A vertical earthquake action evaluation method based on random effect method

Abstract

The present application belongs to the vertical earthquake evaluation technical field, disclose a kind of vertical earthquake action evaluation method based on random effect method, including S1, the ground motion record dataset of southwest region is established;S2, determine as basic input seismic parameter;S3, determine the model equation capable of fully reflecting the V / H spectrum value variation law of target area;S4, the model equation in S3 is carried out multiple nonlinear regression fitting using random effect method;S5, according to the vibration data set established in S1 as training set, combined with the mixed effect expression fitting in S4 coefficient in S3, i.e. the V / H spectrum value model of southwest region is obtained;The present application takes magnitude, fault type, site condition, distance, focal depth as variable, and adopts random effect method to propose V / H spectrum value model suitable for southwest region, to reasonably evaluate the vertical earthquake action of the region.

Description

Technical Field

[0001] This invention relates to the field of vertical seismic assessment technology, specifically to a method for assessing vertical seismic action based on the random effects method. Background Technology

[0002] Currently, seismic response analysis of engineering structures primarily focuses on horizontal seismic forces, generally neglecting vertical seismic forces. It is assumed that the structure's safety factor or load factor is sufficient to withstand the combined effects of gravity and vertical seismic forces. Even when vertical seismic forces are considered, a simplified approach using 0.5 to 0.65 times the horizontal seismic force is adopted. For example, my country's "Code for Seismic Design of Buildings" (GB50011-2016) stipulates that for high-rise buildings or large-span spatial structures, the vertical seismic influence coefficient can be taken as 65% of the corresponding horizontal seismic influence coefficient. However, with the increasing availability of recorded seismic ground motion data in recent years, scholars have discovered many ground motions with very large vertical peak values, some even exceeding the horizontal peak value. Furthermore, investigations into seismic damage to buildings and bridge structures indicate that excessive vertical seismic forces can also be a significant cause of structural failure.

[0003] Currently, research on vertical seismic action mainly revolves around how to establish vertical ground motion response spectra for seismic design or assessment. There are generally two methods: the first is the direct method, which establishes a statistical analysis model based on vertical ground motion data and directly calculates the vertical response spectrum from seismic parameters (magnitude, fault distance, site conditions, fault type, etc.); the second is the indirect method, which establishes a ratio model ("V / H spectral value model") between the vertical and horizontal response spectra based on horizontal and vertical ground motion data, and then indirectly obtains the vertical seismic action by multiplying the horizontal seismic action by this ratio. Most research and design work uses the indirect method.

[0004] It is generally believed that the V / H spectral value is closely related to factors such as magnitude, distance, period, site, and focal mechanism. Studies by Jia Junfeng et al. have shown that the V / H spectral value is relatively large in near-fault areas with fault distances within 20 km, in sites with weak soil layers, in the range of medium-magnitude earthquakes and large-magnitude, long-period earthquakes on reverse faults. Zhao Peipei, Qi Juan, and others believe that the seismic designation of 0.65 times the horizontal seismic force as the vertical seismic force is unreasonable. Xu Longjun and others believe that the dual-track quasi-response spectrum can be used as a reference for predicting the vertical ground motion design spectrum. Anderson, Di Sarno, and others believe that in actual engineering, vertical and horizontal ground motions should be considered together to better reflect the actual situation. He Qiumei and others have shown that the peak ground acceleration ratio of vertical to horizontal ground motions is 0.60, but about 1 / 3 of strong ground motion records have a peak ground acceleration ratio greater than 2 / 3. Wang Yong and others have shown that the V / H spectrum value decreases with the increase of fault distance in the short period, and taking 2 / 3 of the peak ground acceleration of the vertical ground motion as the peak ground acceleration of the horizontal ground motion is unsafe.

[0005] To facilitate seismic hazard analysis, scholars have proposed V / H spectral value models based on regional ground motion data. Tan et al. established a V / H spectral value model for the nearshore area of ​​Sagami Bay, Japan, using moment magnitude, focal distance, focal depth, and tectonic source type as independent variables. Ramadan et al. proposed a V / H spectral value model for Italy, using magnitude, focal distance, focal mechanism, and site effects as variables. Jaimes et al. proposed a vertical and horizontal acceleration response spectral ratio prediction model for soft soil sites in Mexico. Based on the NGA-WEST1 database, Gulerce et al. developed a V / H spectral value model using magnitude, focal distance, fault type, and site conditions as basic parameters. Based on a database of 6989 near-fault ground motions, Bozorgnia et al. proposed a vertical and horizontal acceleration response spectral ratio prediction model using magnitude saturation, fault type, focal depth, fault rupture dip angle, geometric attenuation, regionally correlated inelastic attenuation, site effects, and hanging wall geometry as independent variables. Zolfaghari et al. proposed a V / H spectral value model for the Ireland region, using magnitude, focal distance, fault type, and site conditions as basic parameters. This model is applicable to areas with moment magnitudes of 4.5–7.4, distances less than 200 km, and reverse fault and strike-slip fault mechanisms. Bommer et al. established a V / H spectral value model based on regression analysis of European and Middle Eastern earthquake databases, using magnitude, fault type, focal distance, and site category as parameters. Jaimes et al. proposed a medium-depth V / H spectral value model for rock sites in Mexico, using moment magnitude, distance, and focal depth as variables.

[0006] As can be seen from the research background above, various scholars have proposed corresponding V / H spectral value models for different regions. However, there is no V / H spectral value model applicable to all regions. This indicates that V / H spectral values ​​have strong regional characteristics, and for different regions, a V / H spectral value model that matches the target area should be adopted.

[0007] Southwest my country is characterized by intense plate tectonics and a dense network of deep, active faults, resulting in seismic activity patterns distinct from other regions both domestically and internationally. Since the implementation of my country's new-generation digital seismic observation system, abundant strong ground motion data has been recorded, providing a solid foundation for studying the characteristics of strong ground motions in Southwest China. However, due to the strong regionality of V / H spectral characteristics, existing V / H spectral analysis conclusions may not be applicable to Southwest my country. Therefore, it is essential to study the V / H spectral variation characteristics applicable to Southwest my country and establish a predictive model for it. Summary of the Invention

[0008] This invention aims to provide a method for assessing vertical seismic action based on the random effects method. Using moment magnitude, fault type, site conditions, distance, and focal depth as variables, a V / H spectral value model applicable to the Southwest region is proposed using the random effects method to reasonably assess the vertical seismic action in this region.

[0009] To achieve the above objectives, the present invention provides the following technical solution:

[0010] A method for assessing vertical seismic action based on the random effects method includes the following steps:

[0011] S1. Establish a seismic motion record dataset for the Southwest region;

[0012] S2. Determine the seismic parameters to be used as basic inputs;

[0013] S3. Determine the model equation that can fully reflect the variation law of V / H spectral values ​​in the target area. Its expression is:

[0014]

[0015] In the formula, V is the vertical component acceleration response spectrum value of the seismic motion, H is the arithmetic mean of the horizontal two components acceleration response spectrum values ​​of the seismic motion, h is the focal depth, R is the distance parameter, and M is the focal depth. w Moment magnitude; FM values ​​are: strike-slip faults FM=1, reverse faults FM=2, normal faults FM=3, other faults FM=0; S c Site condition parameters: V s30 >700cm / s, S c =0; 375cm / s≤V s30 ≤700cm / s, Sc =1, V s30 <375cm / s, S c =2; pseudo-depth a8 is 5km; T is the period; the definitions of a0, a1, a3, a4, a5, a6, a7, a8, and a9 are respectively: model fitting parameters;

[0016] S4. The random effects method is used to fit the model equation in S3 using multiple nonlinear regression, and the model equation is expressed as a mixed effects expression as follows:

[0017] log 10 (yi j )=f(M i ,R ij ,θ)+η i +ε ij

[0018]

[0019] In the formula, η represents the inter-event residuals, mainly reflecting the influence of the source effect; ε represents the intra-event residuals, mainly reflecting the influence of path and site effects; δ represents the standard deviation of the total residuals; and τ represents the standard deviation of the inter-event residuals. The standard deviation of the residuals within the event;

[0020] S5. Using the vibration dataset established in S1 as the training set, and combining it with the mixed effect expression in S4, fit the coefficients in S3 to obtain the V / H spectral value model for the Southwest region.

[0021] Furthermore, in S1, the constraints constituting the seismic motion record dataset are:

[0022] The earthquake events occurred between 2008 and 2021; the moment magnitude of the earthquake events ranged from 4.5 to 8.0, and the focal distance was less than 350 km; the recorded ground motions all included ground motions in three directions: north-south, east-west, and vertical.

[0023] Furthermore, in S2, the basic input seismic parameters include: moment magnitude, site conditions, fault type, focal distance, and focal depth; the site conditions represent the equivalent shear wave velocity Vs30 of the soil and rock layers within a depth of 30m below the surface.

[0024] Furthermore, in S5, the earthquake motion dataset established in S1 is used as the training set to fit the coefficients in S3, including both fixed and random effects.

[0025] The model is expressed as a mixture of effects as follows:

[0026] log 10 (yi j )=f(Mi ,R ij ,θ)+η i +ε ij

[0027]

[0028] In the formula, y ij For earthquake motion prediction parameters, M i The magnitude is R. ij η is the distance, θ is the model parameter vector; unlike the fixed effects model, the error term in the mixed effects model is divided into two parts: between events and within events; i Let η be the residual between events. i f(M) represents the random effect of the i-th earthquake. i ,R ij ,θ)+ε ij This represents a fixed effect, ε ij For the in-event residual, η i With ε ij The events are independent and follow a normal distribution; δ is the total residual standard deviation, and τ is the inter-event residual standard deviation. The standard deviation of the residuals within the event;

[0029] The fitting steps for the random effects method are as follows:

[0030] A1: Estimate the fixed effects parameter θ;

[0031] A2: Given θ, estimate τ by maximizing the likelihood function as follows. 2 and

[0032]

[0033] In the formula: N is the number of ground motions, μ ij For the predicted value, y ij For the observed value, n i denoted as the number of records for the i-th earthquake.

[0034] A3: Given θ, τ 2 and Estimate the solution η of the maximum likelihood function for random effects using the following equation. i :

[0035]

[0036] A4: Given η i , for (lny) ij -τc i The new θ value is estimated using a fixed-effects regression equation, where c iThe random effects parameters calculated using the expectation-maximization algorithm are expressed as follows:

[0037] c i =E[η i / τ]

[0038] A5: Repeat steps two, three, and four until the likelihood function of step three is maximized.

[0039] The beneficial effects of the technical solution are:

[0040] The vertical seismic action assessment method based on the random effects method provided by this invention can be applied to the V / H spectral value variation characteristics in southwestern my country and establish its prediction model. Based on this V / H spectral value model, the vertical seismic action in southwestern my country can be reasonably assessed to facilitate seismic hazard analysis.

[0041] The evaluation method provided by this invention is simple to operate and has high evaluation accuracy. Attached Figure Description

[0042] Figure 1 This is a distribution diagram of the inter-event residuals as a function of moment magnitude Mw in embodiment S4 of the present invention.

[0043] Figure 2 In embodiment S4 provided by the present invention, the intra-event residual varies with the source distance R. hyp Distribution map of the changes;

[0044] Figure 3 To utilize the embodiments provided by this invention, under different magnitude raw records, the spectral ratio of the model and the comparison model in S3 varies with R. hyp A diagram showing the relationship between changes;

[0045] Among them, a, d, and g are the results under the condition of minor earthquake, b, e, and h are the results under the condition of moderate earthquake, and c, f, and i are the results under the condition of major earthquake. Detailed Implementation

[0046] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments:

[0047] A method for assessing vertical seismic action based on the random effects method includes the following steps:

[0048] S1. Establish a seismic ground motion record dataset for Southwest China; all data are provided by the National Strong Ground Motion Network Center of the Institute of Engineering Mechanics, China Earthquake Administration, and the dataset must meet the following conditions:

[0049] (1) The earthquake events in question occurred between 2008 and 2021;

[0050] (2) Earthquake event moment magnitude (Mw The distribution range is 4.5–8.0, and the focal distance (R) hyp Less than 350km;

[0051] (3) All recorded ground motions include ground motions in three directions: north-south (NS), east-west (EW), and vertical (UD);

[0052] In accordance with the above requirements, this embodiment selects 52 earthquake events with epicenters located in the southwest region, totaling 4437 ground motions; the dataset includes earthquake events such as the 2008 Wenchuan earthquake, the 2013 Lushan earthquake, the 2014 Ludian earthquake, and the 2017 Jiuzhaigou earthquake;

[0053] S2. Determine the seismic parameters to be used as basic inputs;

[0054] Studies have shown that the V / H spectral value is affected by moment magnitude (M). w Site conditions, fault type (FM), and distance have the most significant impacts. In this embodiment, M is used as an example. w Site conditions (equivalent shear wave velocity of soil and rock layers within 30m depth below the surface—Vs30), FM, R hyp The focal depth (h) serves as the basic input parameter for the V / H spectral value prediction model.

[0055] S3. Determine the model equation that can fully reflect the variation law of V / H spectral values ​​in the target area. Its expression is:

[0056]

[0057] In the formula, V is the vertical component acceleration response spectrum value of the seismic motion, H is the arithmetic mean of the horizontal two components acceleration response spectrum values ​​of the seismic motion, h is the focal depth, R is the distance parameter, and M is the focal depth. w Moment magnitude; FM values ​​are: strike-slip faults FM=1, reverse faults FM=2, normal faults FM=3, other faults FM=0; S c Site condition parameters: V s30 >700, S c =0; 375≤V s30 ≤700, S c =1, V s30 <375, S c =2; pseudo-depth a8 is 5km; T is the period; the definitions of a0, a1, a3, a4, a5, a6, a7, a8, and a9 are respectively: model fitting parameters;

[0058] S4. The random effects method is used to fit the model equation in S3 using multiple nonlinear regression, and the model equation is expressed as a mixed effects expression as follows:

[0059] log 10 (yi j )=f(M i ,R ij ,θ)+η i +ε ij

[0060]

[0061] In the formula, η represents the inter-event residuals, mainly reflecting the influence of the source effect; ε represents the intra-event residuals, mainly reflecting the influence of path and site effects; δ represents the standard deviation of the total residuals; and τ represents the standard deviation of the inter-event residuals. The standard deviation of the residuals within the event;

[0062] S5. Using the vibration dataset established in S1 as the training set, and combining the mixed effect expression in S4, fit the coefficients in S3 to obtain the V / H spectral value model for the Southwest region; the coefficients fitted in S3 include fixed effects and random effects.

[0063] The model is expressed as a mixture of effects as follows:

[0064] log 10 (yi j )=f(M i ,R ij ,θ)+η i +ε ij

[0065]

[0066] In the formula, y ij For earthquake motion prediction parameters, M i The magnitude is R. ij η is the distance, θ is the model parameter vector; unlike the fixed effects model, the error term in the mixed effects model is divided into two parts: between events and within events; i Let η be the residual between events. i f(M) represents the random effect of the i-th earthquake. i ,R ij ,θ)+ε ij This represents a fixed effect, ε ij For the in-event residual, η i With ε ij The events are independent and follow a normal distribution; δ is the total residual standard deviation, and τ is the inter-event residual standard deviation. The standard deviation of the residuals within the event;

[0067] The fitting steps for the random effects method are as follows:

[0068] A1: Estimate the fixed effects parameter θ;

[0069] A2: Given θ, estimate τ by maximizing the likelihood function as follows. 2 and

[0070]

[0071] In the formula: N is the number of ground motions, μ ij For the predicted value, y ij For the observed value, n i denoted as the number of records for the i-th earthquake.

[0072] A3: Given θ, τ 2 and Estimate the solution η of the maximum likelihood function for random effects using the following equation. i :

[0073]

[0074] A4: Given η i , for (lny) ij -τc i The new θ value is estimated using a fixed-effects regression equation, where c i The random effects parameters calculated using the expectation-maximization algorithm are expressed as follows:

[0075] c i =E[η i / τ]

[0076] A5: Repeat steps two, three, and four until the likelihood function of step three is maximized.

[0077] Figure 1 and Figure 2 As shown, different periods (T) are displayed. n At 0.2s, 1s, 3s, 10s, the inter-event residuals and intra-event residuals obtained by the model of this invention as a function of moment magnitude M w and distance from the epicenter R hyp The distribution of changes. Comparing the two figures, it can be seen that the residuals between events are much smaller than the residuals within events overall, indicating that the dispersion of V / H spectrum values ​​is affected by site factors (such as path effect, site effect, etc.) much more than by source factors.

[0078] from Figure 1 It can be seen that the trend line of the residuals between earthquake events is basically horizontal, and the mean of the residuals (± one standard deviation) is close to 0; the mean of the residuals at the large earthquakes is slightly off the horizontal line to zero at the small earthquakes, which is related to the small number of earthquake events.

[0079] from Figure 2As can be seen, the trend line of the residuals within the earthquake event remains basically horizontal, and the mean (± one standard deviation) is close to 0, indicating that the predicted values ​​of the model used in this invention do not have significant deviations.

[0080] like Figure 3 As shown, to verify the effectiveness of the model's prediction results, the prediction results of this invention and those of two existing models (GULF-2017 model and INDIA-2022 model) were compared under different magnitudes and periods (Tn = 0.2, 0.5, 1, 1.5, 2, 3, 4, 5, 10 s) to verify the effectiveness of the model's prediction results. As shown in the figure, in Figure 3 Under the conditions of minor earthquakes in the ADG plot, major earthquakes in the BETH plot, and major earthquakes in the CFI plot, the original earthquake records did not show any particular trend. The relatively dispersed original data points are distributed fairly evenly on both sides of the predicted curve of the model in this paper, indicating that the evaluation model provided by this invention is closer to the original data than the GULF-2017 and INDIA-2022 models. It should be noted that the fact that all three models can simulate the V / H spectral value variation patterns of their respective regions well further demonstrates that V / H spectral values ​​have strong regional characteristics.

[0081] The above descriptions are merely embodiments of the present invention, and common knowledge regarding specific technical solutions or characteristics is not elaborated upon here. It should be noted that those skilled in the art can make various modifications and improvements without departing from the technical solutions of the present invention, and these should also be considered within the scope of protection of the present invention. These modifications and improvements will not affect the effectiveness of the implementation of the present invention or the practicality of the patent. The scope of protection claimed in this application should be determined by the content of its claims, and the specific embodiments described in the specification can be used to interpret the content of the claims.

Claims

1. A method for assessing vertical seismic action based on the random effects method, characterized in that, Includes the following steps: S1. Establish a seismic motion record dataset for the Southwest region; S2. Determine the seismic parameters to be used as basic inputs; S3. Determine the model equation that can fully reflect the variation law of V / H spectral values ​​in the target area. Its expression is: In the formula, V is the vertical component of the ground motion acceleration response spectrum, H is the arithmetic mean of the horizontal two components of the ground motion acceleration response spectrum, and h is the focal depth. M is the distance parameter. w Moment magnitude; FM values ​​are: strike-slip faults FM=1, reverse faults FM=2, normal faults FM=3, other faults FM=0; S c Site condition parameters: V s30 >700cm / s, S c =0;375 cm / s≤V s30 ≤700 cm / s, S c =1, V s30 <375 cm / s, S c =2; pseudo-depth The value is 5km; T is the period; and a0, a1, a3, a4, a5, a6, a7, a8, and a9 are defined as model fitting parameters, respectively. S4. The random effects method is used to fit the model equation in S3 using multiple nonlinear regression, and the model equation is expressed as a mixed effects expression as follows: In the formula, The residuals between events mainly reflect the influence of the source effect; These are the residuals within the event, primarily reflecting the effects of path and site. The standard deviation of the total residuals. The standard deviation of the residuals between events. The standard deviation of the residuals within the event; S5. Using the vibration dataset established in S1 as the training set, and combining it with the mixed effect expression in S4, fit the coefficients in S3 to obtain the V / H spectral value model for the Southwest region.

2. The method for assessing vertical seismic action based on the random effects method according to claim 1, characterized in that: In S1, the constraints constituting the seismic motion record dataset are: The earthquake events occurred between 2008 and 2021; the moment magnitude of the earthquake events ranged from 4.5 to 8.0, and the focal distance was less than 350 km; the recorded ground motions all included ground motions in three directions: north-south, east-west, and vertical.

3. The method for assessing vertical seismic action based on the random effects method according to claim 1, characterized in that: In S2, the basic input seismic parameters include: moment magnitude, site conditions, fault type, focal distance, and focal depth; the site conditions represent the equivalent shear wave velocity V of the soil and rock layers within a depth of 30m below the surface. s30 .

4. The method for assessing vertical seismic action based on the random effects method according to claim 1, characterized in that: In S5, the earthquake motion dataset established in S1 is used as the training set, and the coefficients in S3 are fitted, including fixed effects and random effects. The model is expressed as a mixture of effects as follows: In the formula, For earthquake motion prediction parameters, The magnitude is [missing information]. For distance, This is the model parameter vector; unlike the fixed effects model, the error term in the mixed effects model is divided into two parts: between events and within events. For the residuals between events, This represents the random effect of the i-th earthquake. This represents a fixed effect. For the residual within the event, They are independent and follow a normal distribution; The standard deviation of the total residuals. The standard deviation of the residuals between events. The standard deviation of the residuals within the event; The fitting steps for the random effects method are as follows: A1: Estimating fixed effects parameters ; A2: Given Estimate the likelihood function using the following method. and : In the formula: N is the number of ground motions. For predicted values, For the observed values, The number of records for the i-th earthquake; A3: Given , and Estimate the solution of the maximum likelihood function for random effects using the following equation. : A4: Given ,right Estimate the new fixed effects regression equation Value, of which The random effects parameters calculated using the expectation-maximization algorithm are expressed as follows: A5: Repeat steps two, three, and four until the likelihood function of step three is maximized.

Images