A calculation method and system for seismic displacement of friction pendulum bearings in near-fault regions

Abstract

A method and system for calculating seismic displacement of friction pendulum bearings in the near-fault region. The method for calculating seismic displacement of friction pendulum bearings in the near-fault region is used to calculate the safety factor of near-fault earthquakes. The safety factor is used to multiply the bearing displacement D(H) when only horizontal ground motion is considered to obtain the bearing check displacement D(H+V) when both horizontal and vertical ground motions are considered. The safety factor calculation model constructed by the present invention only needs to input two ground motion intensity parameters to calculate the safety factor at any set guarantee rate. Calculators only need to calculate the bearing displacement under the action of horizontal ground motion (i.e., the bearing displacement D(H) when only horizontal ground motion is considered), and then multiply it by the safety factor to fully consider the influence of vertical ground motion, providing help for seismic calculation.

Description

Technical Field

[0001] The present invention relates to the technical field of earthquake prevention and shock absorption, and particularly to a method and system for calculating seismic displacement of friction pendulum bearings in a near-fault area. Background Art

[0002] The FPB (friction pendulum bearing, as shown in Figure 8 ) has excellent characteristics such as adjusting the structural period, reducing the seismic force of bridge piers, being economical and durable, and is widely used in the seismic isolation design of bridges. Due to its structural characteristics, under seismic action, the FPB will have a large seat displacement, resulting in a series of bridge seismic damages. Therefore, in the field, the seat displacement of the FPB is taken as a damage index for investigation, and in seismic design, it is also necessary to check whether the seat displacement of the FPB is less than the seismic isolation displacement design value to ensure the safety of friction-type seismic isolation bridges during earthquakes.

[0003] Currently, the method for calculating the seat displacement of friction pendulum bearings under horizontal ground motion is relatively complete, but the calculation method for seat displacement under horizontal-vertical combined seismic action is still limited. A large-amplitude vertical ground motion is one of the main characteristics of near-fault ground motion. Currently, there is no consistent conclusion on whether vertical ground motion will affect the displacement response of the FPB, which brings great confusion to the seismic design and safety assessment of friction-type seismic isolation bridges in the near-fault area.

[0004] In current seismic calculations, the finite element software SAP2000 is usually used to generate and select about seven seismic waves according to the site characteristics for calculation and take the average value (sometimes take the maximum value), and the vertical ground motion intensity a VH is considered as a fixed value of 2 / 3. Using such a calculation method to evaluate the safety of the FPB has three deficiencies: 1. In the SAP software, the double-line model is often used to simulate the FPB, and such a constitutive relationship cannot reflect the influence of the action of vertical ground motion on the response of the FPB. 2. Taking the average value of the calculation results will lead to a conservative calculation result, and taking the maximum value may lead to an overly high calculation result. (This reason will be described in detail in the detailed description of the invention.) 3. Considering the vertical ground motion intensity a VH as a fixed value of 2 / 3 is too conservative for near-fault earthquakes. A large number of studies have shown that the situation where a VH is greater than 2 / 3 often occurs in near-fault earthquakes. Detailed Description of the Invention

[0005] To address the above-mentioned deficiencies in the insufficient safety assessment of FPB in the prior art, the present invention proposes a method for calculating the seismic displacement of friction pendulum bearings in the near-fault region, with the emphasis on considering the influence of vertical ground motion on the bearing displacement. The present invention constructs a safety factor calculation model to consider the influence of near-fault vertical ground motion. By using this safety factor calculation model, the displacement safety factor under near-fault seismic action can be quickly calculated. Multiplying this factor by the bearing displacement D(H) obtained by using the existing method considering only horizontal ground motion can obtain the bearing check displacement D(H+V) considering the combined action of horizontal and vertical ground motions.

[0006] A method for calculating the seismic displacement of friction pendulum bearings in the near-fault region proposed by the present invention constructs a safety factor calculation model for calculating the safety factor of near-fault earthquakes. The safety factor is used to multiply the bearing displacement D(H) considering only horizontal ground motion to obtain the bearing check displacement D(H+V) considering the combined action of horizontal and vertical ground motions. The construction of the safety factor calculation model includes the following steps:

[0007] S1. Obtain a seismic wave sample set composed of seismic waves; define the vertical ground motion amplification factor as K, where K is the ratio of the bearing check displacement D(H+V) to the bearing displacement D(H). The bearing check displacement D(H+V) is the bearing displacement considering horizontal and vertical ground motions, and the bearing displacement D(H) is the bearing displacement considering only horizontal ground motion;

[0008] Define the safety factor when the guarantee rate is ψ as K ψ , define K ψ 's basic model as:

[0009] K ψ = f{(PGA, a VH ) ; θ} (1)

[0010] Where f is a mapping function, θ is a set of parameters; PGA is the horizontal ground motion intensity index; a VH is the vertical ground motion intensity index;

[0011] S2. Set the horizontal ground motion intensity index PGA and the vertical ground motion intensity index a VH , and adjust the amplitude of each seismic wave in the seismic wave sample set so that the horizontal ground peak acceleration PGA' of the seismic wave is equal to PGA, and the ratio a' VH of the vertical ground peak acceleration to the horizontal ground peak acceleration is equal to the vertical ground motion intensity index a VH ;

[0012] S3. Calculate the vertical ground motion amplification factor K for each amplitude - adjusted seismic wave; fit the distribution of all vertical ground motion amplification factors K to a Gaussian distribution, where the coordinate system of the Gaussian distribution has K as the abscissa and the ratio f of the statistical frequency to the class interval as the ordinate, and obtain the mean μ and standard deviation σ of the Gaussian distribution; a For the ordinate, obtain the mean μ and standard deviation σ of the Gaussian distribution;

[0013] S4. Substitute the confidence level ψ, mean μ, standard deviation σ, and the Gaussian distribution corresponding to K into the following formula to calculate the simulation value K' of the safety factor ψ , and construct the parameter sample {(PGA, a VH ); K'} ψ};

[0014]

[0015] S5. Update PGA and a VH and loop through steps S2 - S4 to obtain multiple parameter samples {(PGA, a VH ); K'} ψ}; Fit formula (1) with all parameter samples to obtain θ = θ0, then obtain the safety factor calculation model of K ψ as:

[0016] K ψ = f{(PGA, a VH ); θ0} (3).

[0017] Preferably, define θ = {k1, k2, k3, k4}, where k1, k2, k3, and k4 are fitting parameters, and the basic model of the safety factor K ψ in S1 is:

[0018]

[0019] In S5, θ0 = {k ψ1 , k ψ2 , k ψ3 , k ψ4}; k ψ1 , k ψ2 , k ψ3 , and k ψ4 are the fitting results of k1, k2, k3, and k4 respectively;

[0020] K ψ The safety factor calculation model is:

[0021]

[0022] Preferably, the calculation of the bearing check displacement D(H + V) includes the following steps:

[0023] S21. Set the assurance rate ψ and obtain the safety factor K used for calculating the safety factor when the assurance rate is ψ ψ safety factor calculation model;

[0024] S22. Set the horizontal ground motion intensity index PGA and the vertical ground motion intensity index a VH and obtain the safety factor K in combination with the safety factor calculation model ψ ;

[0025] S23. Obtain the support displacement D(H) of the friction pendulum bearing in the target seismic wave considering only the horizontal ground motion;

[0026] S24. Calculate the support check displacement D(H+V), D(H+V) = K ψ ×D(H).

[0027] Preferably, it further includes step S25: Determine whether the friction pendulum bearing is safe under seismic action according to the support check displacement D(H+V).

[0028] Preferably, when determining whether the friction pendulum bearing is safe under seismic action according to the support check displacement D(H+V), compare the support check displacement D(H+V) with the set safety threshold. If the support check displacement D(H+V) is less than or equal to the set safety threshold, it means that the friction pendulum bearing meets the safety requirements.

[0029] The present invention also proposes a seismic displacement calculation system for a friction pendulum bearing in a near-fault area, providing a carrier for the above design method.

[0030] A design system for a friction pendulum bearing proposed by the present invention includes a storage module, and the storage module stores the basic model of K ψ and a computer program, and when the computer program is executed, it realizes the safety verification method of the friction pendulum bearing.

[0031] Preferably, it further includes a processing module, and the processor is used to execute the computer program to realize the safety verification method of the friction pendulum bearing.

[0032] A storage medium proposed by the present invention stores the basic model of K ψ and a computer program, and when the computer program is executed, it realizes the design method of the friction pendulum bearing.

[0033] The advantages of the present invention are as follows:

[0034] (1) A method for calculating the seismic displacement of a friction pendulum bearing in a near-fault area proposed by the present invention uses a safety factor calculation model to calculate the safety factor. Only two ground motion intensity parameters need to be input, namely the horizontal ground motion intensity index PGA and the vertical ground motion intensity index a. VH Then, the safety factor at any set confidence level can be calculated. Combining the safety factor calculated by the safety factor calculation model in the present invention, designers only need to calculate the bearing displacement D(H) when only horizontal ground motion is considered, and then multiply it by this safety factor to fully consider the influence of the magnitude of vertical ground motion on the friction pendulum bearing, providing help for seismic checking and design.

[0035] (2) The safety factor calculation model proposed by the present invention can realize the display of the vertical ground motion law at a set confidence level, such as a 95% confidence level, and ensure the safety assessment of the vertical ground motion displacement.

[0036] (3) In the present invention, only need to construct the safety factor calculation model at a specified confidence level according to the working conditions once, and then the safety factor of any seismic wave at this confidence level can be calculated by using this safety factor calculation model, with wide generality.

[0037] (4) A method for calculating the seismic displacement of a friction pendulum bearing in a near-fault area proposed by the present invention can directly use the safety factor calculation model provided by the present invention to calculate the safety factor under any seismic conditions, and then quickly calculate the vertical displacement of the friction pendulum bearing. Thus, the influence of vertical ground motion can be fully considered during the design of the friction pendulum bearing to ensure safety and at the same time not waste the material performance excessively. Compared with the prior art that requires inputting D(H) and D(H+V) simultaneously when designing a friction pendulum bearing, the present invention obtains D(H+V) based on the safety factor combined with D(H), with high efficiency, simple calculation process, and avoiding calculation deviation caused by artificially selecting seismic waves.

[0038] (5) The seismic displacement calculation system for a friction pendulum bearing in a near-fault area provided by the present invention provides a carrier for the above-mentioned method for calculating the seismic displacement of a friction pendulum bearing in a near-fault area, facilitating the popularization and application of the method. Description of the Drawings

[0039] Figure 1 is a flowchart for constructing a safety factor calculation model;

[0040] Figure 2 is a flowchart for a method for calculating the seismic displacement of a friction pendulum bearing in a near-fault area;

[0041] Figure 3(a) shows the distribution of K corresponding to 121 amplitude-modulated seismic waves when a VH = 1 and PGA = 0.5g in the embodiment;

[0042] Figure 3(b) is the corresponding Gaussian distribution of Figure 3(a);

[0043] Figure 4(a) shows the distribution of K corresponding to 121 amplitude-modulated seismic waves when a VH = 2 and PGA = 0.5g in the embodiment;

[0044] Figure 4(b) is the corresponding Gaussian distribution of Figure 4(a)

[0045] Figure 5 is the fitted surface diagram of the parameter samples in the embodiment;

[0046] Figure 6 is the corresponding relationship between K’ 95 and K 95 corresponding to the seismic wave;

[0047] Figure 7 is the comparison diagram of the safety factor K 95 and the actual value of the vertical ground motion amplification factor in the embodiment;

[0048] Figure 8 is the structural diagram of the existing friction pendulum bearing;

[0049] Illustration: 1. Sliding surface; 2. Anti-sliding bolt; 3. Limit slider; 4. Sliding block; 5. Upper seat plate; 6. Lower seat plate. Detailed implementation method

[0050] Embodiment 1

[0051] In this embodiment, the friction coefficient μf of the friction pendulum bearing is 0.03, the guarantee rate ψ = 95, and the basic model adopted for the safety factor is:

[0052]

[0053] where k1, k2, k3, and k4 are fitting parameters.

[0054] Referring to Figure 1 the shown process, 121 seismic waves are randomly selected in this embodiment.

[0055] Referring to Figure 1 the shown process, the construction steps of the parameter samples {(PGA, a VH ) ; K 95} in this embodiment are as follows:

[0056] The first step: Set the horizontal ground motion intensity index PGA and the vertical ground motion intensity index a VH , and perform amplitude modulation on each seismic wave so that the horizontal ground peak acceleration PGA’ of the seismic wave is equal to PGA, and the ratio a’ of the vertical ground peak acceleration to the horizontal ground peak accelerationVH is equal to the vertical ground motion intensity index a VH ; through simulation, obtain the vertical ground motion amplification factor K of the amplitude-adjusted seismic wave, and obtain a total of 121 K values;

[0057] Second step, fit the distribution of 121 vertical ground motion amplification factors K to a Gaussian distribution, where the coordinate system of the Gaussian distribution takes K as the abscissa and the ratio f of the statistical frequency to the class interval a as the ordinate, and obtain the mean μ and standard deviation σ of the Gaussian distribution.

[0058] In this embodiment, it is equivalent to making a frequency histogram of the distribution of 121 vertical ground motion amplification factors K, and then obtaining the Gaussian distribution of the frequency histogram. Figure 3(a) shows the distribution of K corresponding to 121 seismic waves after amplitude adjustment when a VH = 1 and PGA = 0.5g in this embodiment, and Figure 3(b) is the Gaussian distribution corresponding to Figure 3(a). Figure 4(a) shows the distribution of K corresponding to 121 seismic waves after amplitude adjustment when a VH = 2 and PGA = 0.5g in this embodiment, and Figure 4(b) is the Gaussian distribution corresponding to Figure 4(a).

[0059] Third step, substitute the Gaussian distribution with a confidence level ψ = 95, mean μ, standard deviation σ, and K into the following formula to calculate the simulated safety factor K' 95 , and construct a parameter sample {(PGA, a VH ); K' 95};

[0060]

[0061] Fourth step, loop through the first step to the third step to obtain the corresponding K' VH for different (PGA, a 95 ), construct 50 parameter samples {(PGA, a VH ); K' 95}, and perform parameter fitting on formula (1.1) by combining all parameter samples to determine k1 = 0.735, k2 = 4.132, k3 = 0.086, k4 = 1.14, so as to obtain the safety factor calculation model of the safety factor K 95 as follows:

[0062] K 95 = 0.735×(PGA 4.132 + 0.086)×a VH 1.14 + 1 (3.2)

[0063] Through formula (3.2), the set PGA and a can be directly combinedVH Quickly calculate the safety factor.

[0064] The surface defined by formula (3.2) is as Figure 5 shown.

[0065] The corresponding relationship between the 50 parameter samples obtained in this embodiment for K’ 95 and K 95 is as Figure 6 shown. It can be seen from Figure 6 that in this embodiment, for the same seismic wave, the safety factor K 95 and the simulated value of the safety factor K’ 95 are close, and the goodness of fit reaches 0.98.

[0066] To verify the safety of calculating D(H+V) using the safety factor K 95 in this embodiment, in this embodiment, let PGA = 0.32g, a VH = 1.2, and at this time K 95 = 1.09. In this embodiment, 121 seismic waves are amplitude - modulated to PGA’ = 0.32g, a’ VH = 1.2 and then simulated to obtain the actual values of the vertical ground motion amplification factor as Figure 7 shown. It can be seen that more than 95% of the actual values of the vertical ground motion amplification factor are less than K 95 , indicating that using K 95 in this embodiment can show the influence laws of the vast majority of vertical ground motions and realize the safety assessment of the vertical displacement of the friction pendulum bearing.

[0067] To further verify the safety level of the safety factor K 95 obtained in this embodiment, the following combines several classical seismic waves to conduct a safety assessment of the displacement D(H+V) obtained according to the safety factor K 95 .

[0068]

[0069]

[0070] In the table, D(H) represents the bearing displacement of the friction pendulum bearing adopted in this embodiment when only considering the horizontal ground motion in the corresponding classical seismic wave environment; g represents the unit of PGA, i.e., the acceleration of gravity, g = 9.8m / s 2 ; D(H+V) = K 95 ×D(H), and the K 95 in the table is obtained by corresponding the PGA and a VHObtained by substituting into formula (3.2) for calculation; D”(H+V) is the displacement of the bearing obtained by directly inputting the horizontal ground motion and vertical ground motion for numerical simulation calculation. Combining with the verification of the classical seismic wave in the above table, it can be known that according to the K given by the present invention 95 The D(H+V) calculated by combining D(H) is close to and greater than the D”(H+V) obtained by simulation, ensuring safety.

[0071] According to the safety factor calculation model in the present invention, the safety factor meeting the assurance rate requirement can be calculated. Combining with this safety factor, D(H+V) can be quickly obtained, and then the friction pendulum bearing can be optimized and designed by using the existing design method in combination with the set PGA, a VH , D(H) and the calculated D(H+V).

[0072] The above are only the preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A seismic displacement calculation method for friction pendulum bearings in near-fault regions, characterized in that, Construct a safety factor calculation model to calculate the safety factor of near-fault earthquakes. The safety factor is used to multiply the bearing displacement D(H) considering only horizontal ground motion to obtain the bearing verification displacement D(H+V) considering the combined action of horizontal and vertical ground motions. The construction of the safety factor calculation model includes the following steps: S1. Obtain a seismic wave sample set composed of seismic waves; define the vertical ground motion amplification factor as K, where K is the ratio of the bearing verification displacement D(H+V) to the bearing displacement D(H). The bearing verification displacement D(H+V) is the bearing displacement considering both horizontal and vertical ground motions, and the bearing displacement D(H) is the bearing displacement considering only horizontal ground motion. The safety factor when the assurance rate is ψ is denoted as K ψ , define K ψ 's basic model as: K ψ = f{(PGA, a VH )); θ} (1) where f is a mapping function, θ is a set of parameters; PGA is a horizontal ground motion intensity index; a VH is a vertical ground motion intensity index; S2. Set the horizontal ground motion intensity index PGA and the vertical ground motion intensity index a VH , and adjust the amplitude of each seismic wave in the seismic wave sample set so that the horizontal peak ground acceleration PGA' of the seismic wave is equal to PGA, and the ratio a' of the vertical peak ground acceleration to the horizontal peak ground acceleration VH is equal to the vertical ground motion intensity index a VH ; S3. Calculate the vertical ground motion amplification factor K for each amplitude - adjusted seismic wave; fit the distribution of all vertical ground motion amplification factors K to a Gaussian distribution, where the coordinate system of the Gaussian distribution has K as the abscissa and the ratio f of the statistical frequency to the class interval as the ordinate, and obtain the mean value μ and the standard deviation σ of the Gaussian distribution; a and obtain the mean value μ and the standard deviation σ of the Gaussian distribution; S4. Substitute the Gaussian distribution corresponding to the assurance rate ψ, mean value μ, standard deviation σ, and K into the following formula to calculate the simulated safety factor value K'. ψ , and construct the parameter sample {(PGA, a VH ); K' ψ}; S5. Update PGA and a VH And loop through steps S2 - S4 to obtain multiple parameter samples {(PGA, a VH ); K’ ψ}, fit all the parameter samples to formula (1) to obtain θ = θ0, and then obtain K ψ The safety factor calculation model is as follows: K ψ = f{(PGA, a VH )); θ0} (3).

2. The seismic displacement calculation method of the friction pendulum bearing in the near-fault area according to claim 1, wherein Define θ = {k1, k2, k3, k4}, where k1, k2, k3, and k4 are fitting parameters, and the safety factor K in S1 ψ has the following basic model: In S5, θ0 = {k ψ1 , k ψ2 , k ψ3 , k ψ4}; k ψ1 , k ψ2 , k ψ3 and k ψ4 are the fitting results of k1, k2, k3, and k4 respectively; K ψ The safety factor calculation model of 3. The method for calculating the seismic displacement of the friction pendulum bearing in the near-fault area according to claim 1, wherein The calculation of the bearing verification displacement D(H+V) includes the following steps: S21. Set the assurance rate ψ and obtain the safety factor calculation model for calculating the safety factor K when the assurance rate is ψ. ψ for calculating the safety factor; S22. Set the horizontal ground motion intensity index PGA and the vertical ground motion intensity index a VH , and obtain the safety factor K by combining with the safety factor calculation model ψ ; S23. Obtain the bearing displacement D(H) of the friction pendulum bearing in the target seismic wave considering only horizontal ground motion. S24. Calculate the bearing check displacement D(H+V), where D(H+V)=K ψ ×D(H).

4. The method for calculating the seismic displacement of the friction pendulum bearing in the near-fault area according to claim 3, characterized in that, It also includes step S25: Determine whether the friction pendulum bearing is safe under seismic action according to the bearing verification displacement D(H+V).

5. The seismic displacement calculation method of the friction pendulum bearing according to claim 4, characterized in that, When determining whether the friction pendulum bearing is safe under seismic action according to the bearing verification displacement D(H+V), compare the bearing verification displacement D(H+V) with the set safety threshold. If the bearing verification displacement D(H+V) is less than or equal to the set safety threshold, it means that the friction pendulum bearing meets the safety requirements.

6. A seismic displacement calculation system for a friction pendulum bearing in a near-fault area, characterized in that, including a storage module, in which a basic model and a computer program of K ψ are stored, and when the computer program is executed, it implements the method for calculating the seismic displacement of a near-fault area friction pendulum bearing according to any one of claims 1-5.

7. The near-fault region friction pendulum bearing seismic displacement calculation system according to claim 6, characterized in that It also includes a processing module. The processor is used to execute the computer program to implement the near-fault area friction pendulum bearing seismic displacement calculation method according to any one of claims 1-5.

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