High-precision seismic fluctuation input method and device for SSI (Small Scale Integration) analysis of layered stepped site

Abstract

The invention discloses a high-precision seismic fluctuation input method and device for SSI analysis of a layered stepped site, and the method comprises the steps: building a two-dimensional stepped layered site model, and introducing a Y-shaped artificial boundary to divide the two-dimensional stepped layered site model into a central finite field, a left half infinite field and a right half infinite field; applying a zigzag-paraxial combined boundary on the Y-shaped artificial boundary to simulate the radiation damping effect of the left half infinite domain and the right half infinite domain; respectively solving the seismic response of the one-dimensional horizontal layering field models of the left half infinite domain and the right half infinite domain, and obtaining the free field response of the left boundary and the right boundary of the Y shape through time delay calculation; respectively decomposing respective total field responses into scattered field responses and free field responses, calculating respective infinite domain equivalent node forces and free field node forces according to the scattered field responses and the free field responses, superposing the infinite domain equivalent node forces and the free field node forces to form two groups of final equivalent node force vectors, and respectively applying the two groups of equivalent node force vectors to the left boundary and the right boundary to obtain a final equivalent node force vector. And high-precision input of far-field vibration in layered stepped field SSI analysis is realized.

Description

Technical Field

[0001] This invention belongs to the field of dynamic analysis technology, specifically relating to a high-precision seismic wave input method and device for SSI analysis of stratified stepped sites. Background Technology

[0002] Soil-structure interaction (SSI) analysis is a core component of seismic safety assessments for large-scale infrastructure projects such as dams, nuclear power plants, and long-distance tunnels. The seismic response of these infrastructures is largely controlled by the dynamic coupling effect between the structure and the surrounding site. Complex site topography (such as stepped terrain) often amplifies ground motion, further increasing the seismic resistance requirements of the structure. Therefore, accurate SSI analysis is crucial for ensuring the seismic safety of infrastructure. Current SSI analysis primarily relies on direct methods (such as the finite element method), which requires two key technologies to achieve high-fidelity coupling analysis: first, specialized treatment of the near-field region's truncated boundary to simulate the radiation damping effect of a semi-infinite site; and second, consistent input to the site's seismic response to ensure the accuracy of seismic load application. However, traditional techniques have significant limitations when dealing with stepped, non-horizontally layered sites, failing to meet the SSI analysis requirements in complex scenarios. Specific shortcomings are as follows:

[0003] I. The traditional SSI analysis method has limitations in its applicable scenarios;

[0004] Traditional seismic seismic response analysis (SSI) methods are generally limited to horizontally layered half-space sites, and can only assess the response of sites with regular terrain and horizontally distributed strata. Their applicability to non-horizontally layered sites such as stepped structures is extremely poor. The seismic response of stepped sites is essentially a two-dimensional wave propagation problem. Incident waves (such as P-SV waves) undergo complex reflections and scattering at non-horizontal strata interfaces and step edges, requiring a two-dimensional numerical model to characterize the wavefield evolution. However, existing site seismic response analysis methods (analytical methods, semi-analytical methods, and domain-based numerical methods) are ill-suited for this scenario. Analytical methods are only applicable to homogeneous, regular terrain (such as full-space and half-space) and cannot handle irregular stepped geometries. Semi-analytical methods (such as the classical stiffness matrix method) are only applicable to horizontally layered half-spaces and are ineffective for two-dimensional wave propagation problems. Even domain-based numerical methods (such as the finite element method) have the potential to simulate complex terrain, but lack suitable boundary treatment and seismic input techniques, making accurate analysis difficult.

[0005] Second, the precision of artificial boundary technology is insufficient;

[0006] When performing direct analysis of SSI, the semi-infinite structure-site coupled system needs to be truncated into a bounded computational domain. Then, an artificial boundary is used to simulate the radiation damping effect of the truncated domain to avoid spurious reflections of outgoing waves at the truncated boundary. Existing artificial boundary methods are mainly divided into two categories, but both have shortcomings, as detailed below:

[0007] 1. Absorbing boundary conditions: including local and nonlocal methods; among them, local methods (such as viscous spring boundary, viscous boundary, transmission boundary, infinite element method) are computationally efficient, but they are approximate models and cannot accurately simulate radiation damping. The inherent error will significantly reduce the accuracy of SSI analysis. Moreover, the application of local boundaries for stepped sites in existing studies mostly relies on empirical assumptions, which further limits the accuracy; nonlocal methods (such as boundary element method, proportional boundary finite element method, thin layer method) can achieve high accuracy by solving the initial boundary value problem of infinite domain, but the computational cost is extremely high and it is difficult to apply to large-scale two-dimensional stepped site models.

[0008] 2. Absorbing layer method: This method attenuates the outgoing wave by adding an artificial material layer to the outer boundary of the computational domain. However, traditional absorbing layers (such as the early fully matched layer PML) rely on the global coordinate system and are prone to spurious reflections at the interface between the inner domain and the absorbing layer. They also have poor adaptability to irregular boundaries of stepped sites. Although the improved scaled boundary fully matched layer (SBPML) can overcome some of the limitations, it has not yet been combined with the two-dimensional numerical model of stepped sites and cannot solve the problem of radiation damping simulation in this scenario.

[0009] III. The earthquake input method has significant errors;

[0010] Existing seismic input techniques are divided into two categories: boundary-dependent and boundary-independent. However, neither can meet the precise input requirements of stepped sites. Boundary-dependent methods, such as the wave method and the artificial boundary substructure method, require the calculation of equivalent seismic loads through absorbing boundary conditions. However, their applicability is limited by stress-type artificial boundaries and cannot be adapted to the irregular truncated boundaries of stepped sites. Furthermore, load calculations are easily affected by boundary approximations, making it difficult to guarantee accuracy. Boundary-independent methods, such as the domain reduction method (DRM) and the internal substructure method, can simulate seismic wave fields in local domains and offer high flexibility, but they require prior acquisition of the site's free-field response. However, stepped sites lack effective response assessment methods, making these methods unsuitable for direct application. In addition, some studies use a hybrid wave input method (specifying the free wave field at the lateral boundary and applying an incident wave field at the bottom boundary) to approximate seismic input to stepped sites. However, this method does not consider the influence of reflected waves from the ground at the bottom boundary. When the bottom boundary is close to the observation point, the calculation error can reach as high as 20%, which seriously affects the reliability of SSI analysis results.

[0011] Fourth, core technology requirements have not been met;

[0012] In summary, traditional techniques cannot simultaneously address the two core requirements of SSI analysis for stepped sites: firstly, there is a lack of artificial boundary techniques that can accurately simulate the radiation damping of truncated boundaries in stepped sites, with existing boundaries either lacking sufficient accuracy or being too costly; secondly, there is a lack of consistent seismic input schemes suitable for stepped sites, with existing input methods either limited by boundary type or having excessively large errors. Therefore, there is an urgent need to develop high-precision artificial boundary and seismic input techniques for stepped, non-horizontally layered sites to overcome the limitations of traditional methods and achieve reliable SSI assessment in complex scenarios. Summary of the Invention

[0013] To overcome the shortcomings of existing technologies, this invention provides a high-precision seismic wave input method for SSI analysis of layered stepped sites.

[0014] The second objective of this invention is to provide a high-precision seismic wave input device for SSI analysis of stratified stepped sites.

[0015] The technical solution of the present invention to solve the above-mentioned technical problems is:

[0016] A high-precision seismic wave input method for SSI analysis of stratified stepped sites includes the following steps:

[0017] Step 1: Based on the collected geometric parameters and geological physical and mechanical parameters of the actual stratified stepped site, a two-dimensional stepped forming layer site model consistent with the morphology and geological characteristics of the actual stratified stepped site is built using numerical modeling tools.

[0018] Step 2: Introduce a Y-shaped artificial boundary to divide the semi-infinite domain corresponding to the two-dimensional stepped formation site model into a central finite domain containing the core area of ​​the stepped formation site and the area where the structure is to be constructed, as well as a left semi-infinite domain and a right semi-infinite domain; cut off the left semi-infinite domain and the right semi-infinite domain to form a closed central finite domain, and apply a tortuous-paraxial combination boundary on the Y-shaped artificial boundary to simulate the radiation damping effect of the cut-off left semi-infinite domain and right semi-infinite domain on seismic waves;

[0019] Step 3: Construct one-dimensional horizontally layered site models that perfectly match the stratigraphic characteristics of the left and right semi-infinite domains respectively. Solve the seismic response of the corresponding one-dimensional horizontally layered site models of the left and right semi-infinite domains under the preset far-field ground motion. Based on Snell's law and combined with the time delay effect, calculate the free field response at the left and right boundaries of the Y-shaped artificial boundary. The free field response includes displacement free field response and stress free field response.

[0020] Step 4: Decompose the total displacement field response and total stress field response at the left and right boundaries of the Y-shaped artificial boundary in the layered stepped site into their respective scattered field response and free field response, and calculate the free field nodal force and infinite domain equivalent nodal force at the left and right boundaries respectively. Superimpose the infinite domain equivalent nodal force and free field nodal force at the same boundary to form the final two sets of equivalent nodal force vectors at the left and right boundaries.

[0021] Step 5: Apply the two sets of equivalent nodal force vectors obtained to the nodes of the left and right boundaries of the Y-shaped artificial boundary, respectively. Through the load transfer of nodal forces, the accurate input of seismic waves in the SSI analysis of the far-field ground motion in the stratified stepped site is realized.

[0022] Preferably, in step 1, the geometric parameters include the total horizontal length of the site, the total vertical depth, the slope angle of the stepped soil layer interface, and the step size; the geological physical and mechanical parameters include shear wave velocity, compressive wave velocity, and mass density.

[0023] Preferably, in step 2, the tortuous-paraxial combined boundary is composed of a left tortuous-paraxial boundary and a right tortuous-paraxial boundary, wherein the left tortuous-paraxial boundary is used to simulate the radiation damping effect of the left half of the infinite domain on seismic waves; and the right tortuous-paraxial boundary is used to simulate the radiation damping effect of the right half of the infinite domain on seismic waves.

[0024] Preferably, the specific steps of step 2 are as follows:

[0025] Step 201: Simulate the geometry of the left and right semi-infinite domains using locally tortuous artificial boundaries;

[0026] Step 202: Using a semi-analytical method, the left and right semi-infinite domains are semi-discrete along the local coordinate p direction. Based on the displacement continuity and stress continuity conditions at the interface of adjacent thin layers, all thin layers contained in the left and right semi-infinite domains are coupled and assembled in sequence, and frequency-wavenumber domain displacement linear equations corresponding to the left semi-infinite domain and the right semi-infinite domain are established within the depth range of the region of interest, respectively.

[0027] Step 203: The dynamic characteristics of the submerged homogeneous half-space in the left and right semi-infinite domains are described using an accurate dynamic stiffness matrix; then, the accurate dynamic stiffness matrix is ​​approximated paraxially using the Taylor series expansion method, and third-order and higher small quantities are truncated; based on the approximation results, paraxial boundaries capable of simulating the radiation damping effect of the submerged homogeneous half-space in the left and right semi-infinite domains are established respectively; the paraxial boundaries are described by the paraxial boundary equations of the submerged homogeneous half-space in the left and right semi-infinite domains respectively, wherein the paraxial boundary equation of the submerged homogeneous half-space in the left semi-infinite domain is used to describe the stress-displacement relationship at the top surface of the submerged homogeneous half-space in the left semi-infinite domain; and the paraxial boundary equation of the submerged homogeneous half-space in the right semi-infinite domain is used to describe the stress-displacement relationship at the top surface of the submerged homogeneous half-space in the right semi-infinite domain.

[0028] Step 204: Based on the displacement continuity and stress balance conditions at the interface between the overlying soil layer and the underlying homogeneous half-space in the left half-infinite domain, the obtained linear displacement equations in the frequency domain and wavenumber domain of the left half-infinite domain are coupled and assembled with the obtained paraxial boundary equations of the underlying homogeneous half-space in the left half-infinite domain. After assembly, a quadratic eigenvalue problem 1 is formed. At the same time, based on the displacement continuity and stress balance conditions at the interface between the overlying soil layer and the underlying homogeneous half-space in the right half-infinite domain, the obtained linear displacement equations in the frequency domain and wavenumber domain of the right half-infinite domain are coupled and assembled with the obtained paraxial boundary equations of the underlying homogeneous half-space in the right half-infinite domain. After assembly, a quadratic eigenvalue problem 2 is formed.

[0029] Step 205: Solve the first and second quadratic eigenvalue problems respectively to obtain the dynamic response characteristic parameters of the left and right semi-infinite domains; based on the solution results, derive the dynamic stiffness matrices at the left and right boundaries of the Y-shaped artificial boundary respectively; wherein, the dynamic stiffness matrix at the left boundary is equivalent to the overall dynamic stiffness matrix of the left semi-infinite domain, and the dynamic stiffness matrix at the right boundary is equivalent to the overall dynamic stiffness matrix of the right semi-infinite domain.

[0030] Preferably, in step 3, the one-dimensional finite element artificial boundary method is used to solve the seismic response of the one-dimensional horizontally layered site model corresponding to the left and right half-infinite domains under the preset far-field ground motion; the time phase difference of the seismic wave propagating from the far field to the Y-shaped artificial boundary is determined by Snell's law, and the free field response at the left and right boundaries of the Y-shaped artificial boundary is calculated accordingly.

[0031] Preferably, step 4 consists of the following steps:

[0032] The total displacement and stress responses at the left and right boundaries of the Y-shaped artificial boundary in the stepped site are decomposed into their respective scattered field responses and free field responses. Then, the stress in the free field responses along the left and right boundaries is integrated to obtain two sets of free field nodal force vectors. Combining the tortuous-paraxial combined boundary, the displacements in the free field responses of the left and right boundaries are converted into equivalent nodal forces in the infinite domain. Finally, the equivalent nodal forces in the infinite domain and the free field nodal forces of the same boundary are superimposed to form the final two sets of equivalent nodal force vectors for the left and right boundaries.

[0033] Preferably, in step 5, by establishing the coupled control equations of the central finite domain and the tortuous-paraxial combined boundary, the two sets of equivalent nodal force vectors of the left and right boundaries are substituted into the coupled control equations as input parameters for solving. Then, based on the solution results, the equivalent nodal forces are accurately applied, and finally, high-precision seismic wave input is achieved in the SSI analysis of the stratified stepped site.

[0034] A high-precision seismic wave input device for SSI analysis of stratified stepped sites includes:

[0035] The model building module is used to build a two-dimensional stepped formation site model that is consistent with the morphology and stratigraphic characteristics of the actual stepped formation site based on the collected geometric parameters and geological physical and mechanical parameters of the actual stepped formation site using numerical modeling tools.

[0036] The boundary construction and region division module is used to introduce a Y-shaped artificial boundary to divide the semi-infinite domain corresponding to the two-dimensional stepped formation layer site model into a central finite domain containing the core area of ​​the stepped formation site and the area where the structure is to be constructed, as well as a left semi-infinite domain and a right semi-infinite domain; the left semi-infinite domain and the right semi-infinite domain are truncated to form a closed central finite domain, and a tortuous-paraxial combination boundary is applied to the Y-shaped artificial boundary to simulate the radiation damping effect of the truncated left semi-infinite domain and the right semi-infinite domain on seismic waves;

[0037] The semi-infinite domain seismic response solution module is used to construct one-dimensional horizontally layered site models that perfectly match the stratigraphic characteristics of the left and right semi-infinite domains, respectively. It solves the seismic response of the corresponding one-dimensional horizontally layered site models in the left and right semi-infinite domains under the preset far-field ground motion. Based on Snell's law and combined with the time delay effect, it calculates the free field response at the left and right boundaries of the Y-shaped artificial boundary.

[0038] The response decomposition and equivalent load conversion module is used to decompose the total displacement field response and total stress field response at the left and right boundaries of the Y-shaped artificial boundary in the layered stepped site into their respective scattered field response and free field response, and to calculate the free field nodal force and infinite domain equivalent nodal force at the left and right boundaries respectively. The infinite domain equivalent nodal force and free field nodal force at the same boundary are superimposed to form the final two sets of equivalent nodal force vectors at the left and right boundaries.

[0039] The ground motion input module is used to apply the two sets of equivalent nodal force vectors to the nodes of the left and right boundaries of the Y-shaped artificial boundary, respectively. Through the load transfer of nodal forces, the accurate input of seismic waves in far-field ground motion in SSI analysis of stratified stepped sites is realized.

[0040] An electronic device includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements the steps in the high-precision seismic wave input method for SSI analysis of stratified stepped sites.

[0041] A computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps in the high-precision seismic wave input method for SSI analysis of stratified stepped sites.

[0042] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0043] 1. The high-precision seismic wave input method for SSI analysis of stratified stepped sites proposed in this invention proposes a Y-shaped artificial boundary composed of a left boundary and a right boundary. This divides the semi-infinite domain corresponding to the two-dimensional stepped stratified site model into a central finite domain (including the structure / region of interest), a left semi-infinite domain, and a right semi-infinite domain. Through the combination mechanism of "overlying soil layer tortuous semi-discretization + underlying half-space dynamic stiffness paraxial expansion", a Y-shaped tortuous-paraxial combined boundary is constructed to accurately simulate the radiation damping effect of the left and right semi-infinite domains on seismic waves, thereby adapting to the two-dimensional wave propagation characteristics of stepped non-horizontally stratified sites.

[0044] 2. The high-precision seismic wave input method for SSI analysis of layered stepped sites in this invention establishes a "one-dimensional response-two-dimensional equivalent" seismic input logic. First, based on the stratigraphic characteristics of the left and right semi-infinite domains, the free field response of the one-dimensional horizontally layered site model of each of the left and right semi-infinite domains is calculated. Combined with the tortuous-paraxial combined boundary, the displacement and stress in the free field response are converted into two sets of equivalent nodal forces of the Y-shaped artificial boundary through wave field decomposition. This achieves consistent, low-error (relative error of 1.5%) input of far-field ground motion, thereby solving the accuracy problem of traditional mixed wave input (error of up to 20%). Attached Figure Description

[0045] Figure 1 This is a flowchart illustrating the high-precision seismic wave input method for SSI analysis of stratified stepped sites according to the present invention.

[0046] Figure 2 This is a configuration diagram of the high-precision seismic wave input method for SSI analysis of stratified stepped sites according to the present invention, wherein, Figure 2 (a) is a schematic diagram of a Y-shaped artificial boundary; Figure 2 (b) is a schematic diagram of the local coordinate system.

[0047] Figure 3 The time history (a) and Fourier amplitude spectrum (b) of the Reck wavelet as input ground motion are shown.

[0048] Figure 4 This is a schematic diagram of a stepped, uniform semi-space with a 30° inclined step structure.

[0049] Figure 5 These are schematic diagrams of four different finite element models used to solve the seismic response of a stepped homogeneous site. Figure 5 (a) is a tortuous-paraxial combined boundary model; Figure 5 (b) is a finite element model with a Y-shaped boundary cutoff of a triangle; Figure 5 (c) is a finite element model with a rectangular Y-shaped boundary cutoff; Figure 5 (d) is a finite element model with a Y-shaped boundary cutoff of general geometry.

[0050] Figure 6 yes Figure 5 The diagram shows the displacement time history and magnified distribution of peak displacement along the Earth's surface for the four finite element models at observation point A; among them, Figure 6 (a) and Figure 6 (b) are observation points A and A respectively. and The timeline; Figure 6 (c) and Figure 6 (d) represents the observation point A. and Distribution of peak displacement magnification along the Earth's surface.

[0051] Figure 7 These are wavefield snapshots taken at two selected times, t=1.5s and t=1.6s, where... Figure 7 (a) is the reference model; Figure 7 (b) is a finite element model with a Y-shaped boundary cutoff of a triangle; Figure 7 (c) is a finite element model with a rectangular Y-shaped boundary cutoff; Figure 7 (d) is a finite element model with a Y-shaped boundary cutoff of general geometry.

[0052] Figure 8 This is a schematic diagram of the five Y-shaped boundary truncated finite element models.

[0053] Figure 9 yes Figure 8 The time histories and corresponding relative errors of the five Y-shaped truncated finite element models at observation point A are as follows: Figure 9 (a) and Figure 9 (b) The finite element model and reference model are respectively cut off by five Y-shaped boundaries. and The timeline; Figure 9 (c) and 9(d) are the five Y-shaped boundary truncated finite element models and reference models, respectively. and The relative error.

[0054] Figure 10 It has =30° =60° and Schematic diagram of finite element models of three different stepped shapes of the site with a radius of 90°.

[0055] Figure 11 yes Figure 10 The time histories and corresponding relative errors of the three finite element models at observation point A are as follows: Figure 11 (a) and 11(b) are respectively and The timeline; Figure 11 (c) and 11(d) are respectively and The relative error.

[0056] Figure 12 This is a schematic diagram of a finite element model for solving the seismic response of a stepped, layered site.

[0057] Figure 13 At the angle of incidence The displacement time history and peak surface displacement distribution at observation point A under the action of obliquely incident SV waves are shown below. Figure 13 (a) and Figure 13 (b) are observation points A and A respectively. and The timeline; Figure 13 (c) and Figure 13 (d) are the observation points respectively and Peak distribution along the Earth's surface.

[0058] Figure 14 At two selected times and A snapshot of the wave field below.

[0059] Figure 15 It is used to analyze the slope angle. A schematic diagram of five control models for a stepped site.

[0060] Figure 16 yes Figure 15 The time histories and corresponding relative errors of the five control models at observation point A are as follows: Figure 16 (a) and Figure 16 (b) respectively and The timeline; Figure 16 (c) and Figure 16 (d) are respectively and The relative error. Detailed Implementation

[0061] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0062] Example 1

[0063] See Figure 1 and Figure 2 The high-precision seismic wave input method for SSI analysis of stratified stepped sites of the present invention includes the following steps:

[0064] Step 1: Based on the collected geometric parameters and geological physical and mechanical parameters of the actual stratified stepped site, a two-dimensional stepped site model consistent with the morphology and geological characteristics of the actual stratified stepped site is constructed using numerical modeling tools. The geometric parameters include the total horizontal length, total vertical depth, slope angle of the stepped soil layer interface, and step size. The geological physical and mechanical parameters include shear wave velocity, compressive wave velocity, and mass density.

[0065] Step 2: Introduce a Y-shaped artificial boundary to divide the semi-infinite domain corresponding to the two-dimensional stepped formation site model into a central finite domain containing the core area of ​​the stepped formation site and the proposed structural area, as well as a left and right semi-infinite domains. Truncate the left and right semi-infinite domains to form a closed central finite domain. Apply a tortuous-paraxial composite boundary to the Y-shaped artificial boundary to simulate the radiation damping effect of the truncated left and right semi-infinite domains on seismic waves. The tortuous-paraxial composite boundary is composed of a left tortuous-paraxial boundary and a right tortuous-paraxial boundary. The left tortuous-paraxial boundary is used to simulate the radiation damping effect of the left semi-infinite domain on seismic waves, while the right tortuous-paraxial boundary is used to simulate the radiation damping effect of the right semi-infinite domain on seismic waves.

[0066] In this embodiment, the central finite domain Ω includes layered soil layers and structures (such as tunnels and nuclear island foundations). This central finite domain Ω is non-homogeneous or nonlinear and is discretized using the finite element method, making it the core region for SSI analysis; although the left half-infinite domain With the right half of the infinite domain It also exhibits an irregular geometric shape, but assuming that its depth direction maintains its layered characteristics, it can be simplified into a horizontally layered model, which is then truncated as a far-field wave source region.

[0067] For the layered soil layers contained in the left and right semi-infinite domains, a local coordinate system is introduced within each layered soil layer. ), to describe the geometry of the left and right boundaries; where The axis has the same direction as the x-axis in the original coordinate system. The axis is then aligned with the boundary line of the corresponding boundary (e.g., Figure 2 (b) shown); in each layer of soil Inside, assuming displacement field exist It exhibits a linear variation on the axis, in If the displacement field changes exponentially along the axis, then the expression based on wave theory is:

[0068] (1)

[0069] In the formula: and These represent the wave number and angular frequency, respectively. The imaginary unit; It is along The direction of the axis defines the one-dimensional finite element shape function; where... and They are respectively with the layered soil layers The one-dimensional finite element shape function associated with the two nodes; It is the nodal displacement vector in the frequency-wavenumber domain; the definition of the variable in the frequency-wavenumber domain is represented by a double wavy line;

[0070] Substituting the displacement field expression (i.e., equation (1)) into the wave equation, based on the displacement continuity condition and stress continuity condition at the interface of adjacent thin layers, the wave equations of all thin layers contained in the left half-infinite domain and the right half-infinite domain are coupled and assembled in sequence through the principle of virtual work, and the frequency domain-wavenumber domain displacement linear equation system corresponding to the left half-infinite domain and the frequency domain-wavenumber domain displacement linear equation system corresponding to the right half-infinite domain are established respectively within the depth range of the region of interest.

[0071] (2)

[0072] In the formula: subscript Quantities related to "multi-layered domains"; matrices , and The coefficient matrix assembled from the sublayer matrix corresponds to the quadratic, linear, and constant terms of the displacement, reflecting the physical and mechanical properties of the multilayer medium (such as elastic modulus, density, and continuity of the layer interface).

[0073] The stress vector on the right-hand side of the frequency-wavenumber domain displacement linear equations can be written as:

[0074] (3)

[0075] In the formula: Indicates application to the base of layered soil stress vector (e.g.) Figure 2 (as shown in (a))

[0076] For the underlying homogeneous half-space with left and right semi-infinite domains, the paraxial approximation method is used to simplify its accurate dynamic stiffness matrix, and the interface between the soil layer and the half-space is established. The mapping relationship between stress and displacement at a given point yields the paraxial boundary equation of the underlying homogeneous half-space; where,

[0077] The precise dynamic stiffness matrix is:

[0078] (4)

[0079] in,

[0080] ; (5)

[0081] In the formula: h represents a variable related to the lower homogeneous half-space; and These are P-wave velocity and SV-wave velocity, respectively. Indicates shear modulus;

[0082] The paraxial boundary equation of the homogeneous half-space is:

[0083] (6)

[0084] In the formula: , , This is a coefficient matrix, the values ​​of which are determined by the material properties of the underlying homogeneous half-space.

[0085] Based on soil-half-space interface Based on the displacement continuity condition and stress balance condition at the interface between the overlying soil layer and the underlying homogeneous half-space in the right half-infinite domain, the obtained linear displacement equations in the frequency domain and wavenumber domain are coupled and assembled with the obtained paraxial boundary equations of the underlying homogeneous half-space in the left half-infinite domain (i.e., assembling equations (2) and (6)). After assembly, a quadratic eigenvalue problem 1 is formed. At the same time, based on the displacement continuity condition and stress balance condition at the interface between the overlying soil layer and the underlying homogeneous half-space in the right half-infinite domain, the obtained linear displacement equations in the frequency domain and wavenumber domain of the right half-infinite domain are coupled and assembled with the obtained paraxial boundary equations of the underlying homogeneous half-space in the right half-infinite domain (i.e., assembling equations (2) and (6)). After assembly, a quadratic eigenvalue problem 2 is formed. The quadratic eigenvalue problem 1 and the quadratic eigenvalue problem 2 are solved respectively to obtain the dynamic response characteristic parameters of the left half-infinite domain and the right half-infinite domain. Based on the solution results, Y is derived respectively. The dynamic stiffness matrices at the left and right boundaries of the artificial boundary; wherein, the dynamic stiffness matrix at the left boundary is equivalent to the overall dynamic stiffness matrix of the left half-infinite domain, and the dynamic stiffness matrix at the right boundary is equivalent to the overall dynamic stiffness matrix of the right half-infinite domain.

[0086] The quadratic eigenvalue problem is as follows:

[0087] (7)

[0088] In the formula: , , , where the symbol Represents finite element assembly;

[0089] In conservative systems (i.e., without energy exchange), independent vibrational modes (i.e., eigenvectors in equation (7)) constitute a complete basis set, which means that any radiative displacement in the frequency-wavenumber domain... and any radiation displacement in the frequency domain All can be represented as follows:

[0090] (8)

[0091] In the formula: It is a diagonal matrix, whose diagonal elements Corresponding to all along eigenvalues ​​of the outgoing wave propagating in the negative direction of the axis ; This is the corresponding eigenvector matrix; This is a vector of undetermined coefficients; a single wavy line represents the definition of the variables in the frequency domain.

[0092] To determine the paraxial boundary conditions of the left boundary, it is necessary to calculate the left boundary. Consistent nodal forces on the upper boundary; by assembling the nodal vectors of the layered soil and the lower half-space, the left boundary can be... The nodal force at one of the nodes is represented as:

[0093] (9)

[0094] Where: matrix The detailed calculation process can be found using existing methods;

[0095] Substituting equation (8) into equation (9), we can obtain the left boundary. The mapping relationship between force and displacement is as follows:

[0096] (10)

[0097] Therefore, the left boundary Dynamic stiffness matrix for:

[0098] (11)

[0099] Equation (11) above gives the formula for simulating the left-half infinite field. The radiation-damped left-bending paraxial combined boundary, while the right-half infinite domain Dynamic stiffness matrix It can also be derived using a similar method.

[0100] Step 3: Construct one-dimensional horizontally layered site models that perfectly match the stratigraphic characteristics of the left and right semi-infinite domains respectively. Solve the seismic response of the corresponding one-dimensional horizontally layered site models of the left and right semi-infinite domains under the preset far-field ground motion. Based on Snell's law and combined with the time delay effect, calculate the free field response at the left and right boundaries of the Y-shaped artificial boundary.

[0101] In this embodiment, the one-dimensional finite element artificial boundary method is used to solve the seismic response of the one-dimensional horizontally layered site model corresponding to the left and right semi-infinite domains under the preset far-field ground motion. The time phase difference of the seismic wave propagating from the far field to the Y-shaped artificial boundary is determined by Snell's law, and the free field response at the left and right boundaries of the Y-shaped artificial boundary is calculated accordingly. The free field response includes displacement free field response and stress free field response.

[0102] For the left boundary The free field response on is , , and ;

[0103] For the right boundary The free field response on is , , and ;

[0104] Step 4: Using the wave field superposition method, the left boundary of the Y-shaped artificial boundary in the layered stepped site is... and right boundary The total displacement field response and total stress field response (the total field response is caused by the incident seismic wave and includes both the total displacement field response and the total stress field response) at a given location are decomposed into their respective scattered field responses (using superscript). (represented by) and free field response (using superscript) (represented by), where the free field response is initially unaffected by the central finite field. The influence of structure and topography;

[0105] For the left boundary Then we have:

[0106] (12)

[0107] (13)

[0108] For the right boundary Then we have:

[0109] (14)

[0110] (15)

[0111] Subsequently, the stress in the free field response is integrated along the left and right boundaries respectively to obtain two sets of free field nodal force vectors; combined with the tortuous-paraxial combined boundary (i.e., radiation damping simulation of the scattered field), where...

[0112] The boundary force-displacement equation for the left boundary is:

[0113] (16)

[0114] The boundary force-displacement equation for the right boundary is:

[0115] (17)

[0116] The displacements in the free field responses of the left and right boundaries are converted into equivalent nodal forces in the infinite domain. Finally, the equivalent nodal forces in the infinite domain of the same boundary are superimposed with the free field nodal forces, that is, equations (12) and (14) are substituted into equations (16) and (17) respectively. Then, the resulting expressions are substituted into equations (13) and (15) respectively to form the final two sets of equivalent nodal force vectors for the left and right boundaries:

[0117] (18)

[0118] (19)

[0119] Step 5: By establishing the coupled control equations of the central finite domain and the tortuous-paraxial combined boundary, the two sets of equivalent nodal force vectors on the left and right boundaries are... and The input parameters are substituted into the coupled control equations for solution, and the equivalent nodal forces are accurately applied based on the solution results, ultimately achieving high-precision seismic wave input in SSI analysis of stratified stepped sites.

[0120] Among them, the central finite domain The frequency-dependent finite element equations can be expressed in block matrix form:

[0121] (20)

[0122] in,

[0123] (twenty one)

[0124] Substituting equations (18) and (19) into equation (20), the resulting coupling control equation is:

[0125] (twenty two)

[0126] In the formula: , and These are the mass matrix, damping matrix, and stiffness matrix, respectively. Represents the nodal displacement vector; Represents the nodal force vector; superscript Indicates the relationship with the central finite field Related variables; subscripts , and Representing the central finite field respectively Left boundary and right boundary Nodes on; subscript Indicates at the left boundary and right boundary Common nodes on the composite lines;

[0127] Example 2

[0128] The effectiveness and feasibility of the high-precision seismic wave input method for SSI analysis of stratified stepped sites of the present invention are analyzed through specific cases below;

[0129] Choose the Lake wavelet as the input ground motion; Figure 3 (a) and 3(b) depict the time history and Fourier amplitude spectrum of the Ricker wavelet (the horizontal axis represents frequency, and the vertical axis represents amplitude), respectively. The analytical expression of the Ricker wavelet can be expressed as:

[0130]

[0131] In the formula: , , These represent the amplitude of ground motion, the dominant frequency of the Fourier spectrum, and the time it takes for ground motion to reach its peak value.

[0132] This embodiment will use three different sets of material parameters, as detailed in Table 1:

[0133] Table 1: Material properties of the soil layers used

[0134]

[0135] like Figure 4 As shown, the seismic response of the stepped uniform half-space site under the action of a vertically incident P-wave is first calculated to verify the effectiveness of the method proposed in this invention.

[0136] The site model of the stepped uniform half-space site includes a Furthermore, the structure is an inclined stepped structure with a height difference of 50 meters; the material properties of the stepped uniform half-space site correspond to the data of the first layer listed in Table 1; the incident wave uses a Ricker wavelet, whose characteristic parameters include amplitude. Main frequency and center time In this embodiment, four different finite element models were constructed, namely, as follows: Figure 5 As shown in (a)-5(d), four different finite element models are included: (a) a tortuous-paraxial combined boundary model; (b) a triangular Y-shaped boundary truncated finite element model; (c) a rectangular Y-shaped boundary truncated finite element model; and (d) a Y-shaped boundary truncated finite element model with a general geometry. All four finite element models are spatially discretized using isoparametric quadrilateral elements with side lengths less than one-tenth of the minimum wavelength. In this frequency domain analysis, the following method is used... The frequency step size; point A at the toe of the slope was selected as the key observation point to record the seismic response.

[0137] In vertically incident P-wave ( Under the influence of ), the displacement time histories of the four finite element models at observation point A and the amplified distribution of peak displacement along the ground surface are as follows: Figure 6 As shown, specifically, Figure 6 (a) and Figure 6 (b) The observation points A are given respectively. and The time history is represented by the horizontal axis as time and the vertical axis as displacement; for quantitative comparison, a reference solution obtained from the extended mesh model is also included. Figure 6 (c) and Figure 6 (d) shows respectively and The peak displacement amplification distribution along the Earth's surface; among which, Figure 6 In this context, Reference represents the reference model, Rect represents the rectangular Y-shaped boundary truncated finite element model, General geom represents the Y-shaped boundary truncated finite element model with general geometry, and Only surf represents the tortuous-paraxial combined boundary model.

[0138] Figure 7 Given at two selected times and A snapshot of the wave field; from Figure 7 As can be observed, the wave field snapshots of the three different finite element models perfectly match the reference model, thus verifying the effectiveness of the method proposed in this invention.

[0139] Furthermore, this embodiment is analyzed again. Figure 4 The stepped uniform half-space field shown has an incident angle of [missing information]. The seismic response under the action of inclined incident P-waves focuses on the influence of the combination point location of the Y-shaped boundary and the influence of the slope angle on the performance of the method proposed in this invention.

[0140] Five Y-shaped boundary truncated finite element models were established, such as Figure 8 As shown in (a)-8(d); these Y-shaped boundary truncated finite element models differ in the location of the combination point of the Y-shaped tortuous-paraxial combined boundary; the detailed dimensions of these five Y-shaped boundary truncated finite element models are also marked in Figure 8 middle.

[0141] Figure 9 The time history and corresponding relative error at observation point A were compared. This relative error is defined as the Euclidean norm of the relative error at the selected sampling point as a function of time, used to quantitatively assess the accuracy. Its expression is:

[0142]

[0143] In this context, the superscript (ref) indicates a reference solution;

[0144] Figure 9 (a) and 9(b) illustrate five Y-shaped truncated finite element models (Model 1, Model 2, Model 3, Model 4, and Model 5) and a reference model. and The time history shows that the five Y-shaped boundary truncated finite element models have good consistency throughout the simulation; Figure 9 (c) and 9(d) show the corresponding relative errors, with the relative errors of all Y-shaped boundary truncated finite element models remaining around 4.5%; considering Figure 8 Despite the geometric irregularities of the model shown and the mesh generation differences between the five Y-shaped boundary truncated finite element models and their reference models, the method proposed in this invention still possesses high computational accuracy and robustness.

[0145] Furthermore, this embodiment also discusses the verification of the method proposed in this invention for evaluating sites with different slope angles. Similarly, three Y-shaped boundary-truncated finite element models were developed for three different stepped-shaped sites with slope angles of 30°, 60°, and 90°, as follows: Figure 10 As shown in (a)-10(c).

[0146] Figure 11 The time history at observation point A and the corresponding relative error over time were compared. Figure 11 (a) and 11(b) present three finite element models and their corresponding reference models. and The timeline; Figure 11 (c) and 11(d) show the corresponding relative errors; the relative errors of all Y-shaped boundary truncated finite element models remain around 4%. Furthermore, in the case of… A smaller relative error (i.e., 1.6%) was observed in the stepped field with a radius of 90°, and in this case, the grid division near observation point A was consistent with the reference model; therefore, compared to the 30° and 60° cases, The Y-shaped boundary truncated finite element model has higher computational accuracy.

[0147] Example 3

[0148] This embodiment further analyzes the seismic response of a two-layered, stepped site; such as Figure 12 As shown, the stepped, tiered site consists of two separate areas with... and The slope is composed of stepped sections; the height difference between the two stepped sections is 150m. The material properties of the first and second sections and the lower half-space are shown in Table 1; point A, located at the bottom of the second slope, is selected as the observation point.

[0149] The characteristic of the incident Reich wavelet is its amplitude Main frequency and center time The model uses structured quadrilateral elements for spatial discretization, with the maximum element side length less than 2m to ensure simulation accuracy. In this frequency domain analysis, the frequency increment is set to... The detailed dimensions of the model are also available. Figure 12 The information is provided in the text.

[0150] At the angle of incidence Under the action of obliquely incident SV waves, the displacement time history and the distribution of peak surface displacement at observation point A are as follows: Figure 13 As shown; Figure 13 (a) and Figure 13 (b) The observation points A and A are given respectively. and The timeline; Figure 13 (c) and Figure 13 (d) shows the observation points A and A respectively. and Peak distribution along the Earth's surface; additionally, Figure 14 It also gives the two selected times. and A snapshot of the wave field.

[0151] The results show that the results obtained by the proposed method are in good agreement with the reference results of the reference model, thus verifying the effectiveness of the proposed method.

[0152] Example 4

[0153] To further verify the advantages of the method proposed in this invention, this embodiment conducts a comprehensive comparative analysis of the method proposed in this invention with other commonly used input methods, such as... Figure 15 As shown; for ease of explanation, a model with... A stepped, uniform field is used as a typical case; the material properties correspond to the data for the first layer listed in Table 1; the incident wave uses a Ricker wavelet, whose characteristic parameters include amplitude. Main frequency and center time ;

[0154] In addition to the method proposed in this invention, four control models have been established, such as... Figure 15 As shown, the first two models ( Figure 15 (a) and Figure 15 (b) The combined one-dimensional input is used, but the artificial boundary treatment differs; one uses a local viscous spring (VS) boundary, and the other uses the SBPML model; it can be seen that the combined one-dimensional input means applying left-side free field motion to the left part of the left and bottom boundaries, and right-side free field motion to the right part of the right and bottom boundaries; the other two models (i.e. Figure 15 (c) and Figure 15 (d) Follow the traditional hybrid input method originally developed for non-horizontally layered sites, in which VS boundaries or SBPML are used to absorb scattered waves; in this hybrid input scheme, free wave fields are defined on the two lateral boundaries, while incident wave fields are applied at the bottom.

[0155] These four control models are represented as combined one-dimensional inputs based on viscoelastic boundaries (VS), combined one-dimensional inputs based on scaled boundary perfect matching layers (SBPML), mixed inputs based on viscoelastic boundaries (VS), and mixed inputs based on scaled boundary perfect matching layers (SBPML), as shown in Table 2. It should be noted that in practical applications, the mixed inputs with SBPML models are introduced through DRM, while the other control models use traditional fluctuation methods. The computational model using the method proposed in this invention is as follows: Figure 15 As shown in (e); point A, located at the toe of the slope (see...). Figure 15 These were selected as key observation points; the detailed geometric dimensions of these models are as follows: Figure 15 As shown;

[0156] Table 2: Comparison of the method proposed in this invention with other control models

[0157]

[0158] Figure 16 This shows the observation point A. and The time history and the corresponding relative error that changes over time. Figure 16 (a) and 16(b) show that the results of the method proposed in this invention are in high agreement with the results of the reference model, while there are significant differences between the four control models implemented in the fluctuation method and DRM. Figure 16 (c) and 16(d) show that the relative error of the method proposed in this invention remains below 1.5%, which is much smaller than the relative errors of combined one-dimensional input based on viscoelastic boundary (VS) (15.7%), combined one-dimensional input based on scaled boundary perfect matching layer (SBPML) (13.6%), mixed input based on viscoelastic boundary (VS) (19.2%), and mixed input based on scaled boundary perfect matching layer (SBPML) (10.1%).

[0159] Example 5

[0160] The high-precision seismic wave input device for SSI analysis of stratified stepped sites of the present invention includes:

[0161] The model building module is used to build a two-dimensional stepped formation site model that is consistent with the morphology and stratigraphic characteristics of the actual stepped formation site based on the collected geometric parameters and geological physical and mechanical parameters of the actual stepped formation site using numerical modeling tools.

[0162] The boundary construction and region division module is used to introduce a Y-shaped artificial boundary to divide the semi-infinite domain corresponding to the two-dimensional stepped formation layer site model into a central finite domain containing the core area of ​​the stepped formation site and the area where the structure is to be constructed, as well as a left semi-infinite domain and a right semi-infinite domain; the left semi-infinite domain and the right semi-infinite domain are truncated to form a closed central finite domain, and a tortuous-paraxial combination boundary is applied to the Y-shaped artificial boundary to simulate the radiation damping effect of the truncated left semi-infinite domain and the right semi-infinite domain on seismic waves;

[0163] The semi-infinite domain seismic response solution module is used to construct one-dimensional horizontally layered site models that perfectly match the stratigraphic characteristics of the left and right semi-infinite domains, respectively, and solve the seismic response of the corresponding one-dimensional horizontally layered site models in the left and right semi-infinite domains under the preset far-field ground motion. Based on Snell's law and combined with the time delay effect, the displacement free field response and stress free field response at the left and right boundaries of the Y-shaped artificial boundary are calculated.

[0164] The response decomposition and equivalent load conversion module is used to decompose the total displacement field response and total stress field response at the left and right boundaries of the Y-shaped artificial boundary in the layered stepped site into their respective scattered field response and free field response. The stress in the free field response is integrated along the left and right boundaries to obtain two sets of free field nodal force vectors. Combining the tortuous-paraxial combined boundary, the displacement in the free field response of the left and right boundaries is converted into an infinite domain equivalent nodal force. Finally, the infinite domain equivalent nodal force and the free field nodal force of the same boundary are superimposed to form the final two sets of equivalent nodal force vectors for the left and right boundaries.

[0165] The ground motion input module is used to apply the two sets of equivalent nodal force vectors to the nodes of the left and right boundaries of the Y-shaped artificial boundary, respectively. Through the load transfer of nodal forces, the accurate input of seismic waves in far-field ground motion in SSI analysis of stratified stepped sites is realized.

[0166] Example 6

[0167] The electronic device of the present invention includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements the steps in the high-precision seismic wave input method for SSI analysis of stratified stepped sites.

[0168] Example 7

[0169] The present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps in the high-precision seismic wave input method for SSI analysis of stratified stepped sites.

[0170] The above are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above content. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A high-precision seismic wave input method for SSI analysis of stratified stepped sites, characterized in that, Includes the following steps: Step 1: Based on the collected geometric parameters and geological physical and mechanical parameters of the actual stratified stepped site, a two-dimensional stepped forming layer site model consistent with the morphology and geological characteristics of the actual stratified stepped site is built using numerical modeling tools. Step 2: Introduce a Y-shaped artificial boundary to divide the semi-infinite domain corresponding to the two-dimensional stepped formation site model into a central finite domain containing the core area of ​​the stepped formation site and the area where the structure is to be constructed, as well as a left semi-infinite domain and a right semi-infinite domain; cut off the left semi-infinite domain and the right semi-infinite domain to form a closed central finite domain, and apply a tortuous-paraxial combination boundary on the Y-shaped artificial boundary to simulate the radiation damping effect of the cut-off left semi-infinite domain and right semi-infinite domain on seismic waves; Step 3: Construct one-dimensional horizontally layered site models that perfectly match the stratigraphic characteristics of the left and right semi-infinite domains respectively. Solve the seismic response of the corresponding one-dimensional horizontally layered site models of the left and right semi-infinite domains under the preset far-field ground motion. Based on Snell's law and combined with the time delay effect, calculate the free field response at the left and right boundaries of the Y-shaped artificial boundary. The free field response includes displacement free field response and stress free field response. Step 4: Decompose the total displacement field response and total stress field response at the left and right boundaries of the Y-shaped artificial boundary in the layered stepped site into their respective scattered field response and free field response, and calculate the free field nodal force and infinite domain equivalent nodal force at the left and right boundaries respectively. Superimpose the infinite domain equivalent nodal force and free field nodal force at the same boundary to form the final two sets of equivalent nodal force vectors at the left and right boundaries. Step 5: Apply the two sets of equivalent nodal force vectors obtained to the nodes of the left and right boundaries of the Y-shaped artificial boundary, respectively. Through the load transfer of nodal forces, the accurate input of seismic waves in the SSI analysis of the far-field ground motion in the stratified stepped site is realized.

2. The high-precision seismic wave input method for SSI analysis of stratified stepped sites according to claim 1, characterized in that, In step 1, the geometric parameters include the total horizontal length of the site, the total vertical depth, the slope angle of the stepped soil layer interface, and the step size; the geological physical and mechanical parameters include shear wave velocity, compressive wave velocity, and mass density.

3. The high-precision seismic wave input method for SSI analysis of stratified stepped sites according to claim 1, characterized in that, In step 2, the tortuous-paraxial combined boundary is composed of a left tortuous-paraxial boundary and a right tortuous-paraxial boundary, which are independent of each other. The left tortuous-paraxial boundary is used to simulate the radiation damping effect of the left half of the infinite domain on seismic waves, while the right tortuous-paraxial boundary is used to simulate the radiation damping effect of the right half of the infinite domain on seismic waves.

4. The high-precision seismic wave input method for SSI analysis of stratified stepped sites according to claim 3, characterized in that, The specific steps of step 2 are as follows: Step 201: Simulate the geometry of the left and right semi-infinite domains using locally tortuous artificial boundaries; Step 202: Using a semi-analytical method, the left and right semi-infinite domains are semi-discrete along the local coordinate p direction. Based on the displacement continuity and stress continuity conditions at the interface of adjacent thin layers, all thin layers contained in the left and right semi-infinite domains are coupled and assembled in sequence, and frequency-wavenumber domain displacement linear equations corresponding to the left semi-infinite domain and the right semi-infinite domain are established within the depth range of the region of interest, respectively. Step 203: The dynamic characteristics of the submerged homogeneous half-space in the left and right semi-infinite domains are described using an accurate dynamic stiffness matrix; then, the accurate dynamic stiffness matrix is ​​approximated paraxially using the Taylor series expansion method, and third-order and higher small quantities are truncated; based on the approximation results, paraxial boundaries capable of simulating the radiation damping effect of the submerged homogeneous half-space in the left and right semi-infinite domains are established respectively; the paraxial boundaries are described by the paraxial boundary equations of the submerged homogeneous half-space in the left and right semi-infinite domains respectively, wherein the paraxial boundary equation of the submerged homogeneous half-space in the left semi-infinite domain is used to describe the stress-displacement relationship at the top surface of the submerged homogeneous half-space in the left semi-infinite domain; and the paraxial boundary equation of the submerged homogeneous half-space in the right semi-infinite domain is used to describe the stress-displacement relationship at the top surface of the submerged homogeneous half-space in the right semi-infinite domain. Step 204: Based on the displacement continuity and stress balance conditions at the interface between the overlying soil layer and the underlying homogeneous half-space in the left half-infinite domain, the obtained linear displacement equations in the frequency domain and wavenumber domain of the left half-infinite domain are coupled and assembled with the obtained paraxial boundary equations of the underlying homogeneous half-space in the left half-infinite domain. After assembly, a quadratic eigenvalue problem 1 is formed. At the same time, based on the displacement continuity and stress balance conditions at the interface between the overlying soil layer and the underlying homogeneous half-space in the right half-infinite domain, the obtained linear displacement equations in the frequency domain and wavenumber domain of the right half-infinite domain are coupled and assembled with the obtained paraxial boundary equations of the underlying homogeneous half-space in the right half-infinite domain. After assembly, a quadratic eigenvalue problem 2 is formed. Step 205: Solve the first and second quadratic eigenvalue problems respectively to obtain the dynamic response characteristic parameters of the left and right semi-infinite domains; based on the solution results, derive the dynamic stiffness matrices at the left and right boundaries of the Y-shaped artificial boundary respectively; wherein, the dynamic stiffness matrix at the left boundary is equivalent to the overall dynamic stiffness matrix of the left semi-infinite domain, and the dynamic stiffness matrix at the right boundary is equivalent to the overall dynamic stiffness matrix of the right semi-infinite domain.

5. The high-precision seismic wave input method for SSI analysis of stratified stepped sites according to claim 4, characterized in that, In step 3, the one-dimensional finite element artificial boundary method is used to solve the seismic response of the one-dimensional horizontally layered site model corresponding to the left and right semi-infinite domains under the preset far-field ground motion. The time phase difference of the seismic wave propagating from the far field to the Y-shaped artificial boundary is determined by Snell's law, and the free field response at the left and right boundaries of the Y-shaped artificial boundary is calculated accordingly.

6. The high-precision seismic wave input method for SSI analysis of stratified stepped sites according to claim 5, characterized in that, The specific steps of step 4 are as follows: The total displacement and stress responses at the left and right boundaries of the Y-shaped artificial boundary in the stepped site are decomposed into their respective scattered field responses and free field responses. Then, the stress in the free field responses along the left and right boundaries is integrated to obtain two sets of free field nodal force vectors. Combining the tortuous-paraxial combined boundary, the displacements in the free field responses of the left and right boundaries are converted into equivalent nodal forces in the infinite domain. Finally, the equivalent nodal forces in the infinite domain and the free field nodal forces of the same boundary are superimposed to form the final two sets of equivalent nodal force vectors for the left and right boundaries.

7. The high-precision seismic wave input method for SSI analysis of stratified stepped sites according to claim 6, characterized in that, In step 5, by establishing the coupled control equations of the central finite domain and the tortuous-paraxial combined boundary, the two sets of equivalent nodal force vectors of the left and right boundaries are substituted into the coupled control equations as input parameters for solving. Then, based on the solution results, the equivalent nodal forces are accurately applied, and finally, high-precision seismic wave input is achieved in the SSI analysis of the stratified stepped site.

8. A high-precision seismic wave input device for SSI analysis of stratified stepped sites, characterized in that, include: The model building module is used to build a two-dimensional stepped formation site model that is consistent with the morphology and stratigraphic characteristics of the actual stepped formation site based on the collected geometric parameters and geological physical and mechanical parameters of the actual stepped formation site using numerical modeling tools. The boundary construction and region division module is used to introduce a Y-shaped artificial boundary to divide the semi-infinite domain corresponding to the two-dimensional stepped formation layer site model into a central finite domain containing the core area of ​​the stepped formation site and the area where the structure is to be constructed, as well as a left semi-infinite domain and a right semi-infinite domain; the left semi-infinite domain and the right semi-infinite domain are truncated to form a closed central finite domain, and a tortuous-paraxial combination boundary is applied to the Y-shaped artificial boundary to simulate the radiation damping effect of the truncated left semi-infinite domain and the right semi-infinite domain on seismic waves; The semi-infinite domain seismic response solution module is used to construct one-dimensional horizontally layered site models that perfectly match the stratigraphic characteristics of the left and right semi-infinite domains, respectively. It solves the seismic response of the corresponding one-dimensional horizontally layered site models in the left and right semi-infinite domains under the preset far-field ground motion. Based on Snell's law and combined with the time delay effect, it calculates the free field response at the left and right boundaries of the Y-shaped artificial boundary. The response decomposition and equivalent load conversion module is used to decompose the total displacement field response and total stress field response at the left and right boundaries of the Y-shaped artificial boundary in the layered stepped site into their respective scattered field response and free field response, and to calculate the free field nodal force and infinite domain equivalent nodal force at the left and right boundaries respectively. The infinite domain equivalent nodal force and free field nodal force at the same boundary are superimposed to form the final two sets of equivalent nodal force vectors at the left and right boundaries. The ground motion input module is used to apply the two sets of equivalent nodal force vectors to the nodes of the left and right boundaries of the Y-shaped artificial boundary, respectively. Through the load transfer of nodal forces, the accurate input of seismic waves in far-field ground motion in SSI analysis of stratified stepped sites is realized.

9. An electronic device, characterized in that, The electronic device includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements the steps in the high-precision seismic wave input method for SSI analysis of stratified stepped sites as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the high-precision seismic wave input method for SSI analysis of stratified stepped sites as described in any one of claims 1 to 7.

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