Residual deformation acquisition method and device for isolation structure and storage medium

Abstract

This application relates to the field of seismic isolation bearing design technology. Specifically, an embodiment discloses a method, device, and storage medium for obtaining the residual deformation of a seismic isolation structure. The method includes: obtaining the equivalent yield displacement of the seismic isolation layer: where is the minimum yield displacement of all seismic isolation bearings; obtaining the equivalent yield-to-weight ratio of the seismic isolation structure: , where is the pre-yield stiffness of the i-th seismic isolation bearing, is the equivalent yield force, and G is the total weight of the upper structure of the seismic isolation layer; obtaining the equivalent post-yield stiffness ratio of the seismic isolation layer: , where is the post-yield stiffness of the i-th seismic isolation bearing; obtaining the equivalent ductility coefficient of the seismic isolation layer: , where D is the maximum horizontal displacement of the seismic isolation layer; obtaining the residual deformation calculation formula of the seismic isolation structure: , , and using the residual deformation calculation formula of the seismic isolation structure to obtain the residual deformation d of the seismic isolation structure. α , where is the guarantee rate, is the exponential parameter, is the stiffness ratio after yielding of the isolation layer, is the yield displacement of the isolation layer, is the yield-weight ratio of the isolation structure, and is the ductility coefficient of the isolation layer.

Description

Technical Field

[0001] This application relates to the field of seismic isolation bearing design technology, specifically to a method, device, and storage medium for obtaining residual deformation of a seismic isolation structure. Background Technology

[0002] In seismically isolated buildings, seismic isolation bearings are key components for achieving seismic isolation. Besides requiring good horizontal deformation capacity, seismic isolation bearings also need reliable vertical bearing capacity, suitable damping performance, and good deformation recovery capability. Deficiencies in any of these properties will affect the seismic isolation effect of the structure, and consequently, the evaluation of the seismic toughness of the isolated building. Previous studies have focused more on the horizontal deformation, vertical bearing capacity, and damping performance of seismic isolation bearings, while research on their deformation recovery capability is relatively limited. Furthermore, existing research indicates that residual deformation of the isolation layer in a seismic isolation structure not only compromises the structural recoverability but also weakens the effectiveness of the isolation device under aftershocks. Therefore, research on the residual deformation of the isolation layer in seismic isolation structures has significant engineering implications.

[0003] Existing technologies can clearly define the limits of residual deformation in seismic isolation systems, but they do not provide specific calculation methods for residual deformation. Furthermore, the equivalent linear method for the design of existing seismic isolation structures can only obtain the maximum displacement of the seismic isolation structure during calculation and analysis, but cannot obtain the residual deformation of the seismic isolation structure. Summary of the Invention

[0004] The purpose of this application is to provide a method, device, and storage medium for obtaining the residual deformation of a seismic isolation structure, in order to solve the problems in the prior art that do not provide a specific calculation method for the residual deformation, and that the equivalent linear method for the design of existing seismic isolation structures can only obtain the maximum displacement of the seismic isolation structure during calculation and analysis, but cannot obtain the residual deformation of the seismic isolation structure.

[0005] To achieve the above objectives, embodiments of this application provide a method for obtaining the residual deformation of a seismic isolation structure, comprising:

[0006] Obtain the equivalent yield displacement of the seismic isolation layer : ,in This represents the minimum yield displacement of all seismic isolation bearings;

[0007] Obtain the equivalent yield-to-weight ratio of the seismic isolation structure : , ,in Let be the pre-yield stiffness of the i-th seismic isolation bearing. G is the equivalent yield force, and G is the total weight of the superstructure above the seismic isolation layer.

[0008] Obtain the equivalent yield stiffness ratio of the seismic isolation layer : ,in Let be the post-yield stiffness of the i-th seismic isolation bearing;

[0009] Obtain the equivalent ductility coefficient of the seismic isolation layer : , where D is the maximum horizontal displacement of the isolation layer;

[0010] Formula for calculating residual deformation of seismic isolation structure: , The residual deformation d of the seismic isolation structure is obtained using the formula for calculating the residual deformation of the seismic isolation structure. α ,in, To guarantee the rate, For exponential parameters, The ratio of the seismic isolation layer after yielding. This represents the yield displacement of the seismic isolation layer. The yield-to-weight ratio of the seismic isolation structure. This is the ductility coefficient of the seismic isolation layer.

[0011] To achieve the above objectives, this application also provides a residual deformation acquisition device for a seismic isolation structure, comprising: a memory; and a processor connected to the memory, the processor being configured to perform the steps of the method described above.

[0012] To achieve the above objectives, this application also provides a computer storage medium having a computer program stored thereon, wherein the computer program, when executed by a machine, implements the steps of the method described above.

[0013] The embodiments of this application have the following advantages:

[0014] By analyzing the distribution pattern of residual deformation of seismic isolation bearings using the above methods, a calculation formula for the residual deformation of seismic isolation bearings under seismic loading is given through probabilistic statistical methods, providing a certain basis for the toughness design of seismic isolation structures. With the calculation formula for the residual deformation of seismic isolation structures, and combining this formula with the maximum displacement of the seismic isolation structure obtained by the equivalent linear method, the residual deformation of the seismic isolation structure can be calculated. The calculation method provided in this application has high estimation accuracy. Attached Figure Description

[0015] To more clearly illustrate the embodiments of this application or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0016] Figure 1A flowchart illustrating a method for obtaining the residual deformation of a seismic isolation structure, provided for at least one embodiment of this application;

[0017] Figure 2 A bilinear model decomposition diagram of a method for obtaining the residual deformation of a seismic isolation structure provided in at least one embodiment of this application;

[0018] Figure 3 A simplified diagram of residual deformation calculation for a method of obtaining residual deformation of a seismic isolation structure provided in at least one embodiment of this application;

[0019] Figure 4 A schematic diagram of the theoretical maximum residual deformation of a method for obtaining the residual deformation of a seismic isolation structure provided in at least one embodiment of this application;

[0020] Figure 5 The theoretical maximum residual deformation of different lead-core rubber seismic isolation bearings for a method of obtaining residual deformation of a seismic isolation structure provided in at least one embodiment of this application;

[0021] Figure 6 Characteristics of 100 seismic wave response spectra of a method for obtaining residual deformation of a seismic isolation structure provided in at least one embodiment of this application;

[0022] Figure 7 Statistical results of the maximum residual deformation of a method for obtaining residual deformation of a seismic isolation structure provided in at least one embodiment of this application;

[0023] Figure 8 Residual deformation distribution diagrams of various models for a method of obtaining residual deformation of a seismic isolation structure provided in at least one embodiment of this application;

[0024] Figure 9 The residual deformation acquisition method for a seismic isolation structure provided in at least one embodiment of this application is described in section d. rmax / θ and K c Relationship curve diagram;

[0025] Figure 10 Examples d of a method for obtaining the residual deformation of a seismic isolation structure provided in at least one embodiment of this application rmax Statistical results of / θ;

[0026] Figure 11 Statistical results of p-values ​​of residual deformation KS test for each example of a method for obtaining residual deformation of a seismic isolation structure provided in at least one embodiment of this application;

[0027] Figure 12 A graph showing the relationship between the exponential distribution parameter θ and other parameters of a method for obtaining the residual deformation of a seismic isolation structure provided in at least one embodiment of this application;

[0028] Figure 13 The residual deformation values ​​of each seismic wave are calculated for a method for obtaining the residual deformation of a seismic isolation structure provided in at least one embodiment of this application.

[0029] Figure 14 The exponential distribution parameter θ and the theoretical maximum residual deformation d of a method for obtaining the residual deformation of a seismic isolation structure provided in at least one embodiment of this application. rmax Statistical relationship diagram;

[0030] Figure 15 The residual deformation d of a method for obtaining the residual deformation of a seismic isolation structure provided in at least one embodiment of this application. r Statistical relationship between peak acceleration A and peak acceleration A;

[0031] Figure 16 The residual deformation d of a method for obtaining the residual deformation of a seismic isolation structure provided in at least one embodiment of this application. r Statistical relationship between yield weight ratio η;

[0032] Figure 17 The exponential distribution parameter θ and the maximum support deformation d of a method for obtaining the residual deformation of a seismic isolation structure provided in at least one embodiment of this application. max Statistical relationship diagram;

[0033] Figure 18 Error diagram of fitting formula calculation for a method for obtaining residual deformation of a seismic isolation structure provided in at least one embodiment of this application;

[0034] Figure 19 The residual deformation acquisition method for a seismic isolation structure provided in at least one embodiment of this application uses peak ground acceleration (PGA) of 1 m / s² for five types of sites. 2 Corresponding average reaction spectrum;

[0035] Figure 20 Error diagram of fitting formula calculation for a method for obtaining residual deformation of a seismic isolation structure provided in at least one embodiment of this application;

[0036] Figure 21 Different seismic groupings and peak ground accelerations (PGA) of seismic waves for obtaining residual deformation of a seismic isolation structure, provided in at least one embodiment of this application. 2 Corresponding average reaction spectrum;

[0037] Figure 22 Error diagram of fitting formula calculation for a method for obtaining residual deformation of a seismic isolation structure provided in at least one embodiment of this application;

[0038] Figure 23 Error diagram of fitting formula calculation for a method for obtaining residual deformation of a seismic isolation structure provided in at least one embodiment of this application;

[0039] Figure 24 A flowchart illustrating the calculation of residual deformation of a seismic isolation structure, provided for at least one embodiment of this application;

[0040] Figure 25 A simplified diagram of a seismic isolation structure for a method of obtaining residual deformation of a seismic isolation structure provided in at least one embodiment of this application;

[0041] Figure 26 A diagram showing the arrangement of seismic isolation supports for a method of obtaining the residual deformation of a seismic isolation structure, provided for at least one embodiment of this application.

[0042] Figure 27 A seismic response spectrum of a method for obtaining the residual deformation of a seismic isolation structure provided in at least one embodiment of this application;

[0043] Figure 28 A comparison diagram of time history analysis and estimation results of a method for obtaining residual deformation of a seismic isolation structure provided in at least one embodiment of this application;

[0044] Figure 29 A block diagram of a residual deformation acquisition device for a seismic isolation structure provided in at least one embodiment of this application. Detailed Implementation

[0045] The following specific embodiments illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0046] It should be noted that the steps in the claims and description of this application may be performed substantially in parallel or in reverse order under appropriate circumstances, depending on the function involved.

[0047] Furthermore, the technical features involved in the different embodiments of this application described below can be combined with each other as long as they do not conflict with each other.

[0048] One embodiment of this application provides a method for obtaining the residual deformation of a seismic isolation structure, referencing... Figure 1 , Figure 1 The flowchart illustrates a method for obtaining the residual deformation of a seismic isolation structure provided in at least one embodiment of this application. It should be understood that the method may also include additional boxes not shown and / or the boxes shown may be omitted, and the scope of this application is not limited in this respect.

[0049] At step 101, the equivalent yield displacement of the seismic isolation layer is obtained. : ,in This represents the minimum yield displacement of all seismic isolation bearings.

[0050] At step 102, the equivalent yield-to-weight ratio of the seismic isolation structure is obtained. : , ,in Let be the pre-yield stiffness of the i-th seismic isolation bearing. G represents the equivalent yield force, and G represents the total weight of the superstructure above the isolation layer.

[0051] In step 103, the equivalent post-yield stiffness ratio of the seismic isolation layer is obtained. : ,in Let be the post-yield stiffness of the i-th seismic isolation bearing.

[0052] At step 104, the equivalent ductility coefficient of the seismic isolation layer is obtained. : , where D is the maximum horizontal displacement of the isolation layer.

[0053] In step 105, the formula for calculating the residual deformation of the seismic isolation structure is obtained: , The residual deformation d of the seismic isolation structure is obtained using the formula for calculating the residual deformation of the seismic isolation structure. α ,in, To guarantee the rate, For exponential parameters, The ratio of the seismic isolation layer after yielding. This represents the yield displacement of the seismic isolation layer. The yield-to-weight ratio of the seismic isolation structure. This is the ductility coefficient of the seismic isolation layer.

[0054] In some embodiments, the residual deformation of the single-degree-of-freedom model of the seismic isolation system is first discussed. The mechanical constitutive model adopts a stiffness-free degenerate bilinear hysteresis model. For ease of analysis, the stiffness-free degenerate bilinear hysteresis model is decomposed into an elastic element and an ideal elastoplastic element, such as... Figure 2 As shown.

[0055] Figure 2 China F y For the yield force of the bilinear model of the seismic isolation bearing, F y1 d represents the yield force of the ideal elastic-plastic element after decomposition. y K represents the yield displacement, k0 represents the pre-yield stiffness of the bilinear model, and k1 represents the pre-yield stiffness of the ideal elastoplastic element after decomposition. pThis represents the post-yield stiffness of the bilinear model, i.e., the stiffness of the elastic elements after decomposition. Based on the equivalence relations before and after decomposition, we can obtain:

[0056] (1)

[0057] (2)

[0058] make Let ρ be the ratio of the stiffness after yielding to the stiffness before yielding in the bilinear model, hereinafter referred to as the post-yield stiffness ratio.

[0059] (3)

[0060] (4)

[0061] Assume point A is the final stopping position of the support, such as Figure 3 As shown, let the distance from point A to the initial starting position o be d. r This refers to residual deformation. Here, we only discuss residual deformation in the positive direction; deformation in the negative direction is similar to that in the positive direction. In the diagram, F1 represents the internal force of the ideal elastoplastic element corresponding to point A, and F2 represents the internal force of the elastic element corresponding to point A. Their expressions are:

[0062] (5)

[0063] Since the internal force of the support is zero when it is in the stopped position, only the ideal elastoplastic element provides the internal force to balance the internal force of the elastic element. Therefore, F1 is...

[0064] (6)

[0065] In an ideal elastoplastic element, the range of internal forces that can be provided is [-F]. y1 F y1 ],therefore

[0066] (7)

[0067] Substituting equations (4) and (6) into equation (7), we get

[0068] (8)

[0069] make (9)

[0070] d rmax Defined as the theoretical maximum residual deformation. According to d... rmax The calculation process can be represented graphically, such as... Figure 4 As shown in the figure, the parameters are... Figure 2The parameters in the diagram have the same meaning. The solid red line represents the possible position of the support when the vibration stops. Each point on the solid red line can satisfy the internal force equilibrium condition. However, the final stopping position of the support needs to be determined based on the displacement and velocity of the support at the end of the seismic motion. Here, the end of the seismic motion does not mean that the support stops moving, because at the end of the seismic motion, the velocity of the support may not be zero, and the position of the support may not be at the internal force equilibrium point. In this case, the support will undergo free decay motion until it comes to rest. Therefore, the residual deformation value of the support is related to the characteristics of the input seismic motion and is a random variable.

[0071] Figure 5 The figure shows the theoretical maximum residual deformation value (drmax) of a commonly used lead-core rubber seismic isolation bearing. The horizontal axis represents the effective diameter (D) of the bearing. S2 is the second shape factor of the bearing, and G is the rubber shear modulus. The bearing mechanical parameters are from the literature. As can be seen from the figure, the theoretical maximum residual deformation increases with the increase of the effective diameter of the lead-core rubber bearing. For the same effective diameter, the smaller the second shape factor and the smaller the rubber shear modulus, the greater the theoretical maximum residual deformation. For lead-core rubber seismic isolation bearings, the post-yield stiffness ratio (ρ) is relatively stable, generally 1 / 13. The larger the effective diameter of the bearing, the smaller the second shape factor and the smaller the rubber shear modulus, resulting in a larger yield displacement and thus a larger theoretical maximum residual deformation.

[0072] In addition, residual deformation d r It will not exceed the maximum deformation of the support during the movement. However, under the action of rare and extremely rare earthquakes, the maximum deformation of the seismic isolation support of the seismic isolation structure is often large. Equation (9) still plays a controlling role in the maximum residual deformation.

[0073] In some embodiments, the residual deformation of the seismic isolation bearing is a random variable. Although the theoretical maximum residual deformation was obtained from the analysis in the aforementioned embodiments, the case where the residual deformation reaches the maximum residual deformation value under actual seismic loading is very rare, and the specific value of the residual deformation needs further study. This embodiment excites a single-degree-of-freedom seismic isolation model using actual seismic motion, and then statistically analyzes the distribution law of the actual residual deformation.

[0074] Analysis model and input description:

[0075] This embodiment analyzes a single-degree-of-freedom model. The mechanical constitutive model is a stiffness-free degenerate bilinear hysteresis model, where the ratio of pre-yield stiffness to post-yield stiffness ranges from 7 to 16, with intervals of 1. That is, the post-yield stiffness ratio ρ ranges from 1 / 16 to 1 / 7. The yield displacement d... yThe initial damping ratios are 2~11mm, with 1mm intervals, and the yield-to-weight ratios η are 0.01~0.055, with 0.005 intervals. The single-degree-of-freedom model can be determined based on the post-yield stiffness ratio, yield displacement, and yield-to-weight ratio. The initial damping ratio is 0.05 for all models, resulting in a total of 1000 seismic isolation models.

[0076] The input ground motion data were obtained from the Pacific Earthquake Engineering Research Center (PEER) Strong Motion Database, and 100 natural waves were selected from the second group of earthquake groups according to the Class II site classification in the "Building Isolation Design Standard" (hereinafter referred to as the "Isolation Standard"). The seismic wave response spectrum characteristics are as follows: Figure 6 As shown.

[0077] Peak ground accelerations were taken as 2-11 m / s². 2 1m / s interval 2 This means it includes 10 seismic scenarios. Therefore, this embodiment contains a total of 10,000 calculation cases, with each of the 10 seismic scenarios acting on 1,000 single-degree-of-freedom isolation models. In addition, to allow the supports sufficient time to decay to rest, 10,000 data points with a value of 0 were added to each seismic wave data, and OpenSeesPy was used to calculate the residual deformation under various ground motions.

[0078] Analysis results:

[0079] Based on the calculation and analysis, the residual deformation value of each model can be obtained for each seismic wave (the residual deformation values ​​in this application are all absolute values ​​of residual deformation). Figure 7 The maximum residual deformation values ​​for each example under 100 seismic excitations were statistically analyzed.

[0080] from Figure 7 As can be seen, under actual seismic excitation, the maximum value of residual deformation did not exceed its theoretical maximum residual deformation value, verifying the rationality of the formula for calculating the maximum theoretical residual deformation value proposed in the aforementioned embodiments.

[0081] Figure 8 The statistical distribution of residual deformation of some models under 100 seismic waves is presented. As can be seen from the frequency curves in the figure, the distribution of residual deformation differs for different yield displacements (dy), post-yield stiffness (ρ), yield-to-weight ratio (η), and peak ground acceleration (A). However, all frequency curves exhibit a monotonically decreasing trend, similar to an exponential distribution. Nevertheless, based on the conclusions of the aforementioned embodiments, for a given yield displacement and post-yield stiffness ratio, the residual deformation has a definite range of values. Therefore, this application initially assumes that the residual deformation of the seismic isolation structure approximately follows a truncated exponential distribution.

[0082] Discussion of residual deformation distribution:

[0083] Based on the aforementioned analysis results, it is initially assumed that the residual deformation of the seismic isolation structure follows a truncated exponential distribution, and its probability density function f(x) is given by equation (10).

[0084] (10)

[0085] (11)

[0086] In the formula, θ is the parameter of the exponential distribution, whose maximum likelihood estimate can be represented by the sample mean; Kc is the truncated conditional probability coefficient; and x is the residual deformation value. Figure 9 d is given rmax / θ and K c Relationship curve graph.

[0087] from Figure 9 It can be seen from this that when the theoretical maximum residual deformation d rmax When the ratio of the residual deformation to the mean is greater than 5, the truncation conditional probability coefficient Kc is close to 1. At this time, the probability density function after truncation is no different from the original probability density function. Figure 10 The theoretical maximum residual deformation d for each example in this application is given. rmax The statistical results of the ratio to the mean residual deformation are shown in the figure, where θ is the sample mean.

[0088] from Figure 10 As can be seen from the data, the theoretical maximum residual deformation d is achieved in 97.8% of the examples in this application. rmax Since the ratio of the residual deformation to the mean residual deformation is greater than 5, the residual deformation of the isolation structure discussed in this application is not significantly different, whether based on the truncated exponential distribution assumption or the exponential distribution assumption. For ease of analysis, the following discussion in this application assumes that the residual deformation of the isolation structure follows an exponential distribution, with its probability density function and cumulative distribution function being equations (12) and (13).

[0089] (12)

[0090] (13)

[0091] In the formula, F(x) is the cumulative distribution function of the residual deformation.

[0092] To further verify the reasonableness of the assumptions, the Kolmogorov-Sminov (KS) test was performed on the residual deformation data of the examples using SPSS software. The significance level was set at 0.05. The statistical results of the p-values ​​of the residual deformation KS test for 10,000 examples are as follows. Figure 9 As shown.

[0093] from Figure 11As can be seen, the p-value of the KS test for 90% of the examples is not less than 0.05, indicating that the residual deformation of the vast majority of examples conforms to the assumption of an exponential distribution. Therefore, the assumption that the residual deformation is exponentially distributed in this application is reasonable to a certain extent.

[0094] The foregoing embodiments clarify that the residual deformation of the seismic isolation structure can be treated according to an exponential distribution. However, in structural design, more attention is paid to the specific value of the residual deformation. Therefore, this embodiment will study the value of the residual deformation of the seismic isolation structure.

[0095] Method for determining residual deformation:

[0096] Assume the residual deformation takes the value of Since the residual deformation follows an exponential distribution, the actual residual deformation is less than... The probability α is (15)

[0097] get (16)

[0098] In equation (16), α also represents the actual residual deformation being less than 1 / 3. The guarantee rate.

[0099] In engineering, the average value of the calculation results is often taken. As a representative value of the result. For residual deformations that follow an exponential distribution, its mean is... for According to equation (16), its guarantee rate α can be obtained as follows:

[0100] (17)

[0101] Therefore, take the average value. As a representative value of residual deformation, its guarantee rate is 63.2%.

[0102] In addition, in engineering, a value with a 95% guarantee rate is often taken as a representative value, and it is calculated according to formula (15).

[0103] (18)

[0104] Therefore, take As a representative value of residual deformation, its guarantee rate is 95%.

[0105] As can be seen from the above analysis, regardless of ,still All are related to the exponential distribution parameters of residual deformation Therefore, it is necessary to determine the exponential distribution parameters of the residual deformation. Based on this, this application will analyze the parameters of the exponential distribution. Influencing factors and statistical parameters The relationship with influencing factors, and the fitting parameters. The calculation formula is then used to clarify the value of the residual deformation.

[0106] Factors affecting residual deformation:

[0107] This embodiment first analyzes the exponential distribution parameters. The relationship between the parameters yield-weight ratio η, post-yield stiffness ratio ρ, yield displacement dy, and peak acceleration A, and the exponential distribution parameters. Take the sample mean. Figure 12 Given The curves showing the relationship between the parameters and the average values ​​for each working condition in the graph represent 1000 calculations for a single parameter. The average value, as shown in Figure (a), refers to the average value of each working condition when η is 0.01, corresponding to a total of 1000 calculation cases with 10 types of ρ, 10 types of A, and 10 types of dy. The average value.

[0108] from Figure 12 As can be seen from this, when only a single parameter is changed, as η and ρ decrease, and dy and A increase, All of these values ​​increase. This indicates that increasing the yield-weight ratio of the seismic isolation structure and the post-yield stiffness ratio of the seismic isolation layer, as well as reducing the yield displacement of the seismic isolation layer, can reduce the residual deformation of the seismic isolation layer. The greater the seismic force, the greater the residual deformation of the seismic isolation layer.

[0109] When ρ decreases or dy increases The increase is mainly due to the fact that when ρ decreases or dy increases, according to equation (9), the theoretical maximum residual deformation d rmax The larger the value, the wider the possible distribution of residual deformation values, such as Figure 4 As shown, the higher the probability of the residual deformation reaching a large value, the greater the expected value of the residual deformation will be when ρ decreases or dy increases, all other things being equal. Figure 13 The residual deformation values ​​calculated for each of the 100 seismic waves are given in some examples.

[0110] from Figure 13 As can be seen from the actual calculation, under the same peak ground acceleration and yield-to-weight ratio, the theoretical maximum residual deformation d rmax The larger the value, the wider the possible distribution of residual deformation values. Furthermore, the figure also shows that the theoretical maximum residual deformation d... rmax When the values ​​are the same, the residual deformation values ​​may have similar distributions. Figure 14 The theoretical maximum residual deformation d is given. rmax The statistical graph of the residual deformation mean of each example, that is, with Statistical relationship diagram.

[0111] from Figure 14 As can be seen from this, the theoretical maximum residual deformation d rmax and There is a good correspondence, and as the theoretical maximum residual deformation increases, The increase further illustrates that the expected value of the residual deformation is greater when ρ decreases or dy increases.

[0112] When the peak acceleration A increases An increase indicates that a greater peak ground acceleration (PGA) leads to a greater residual deformation. However, the residual deformation here refers to the statistical mean of the residual deformation; this relationship may not necessarily exist for a single seismic excitation. Figure 15 As shown.

[0113] from Figure 15 As can be seen, the statistical mean of residual deformation increases with increasing peak ground acceleration (PGA). However, for a single seismic wave, the residual deformation does not increase with increasing PGA, but rather fluctuates irregularly. A similar phenomenon exists regarding the effect of the yield-to-weight ratio on the residual deformation of seismic isolation structures. Figure 16 As shown.

[0114] from Figure 16 As can be seen, the statistical mean of residual deformation decreases with increasing yield-to-weight ratio. However, for a single seismic wave, the residual deformation does not decrease with increasing yield-to-weight ratio, but rather exhibits irregular fluctuations. This statistical relationship between residual deformation, peak ground acceleration, and yield-to-weight ratio may be related to the nonlinear characteristics of seismic waves and isolation structures; the specific reasons require further investigation.

[0115] Furthermore, as ρ decreases or dy increases, the maximum displacement of the isolation layer also increases. In fact, as η decreases or A increases, the maximum displacement of the isolation layer also increases, which is consistent with the influence law on residual deformation. Figure 17 As shown.

[0116] from Figure 17 As can be seen, there is a correlation between the residual deformation and the maximum deformation of the seismic isolation layer. However, this correlation is based on three of the four parameters being fixed; essentially, the factors influencing the residual deformation remain four. Nevertheless, the influence of peak acceleration on the residual deformation can be replaced by the maximum deformation. This approach has three advantages:

[0117] (1) According to dimensional analysis, if the residual deformation calculation formula includes acceleration, the calculation formula needs to include the quadratic expression of time to obtain the displacement result. The result in unit displacement cannot be obtained by relying solely on the combination of several parameters. (2) The maximum displacement is a comprehensive parameter. It is the result determined by the combined action of the superstructure, the isolation layer and the seismic wave, and has a good comprehensive effect. (3) In terms of data richness, the data distribution of the maximum displacement is much wider than that of the acceleration. This is because the acceleration parameter has only 10 values, while the maximum displacement has far more than 10 values. Using the maximum displacement as the influencing parameter results in higher data quality.

[0118] Of course, using maximum deformation instead of peak acceleration also has drawbacks. For example, if the residual deformation includes maximum displacement, then the maximum displacement of the isolation structure must be analyzed first to obtain the residual displacement of the isolation structure. However, if the calculation formula uses peak acceleration, the residual deformation can be determined directly from the influencing parameters without calculation. However, compared to its advantages, this drawback can be overcome.

[0119] Based on this, when fitting the expression for the exponential distribution parameters, this application takes the maximum displacement, yield displacement, post-yield stiffness ratio, and yield-weight ratio as variables.

[0120] Formula for calculating the exponential parameter:

[0121] Based on the foregoing analysis, the expression for calculating the exponential distribution parameters includes four parameters: maximum displacement, yield displacement, post-yield stiffness ratio, and yield-to-weight ratio. Furthermore, given the good correspondence between the theoretical maximum residual deformation and the exponential parameters, the yield displacement and post-yield stiffness ratio can be combined into a single variable representing the theoretical maximum residual deformation. As the unit of the exponential parameters is displacement, and the unit of the theoretical maximum residual deformation is also displacement, while the yield-to-weight ratio is dimensionless, the maximum displacement should also be combined with a dimensionless variable to ensure the final expression is in units of length. Removing the maximum displacement and using the yield displacement (i.e., the ductility coefficient) is a commonly used method for dimensionless reduction. Therefore, in this embodiment, the expression for the fitted exponential parameters is as follows:

[0122] (17)

[0123] in (18)

[0124] From equation (17), it can be seen that only drmax in f2 is a length unit, while the units of the other individual parameters are all 1. Therefore, f2 should be a linear function of drmax. In addition, the value of f2 at special points needs to meet certain requirements. For example, when the ductility coefficient μ is less than or equal to 1, it indicates that the isolation structure has not yielded, and the residual deformation should be 0; when the stiffness ratio ρ after yielding is equal to 1, it indicates that the isolation structure is elastic, and the residual deformation should be 0; when the yield-weight ratio is infinite, the corresponding yield force of the isolation layer is infinite, and the isolation layer will not yield, and the residual deformation should be 0. Finally, based on the relationship curves between the aforementioned individual variables and the exponential parameters, it can be preliminarily assumed that the form of the formula for calculating the residual deformation exponential distribution parameter is as follows:

[0125] (19)

[0126] In the formula, β1, β2, β3, β4, and β5 are the fitting parameters. This application uses the curve_fit function in Python for fitting. The fitting results are shown in Table 1:

[0127] Table 1 Fitting results of residual deformation exponential distribution parameters

[0128]

[0129] Therefore, the formula for calculating the residual deformation exponent distribution parameter is:

[0130] (20)

[0131] The error in calculating the residual deformation exponent distribution parameters according to the above formula is as follows: Figure 18 As shown:

[0132] from Figure 18 As can be seen, when calculating the residual deformation index distribution parameters according to the fitting formula, the calculation error is controlled within 10% for 62% of the cases and within 20% for 96% of the cases, indicating that the fitting formula has high estimation accuracy.

[0133] Accuracy of the fitting formula:

[0134] Since the aforementioned analysis data all come from the same set of seismic wave calculation results, in order to further illustrate the applicability and estimation accuracy of the fitting formula, this embodiment will select seismic waves of 5 types of sites corresponding to the second group based on the response spectrum of the seismic isolation standard and the site category and seismic group of the seismic designation, with 100 seismic waves for each type of site, and analyze the distribution parameters of the seismic isolation residual deformation index. The seismic wave response spectrum characteristics are as follows: Figure 19 As shown.

[0135] The residual deformation index distribution parameters were calculated using the above seismic waves and compared with the results calculated by formula (20). The statistical error was controlled within 20%, such as... Figure 20 As shown.

[0136] from Figure 20 As can be seen from the data, formula (20) has a high estimation accuracy for the residual deformation of the isolation model under seismic wave excitation in sites of Class II, III, and IV, but a low estimation accuracy for the residual deformation in sites of I0 and I1. This may be because there are fewer seismic waves in Class I sites, and most seismic waves are low in the long period. When selecting seismic waves, in order to match the average response spectrum with the standard response spectrum, some seismic waves will be much larger, which makes the distribution of the calculation results inconsistent with the distribution of other results. In addition, the displacement values ​​of the isolation supports calculated by seismic waves in Class I0 and I1 sites are small, and the maximum displacement value may be less than the theoretical maximum residual deformation, which makes the distribution of residual deformation not conform to the exponential distribution, resulting in low calculation accuracy.

[0137] In addition to analyzing seismic waves from different sites, this embodiment also analyzes seismic waves from different seismic groups at Class II sites, with 100 seismic waves in each group. The distribution parameters of the seismic isolation residual deformation index and the seismic wave response spectrum characteristics are analyzed as follows: Figure 21 As shown.

[0138] The residual deformation index distribution parameters were calculated using the above seismic waves and compared with the results calculated by formula (20). The statistical error was controlled within 20%, such as... Figure 22 As shown.

[0139] from Figure 22 As can be seen from the above, formula (20) has a high estimation accuracy for the residual deformation of the isolation model under seismic wave excitation in different seismic groups.

[0140] In addition, this embodiment also compares the impact of the characteristic period on the estimation accuracy of formula (20), such as Figure 23 As shown.

[0141] from Figure 23 As can be seen from the above, under the same characteristic period, formula (20) has higher estimation accuracy for seismic waves at Class II sites than for seismic waves at Class I0 sites.

[0142] In summary, except for the fact that formula (20) cannot be used to estimate the residual deformation of seismic isolation structures on sites of type I0 and I1, other seismic isolation structures have high estimation accuracy.

[0143] Based on the above analysis, the residual deformation d of the seismic isolation structure can be obtained. α for

[0144] (twenty one)

[0145] In the formula, To ensure a high success rate, either 63.2% or 95% can be used.

[0146] For the exponential parameter, its calculation formula is:

[0147] (twenty two)

[0148] In the formula The ratio of the seismic isolation layer after yielding; This represents the yield displacement of the seismic isolation layer. The yield-to-weight ratio of the seismic isolation structure; This is the ductility coefficient of the seismic isolation layer.

[0149] Since the actual seismic isolation structure uses a combination of various types of bearings, and the post-yield stiffness ratio, yield displacement, and yield-weight ratio of each type of bearing are different, this application uses the equivalent post-yield stiffness ratio, equivalent yield displacement, and equivalent yield-weight ratio to calculate the equivalent residual deformation of the seismic isolation structure when performing actual seismic isolation structure analysis. The specific calculation process is as follows:

[0150] ① Determine the guarantee rate We can take 63.2%, which corresponds to the mean level of the time history analysis;

[0151] ② Obtain the equivalent yield displacement of the seismic isolation layer :

[0152] (twenty three)

[0153] In the above formula This represents the minimum yield displacement of all seismic isolation bearings.

[0154] ③ Obtain the equivalent yield-to-weight ratio of the seismic isolation structure :

[0155] (twenty four)

[0156] (25)

[0157] In the above formula Let be the pre-yield stiffness of the i-th seismic isolation bearing. For a natural rubber bearing, This refers to elastic stiffness;

[0158] G represents the equivalent yield force, and G represents the total weight of the superstructure above the isolation layer.

[0159] ④ Obtain the equivalent post-yield stiffness ratio of the seismic isolation layer :

[0160] (26)

[0161] In the above formula Let be the post-yield stiffness of the i-th seismic isolation bearing. For a natural rubber bearing, This refers to elastic stiffness; Same as formula (24).

[0162] ⑤ Obtain the equivalent ductility coefficient of the seismic isolation layer :

[0163] (27)

[0164] In the above formula, D represents the maximum horizontal displacement of the isolation layer.

[0165] ⑥ Substituting the parameter values ​​obtained from ① to ⑤ into equations (21) and (22), the equivalent residual deformation of the seismic isolation structure can be obtained. .

[0166] To further clarify the process of calculating the residual deformation of a seismically isolated structure based on the method of this application, this embodiment uses an actual seismically isolated structure as an example for illustration. The simplified model diagram and support layout diagram are as follows: Figures 25-26 As shown.

[0167] This project has a total of 32 seismic isolation bearings. The parameters of the seismic isolation bearings are shown in Table 2.

[0168] Table 2 Seismic Isolation Bearing Parameter Table

[0169]

[0170] The seismic fortification intensity of this example is 7 degrees (0.15g), and the peak ground acceleration under rare earthquake action is 310 gal. The design earthquake group is Group 3, site class II, with a site characteristic period of 0.45s. The site characteristic period is taken as 0.50s for rare earthquake analysis. The structural form is a frame structure, and the total weight of the model is 82963kN.

[0171] According to equation (23), we know that:

[0172] According to equations (24) and (25), we get

[0173]

[0174]

[0175] According to equation (26), we get

[0176]

[0177] Analysis by other software showed that the maximum displacement of the seismic isolation structure under rare earthquakes was 195 mm. Therefore, according to equation (27), the following can be calculated:

[0178]

[0179] Substituting the results of the above calculations into equation (22), we get:

[0180]

[0181] The guarantee rate is 63.2%, and Substituting into equation (23) yields the following result:

[0182] Therefore, the equivalent residual deformation of the model under rare earthquake conditions is 3.42 mm.

[0183] To verify the rationality of the equivalent residual deformation calculation results in this example, time history analysis was performed on the example using seven seismic waves, and the average residual deformation of each isolation bearing under the action of the seven seismic waves was calculated. The response spectra of the seven seismic waves are shown below. Figure 27 As shown.

[0184] The time history analysis compares the average residual deformation of each support with the estimated value obtained by the method proposed in this application. Figure 28 As shown. From Figure 28 As can be seen from the time history analysis, the residual deformation of each support is between 3.7 and 3.8 mm, and the error between the result estimated by the method proposed in this application is within 10%, indicating that the calculation method for residual deformation of seismic isolation structure proposed in this application has high estimation accuracy.

[0185] Figure 29 A module block diagram of a residual deformation acquisition device for a seismic isolation structure provided for at least one embodiment of this application. The device includes:

[0186] The memory 201; and the processor 202 connected to the memory 201, the processor 202 being configured to implement the aforementioned method embodiments, which will not be described again here.

[0187] This application may be a method, apparatus, system, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for performing various aspects of this application.

[0188] Note that, unless otherwise explicitly stated, all features disclosed in this specification (including any appended claims, abstract, and drawings) may be replaced by alternative features for achieving the same, equivalent, or similar purpose. Therefore, unless explicitly stated otherwise, each disclosed feature is merely one example of a set of equivalent or similar features. Where used, "further," "preferably," "even further," and "more preferably" are simply starting points for describing another embodiment based on the foregoing embodiments, the combination of which with the foregoing embodiments constitutes the complete configuration of another embodiment. Any combination of several "further," "preferably," "even further," or "more preferably" settings following the same embodiment constitutes yet another embodiment.

Claims

1. A method for obtaining the residual deformation of a seismic isolation structure, characterized in that, include: Obtain the equivalent yield displacement of the seismic isolation layer : ,in This represents the minimum yield displacement of all seismic isolation bearings; Obtain the equivalent yield-to-weight ratio of the seismic isolation structure : , ,in Let be the pre-yield stiffness of the i-th seismic isolation bearing. G is the equivalent yield force, and G is the total weight of the superstructure above the seismic isolation layer. Obtain the equivalent yield stiffness ratio of the seismic isolation layer : ,in Let be the post-yield stiffness of the i-th seismic isolation bearing; Obtain the equivalent ductility coefficient of the seismic isolation layer : , where D is the maximum horizontal displacement of the isolation layer; Formula for calculating residual deformation of seismic isolation structure: , The residual deformation d of the seismic isolation structure is obtained using the formula for calculating the residual deformation of the seismic isolation structure. α ,in, To guarantee the rate, For exponential parameters, The ratio of the seismic isolation layer after yielding. This represents the yield displacement of the seismic isolation layer. The yield-to-weight ratio of the seismic isolation structure. This is the ductility coefficient of the seismic isolation layer.

2. The method for obtaining the residual deformation of a seismic isolation structure according to claim 1, characterized in that, The formula for calculating the residual deformation of the seismic isolation structure specifically includes: The stiffnessless degenerate bilinear hysteresis model is decomposed into an elastic element and an ideal elastoplastic element, using the formula: ， The theoretical maximum residual deformation is obtained, where d y K represents the yield displacement, k0 represents the pre-yield stiffness of the bilinear model, and k... p The post-yield stiffness of the bilinear model. ρ is the ratio of stiffness after yielding to stiffness before yielding in the bilinear model.

3. The method for obtaining the residual deformation of a seismic isolation structure according to claim 2, characterized in that, The formula for calculating the residual deformation of the seismic isolation structure specifically includes: A single-degree-of-freedom model is determined based on the post-yield stiffness ratio, yield displacement, and yield-weight ratio. Earthquake motion is input, and the residual deformation value of each model is calculated for each seismic wave. The mechanical constitutive model of the single-degree-of-freedom model is a stiffness-free degenerate bilinear hysteresis model. The ratio of pre-yield stiffness to post-yield stiffness is taken as 7~16, with an interval of 1, i.e., the post-yield stiffness ratio ρ is taken as 1 / 16~1 / 7. The yield displacement d... y The values ​​range from 2 to 11 mm, with an interval of 1 mm. The yield-to-weight ratio η ranges from 0.01 to 0.055, with an interval of 0.

005.

4. The method for obtaining the residual deformation of a seismic isolation structure according to claim 3, characterized in that, The formula for calculating the residual deformation of the seismic isolation structure specifically includes: Assuming the residual deformation of the seismic isolation structure follows an exponential distribution, its probability density function and cumulative distribution function are given by: , , Where F(x) is the cumulative distribution function of the residual deformation, f(x) is the probability density function, θ is the exponential distribution parameter, its maximum likelihood estimate is represented by the sample mean, and x is the residual deformation value.

5. The method for obtaining the residual deformation of a seismic isolation structure according to claim 4, characterized in that, The formula for calculating the residual deformation of the seismic isolation structure specifically includes: For residual deformations that follow an exponential distribution, take their average value. As a representative value of residual deformation.

6. The method for obtaining the residual deformation of a seismic isolation structure according to claim 5, characterized in that, The formula for calculating the residual deformation of the seismic isolation structure specifically includes: When fitting the expression for the exponential distribution parameters, the maximum displacement, yield displacement, post-yield stiffness ratio, and yield-weight ratio are taken as the variables.

7. A device for obtaining residual deformation of a seismic isolation structure, characterized in that, include: Memory; as well as A processor connected to the memory, the processor being configured to perform the steps of the method as described in any one of claims 1 to 6.

8. A computer storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a machine, it implements the steps of the method as described in any one of claims 1 to 6.

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