A simplified input method and system for seismic loads applicable to stratified soil foundations

Abstract

This invention proposes a simplified input method and system for seismic loads on layered soil foundations, belonging to the field of earthquake engineering technology. The method includes: constructing a finite domain model of the layered foundation and setting viscoelastic artificial boundaries; obtaining the constraint nodal forces at the boundary nodes through static analysis; performing equivalent boundary condition processing based on matrix decomposition to eliminate theoretical inconsistencies in static and dynamic analysis; assuming vertical seismic wave incidence, solving for the free-field response considering the initial transmission, reflection, and reverse re-incidence processes of the wave at the layered interface, and calculating the equivalent seismic nodal forces; finally, superimposing the equivalent static constraint nodal forces and equivalent seismic nodal forces and applying them in batches to the boundary nodes. This invention, through equivalent processing of static and dynamic boundaries and free-field analysis considering multiple transmission and reflection, avoids inconsistencies in boundary conditions and inaccurate wave propagation simulations in the seismic response analysis of layered soil foundations, making it more suitable for practical engineering implementation.

Description

Technical Field

[0001] This invention belongs to the field of earthquake engineering technology, and in particular relates to a simplified input method and system for seismic loads applicable to layered soil foundations. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] With the rapid development of large-scale geotechnical engineering projects such as high earth-rock dams, offshore wind power, and underground structures, seismic response analysis of layered soil foundation-structure interaction systems has become a crucial aspect of engineering design. In the numerical simulation of semi-infinite layered soil foundations, how to reasonably simulate the infinite domain radiation effect and how to accurately input seismic loads are the two core issues affecting the calculation accuracy.

[0004] In existing technologies, viscoelastic artificial boundaries and other dynamic artificial boundaries are often used to simulate the radiation damping effect of an infinite foundation. These boundaries are derived based on wave theory and can effectively absorb outwardly propagating scattered waves.

[0005] However, in engineering practice requiring coupled static and dynamic analysis, the initial geostress field is typically established using fixed-constraint boundaries for static analysis, while subsequent dynamic analysis requires switching to artificial boundaries. Because the theoretical foundations of static and dynamic artificial boundaries are inconsistent, this switch in boundary conditions can easily lead to distortion of the initial geostress field, consequently causing errors in subsequent seismic response calculations.

[0006] Furthermore, regarding seismic input, existing methods often directly apply seismic load input methods suitable for homogeneous foundations to stratified soil foundations, failing to fully consider the transmission and reflection effects that occur when seismic waves pass through interfaces between different soil layers. Although some improved methods in existing technologies consider the initial transmission and reflection of waves at the interface, they cannot account for the subsequent transmission and reflection processes of waves at deeper interfaces, resulting in unsatisfactory seismic response predictions for deep soils. Summary of the Invention

[0007] To overcome the shortcomings of the prior art, this invention provides a simplified input method and system for seismic loads applicable to layered soil foundations. By using static and dynamic boundary consistency equivalent processing and considering free field analysis with multiple transmission and reflection, it can avoid inconsistent boundary conditions and inaccurate wave propagation simulation in the seismic response analysis of layered soil foundations, making it more suitable for practical implementation in engineering.

[0008] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions: The first aspect of the present invention provides a simplified input method for seismic loads applicable to layered soil foundations.

[0009] A simplified input method for seismic loads applicable to stratified soil foundations includes: A finite-domain model of a layered foundation is constructed, and an infinite-domain-finite-domain computational model is obtained by setting a viscoelastic artificial boundary. By performing static analysis on the infinite-domain-finite-domain computational model, the constraint node forces at the boundary nodes of the finite domain are obtained, which are consistent with the initial static state of the infinite-domain-finite-domain computational model. Based on the matrix decomposition method, the initial static boundary conditions are equivalently processed to obtain the equivalent static constraint nodal forces that eliminate the theoretical inconsistency of the artificial boundary of the sticky spring in static and dynamic analysis. By assuming that the seismic wave is incident perpendicularly, the initial transmission and reflection events of the wave at the layered interface are solved, as well as the single transmission and reflection of the reverse re-incident wave. The delay method is used to solve the free field response of the infinite-domain to finite-domain computational model, as well as the equivalent seismic nodal force consistent with the parameters of the viscoelastic spring. By superimposing the equivalent static constraint nodal forces and the equivalent seismic nodal forces, the calculation files of the layered foundation model are modified in batches, and the superimposed nodal forces are applied at the boundary nodes of the finite domain.

[0010] Furthermore, the model boundary of the layered foundation finite domain model adopts a viscoelastic dynamic artificial boundary, and physical elements are set in the normal and tangential directions of each boundary node. The physical elements are composed of spring elements and damping elements connected in parallel.

[0011] Furthermore, the acquisition of the constraint node forces includes: applying an initial geostress field and the corresponding external load to the model by constraining all three degrees of freedom of the outer boundary of the finite domain except for the top; and extracting the node numbers and constraint reactions at the boundary of the finite domain after performing static analysis.

[0012] Furthermore, the realization of the theoretical consistency includes: first, constructing a global equilibrium equation for a finite region, and associating nodal force vectors with the global stiffness matrix and nodal displacement vectors; then, dividing the global stiffness matrix into blocks according to internal nodes and boundary nodes to obtain a block matrix containing components caused by external forces and constraint reaction forces; and replacing constraint reaction forces by applying equivalent forces corresponding to actual boundary conditions to achieve theoretical consistency between static and dynamic analyses at the physical starting point.

[0013] Furthermore, the determination of the free-field response includes: determining the reflectivity and transmittance of seismic waves when they are vertically incident based on the wave impedance of each soil layer interface; for seismic waves vertically incident from the bottom boundary, tracing the initial transmission and initial reflection processes of the seismic waves at the interfaces of each soil layer; subsequently, tracing the first transmission and first reflection processes of the reverse re-incident waves generated by the initial reflected waves at the interfaces below each layer; and, based on the time delay method and the wave superposition principle, superimposing the initial transmitted wave, the initial reflected wave, the reverse re-incident wave, and the corresponding secondary transmitted and reflected waves to construct the free-field displacement response and free-field velocity response within each soil layer, respectively.

[0014] Furthermore, the determination of the equivalent seismic nodal force includes: deriving the stress tensor generated by free-field ground motion at the boundary based on the basic assumptions of elasticity and the free-field displacement response; obtaining the control area, damping coefficient, spring stiffness coefficient, and cosine vector of the outward normal direction for each boundary node; calculating the additional resistance term introduced by the spring and damper based on the free-field displacement response, free-field velocity response, damping coefficient, and spring stiffness coefficient; calculating the resistance term that the infinite-domain medium should provide at the boundary based on the free-field stress tensor, the control area, and the cosine vector of the outward normal direction; and determining the difference between the resistance term and the additional resistance term as the equivalent seismic nodal force applied to the boundary node.

[0015] Furthermore, applying superimposed nodal forces at the boundary nodes of the finite domain includes: using file read / write functions in Matlab to batch modify the foundation model calculation file; creating a set of boundary nodes in the modified calculation file and establishing an amplitude function corresponding to the seismic wave time history; and applying the total equivalent nodal forces in batches to the corresponding boundary nodes in the form of concentrated nodal forces; wherein, the total equivalent nodal forces are expressed as: ; in, Indicates the total equivalent nodal force; This represents the nodal constraint reaction force consistent with the initial ground field, i.e., the equivalent static constraint nodal force; This represents the equivalent nodal force of an earthquake.

[0016] A second aspect of the present invention provides a simplified seismic load input system suitable for layered soil foundations.

[0017] A simplified seismic load input system suitable for stratified soil foundations includes: The computational model building module is configured to: construct a layered foundation finite domain model and obtain an infinite domain-finite domain computational model by setting viscoelastic artificial boundaries; The static analysis module is configured to: perform static analysis on the infinite-domain-finite-domain computational model to obtain the constraint node forces at the finite-domain boundary nodes that are consistent with the initial static state of the infinite-domain-finite-domain computational model; The static constraint nodal force equivalent module is configured to: perform equivalent processing on the initial static boundary conditions based on the matrix decomposition method, so as to obtain equivalent static constraint nodal forces that eliminate the theoretical inconsistency of the artificial boundary of the sticky spring in static and dynamic analysis. The seismic nodal force equivalent module is configured to: solve for the initial transmission and reflection events of the wave at the layered interface, as well as the single transmission and reflection of the reverse re-incident wave, by assuming that the seismic wave is perpendicularly incident; and solve for the free field response of the infinite-domain to finite-domain computational model and the equivalent seismic nodal force consistent with the parameters of the viscoelastic spring using the delay method. The seismic load input module is configured to: batch modify the layered foundation model calculation file by superimposing the equivalent static constraint nodal forces and the equivalent seismic nodal forces, and apply the superimposed nodal forces at the boundary nodes of the finite domain.

[0018] A third aspect of the invention provides a computer-readable storage medium having a program stored thereon that, when executed by a processor, implements the steps of a simplified seismic load input method for layered soil foundations as described in the first aspect of the invention.

[0019] A fourth aspect of the present invention provides an electronic device including a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the steps of a simplified input method for seismic loads applicable to stratified soil foundations as described in the first aspect of the present invention.

[0020] The above one or more technical solutions have the following beneficial effects: This invention extracts the constraint reactions of finite domain boundary nodes through static analysis and performs equivalent processing on the initial static boundary conditions based on matrix decomposition to obtain equivalent static constraint nodal forces consistent with the initial geostress field. In subsequent dynamic analysis, these equivalent static constraint nodal forces are applied to replace the original fixed constraint boundaries, achieving theoretical unification between static boundary conditions and viscoelastic dynamic artificial boundaries. This method avoids the distortion of the initial geostress field caused by inconsistencies between static and dynamic boundary conditions, ensuring the continuity and consistency of the static-dynamic coupled analysis at the physical starting point, and providing a reliable initial state for high-precision seismic response analysis.

[0021] This invention, during the seismic load input process, assumes vertical incidence of seismic waves and solves for the initial transmission and reflection events at layered interfaces, as well as the single transmission and reflection processes of the back-reflection waves generated by the reflected waves at deeper interfaces. It then employs a delay method to superimpose these multiple transmissions and reflections, constructing the free-field displacement and velocity responses within each soil layer. This method not only considers the initial transmission and reflection at the interfaces but also traces the back-reflection waves and their subsequent propagation. Compared to existing methods that only consider initial transmission and reflection, it can more realistically simulate the complex propagation characteristics of seismic waves in layered foundations, significantly improving the accuracy of seismic response prediction in deep soils.

[0022] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0023] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0024] Figure 1 This is a flowchart of adding artificial boundaries and equivalent nodal forces in Embodiment 1 of the present invention.

[0025] Figure 2 This is a schematic diagram of a multi-layer foundation model in Embodiment 1 of the present invention.

[0026] Figure 3 This is a schematic diagram of seismic data in Embodiment 1 of the present invention; wherein, Figure 3 In the text, (a) represents the input seismic velocity time history. Figure 3 (b) in the figure represents the input ground motion power spectral density.

[0027] Figure 4 This is a schematic diagram of adding spring and damper elements to artificial boundary nodes in Embodiment 1 of the present invention.

[0028] Figure 5 This is a schematic diagram of applying equivalent nodal forces to artificial boundary nodes in Embodiment 1 of the present invention.

[0029] Figure 6 This is a displacement time history diagram of observation point A in Embodiment 1 of the present invention.

[0030] Figure 7 This is a displacement time history diagram of observation point B in Embodiment 1 of the present invention. Detailed Implementation

[0031] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0032] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations of the present invention.

[0033] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0034] Example 1 This embodiment discloses a simplified input method for seismic loads applicable to stratified soil foundations.

[0035] like Figure 1 As shown, a simplified input method for seismic loads suitable for stratified soil foundations includes: Step S1: Construct a finite domain model of a layered foundation, and obtain an infinite domain-finite domain computational model by setting a viscoelastic artificial boundary; Step S2: By performing static analysis on the infinite-domain-finite-domain computational model, obtain the constraint node forces at the boundary nodes of the finite domain that are consistent with the initial static state of the infinite-domain-finite-domain computational model. Step S3: Based on the matrix decomposition method, perform equivalent processing on the initial static boundary conditions to obtain equivalent static constraint nodal forces that eliminate the theoretical inconsistency between the artificial boundary of the sticky spring in static and dynamic analysis. Step S4: By assuming that the seismic wave is incident perpendicularly, solve for the initial transmission and reflection events of the wave at the layered interface, as well as the single transmission and reflection of the reverse re-incident wave; use the delay method to solve for the free field response of the infinite-domain-finite-domain calculation model, and the equivalent seismic nodal force consistent with the parameters of the viscoelastic spring. Step S5: By superimposing the equivalent static constraint nodal forces and the equivalent seismic nodal forces, the layered foundation model calculation file is modified in batches, and the superimposed nodal forces are applied at the boundary nodes of the finite domain.

[0036] Based on the above process, this invention, through equivalent treatment of static and dynamic boundary consistency and free-field analysis considering multiple transmission and reflection, can avoid inconsistent boundary conditions and inaccurate wave propagation simulation in the seismic response analysis of layered soil foundations, making it more suitable for practical implementation in engineering. To facilitate understanding of the technical solution of this invention, the specific implementation methods of this invention will be further explained and described below.

[0037] In step S1, a layered foundation finite domain model is constructed, and an infinite domain-finite domain computational model is obtained by setting a viscoelastic artificial boundary.

[0038] like Figure 2 As shown, the finite domain model of the layered foundation along the vertical direction ( z The axis divides the foundation into layers 1 through 2 from bottom to top. n The soil layers are layered, and each layer has independent physical and mechanical properties, including density. ρ shear modulus G Damping ratio λ and layer thickness h The foundation has an infinite element boundary at its base to receive input excitation signals. f 0; The soil layers are separated by horizontal interfaces (interface 0 to interface 1). n ) connected, Figure 2 The image uses arrow vectors of different hues to illustrate the propagation and evolution of waves in various media layers, including the upward wave. f 1,i With downward wave f 2,i At the interface between adjacent soil layers, the laws of wave reflection and transmission apply. For example... Figure 2 As shown in the magnified region in the middle, the incident wave f in It decomposes into transmitted waves when passing through the interface. f tr With reflected waves f re By establishing continuity conditions for interlayer displacement and stress, it is possible to calculate any point A within the foundation at a micro-incremental height Δ. h Accurate characterization of dynamic response under conditions.

[0039] Step S1 can be implemented in the following way: Step S1.1: The model boundary adopts a viscoelastic dynamic artificial boundary. Physical elements are set in the normal and tangential directions of each boundary node. The physical element is composed of spring elements and damping elements connected in parallel. The parameters of the spring elements and damping elements are calculated according to the following formula: ; ; In the formula, , These are the correction factors for the tangential and normal directions of the viscoelastic boundary, respectively. It is the mass density of the medium; It is the shear modulus of the medium; This represents the distance from the scattering source to the artificial boundary; , These represent the transverse wave velocity and the longitudinal wave velocity in the medium, respectively. This represents the area controlled by the node. It should be noted that for boundary nodes at soil layer interfaces, the physical element coefficients can be taken as the average of the parameters of the upper and lower soil layers.

[0040] Step S1.2: Use the fopen and fprintf functions in Matlab to modify the foundation model calculation file and create the sticky spring components in batches.

[0041] In step S2, by performing static analysis on the infinite-domain-finite-domain computational model, the constraint node forces at the boundary nodes of the finite domain are obtained, which are consistent with the initial static state of the infinite-domain-finite-domain computational model.

[0042] In the specific implementation process, firstly, all three degrees of freedom of the outer boundary of the finite domain except for the top are constrained, and an initial geostress field and the corresponding external load are applied to the model; then, after performing static analysis, the node numbers and constraint reactions at the boundary of the finite domain are extracted. .

[0043] In step S3, based on the matrix decomposition method, the initial static boundary conditions are equivalently processed to obtain equivalent static constraint nodal forces that eliminate the theoretical inconsistencies in static and dynamic analysis of the artificial boundary of the sticky spring. This can be achieved specifically through the following methods: Step S3.1: For static analysis, the global equilibrium equations for the finite region are as follows: ; in,{ F} represents the nodal force vector, [ K ] is the global stiffness matrix that includes all finite element contributions, { U} represents the nodal displacement vector.

[0044] Step S3.2: Internal nodes are not directly affected by the reaction forces at the boundaries, while the nodal forces at boundary nodes are the result of the combined action of external loads and boundary constraint reaction forces, i.e.: ; Among them, subscript I and B These represent parameters related to internal nodes and boundary nodes (at the intersection of finite and infinite fields), respectively. K II , K IB , K BI and K BB A block matrix representing the global stiffness matrix; superscript e and r These represent the components caused by external forces and constraint reaction forces, respectively.

[0045] Step S3.3: Due to the existence of artificial boundary constraints, for the known boundary displacement {U} B} = {U B0}, [ K Since it is positive definite, we can conclude that: ; ; Step S3.4, let We can obtain: ; ; The existence of artificial boundaries provides a virtual support, eliminating rigid motion within the finite field; therefore, the infinite-field-finite-field system is stable. At this point, { U B The solution to} is unique. U B} = { U B0}.in this case,{ U I The solution to the problem will not change. That is, applying an equivalent force corresponding to the actual boundary conditions to replace the reaction force will not change the original static equilibrium state of the finite field.

[0046] Step S3.5: Based on the above analysis, applying constraint nodal forces at the boundary nodes of the finite domain, consistent with the initial static state of the model, avoids inconsistencies between the static and dynamic conditions of the artificial boundary. That is, the initial static state analysis performed before dynamic analysis can be treated as a quasi-static problem by applying equivalent nodal forces consistent with the initial state, thus ensuring a physically consistent starting point in both static and dynamic analyses. It should be noted that implementing equivalent nodal forces does not involve removing the artificially defined boundaries.

[0047] In step S4, by assuming perpendicular incidence of the seismic wave, the initial transmission and reflection events at the layered interface, as well as the single transmission and reflection of the reverse re-incident wave, are solved. The free-field response of the infinite-domain to finite-domain computational model, and the equivalent seismic nodal force consistent with the parameters of the viscoelastic spring, are solved using the delay method. Specifically, this can be achieved through the following methods: Step S4.1: Under multi-layered soil foundation conditions, the amplitude variation of seismic waves during vertical incidence is determined according to the following formula: ; ; In the formula, , These represent the reflectivity and transmittance of seismic waves, respectively. Indicates the amplitude of seismic waves, its subscript , and These represent incident wave, transmitted wave, and reflected wave, respectively. It is the ratio of the wave impedances of the two media; and These represent soil density and wave velocity, respectively.

[0048] Step S4.2: For the free field displacement of the layered foundation incident at the bottom boundary, only the first... i The initial transmission and reflection process of the incident wave at the interface of the soil layers, and the process of the initial reflected wave at the second... i The process of one transmission and one reflection of the reverse re-incident wave generated at the interface below the layer. The wave incident vertically from the bottom is... u 0( t ) ( Based on the time delay method and the principle of wave superposition, the first... i Layer (1 < i < n Transmitted waves within soil units f tr,i Determine by the following formula: ; in, ; ; ; This represents the distance from the soil node to the bottom of the i-th layer; h It refers to the thickness of the layer; subscript i , k , m and j These represent the soil layer number or interface, respectively. and The transmission coefficients of the uplink and downlink waves, respectively. = The first term in the transmitted wave expression is used to characterize the first term. i The influence of each soil layer below the first layer on the initial upward wave; the second term is used to characterize the first layer. i The influence of the reverse re-incident waves of each soil layer above the layer on the soil unit.

[0049] Step S4.3: For the reflected wave, it can be expressed as: ; in, , , , .

[0050] Step S4.4: According to the stacking principle, the first... iLayer (1 < i < n The free-field displacement of the soil can be expressed as: ; ; ; Step S4.5, correspondingly, the first i Layer (1 < i < n The velocity of the soil within the soil is: ; ; .

[0051] Step S4.6, based on the fundamental assumptions of elasticity, the equivalent seismic nodal forces at each boundary node can be calculated using the following formula: ; In the formula, The physical meaning is to eliminate the additional resistance caused by the introduction of springs and dampers; It is the stress tensor generated at the boundary by free field vibration; , These are the damping coefficient and spring stiffness coefficient of the boundary node, respectively; , These are the displacement vector and velocity vector of the earthquake, respectively. It is the cosine vector of the outer normal direction of the boundary.

[0052] Step S4.7, the displacement response and velocity response of the incident wave field are determined according to the relationship between the out-of-bounds normal direction and the coordinate axis direction, respectively. x axis, y When the z-axis or z-axis is parallel, the corresponding displacement and velocity response expressions are as follows: ; 1) When the direction of the out-of-plane normal is... x When the axes are parallel: ; 2) When the direction of the out-of-plane normal is... y When the axes are parallel: ; 3) When the direction of the out-of-plane normal is... z When the axes are parallel: ; Step S4.8, taking the P wave as an example, establish a horizontally perpendicular direction as...x shaft and y The axis, vertically upward direction is z In a spatial coordinate system along the positive axis, the free field strain, according to the geometric equations in elasticity, is: ; Step S4.9: Based on the geometric equations of elasticity The stress expressions for each direction at the node can be obtained, and then the expression for the free field stress tensor can be calculated: ; In the formula, The first Lamé constant, This is the shear modulus of the medium.

[0053] Step S4.10, the displacement vector of the incident wave is The velocity vector is The free field stress tensor is: ; Step S4.11: According to one-dimensional wave theory, we know that: ; Step S4.12: Constrain all three degrees of freedom of the outer boundary of the finite domain except the top, apply a unit pressure of 1 Pa to the constrained boundary and perform static analysis; Step S4.13: Extract the equivalent nodal area (constraint reaction force) corresponding to each node of the finite domain boundary. A b With three-dimensional spatial coordinates; Step S4.14, for the bottom boundary ,and x Spring stiffness coefficient when the shaft is parallel get: ; Step S4.15, for x Direction positive direction boundary : ; Step S4.16, x Negative direction boundary : ; Step S4.17, y Direction positive direction boundary : ; Step S4.18, y Direction positive direction boundary : ; In the formula, the superscript of the nodal force indicates the direction of the outward normal to the boundary surface where the node is located; it is positive if it is in the same direction as the coordinate axis and negative if it is opposite. The subscripts, in order, represent the node name and the direction of the nodal force, respectively. Similarly, the derivation process of the equivalent nodal force is the same when SH waves and SV waves propagate in the soil medium.

[0054] In step S5, the layered foundation model calculation file is modified in batches by superimposing equivalent static constraint nodal forces and equivalent seismic nodal forces, and the superimposed nodal forces are applied at the boundary nodes of the finite domain. This can be achieved specifically through the following method: Step S5.1: The actual nodal force at the boundary node of the finite domain needs to simultaneously satisfy the constraint effect of the initial boundary and the free field fluctuation condition. Therefore, the actual applied total equivalent nodal force is: ; in, The nodal constraint reaction forces are consistent with the initial ground field; This is the earthquake equivalent nodal force.

[0055] Step S5.2: Using the fopen and fprintf functions in Matlab, the node set is created in batches, the magnitude function is established, and the concentrated nodal force is applied to complete the application of the total equivalent nodal force.

[0056] To further illustrate the beneficial effects of the present invention, the following experiment was conducted in this embodiment: A three-dimensional foundation model with dimensions of 200 m × 200 m × 100 m was established. The soil layers in the model, from bottom to top, were labeled C1 to C5, with each layer having a thickness of 20 meters. The soil exhibits depth-dependent elastic properties, with an effective unit weight of 6.0 kN / m³. Detailed material parameters for all soil layers in the model are shown in Table 1. A seismic wave load, specifically a P-wave, was input at the bottom boundary of the model. Its velocity-time history curve and corresponding power spectral density are shown in Table 1. Figure 3 As shown in (a) and (b) above, the model analysis employed a static-dynamic workflow: a 1-second initial static stress step and a 2-second seismic loading step, with a seismic wave sampling frequency of 100 Hz. Using the above input method, nodal loads corresponding to the initial stress field and equivalent seismic forces were applied to the numerical model.

[0057] Table 1 Soil parameters

[0058] First, calculate the control area of ​​each boundary node, and determine the spring stiffness coefficient and damping coefficient accordingly. Then, apply equivalent nodal forces and viscoelastic artificial boundary conditions, as follows: Figure 4 , Figure 5 As shown.

[0059] like Figure 6 and Figure 7 The displacement time histories of observation points A and B, as shown, indicate that during the pre-earthquake phase (t = 0 to 1 second), the model was in static equilibrium, and soil displacement was zero. Furthermore, Figure 6 , Figure 7 The displacement-time history curves (t = 1–3 s) of points A and B under the action of a vertically incident P-wave are also presented, employing four methods: a far-boundary reference solution (baseline value), an input method for homogeneous soil introduced into layered soil (Method 1), considering only the initial propagation and reflection events of the incident wave at each interface (Method 2), and the method of this invention. The baseline value is obtained from a numerical model with truncated boundaries, which are set sufficiently far from the region of interest; while Method 1 directly introduces the input method for homogeneous soil into the layered soil scenario. Clearly, compared to the other two methods, the method of this invention is almost completely consistent with the reference solution at the two peaks, and the overall curve shape is also closer to the baseline value. This means that it maintains high accuracy in complex response simulations, especially in the recovery of key peak features, and can meet the requirements of high-precision engineering and practical applications.

[0060] Example 2 This embodiment discloses a simplified seismic load input system suitable for stratified soil foundations.

[0061] A simplified seismic load input system suitable for stratified soil foundations includes: The computational model building module is configured to: construct a layered foundation finite domain model and obtain an infinite domain-finite domain computational model by setting viscoelastic artificial boundaries; The static analysis module is configured to: perform static analysis on the infinite-domain-finite-domain computational model to obtain the constraint node forces at the finite-domain boundary nodes that are consistent with the initial static state of the infinite-domain-finite-domain computational model; The static constraint nodal force equivalent module is configured to: perform equivalent processing on the initial static boundary conditions based on the matrix decomposition method, so as to obtain equivalent static constraint nodal forces that eliminate the theoretical inconsistency of the artificial boundary of the sticky spring in static and dynamic analysis. The seismic nodal force equivalent module is configured to: solve for the initial transmission and reflection events of the wave at the layered interface, as well as the single transmission and reflection of the reverse re-incident wave, by assuming that the seismic wave is perpendicularly incident; and solve for the free field response of the infinite-domain to finite-domain computational model and the equivalent seismic nodal force consistent with the parameters of the viscoelastic spring using the delay method. The seismic load input module is configured to: batch modify the layered foundation model calculation file by superimposing the equivalent static constraint nodal forces and the equivalent seismic nodal forces, and apply the superimposed nodal forces at the boundary nodes of the finite domain.

[0062] Example 3 The purpose of this embodiment is to provide a computer-readable storage medium.

[0063] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the steps of a simplified seismic load input method for layered soil foundations as described in Embodiment 1 of this disclosure.

[0064] Example 4 The purpose of this embodiment is to provide an electronic device.

[0065] An electronic device includes a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps in a simplified seismic load input method for stratified soil foundations as described in Embodiment 1 of this disclosure.

[0066] The steps and methods involved in the apparatuses of Embodiments 2, 3, and 4 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0067] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0068] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A simplified input method for seismic loads applicable to stratified soil foundations, characterized in that, include: A finite-domain model of a layered foundation is constructed, and an infinite-domain-finite-domain computational model is obtained by setting a viscoelastic artificial boundary. By performing static analysis on the infinite-domain-finite-domain computational model, the constraint node forces at the boundary nodes of the finite domain are obtained, which are consistent with the initial static state of the infinite-domain-finite-domain computational model. Based on the matrix decomposition method, the initial static boundary conditions are equivalently processed to obtain the equivalent static constraint nodal forces that eliminate the theoretical inconsistency of the artificial boundary of the sticky spring in static and dynamic analysis. By assuming that the seismic wave is incident perpendicularly, the initial transmission and reflection events of the wave at the layered interface are solved, as well as the single transmission and reflection of the reverse re-incident wave. The delay method is used to solve the free field response of the infinite-domain to finite-domain computational model, as well as the equivalent seismic nodal force consistent with the parameters of the viscoelastic spring. By superimposing the equivalent static constraint nodal forces and the equivalent seismic nodal forces, the calculation files of the layered foundation model are modified in batches, and the superimposed nodal forces are applied at the boundary nodes of the finite domain.

2. The simplified seismic load input method for layered soil foundations as described in claim 1, characterized in that, The model boundary of the layered foundation finite domain model adopts a viscoelastic dynamic artificial boundary, and physical elements are set in the normal and tangential directions of each boundary node. The physical elements are composed of spring elements and damping elements connected in parallel.

3. The simplified seismic load input method for layered soil foundations as described in claim 1, characterized in that, The acquisition of the constraint node forces includes: applying an initial geostress field and the corresponding external load to the model by constraining all three degrees of freedom of the outer boundary of the finite domain except for the top; and extracting the node numbers and constraint reactions at the boundary of the finite domain after static analysis.

4. The simplified seismic load input method for layered soil foundations as described in claim 1, characterized in that, The realization of the theoretical consistency includes: First, a global equilibrium equation for a finite region is constructed, and the nodal force vectors are associated with the global stiffness matrix and the nodal displacement vectors. Then, the global stiffness matrix is ​​divided into blocks according to internal nodes and boundary nodes to obtain a block matrix containing components caused by external forces and constraint reaction forces. The constraint reaction forces are replaced by applying equivalent forces corresponding to the actual boundary conditions to achieve theoretical consistency between static and dynamic analysis at the physical starting point.

5. The simplified seismic load input method for layered soil foundations as described in claim 1, characterized in that, The determination of the free-field response includes: determining the reflectivity and transmittance of seismic waves when they are vertically incident based on the wave impedance of each soil layer interface; for seismic waves vertically incident from the bottom boundary, tracing the initial transmission and initial reflection processes of the seismic waves at the interfaces of each soil layer; subsequently, tracing the first transmission and first reflection processes of the reverse re-incident waves generated by the initial reflected waves at the interfaces below each layer; and, based on the time delay method and the wave superposition principle, superimposing the initial transmitted wave, the initial reflected wave, the reverse re-incident wave, and the corresponding secondary transmitted and reflected waves to construct the free-field displacement response and free-field velocity response within each soil layer.

6. The simplified seismic load input method for layered soil foundations as described in claim 1, characterized in that, The determination of the equivalent seismic nodal force includes: deriving the stress tensor generated at the boundary by free-field ground motion based on the basic assumptions of elasticity and the free-field displacement response; obtaining the control area, damping coefficient, spring stiffness coefficient, and cosine vector of the outward normal direction for each boundary node; calculating the additional drag term introduced by the spring and damper based on the free-field displacement response, free-field velocity response, damping coefficient, and spring stiffness coefficient; calculating the resistance term that the infinite-domain medium should provide at the boundary based on the free-field stress tensor, the control area, and the cosine vector of the outward normal direction; and determining the difference between the resistance term and the additional drag term as the equivalent seismic nodal force applied to the boundary node.

7. The simplified seismic load input method for layered soil foundations as described in claim 1, characterized in that, Applying superimposed nodal forces at the boundary nodes of the finite domain includes: using file read / write functions in Matlab to batch modify the foundation model calculation file; creating a set of boundary nodes in the modified calculation file and establishing an amplitude function corresponding to the seismic wave time history; and applying the total equivalent nodal forces in batches to the corresponding boundary nodes in the form of concentrated nodal forces; wherein, the total equivalent nodal forces are expressed as: ； in, Indicates the total equivalent nodal force; This represents the nodal constraint reaction force consistent with the initial ground field, i.e., the equivalent static constraint nodal force; This represents the equivalent nodal force of an earthquake.

8. A simplified seismic load input system suitable for stratified soil foundations, characterized in that, include: The computational model building module is configured to: construct a layered foundation finite domain model and obtain an infinite domain-finite domain computational model by setting viscoelastic artificial boundaries; The static analysis module is configured to: perform static analysis on the infinite-domain-finite-domain computational model to obtain the constraint node forces at the finite-domain boundary nodes that are consistent with the initial static state of the infinite-domain-finite-domain computational model; The static constraint nodal force equivalent module is configured to: perform equivalent processing on the initial static boundary conditions based on the matrix decomposition method, so as to obtain equivalent static constraint nodal forces that eliminate the theoretical inconsistency of the artificial boundary of the sticky spring in static and dynamic analysis. The seismic nodal force equivalent module is configured to: solve for the initial transmission and reflection events of the wave at the layered interface, as well as the single transmission and reflection of the reverse re-incident wave, by assuming that the seismic wave is perpendicularly incident; and solve for the free field response of the infinite-domain to finite-domain computational model and the equivalent seismic nodal force consistent with the parameters of the viscoelastic spring using the delay method. The seismic load input module is configured to: batch modify the layered foundation model calculation file by superimposing the equivalent static constraint nodal forces and the equivalent seismic nodal forces, and apply the superimposed nodal forces at the boundary nodes of the finite domain.

9. A computer-readable storage medium having a program stored thereon, characterized in that, When executed by the processor, the program implements the steps in the simplified seismic load input method for layered soil foundations as described in any one of claims 1-7.

10. An electronic device, comprising a memory, a processor, and a program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the simplified seismic load input method for layered soil foundations as described in any one of claims 1-7.

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