Efficient reaction spectrum method for anti-seismic analysis of soil-structure interaction

Abstract

The embodiment of the invention discloses an efficient response spectrum method for soil-structure interaction anti-seismic analysis. The efficient response spectrum method comprises the steps that a finite element model of a to-be-analyzed soil-structure system is obtained; performing modal analysis on the structure model under the rigid foundation, and calculating the effective inherent frequency and modal vector of each order of the soil-structure system; according to the effective inherent frequency and the modal vector of each order, calculating a modal participation coefficient of each effective modal and a cross correlation coefficient between the effective modals; a model bottom response spectrum is obtained according to earthquake risk analysis of a specific site, and for an engineering site without earthquake risk analysis of the specific site, the model bottom response spectrum is obtained through inversion of a ground surface design spectrum through an inversion method; and determining the peak response of the structure according to the bottom response spectrum of the model. According to the embodiment of the invention, soil-structure interaction is considered in the structural seismic analysis response spectrum method, and the execution efficiency is relatively high.

Description

Technical Field

[0001] The embodiments of the present invention relate to the technical field of structural seismic analysis, and in particular to an efficient response spectrum method for seismic analysis of soil-structure interaction. Background Art

[0002] The uncertainty of ground motion leads to a large discreteness in structural responses, making it difficult to quantitatively carry out structural design. The design response spectrum is a statistical representative of ground motion on a certain type of site. The response spectrum method based on the design response spectrum can give the peak value of the structural response under the representative ground motion, which is applicable to the seismic design of engineering structures and has been incorporated into the seismic design codes of many countries, such as the "Code for Seismic Design of Buildings GB50011-2010" in China, etc.

[0003] With the development of modern engineering construction, the dynamic systems under earthquake actions are more complex. For example, multiple materials and damping shock absorbers result in non-proportionally damped systems, and large-span structures need to consider the multi-point excitation effect of non-uniform ground motion. In response to these challenges, the response spectrum method has also developed accordingly. For example, the response spectrum method for non-proportionally damped systems based on complex modal analysis technology, the multi-point excitation response spectrum method based on pseudo-static displacement decomposition, and the response spectrum method considering the combined action of inertial load and damping load. In addition, with the development of structural seismic analysis from elastic to elastoplastic, an elastoplastic response spectrum method based on elastoplastic response spectrum and modal Pushover analysis has been proposed. Some of the results of these new response spectrum methods have also been incorporated into relevant structural seismic design codes. For example, the elastoplastic response spectrum method has been incorporated into the "Code for Seismic Design of Urban Rail Transit Structures GB50909-2014" in China for the seismic design of bridge structures. The above structural seismic analysis methods are usually based on the assumption of a rigid foundation. However, there is usually a certain thickness of soil layer between the underlying bedrock and the foundation of most structures. When the site conditions are poor, there is an obvious dynamic interaction between the infinite soil mass and the structure. Therefore, when the soil-structure interaction has a significant impact, the soil-structure interaction needs to be considered in the structural design.

[0004] With the development of the analysis of soil-structure interaction, researchers have also proposed a response spectrum method considering soil-structure interaction, which can be divided into three categories according to the used soil-structure interaction models. The first category is the foundation vibration problem of ground structures such as high-rise buildings and bridges. A substructure analysis model is established, where the structure and the foundation are simulated by finite elements, and the soil body is simulated by a lumped parameter model without considering the non-uniform excitation of ground motion. The lumped parameter model of the soil body without damper elements is a proportional damping dynamic system, and the standard response spectrum method is used to solve it; the lumped parameter model of the soil body with damper elements results in a non-proportional damping system, and the non-proportional damping response spectrum method is used for solution. The second category is the pile-soil interaction problem of bridge structures. The substructure method is adopted to establish the calculation models of the structure and the pile foundation. The pile bottom is fixed, and the action of the soil on the pile side is simulated by a distributed spring system without considering the non-uniform change of ground motion along the pile, avoiding the problems of non-proportional damping and multi-point excitation. The entire soil-structure system can be directly solved by the response spectrum method; or the fixed boundary at the pile bottom is changed to a viscous boundary, and a response spectrum method for a non-proportional damping system is developed. Due to the neglect of the degrees of freedom of the soil body in the above two types of substructure models, the calculation accuracy is reduced compared with the integral analysis model. The third category is the soil-structure interaction problem of ground structures such as high-rise buildings under earthquake action. An integral analysis model of the structure and a part of the soil nearby is established, and finite element simulation is used. The side boundary of the model adopts treatment methods such as free boundary, elastic boundary composed of springs, and normal constraints, and consistent earthquake excitation is input at the bottom boundary of the model. The integral model of the soil-structure system is directly solved by the response spectrum method. Compared with the substructure analysis model, the integral analysis model can more accurately consider the dynamic interaction between the soil and the structure. However, the existing methods require modal analysis of the entire soil-structure system, with low execution efficiency and increased time cost for the response spectrum method and structural seismic analysis. Summary of the Invention

[0005] An embodiment of the present invention provides an efficient response spectrum method for soil-structure interaction seismic analysis to solve the above technical problems.

[0006] In a first aspect, an embodiment of the present invention provides an efficient response spectrum method for soil-structure interaction seismic analysis, including:

[0007] Obtain a finite element model of the soil-structure system to be analyzed, where the bottom of the model is fixed and the side uses roller boundaries;

[0008] Perform modal analysis on the structural model under a rigid foundation to obtain the initial eigenvalue and initial mode of each order;

[0009] Calculate the effective natural frequencies and mode vectors of each order of the soil-structure system according to the initial eigenvalue and mode of each order;

[0010] Calculate the modal participation coefficients of each effective mode and the cross-correlation coefficients between effective modes according to the effective natural frequencies and modal vectors of each order.

[0011] Obtain the base response spectrum of the soil-structure model according to the seismic hazard analysis of a specific site. For engineering sites without seismic hazard analysis of a specific site, the base response spectrum of the soil-structure model is inversed from the surface design spectrum by an inversion method.

[0012] Determine the peak response of the structure according to the base response spectrum of the soil-structure model.

[0013] Among them, the effective mode of the soil-structure system refers to the mode in the soil-structure system that is mainly dominated by the structural vibration or makes a major contribution to the structural dynamic response, and the effective natural frequency refers to the frequency corresponding to the effective mode.

[0014] In a second aspect, an embodiment of the present invention provides an electronic device, and the electronic device includes:

[0015] One or more processors;

[0016] A memory for storing one or more programs,

[0017] When the one or more programs are executed by the one or more processors, the one or more processors implement the efficient response spectrum method for soil-structure interaction seismic analysis described in any embodiment.

[0018] In a third aspect, an embodiment of the present invention further provides a computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, it implements the efficient response spectrum method for soil-structure interaction seismic analysis described in any embodiment.

[0019] An embodiment of the present invention provides an efficient response spectrum method for soil-structure interaction seismic analysis, which is used to calculate the seismic response of a structure considering soil-structure interaction. This method considers soil-structure interaction on the basis of the traditional response spectrum method and has high calculation efficiency. It has the following beneficial results:

[0020] 1) This method can directly obtain the effective natural frequencies and modes of the soil-structure system, avoiding modal analysis of the overall model of the soil-structure system.

[0021] 2) This method can directly use the effective modes of the soil-structure system for modal superposition, and the execution efficiency is improved compared with the traditional method. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0023] Figure 1 It is a modal nephogram of a soil-structure system provided by an embodiment of the present invention;

[0024] Figure 2 They are the first two effective modes of the soil-structure system provided by an embodiment of the present invention. Among them, Figure 2 (a) is the first-order mode, Figure 2 (b) is the second-order mode;

[0025] Figure 3 It is a flow chart of an efficient response spectrum method for seismic analysis of soil-structure interaction provided by an embodiment of the present invention;

[0026] Figure 4 It is a ground design response spectrum diagram provided by an embodiment of the present invention;

[0027] Figure 5 It is a result comparison diagram between the method of this embodiment and the traditional method provided by an embodiment of the present invention;

[0028] Figure 6 It is a schematic structural diagram of an electronic device provided by an embodiment of the present invention. Specific Embodiments

[0029] To make the objectives, technical solutions, and advantages of the present invention clearer, the following will clearly and completely describe the technical solutions of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope protected by the present invention.

[0030] In the description of the present invention, it should be noted that the orientation or positional relationship indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation of the present invention. In addition, the terms "first", "second", "third" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0031] In the description of the present invention, it should also be noted that, unless otherwise clearly specified and limited, the terms "installation", "connection", and "coupling" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the communication inside two components. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0032] An efficient response spectrum method for seismic analysis of soil-structure interaction provided by an embodiment of the present invention proposes the concept of effective modes of the soil-structure system, calculates the effective modes of the soil-structure system, and then selects the effective modes for mode superposition, avoiding modal analysis of the entire soil-structure system and improving the execution efficiency of the response spectrum method. To illustrate this method, first, the concept of the effective modes of the structure in the soil-structure system is described.

[0033] Specifically, taking the soil-structure system with a two-degree-of-freedom lumped mass model of the superstructure as an example, the effective modes of the soil-structure system are elaborated. In this system, the masses of the two degrees of freedom are 224t and 130t respectively, and the lateral stiffnesses are 201MN / m and 428MN / m. The radius of the soil domain in the soil-structure system is 100m, the grid size is 0.5m, and the soil is discretized using tetrahedral elements. Fixed boundary conditions are adopted at the truncated boundary of the soil, and the shear wave velocity of the site is 200m / s. Figure 1 The first six-order mode contour maps of the soil-structure system are given. From Figure 1 it can be seen that the first six-order modes of the soil-structure system are mainly dominated by soil vibration, that is, the local modes of the soil, and the effective modes that play an important role in the seismic response of the structure need to be selected from a large number of modes. The first-order and second-order effective modes of the soil-structure system are located at the 8th order mode and the 335th order mode of the soil-structure system respectively. Figure 2 The first two-order effective mode contour maps of the soil-structure system are given. These two-order modes are mainly dominated by structural vibration, while the vibration of the lower soil is small. At this time, these two-order modes can be regarded as the effective modes of the soil-structure system, that is, the modes that are mainly dominated by structural vibration or play a controlling role in the dynamic response of the structure in the soil-structure system are the effective modes of the soil-structure system, and the corresponding frequencies are the effective natural frequencies.

[0034] Based on the above concept, the calculation method of the effective modes of the soil-structure system is described below. In a specific embodiment, the calculation method of the effective modes may include the following steps:

[0035] Step 1: Given the initial eigenvalue λ (1) and the modal vector Φ (1), select the sum of the squares of the natural frequencies and the modes of the structure under the fixed base as the initial eigenvalues and mode vectors, where Φ (1) is the dimension of the soil-structure system, and the corresponding values of the soil degrees of freedom are zero. Further, if N orders are required in the response spectrum method, N sets of initial eigenvalues and mode vectors are set, and finally N sets are obtained by cyclic update. Usually, 3 sets can meet the calculation requirements.

[0036] Step 2: Repeat equations (1) to (4) until the set error and modal similarity conditions are met:

[0037]

[0038] When performing modal analysis on the soil-structure system, dense eigenvalue problems may occur in the soil, especially under poor site conditions. Therefore, when performing iterative calculations, an iterative exit condition needs to be introduced. Using the similarity of the mode vectors as the iterative exit condition, the two mode vectors are respectively the mode vectors of the upper structure degrees of freedom part in the soil-structure system (this vector is part of Φ (i+1) and can be extracted from it) and the mode vector of the fixed-base structure. The cosine similarity is used to judge the similarity degree of the two vectors. Cosine similarity is a method to evaluate the similarity of two vectors in a multi-dimensional space by measuring the cosine value of the angle between the two vectors. The cosine value between the two mode vectors can be determined by equation (5):

[0039]

[0040] where Similarity represents the similarity degree, cosθ represents the cosine value of the angle between the two mode vectors, and Φ1 and Φ0 represent the two mode vectors respectively.

[0041] Based on the above calculation method of the effective natural frequencies and modes of the soil-structure system, the principle of the efficient response spectrum method is described below.

[0042] According to the effective natural frequencies and mode vectors of each order, calculate the modal participation coefficients and cross-correlation coefficients, including:

[0043] Calculate the modal participation coefficients of each effective mode according to the following formula:

[0044]

[0045] where M represents the mass matrix of the soil-structure system, I represents the column vector with all elements being 1, Sj represents the index of the effective mode, γ Sj and Φ Sj represent the modal participation coefficient and mode vector of the Sj-th effective mode respectively, and T represents the transpose of the matrix.

[0046] Calculate the cross-correlation coefficient between effective modes according to the following formula:

[0047]

[0048] where Sj and Sl are the indices of two effective modes, and β jl represents the cross-correlation coefficient between the Sj-th effective mode and the Sl-th effective mode, ω Sj and ζ Sj represent the Sj-th effective natural frequency and modal damping ratio respectively, and ω Sl and ζ Sl represent the Sl-th effective natural frequency and modal damping ratio respectively.

[0049] Obtain the peak values of each single-degree-of-freedom equation according to the response spectrum theory, and then combine the peak responses of each order of modes by the Complete Quadratic Combination (CQC) method, that is:

[0050]

[0051] where Sj and Sl represent the indices of two effective modes respectively, γ Sj , ω Sj , Φ Sj and ζ Sj represent the modal participation coefficient, effective natural frequency, modal vector and modal damping ratio of the Sj-th effective mode respectively, γ Sl , ω Sl , Φ Sl and ζ Sl represent the modal participation coefficient, effective natural frequency, modal vector and modal damping ratio of the Sl-th effective mode respectively, S g (ω Sj , ζ Sj ) and S g (ω Sl , ζ Sl ) are the peak values of the soil-structure model bottom response spectrum corresponding to the Sj and Sl order modes respectively, * represents the multiplication of the elements at the corresponding positions of the vectors, and N represents the number of effective modes.

[0052] Based on the above principle, Figure 3 is the flowchart of an efficient response spectrum method for soil-structure interaction seismic analysis provided by an embodiment of the present invention. This method is applicable to the case of structural seismic analysis of soil-structure systems and is executed by an electronic device. As Figure 4 shown, this method specifically includes:

[0053] S110. Determine M, C, and K of the system according to the established soil-structure calculation model.

[0054] S120. Perform modal analysis on the structural model under the rigid foundation to determine the initial eigenvalue λ of each order (1) and the modal vector Φ (1) .

[0055] S130. According to the M and K matrices obtained in Step 1 and the initial conditions obtained in S120, execute the calculation method of the effective natural frequency and mode shown in the above Step 1 and Step 2 to obtain the effective natural frequency ω of the soil-structure system at the Sj-th order Sj and the modal vector Φ Sj .

[0056] S140. Calculate γ Sj , δ Sj (t) and β jl and substitute them into Equation (10) to obtain the peak displacement response of the structure

[0057] Optionally, Equation (10) can also use the SRSS combination method to calculate the peak response of the structure, further improving the calculation efficiency

[0058] To illustrate the effectiveness of the method of this embodiment, an application example of the method of this embodiment is given below. The problem description of this application example is as follows

[0059] Three ground structures with different heights are selected, including 5-story, 10-story and 20-story. The section information of the structural beams and columns is shown in Table 1; a typical site is selected, and the physical parameters of the site are shown in Table 2. The site is a layered site with a thickness of 50m. It is assumed that the soil layer of the site is a linear elastic material. The damping ratio of each order mode of the soil-structure system is 5%. It is assumed that the ground structure is located in a seismic intensity zone of VII degree, and the peak ground acceleration of the site is 0.15g. The design response spectrum is shown in Figure 4 . Six artificial earthquake records are generated by using the ground design response spectrum and the artificial earthquake synthesis technology. The earthquake records at the bottom of the model are obtained by inverting the surface records

[0060] Table 1. Material parameters

[0061]

[0062] Table 2 Site information

[0063]

[0064] In this embodiment, the seismic response of the structure obtained by the mode superposition method is used as a reference, and the first 1000 order system modes of the soil-structure system are selected for mode superposition Figure 5The structural responses calculated by using the proposed efficient response spectrum method are given. It can be seen that the average errors between the structural responses obtained by the proposed method and the seismic responses obtained by the mode superposition method under 6 seismic records are less than 8.23%, 7.99% and 11.2% respectively. It shows that the proposed method can obtain accurate structural seismic responses, and the calculation efficiency is improved due to the removal of many modes of the soil body.

[0065] In summary, this embodiment provides an efficient response spectrum method for seismic analysis of soil-structure interaction to calculate the seismic response of the structure in the soil-structure system. This method considers the soil-structure interaction on the basis of the traditional response spectrum method and has high calculation efficiency. It has the following beneficial results:

[0066] 1) This method can directly obtain the effective modes of the soil-structure system, avoiding the modal analysis of the overall model of the soil-structure system.

[0067] 2) This method can directly use the effective modes in the soil-structure system for mode superposition, and the execution efficiency is improved compared with the traditional method.

[0068] Figure 6 The structural schematic diagram of an electronic device provided by an embodiment of the present invention is as Figure 6 shown. The device includes a processor 60, a memory 61, an input device 62 and an output device 63; the number of processors 60 in the device can be one or more; the processors 60, the memory 61, the input device 62 and the output device 63 in the device can be connected through a bus or other means, Figure 6 and the connection through the bus is taken as an example here.

[0069] The memory 61, as a computer-readable storage medium, can be used to store software programs, computer-executable programs and modules, such as the program instructions / modules corresponding to the efficient response spectrum method for seismic analysis of soil-structure interaction in the embodiment of the present invention. The processor 60 executes various functional applications and data processing of the device by running the software programs, instructions and modules stored in the memory 61, that is, realizes the above-mentioned efficient response spectrum method for seismic analysis of soil-structure interaction.

[0070] The memory 61 may mainly include a program storage area and a data storage area. Among them, the program storage area may store an operating system and application programs required for at least one function; the data storage area may store data created according to the use of the terminal, etc. In addition, the memory 61 may include a high-speed random access memory, and may also include a non-volatile memory, such as at least one magnetic disk storage device, a flash memory device, or other non-volatile solid-state storage devices. In some instances, the memory 61 may further include a memory remotely provided with respect to the processor 60, and these remote memories may be connected to the device through a network. Examples of the above network include but are not limited to the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0071] The input device 62 may be used to receive input digital or character information, and generate key signal inputs related to user settings and function controls of the device. The output device 63 may include a display device such as a display screen.

[0072] An embodiment of the present invention also provides a computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, it implements the efficient response spectrum method for soil-structure interaction seismic analysis in any embodiment.

[0073] The computer storage medium of the embodiment of the present invention may adopt any combination of one or more computer-readable media. The computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium. The computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the above. More specific examples (non-exhaustive list) of the computer-readable storage medium include: an electrical connection having one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In this document, the computer-readable storage medium may be any tangible medium that contains or stores a program, and this program may be used by or in combination with an instruction execution system, apparatus, or device.

[0074] The computer-readable signal medium may include a data signal propagated in a baseband or as part of a carrier wave, which carries the computer-readable program code. Such a propagated data signal may take various forms, including but not limited to an electromagnetic signal, an optical signal, or any suitable combination of the above. The computer-readable signal medium may also be any computer-readable medium other than the computer-readable storage medium, and this computer-readable medium may send, propagate, or transmit a program for use by or in combination with an instruction execution system, apparatus, or device.

[0075] The program code contained on a computer-readable medium can be transmitted with any appropriate medium, including but not limited to wireless, wire, optical fiber cable, RF, etc., or any suitable combination of the above.

[0076] The computer program code for performing the operations of the present invention can be written in one or more programming languages or combinations thereof. The programming languages include object-oriented programming languages such as Java, Smalltalk, C++, and also include conventional procedural programming languages such as C language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, executed as an independent software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer can be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computer (for example, by using an Internet service provider to connect through the Internet).

[0077] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. An efficient response spectrum method for seismic analysis of soil-structure interaction, characterized in that: include: Obtain a finite element model of the soil-structure system to be analyzed, where the bottom of the model is fixed and the sides use roller boundaries; Perform modal analysis on the structural model under the rigid foundation to obtain the initial eigenvalue and initial mode of each order; According to the initial eigenvalue and mode of each order, the effective natural frequency and mode vector of each order of soil-structure system are calculated; According to the effective natural frequencies and modal vectors of each order, the modal participation coefficients of each effective mode and the mutual correlation coefficients between the effective modes are calculated; The bottom response spectrum of the soil-structure model is obtained according to the seismic hazard analysis of the specific site. For the engineering site without the seismic hazard analysis of the specific site, the bottom response spectrum of the soil-structure model is obtained by inverting the surface design spectrum through the inversion method. determining a peak response of the structure according to a bottom response spectrum of the soil-structure model; The effective mode of the soil-structure system refers to the mode in the soil-structure system that is dominated by structural vibration or contributes mainly to the structural dynamic response, and the effective natural frequency refers to the frequency corresponding to the effective mode.

2. The method according to claim 1, characterized in that The method of calculating effective natural frequencies and modal vectors of each order of the soil-structure system according to the initial eigenvalues ​​and modal vectors of each order includes: According to the initial eigenvalue λ of each order (1) and the initial modal vector Φ (1) , repeat the operations of formula (1) to formula (3) until the iteration termination condition is met: Among them, Φ (1) is the dimension of the soil-structure system, and the corresponding value of the soil freedom part is zero; M represents the mass matrix of the soil-structure system; i represents the number of iterations, λ (i) and Φ (i) denote the eigenvalue and mode vector of the i-th iteration, respectively, and λ (i+1) and Φ (i+1) denote the eigenvalue and mode vector of the i+1th iteration respectively; T denotes the transpose of the matrix; represents the mode vector of the i+1th iteration before regularization; The iteration termination condition is: And the similarity conditions of the modal vectors of the upper structure freedom part and the modal vectors of the fixed foundation structure in the soil-structure system.

3. The method according to claim 2, characterized in that The modal vector similarity condition is determined in the following way: From the modal vector Φ (i+1) extracting the modal vectors of the upper structure freedom part of the soil-structure system; Calculate the cosine similarity between the extracted modal vector and the modal vector of the fixed base structure; If the cosine similarity is greater than a set threshold, it is determined that the modal vector similarity condition is met.

4. The method according to claim 1, characterized in that: The method of calculating the modal participation coefficient and the mutual correlation coefficient between the effective modes according to the effective natural frequencies and modal vectors of each order includes: The modal participation coefficient of each effective mode is calculated according to the following formula: Where M represents the mass matrix of the soil-structure system, I represents a column vector whose elements are all 1, Sj represents the index of the effective mode, and γ Sj and Φ Sj They represent the modal participation coefficient and modal vector of the Sj-th order effective mode, respectively, and T represents the transpose of the matrix; The mutual correlation coefficient between effective modes is calculated according to the following formula: Among them, Sj and Sl are the indices of the two effective modes, β jl represents the mutual correlation coefficient between the Sj-th order effective mode and the Sl-th order effective mode, ω Sj and Sj They represent the effective natural frequency and modal damping ratio of the Sj-th order effective mode, ω Sl and Sl They respectively represent the effective natural frequency and modal damping ratio of the S1th order effective mode.

5. The method according to claim 1, characterized in that Determining the peak response of the structure according to the bottom response spectrum of the soil-structure model includes: According to the following formula, the peak response of the structure |u(t)| max : Among them, Sj and Sl represent the indexes of two valid modes respectively, γ Sj ,ω Sj , Φ Sj and Sj They represent the modal participation coefficient, effective natural frequency, modal vector and modal damping ratio of the Sj-th order effective mode, respectively. Sl ,ω Sl , Φ Sl and Sl They represent the modal participation coefficient, effective natural frequency, modal vector and modal damping ratio of the Sl-th order effective mode, respectively. g (ω Sj ,ζ Sj ) and S g (ω Sl ,ζ Sl ) are the peak values ​​of the model bottom response spectrum corresponding to the Sj and Sl order modes, * represents the multiplication of the elements at the corresponding positions of the vectors, and N represents the number of effective modes.

6. An electronic device, characterized in that: include: one or more processors; a memory for storing one or more programs, When the one or more programs are executed by the one or more processors, the one or more processors implement the efficient response spectrum method for seismic analysis of soil-structure interaction as described in any one of claims 1-5.

7. A computer-readable storage medium, characterized in that: A computer program is stored thereon, and when the program is executed by a processor, the efficient response spectrum method for seismic analysis of soil-structure interaction as described in any one of claims 1-5 is implemented.

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