Method for determining rainfall and earthquake combination coefficient based on Couple function and risk consistency principle

Abstract

The invention discloses a method for determining rainfall and earthquake combination coefficients based on a Couple function and a risk consistency principle. The method comprises the following steps: S1, preferably selecting rainfall-earthquake joint probability distribution; s2, station yard roadbed response analysis under the rainfall-earthquake action; s3, determining the vulnerability of the station yard roadbed under the rainfall-earthquake action; s4, determining the failure risk of the station yard roadbed under the rainfall-earthquake action; and S5, determining rainfall and earthquake combination coefficients based on a risk consistency principle. According to the method, the problem of how to consider rainfall and earthquake actions simultaneously in railway yard roadbed anti-seismic checking calculation is solved, rainfall events and earthquake events can be considered simultaneously, rainfall parameters and earthquake parameters are combined by utilizing the Copula theory, the rainfall and earthquake actions can be considered simultaneously in railway yard roadbed anti-seismic checking calculation, and the calculation accuracy of the railway yard roadbed anti-seismic checking calculation is improved. The method can be used for guiding and carrying out railway yard roadbed design checking calculation under the rainfall-earthquake action so as to improve the efficiency and accuracy of yard roadbed analysis.

Description

Technical Field

[0001] The present invention belongs to the technical field of station roadbed engineering in the transportation industry, and relates to a method for determining a rainfall and earthquake combination coefficient, and specifically relates to a method for determining a rainfall and earthquake combination coefficient based on a Couple function and a risk consistency principle. Background Art

[0002] my country's railway infrastructure construction has entered a new round of peak. Many major projects such as railway station subgrades are subjected to various natural environmental loads during use, such as earthquakes, rainfall and other violent internal and external dynamic effects. At present, the seismic verification of railway station subgrades in my country mainly refers to the "Railway Engineering Seismic Design Code" GB 50111-2006 (2009 edition) and other relevant specifications, and the earthquake is applied in an equivalent static manner without considering the rainfall-earthquake coupling effect. In fact, this rainfall-earthquake coupling effect will not only change the dynamic characteristics of the railway station subgrade, but also impose additional loads on the station subgrade, which will have a certain impact on the dynamic response of the station subgrade. It can be seen that how to consider the effects of rainfall and earthquakes at the same time in the seismic verification is particularly urgent. Summary of the invention

[0003] In order to solve the design verification problem of railway station subgrade under the coupled working conditions of rainfall and earthquake, the present invention provides a method for determining the combined coefficient of rainfall and earthquake based on the Couple function and the risk consistency principle. The method is practical and can be used to guide the design verification of railway station subgrade under the action of rainfall and earthquake, so as to improve the efficiency and accuracy of station subgrade analysis.

[0004] The objective of the present invention is achieved through the following technical solutions:

[0005] A method for determining a rainfall and earthquake combination coefficient based on a Couple function and a risk consistency principle comprises the following steps:

[0006] Step S1, optimizing rainfall-earthquake joint probability distribution:

[0007] Based on the AIC criterion, the probability model of rainfall and earthquake edge distribution is optimized, and on this basis, the Copula function is optimized to form the joint probability distribution model and joint probability density function of rainfall parameters and earthquake parameters;

[0008] Step S2: Analysis of station subgrade response under rainfall-earthquake action:

[0009] Obtain soil-water characteristic curves, saturation-related strength parameters, and saturation-related dynamic parameters, and use finite difference element methods to obtain the station subgrade response under different rainfall and earthquake effects, providing basic data for the establishment of station subgrade vulnerability;

[0010] Step S3: Determine the vulnerability of the station roadbed under rainfall-earthquake action:

[0011] Determine the relationship between action intensity and station subgrade response, the limit state corresponding to the deterministic demand level, and establish a station subgrade vulnerability model under rainfall-earthquake action based on Bayesian updating;

[0012] Step S4: Determine the failure risk of the station roadbed under the action of rainfall and earthquake:

[0013] Based on the optimal joint probability density function in step 1 and the station roadbed vulnerability model in step 3, a convolution calculation of the rainfall-earthquake joint probability distribution and the station roadbed vulnerability under rainfall-earthquake action is carried out to determine the failure risk of the station roadbed under rainfall-earthquake action;

[0014] Step S5: Determine the rainfall and earthquake combination coefficient based on the risk consistency principle

[0015] Based on the failure risk of the station roadbed in step 4, determine the reliability index of the station roadbed and the rainfall intensity corresponding to the cumulative earthquake risk probability equal to the cumulative joint risk probability, and finally determine the rainfall and earthquake combination coefficient based on the standard combination expression of the action effect.

[0016] Compared with the prior art, the present invention has the following advantages:

[0017] The present invention solves the problem of how to simultaneously consider rainfall and earthquake effects in the seismic verification of railway station roadbed. The method can simultaneously consider rainfall events and earthquake events, and combines rainfall parameters and earthquake parameters by using Copula theory, so as to realize simultaneous consideration of rainfall and earthquake effects in the seismic verification of railway station roadbed. The method can be used to guide the design verification of railway station roadbed under rainfall-earthquake effects, so as to improve the efficiency and accuracy of station roadbed analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a flow chart of the method for determining the combined coefficient of rainfall and earthquake based on the Couple function and the risk consistency principle;

[0019] Figure 2 It is the result diagram of the optimal result of the rainfall-earthquake joint probability distribution;

[0020] Figure 3 It is the analysis result of the station roadbed response under the action of rainfall and earthquake;

[0021] Figure 4 It is the vulnerability model of station roadbed under rainfall-earthquake action;

[0022] Figure 5 is the risk of station roadbed failure under rainfall-earthquake action;

[0023] Figure 6 is the failure probability diagram under a certain IM, and the combination coefficient is 0.415. DETAILED DESCRIPTION

[0024] The technical solution of the present invention is further described below in conjunction with the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be included in the protection scope of the present invention.

[0025] The present invention provides a method for determining the rainfall and earthquake combination coefficient based on the Couple function and the risk consistency principle, such as Figure 1 As shown, the method comprises the following steps:

[0026] Step S1, optimizing rainfall-earthquake joint probability distribution:

[0027] The rainfall and earthquake marginal distribution probability models are optimized based on the AIC criterion, and on this basis, the Copula function is optimized to form the joint probability distribution model and joint probability density function of rainfall parameters and earthquake parameters.

[0028] The specific steps are as follows:

[0029] Step S1-1: Based on the study area, rainfall and earthquake records are selected from the meteorological database and the seismic database to form a rainfall-earthquake database.

[0030] In this step, rainfall and earthquake records are taken from meteorological databases and seismic databases of authoritative institutions at home and abroad.

[0031] Step S1-2: Based on the AIC criterion, the probability distribution model that best matches the rainfall parameters and the earthquake parameters is selected, and the optimal marginal distribution probability model of the rainfall parameters and the earthquake parameters is established.

[0032] Step S1-3: Generate empirical distribution data based on the optimal marginal distribution probability model of step S1-2, and select the Copula function that best matches the empirical distribution function based on the AIC criterion.

[0033] Step S1-4: Based on the optimal marginal distribution model of step S1-2 and the optimal Copula function of step S1-3, according to Copula theory, an optimal joint distribution probability model of rainfall parameters and earthquake parameters is established, and the Copula joint probability density function is obtained.

[0034] In this step, the Copula joint probability density function is as follows:

[0035] f R-E (RI,IM)=c(RI,IM)·f(RI)·f(IM)

[0036] Where c(RI,IM) is the probability density distribution function of the optimal Copula function, RI is the rainfall intensity, IM is the earthquake intensity, f(RI) and f(IM) are the optimal marginal probability density distribution functions of rainfall and earthquake, respectively.

[0037] Step S2: Analysis of station subgrade response under rainfall-earthquake action:

[0038] Obtain soil-water characteristic curves, saturation-related strength parameters, and saturation-related dynamic parameters, and use finite difference element methods to obtain the station field subgrade response under different rainfall and earthquake effects, providing basic data for the establishment of station field subgrade vulnerability. The specific steps are as follows:

[0039] Step S2-1, determine the soil-water characteristic curve of the geotechnical material used based on the filter paper method, soil-water characteristic curve instrument, etc., for calibrating the relationship between saturation and permeability coefficient; determine the saturation-related strength parameters and saturation-related dynamic parameters of the geotechnical material used based on static triaxial tests and dynamic triaxial tests.

[0040] In this step, the soil-water characteristic curve, strength parameters, and dynamic parameters can be determined by experiments or based on reliable literature.

[0041] Step S2-2: Based on the soil-water characteristic curve of the geotechnical material obtained in step S2-1, a rainfall infiltration boundary processing function and a real-time update function of the unsaturated zone permeability coefficient are established to simulate the saturated and unsaturated permeability process of the railway station subgrade under rainfall conditions.

[0042] Step S2-3, based on the saturation-related strength parameters and dynamic saturation-related mechanical parameters of the geotechnical materials obtained in step S2-1, establish a real-time update function of shear modulus, bulk modulus, cohesion, and friction angle coefficient to simulate the dynamic response process of the railway station subgrade under the action of earthquake under different rainfall conditions.

[0043] Step S2-4: input different rainfall effects and different earthquake effects to obtain the response of the railway station subgrade.

[0044] In this step, the distribution of different rainfall effects and different earthquake effects is coordinated with the optimal joint distribution model of rainfall parameters and earthquake parameters determined in step S1.

[0045] Step S3: Determine the vulnerability of the station roadbed under rainfall-earthquake action:

[0046] Determine the relationship between the action intensity and the station roadbed response, the limit state corresponding to the deterministic demand level, and establish the station roadbed vulnerability model under rainfall-earthquake action based on Bayesian updating. The specific steps are as follows:

[0047] Step S3-1: Based on the response of the railway station roadbed in step S2-4, the Bayesian update method is used to determine the relationship between the rainfall intensity, the earthquake intensity and the station roadbed response.

[0048] In this step, the relationship between rainfall intensity, earthquake intensity and station subgrade response, that is, the probability demand model, can be expressed in logarithmic space as:

[0049] ln(EDP)=θ0+θ RI ln(RI)+θ IM ln(IM)+σε

[0050] Where EDP is the demand parameter, θ=(θ0,θ IM ,θ RI ) are unknown parameters of the model, σ and ε are model errors, and the Bayesian update method can be used to estimate the model parameters:

[0051] g(Θ)=κL(Θ)p(Θ)

[0052] Where g(Θ) is the posterior distribution of the model parameter Θ; κ is the standardized model parameter; L(Θ) is the maximum likelihood function; and p(Θ) is the prior distribution of the model parameter Θ. L(Θ) can be constructed in the following form:

[0053]

[0054] Where k[·] is the marginal probability density function of the parameter; hi l (Θ) is the actual calculated value of the railway station subgrade response; M is the size of the actual calculated response data set.

[0055] Step S3-2: Based on the test data and measured data, determine the limit state corresponding to the deterministic capacity level of the railway station subgrade.

[0056] In this step, in the absence of test data and measured data, the limit state corresponding to the deterministic capacity level can use permanent displacement as a parameter and take values ​​of 0.05, 0.1, and 0.15.

[0057] Step S3-3: Establish a vulnerability model based on the results of steps S3-1 and S3-2.

[0058] In this step, the vulnerability model takes the following form:

[0059] F R (RI,IM,Θ)=P(C≤D(RI,IM,Θ)|RI,IM,Θ)

[0060] Where C is the deterministic capacity level, and D(RI,IM,Θ) is the above-mentioned probabilistic demand model. At the same time, in order to consider the uncertainty of rainfall and earthquake effects, the vulnerability model is calculated as follows:

[0061]

[0062] Step S4: Determine the failure risk of the station roadbed under the action of rainfall and earthquake:

[0063] Based on the optimal joint probability density function in step 1 and the station roadbed vulnerability model in step 3, the convolution calculation of the rainfall-earthquake joint probability distribution and the station roadbed vulnerability under rainfall-earthquake action is carried out to determine the failure risk of the station roadbed under rainfall-earthquake action.

[0064] In this step, the station roadbed failure risk R f Take the following form:

[0065]

[0066] Step S5: Determine the rainfall and earthquake combination coefficient based on the risk consistency principle

[0067] Based on the failure risk of the station roadbed in step 4, determine the reliability index of the station roadbed and the rainfall intensity corresponding to the cumulative earthquake risk probability equal to the cumulative joint risk probability, and finally determine the rainfall and earthquake combination coefficient based on the standard combination expression of the action effect. The specific steps are as follows:

[0068] Step S5-1: Based on the failure risk of the station roadbed in step S4, the failure probability and reliability index of the station roadbed are calculated.

[0069] In this step, the failure probability and reliability index of the station roadbed are calculated as follows:

[0070] R f =Φ(-β)

[0071] In the formula, R f is the failure risk of the station roadbed, and β is the reliability index.

[0072] Step S5-2: Determine the corresponding rainfall intensity based on the cumulative earthquake risk probability that is equal to the cumulative joint risk probability.

[0073] Step S5-3: Establish a standard combination expression of effects based on the risk consistency principle and determine the rainfall and earthquake combination coefficients.

[0074] In this step, the rainfall and earthquake combination coefficient is calculated as follows:

[0075]

[0076] Where, IMr is the cumulative earthquake risk probability equal to the cumulative joint risk probability, and γ is the combination coefficient.

[0077] The optimal results of rainfall-earthquake joint probability distribution are as follows: Figure 2 The analysis results of the station subgrade response under rainfall-earthquake action are shown in Figure 3 The vulnerability model of the station subgrade under rainfall-earthquake action is shown in Figure 4 As shown in the figure; the risk of station subgrade failure under rainfall-earthquake action is as follows Figure 5 As shown; the failure probability under a certain IM is Figure 6 shown.

Claims

1. A method for determining the combined coefficient of rainfall and earthquake based on the Couple function and the risk consistency principle, characterized in that The method comprises the following steps: Step S1, optimizing rainfall-earthquake joint probability distribution: Based on the AIC criterion, the probability model of rainfall and earthquake edge distribution is optimized, and on this basis, the Copula function is optimized to form the joint probability distribution model and joint probability density function of rainfall parameters and earthquake parameters; Step S2: Analysis of station subgrade response under rainfall-earthquake action: Obtain soil-water characteristic curves, saturation-related strength parameters, and saturation-related dynamic parameters, and use finite difference element methods to obtain the station subgrade response under different rainfall and earthquake effects, providing basic data for the establishment of station subgrade vulnerability; Step S3: Determine the vulnerability of the station roadbed under rainfall-earthquake action: Determine the relationship between action intensity and station subgrade response, the limit state corresponding to the deterministic demand level, and establish a station subgrade vulnerability model under rainfall-earthquake action based on Bayesian updating; Step S4: Determine the failure risk of the station roadbed under the action of rainfall and earthquake: Based on the optimal joint probability density function in step 1 and the station roadbed vulnerability model in step 3, a convolution calculation of the rainfall-earthquake joint probability distribution and the station roadbed vulnerability under rainfall-earthquake action is carried out to determine the failure risk of the station roadbed under rainfall-earthquake action; Step S5: Determine the rainfall and earthquake combination coefficient based on the risk consistency principle Based on the failure risk of the station roadbed in step 4, determine the reliability index of the station roadbed and the rainfall intensity corresponding to the cumulative earthquake risk probability equal to the cumulative joint risk probability, and finally determine the rainfall and earthquake combination coefficient based on the standard combination expression of the action effect.

2. The method for determining the combined coefficient of rainfall and earthquake based on the Couple function and the risk consistency principle according to claim 1, characterized in that The specific steps of step S1 are as follows: Step S1-1, based on the study area, select rainfall and earthquake records from the meteorological database and the seismic database to form a rainfall-earthquake database; Step S1-2, selecting the probability distribution model that best matches the rainfall parameters and the earthquake parameters based on the AIC criterion, and establishing the optimal marginal distribution probability model of the rainfall parameters and the earthquake parameters; Step S1-3, based on the optimal marginal distribution probability model of step S1-2, generate empirical distribution data, and based on the AIC criterion, select the Copula function that best matches the empirical distribution function; Step S1-4: Based on the optimal marginal distribution model of step S1-2 and the optimal Copula function of step S1-3, according to Copula theory, an optimal joint distribution probability model of rainfall parameters and earthquake parameters is established, and the Copula joint probability density function is obtained.

3. The method for determining the rainfall and earthquake combination coefficient based on the Couple function and the risk consistency principle according to claim 2, characterized in that The Copula joint probability density function is shown as follows: f R-E (RI,IM)=c(RI,IM)·f(RI)·f(IM) Where c(RI,IM) is the probability density distribution function of the optimal Copula function, RI is the rainfall intensity, IM is the earthquake intensity, f(RI) and f(IM) are the optimal marginal probability density distribution functions of rainfall and earthquake, respectively.

4. The method for determining the rainfall and earthquake combination coefficient based on the Couple function and the risk consistency principle according to claim 1, characterized in that The specific steps of step S2 are as follows: Step S2-1, determining the soil-water characteristic curve of the geotechnical material used, which is used to calibrate the relationship between saturation and permeability coefficient; determining the saturation-related strength parameters and saturation-related dynamic parameters of the geotechnical material used; Step S2-2: Based on the soil-water characteristic curve of the geotechnical material obtained in step S2-1, a rainfall infiltration boundary processing function and a real-time update function of the unsaturated zone permeability coefficient are established to simulate the saturated and unsaturated permeability process of the railway station subgrade under rainfall conditions; Step S2-3, based on the saturation-related strength parameters and dynamic saturation-related mechanical parameters of the geotechnical materials obtained in step S2-1, a real-time update function of shear modulus, bulk modulus, cohesion, and friction angle coefficient is established to simulate the dynamic response process of the railway station subgrade under the action of earthquake under different rainfall conditions; Step S2-4: input different rainfall effects and different earthquake effects to obtain the response of the railway station subgrade.

5. The method for determining the combined coefficient of rainfall and earthquake based on the Couple function and the risk consistency principle according to claim 1, characterized in that The specific steps of step S3 are as follows: Step S3-1, based on the response of the railway station roadbed, using the Bayesian update method to determine the relationship between the rainfall intensity, the earthquake intensity and the station roadbed response; Step S3-2, based on the test data and measured data, determining the limit state corresponding to the deterministic capacity level of the railway station subgrade; Step S3-3: Establish a vulnerability model based on the results of steps S3-1 and S3-2.

6. The method for determining the rainfall and earthquake combination coefficient based on the Couple function and the risk consistency principle according to claim 5, characterized in that In step S3-1, the relationship between rainfall intensity, earthquake intensity and station roadbed response, i.e., the probability demand model, is expressed in logarithmic space as: ln(EDP)=θ0+θ RI ln(RI)+θ IM ln(IM)+in Where EDP is the demand parameter, θ=(θ0,θ IM ,θ RI ) are unknown model parameters, σ and ε are model errors, and the Bayesian update method is used to estimate the model parameters: g(Θ)=κL(Θ)p(Θ) Where g(Θ) is the posterior distribution of the model parameter Θ; κ is the standardized model parameter; L(Θ) is the maximum likelihood function; p(Θ) is the prior distribution of the model parameter Θ; The L(Θ) is constructed in the following form: Where k[·] is the marginal probability density function of the parameter; hi l (Θ) is the actual calculated value of the railway station subgrade response; M is the size of the actual calculated response data set.

7. The method for determining the rainfall and earthquake combination coefficient based on the Couple function and the risk consistency principle according to claim 5, characterized in that In step S3-3, the vulnerability model is in the following form: F R (RI,IM,Θ)=P(C≤D(RI,IM,Θ)|RI,IM,Θ) Where C is the deterministic capacity level, and D(RI,IM,Θ) is the probabilistic demand model. At the same time, in order to consider the uncertainty of rainfall and earthquake effects, the vulnerability model is calculated as follows:

8. The method for determining the combined coefficient of rainfall and earthquake based on the Couple function and the risk consistency principle according to claim 1, characterized in that In step S4, the station roadbed failure risk R f Take the following form:

9. The method for determining the combined coefficient of rainfall and earthquake based on the Couple function and the risk consistency principle according to claim 1, characterized in that The specific steps of step S5 are as follows: Step S5-1, based on the station field roadbed failure risk in step S4, calculating the station field roadbed failure probability and reliability index; Step S5-2, determining a corresponding rainfall intensity based on a cumulative earthquake risk probability that is equal to the cumulative joint risk probability; Step S5-3: Establish a standard combination expression of effects based on the risk consistency principle and determine the rainfall and earthquake combination coefficients.

10. The method for determining the rainfall and earthquake combination coefficient based on the Couple function and the risk consistency principle according to claim 9, characterized in that In step S5-1, the failure probability and reliability index of the station roadbed are calculated as follows: R f =Φ(-β) In the formula, R f is the failure risk of station roadbed, and β is the reliability index. In step S5-3, the rainfall and earthquake combination coefficient is calculated as follows: Where, IM r is the cumulative earthquake risk probability equal to the cumulative joint risk probability, and γ is the combination coefficient.

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