, the expected value of the reduction factor is determined by weighted averaging, and its expression is as follows:

[0027] (8)

[0028] In the formula, m is the total number of segments; w k For weighting coefficients, through Wd,k / W d,max The calculation determines that, where W d,k W represents the width of the k-th segment where the falling objects accumulate. d,max The maximum width of all areas where falling objects accumulate;

[0029] Step 7: The post-earthquake road network blockage vulnerability determined in Step 6 is integrated over the domain of the unknown parameter Θ. This quantifies the impact of the uncertainty of the unknown parameters on the post-earthquake road network blockage vulnerability.

[0030] (9).

[0031] The beneficial effects of this invention are as follows: The building debris accumulation range prediction model based on Bayesian theory considers various damage states of buildings under earthquake action, including complete building collapse and damage to non-structural components. Based on Bayesian theory, the posterior probability distribution of unknown parameters of the prediction model can be obtained, thereby quantifying the cognitive uncertainty from the model parameters in post-earthquake road blockage vulnerability assessment. This invention not only helps improve the accuracy of post-earthquake road blockage risk assessment but also contributes to the rational planning of post-disaster rescue and evacuation routes. Attached Figure Description

[0032] Figure 1 This is a general concept diagram of the present invention;

[0033] Figure 2 The following are detailed floor plans and beam / column reinforcement drawings for four buildings: (a) a 6-story office building; (b) reinforcement details of the frame columns of the 6-story office building (mm); (c) reinforcement details of the frame beams of the 6-story office building (mm); (d) 8-story and 10-story residential buildings; (e) reinforcement details of the frame columns of the 8-story and 10-story residential buildings (mm); (f) reinforcement details of the frame beams of the 8-story and 10-story residential buildings (mm); (g) a 4-story retail store; (h) reinforcement details of the corner columns of the 4-story retail store (mm); (i) reinforcement details of the other frame columns of the 4-story retail store (mm); and (j) reinforcement details of the frame beams of the 4-story retail store (mm).

[0034] Figure 3 Contour map showing the maximum width of the area where debris accumulates from falling buildings;

[0035] Figure 4 Contour map showing the maximum length of the area where falling objects accumulate;

[0036] Figure 5 A map showing the distribution of the city's road network and buildings along the street;

[0037] Figure 6 The vulnerability of urban road networks to blockage after an earthquake. Detailed Implementation

[0038] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0039] This invention proposes a model for estimating the distribution range of post-earthquake building ruins based on Bayesian theory and a method for estimating the congestion vulnerability of urban road networks. A specific implementation example of the method includes the following steps:

[0040] Step 1: This invention selects 22 far-field, 14 near-field pulseless, and 14 near-field pulsed ground motions from the ACT-63 strong ground motion database, each of which includes two horizontal components. Furthermore, Iunio Iervolino, Eugenio Chioccarelli, and Georgios Baltzopoulos, in their paper "Inelastic displacement ratio of near-source pulse-like ground motions," suggest a ratio of 0.7 to 1.0 between the structure's natural period and the pulse period, which was used to select 3 acceleration time history curves from the 14 near-field pulsed ground motions. In addition, based on the target response spectrum curves provided by my country's seismic design code, 10 acceleration time history curves with a PGA less than 0.2g were supplemented from the Pacific Earthquake Engineering Center (PAC). Therefore, a total of 85 acceleration time history curves are used for the nonlinear dynamic time history analysis in the following steps. Detailed acceleration time history data is summarized in Table 1.

[0041] Table 1. Detailed information on acceleration time history data

[0042]

[0043] Step 2: Based on the physics engine technology BCB (Bullet Constraints Builder), nonlinear dynamic time history calculations were performed on the Blender platform for a 6-story reinforced concrete frame office building, an 8-story and a 10-story reinforced concrete frame residential building, and a 4-story reinforced concrete frame retail building, respectively. Figure 2 As shown. Furthermore, 340 images of falling objects were obtained, and an envelope map of the object distribution area was drawn using CAD software. The maximum width and maximum length values ​​of the envelope map were further determined.

[0044] Step 3, based on the falling object distribution data determined in Step 2, firstly, a prediction model for the maximum width of the post-earthquake falling object accumulation area based on Bayesian theory is given, namely...

[0045] (10)

[0046] In the formula, W debris(x, Θ) represents the maximum width of the debris accumulation area; W is the building width; H is the building height; PGA is the peak ground acceleration; α is the inclination angle of the debris accumulation area, taken as 30°. 。 k is a constant 0.5; h i The explanatory function is defined with h1=1.0 and h2= h3 represents the opening ratio of the infill wall, and h4 represents the building's function. The building's function can be described using a label coding system, with labels 0.5, 0.3, and 0.7 representing office building, residential building, and retail mall, respectively. Additionally, W... lane The width of the road lane is set to 3.5 meters, which is used to implement the infinitesimal hardening of the interpretation function h2.

[0047] Based on the Bayesian update criterion, the posterior PDF, f´(Θ), of the unknown parameters of the model is determined, and then the posterior estimate sample of parameter Θ is obtained by the MCMC sampling method. The statistical results are summarized in Table 2.

[0048] Table 2. Posterior statistics of unknown parameters in the prediction model for the maximum width of the debris accumulation area.

[0049]

[0050] This invention takes a residential building with a width of 15 meters, a height of 20 meters, and an opening ratio of 0.4 as an example, and determines the contour lines of the maximum width distribution of the predicted falling object accumulation area on its front side, such as... Figure 3 As shown.

[0051] Secondly, a prediction model for the maximum length of post-earthquake debris accumulation areas based on Bayesian theory is presented, namely...

[0052] (11)

[0053] In the formula, L debris (x, Θ) represents the maximum length of the area where the falling objects accumulate; L is the building length; l d For the determination term of the prediction model, the side length of the building plan in the direction of the falling object is taken; h i To interpret the function, we take h1=1.0 and h2= / W lane h3 represents the opening ratio of the infill wall, and h4 represents the building's function.

[0054] Here, taking only the length of the maximum falling object accumulation area on the right as an example, the posterior statistics of the prediction model parameters are summarized in Table 3.

[0055] Table 3. Posterior statistics of unknown parameters in the prediction model for the maximum length of the debris accumulation area.

[0056]

[0057] Similarly, taking an office building 15 meters wide and 15 meters long with an opening ratio of 0.3 as an example, the contour lines of the predicted maximum length distribution of the falling object accumulation area on its front side are shown, such as... Figure 4 As shown.

[0058] Step 4, this invention takes a real road network as an example, such as... Figure 5 As shown, this paper illustrates the congestion vulnerability of urban road networks after an earthquake, considering the obstruction effect of building debris. This invention assumes that rescue vehicles have the highest traffic priority after an earthquake and calculates the congestion probability of road segments 7→8, 8→11, 7→10, 10→11, 17→18, and 18→11. The calculation results are plotted on [the graph]. Figure 6 Taking the path from node 7 to node 11 as an example, its blocking probability can be calculated and determined by the following formula.

[0059] (12)

[0060] In the formula, N r p represents the total number of roads in the road network. i This represents the congestion probability of the i-th road in the road network.

[0061] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions and implementation processes of the present invention, and are not intended to limit them. Those skilled in the art should understand that modifications can be made to the technical solutions described in the embodiments, or equivalent substitutions can be made to some of the technical features, but these modifications or substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A probabilistic prediction model for the distribution range of post-earthquake building ruins and a method for estimating the congestion vulnerability of urban road networks, characterized in that, The steps are as follows: Step 1: Select target ground motion records. Based on the target response spectrum curve provided in the "Code for Seismic Design of Buildings", download the target ground motion records from the Pacific Earthquake Engineering Center of the United States or obtain the target ground motion records from the ground motion database recommended by the code and research report. Then, based on the relationship between the pulse period of the near-field pulse ground motion and the natural period of the structure, filter the pulse-type ground motion records from the target ground motion records. Step 2: Based on the discrete element method, perform nonlinear dynamic time history calculations on the building structure under seismic loading to obtain the distribution data of falling objects after the earthquake; wherein, the ground motion used for the nonlinear dynamic time history calculation is obtained from Step 1, or the falling object distribution data is obtained from post-earthquake satellite image data; Step 3: Based on the distribution data of fallen building objects determined in Step 2, propose a prediction model for the distribution range of fallen building objects after the earthquake based on Bayesian theory. The prediction model for the distribution range of falling objects from buildings after an earthquake, based on Bayesian theory, is as follows: (1) In the formula, E (x,Θ) is a prediction model for the distribution range of falling objects from buildings after an earthquake, based on Bayesian theory. IM It is an index of seismic intensity; d A deterministic model for predicting the distribution range of falling objects from buildings, described by the theoretical model in the "Standards and Specifications for Comprehensive Urban Disaster Prevention Planning"; γ (x,θ) is the error correction term of the prediction model for the distribution range of falling objects from buildings after an earthquake based on Bayesian theory, where θ is the coefficient vector in the error correction term; σε The error of the prediction model for the distribution range of falling objects from buildings after an earthquake, based on Bayesian theory, follows a mean of 0 and a standard deviation of . σ The normal distribution; Θ=(θ, σ ) represents the unknown parameters of the prediction model for the distribution range of falling objects from buildings after an earthquake based on Bayesian theory; Step 4, based on the Bayesian update criterion, the posterior probability density function of the unknown parameter Θ in Step 3 is expressed as: (3) In the formula, the proportionality coefficient k =[∫ L (Θ) f (Θ)dΘ] -1 , used to ensure f The integral of ´(Θ) is 1; L (Θ) denotes the likelihood function; dΘ denotes the differential with respect to the unknown parameter Θ; to reflect the objective fact of lacking prior information, the prior probability density function of the unknown parameter Θ is... f (Θ) is represented as: (4) Step 5: Based on the posterior probability density function of the unknown model parameter Θ determined in Step 4, f ´(Θ) obtains the posterior estimate of the unknown parameter Θ of the model through the MCMC sampling method; the Metropolis-Hastings algorithm is used to implement MCMC sampling, wherein the number of samples is determined by whether the samples meet the variance requirements, and the variance threshold is set at 10%~50%; Step 6: The post-earthquake road network congestion is described by the ratio of the remaining road capacity to the pre-earthquake capacity, i.e., the congestion probability is written as: (5) In the formula, C post and C o These represent the road capacity before and after the earthquake, respectively; the symbol |·| represents the absolute value; λ t To define the threshold for road traffic congestion, a value of 0.45 was used; the pre-earthquake design capacity of the road network was determined based on the "Code for Design of Urban Road Engineering"; IM| Θ) represents the blocking probability of IM given an unknown parameter Θ; Therefore, the remaining traffic capacity of the urban road network after the earthquake is expressed as follows: (6) In the formula, C j,in To regulate the prescribed road capacity; f d This is a driver correction factor, with a value ranging from 0.9 to 1.0; f c The road width reduction factor is expressed as: f c = W e / W in ,in, W in This refers to the road width before the earthquake. W e The ruins of buildings after an earthquake will reduce the effective width of roads; N The formula for calculating the number of remaining lanes on a road after an earthquake is as follows: (7) In the formula, the symbol ⌊·⌋ indicates rounding down; d min This represents the minimum width for vehicle passage; 0.3 is the safety redundancy for vehicle passage; and the road width reduction factor. f c Considering the impact of the length of the debris accumulation area, the post-earthquake road is divided into several sections based on the location and length of the debris accumulation area, and the reduction factor for each section is calculated. f c,k Finally, the expected value of the reduction factor is determined by weighted averaging, and its expression is as follows: (8) In the formula, m The total number of segments; w k For weighting coefficients, through W d,k / W d,max The calculation determines that, W d,k Indicates the first k The width of each section where falling objects accumulate. W d,max The maximum width of all areas where falling objects accumulate; Step 7: The post-earthquake road network blockage vulnerability determined in Step 6 is integrated over the domain of the unknown parameter Θ. This quantifies the impact of the uncertainty of the unknown parameter on the post-earthquake road network blockage vulnerability. (9)。 2. The probabilistic prediction model for the distribution range of post-earthquake building ruins and the method for estimating the congestion vulnerability of urban road networks according to claim 1, characterized in that, The error correction term for the prediction model of the distribution range of falling building debris after an earthquake based on Bayesian theory is written as follows: (2) In the formula, h i This represents a dimensionless interpretation function, which indicates a physical quantity that may affect the random distribution of falling debris after an earthquake. i For the first i An explanatory function; to capture potential biases independent of variable x in the Bayesian theory-based prediction model for the distribution range of falling buildings after an earthquake, let h 1(x) = 1.0; The explanatory function in the error correction term is determined by the stepwise elimination method or by referring to existing literature.

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