Numerical simulation method for dynamic large deformation of embankment on liquefiable ground during earthquake

Abstract

The present application belongs to the technical field of earthquake prediction of building engineering, and particularly relates to a numerical simulation method for dynamic large deformation of embankment on liquefied site during earthquake. First, an embankment engineering structure model is established, and a background grid of finite elements for seismic large deformation analysis is generated by dividing the polygonal proportional boundary element grid in the structure model. Then, initial stress of deformation information of each engineering part of the embankment during filling and water storage process is obtained through static analysis, and seismic motion data is set based on the initial stress and according to the geographical position of the embankment engineering. Finally, dynamic motion is input to the finite element background grid according to the seismic motion data for dynamic analysis to obtain dynamic deformation information of each engineering part of the embankment after earthquake. The present application can truly reflect the deformation development mode, physical mechanism and influencing factors of the embankment on liquefied site during earthquake through numerical simulation, and is convenient for directly finding the weak parts of the embankment engineering structure for seismic resistance, so as to optimize the design of the embankment engineering structure, improve the seismic fortification level, and ensure the safety of the embankment engineering facilities and personnel.

Description

Technical Field

[0001] This invention belongs to the field of earthquake prediction technology in building engineering, and specifically relates to a numerical simulation method for dynamic large deformation of dams in earthquake liquefaction sites. Background Technology

[0002] Floods are among the most severe natural disasters in my country. Dikes are a primary engineering measure in flood control and disaster reduction, and a crucial component of the flood control system. my country possesses a vast network of dikes, mainly distributed in the alluvial plains of the middle and lower reaches of rivers. These dikes serve as a barrier to flood safety in my country's socio-economic development zones. As is well known, my country is also a country prone to earthquakes, with approximately half of the country located in areas with seismic intensity of 7 degrees or higher. Earthquakes are incredibly powerful, capable of destroying a city in seconds. If a dike is damaged by an earthquake, leading to flooding, the consequences could be unimaginable. Therefore, the earthquake resistance of dikes is of paramount importance. Existing earthquake damage surveys indicate that dike damage caused by earthquakes is closely related to topography and geological conditions, and is primarily caused by foundation liquefaction. Dikes are mainly constructed on low terraces and high floodplains of rivers, lakes, and seas. The soil at these sites is often recently deposited sandy soil with a loose structure, shallow burial depth, and a saturated state. Sudden earthquakes easily cause soil liquefaction, leading to large deformations in the dikes, such as settlement and lateral displacement of several meters. How to adopt reasonable seismic countermeasures are core issues in the seismic design of dams on seismically liquefiable sites. Accurately obtaining the large deformation characteristics of dams on seismically liquefiable sites and revealing their failure mechanisms are key to solving these problems.

[0003] However, current research in my country on safety evaluation and analysis methods for dams on seismically liquefied sites, as well as on seismic damage mechanisms, is still severely lacking. The analysis method recommended in current dam engineering design codes is still based on the single safety factor method according to the rigid body limit equilibrium theory. This method ignores the granular characteristics of the soil and only considers the stress state of the slip surface, failing to account for the deformation of the sliding body and the dam structure, and neglecting the coupling relationship between liquefaction and deformation. Clearly, it cannot analyze the large deformation problems of dams caused by seismic liquefaction. Since the 20th century, numerous earthquakes worldwide have caused the failure of dams due to foundation liquefaction. While seismic damage induction can obtain the true state of dams after failure, it is difficult to elucidate the failure mechanism. Numerical simulation methods, demonstrating seismic damage to dams, can reveal the deformation development pattern, physical mechanism, and influencing factors, and can predict potential dam hazards caused by earthquakes, thereby preventing disasters. Therefore, seismic damage induction is a passive method; a dynamic method is needed to understand the deformation development process and failure mechanism of dams on seismically liquefied sites to meet the needs of earthquake prediction. Summary of the Invention

[0004] Therefore, this invention provides a numerical simulation method for dynamic large deformation of dams in earthquake liquefaction sites. By numerically simulating the entire process of soil liquefaction and seismic deformation and progressive failure of dams in earthquake liquefaction sites, it can realistically reflect the deformation development mode, physical mechanism and influencing factors of dams in earthquake liquefaction sites, and can provide a basis for seismic design.

[0005] According to the design scheme provided by this invention, a numerical simulation method for dynamic large deformation of dams in earthquake liquefaction sites is provided, comprising the following:

[0006] A structural model of the dam project is established, and the background mesh of the finite element method for seismic large deformation analysis is generated by dividing the polygonal scale boundary element mesh in the structural model.

[0007] The initial stress of each engineering part of the dam during the filling and water impoundment process was obtained through static analysis;

[0008] Ground motion data were set based on initial stress and according to the geographical location of the dam project;

[0009] Based on the seismic motion data, the seismic motion is input into the finite element background mesh for dynamic analysis to obtain the dynamic deformation information of various engineering parts of the dam after the earthquake.

[0010] As a numerical simulation method for large dynamic deformation of dams in seismic liquefaction sites in this invention, the establishment of the dam engineering structural model further includes: first, acquiring relevant data for dam engineering modeling, and using drawing modeling line segments to describe the dam engineering morphology and calculation analysis domain, wherein the relevant data for modeling includes at least the simulation range, typical elevation, dam material analysis, and foundation layer distribution; then, performing polygonal scale boundary element meshing on the constructed model, and recording key boundary data, wherein the key boundary data includes: dam engineering outline, material partitioning lines, and strata layering lines.

[0011] As a numerical simulation method for large dynamic deformation of dams in seismic liquefaction sites in this invention, the background mesh for seismic large deformation analysis is further generated by dividing the polygonal scale boundary element mesh in the structural model. This includes: first, determining the calculation analysis domain of the model based on the dam engineering model; then, setting the number of segments of each line segment in the analysis domain and the densification points in the closed area, and generating the background mesh by identifying the densification points and dividing the densification point positions into meshes.

[0012] As a numerical simulation method for dynamic large deformation of dams in earthquake liquefaction sites in this invention, the initial stress of deformation information of various engineering parts of the dam during filling and water impoundment is obtained through static analysis. This includes: firstly, preprocessing the background network, which includes: applying gravity load and water pressure load to the model, and setting the plastic deformation characteristics of the foundation material and the dam body; then, calculating and analyzing the static stress of the background mesh finite element according to the time step during the filling and water impoundment process, and outputting the initial stress data after static calculation and analysis. The initial stress data includes: deformation information of stress and strain of various parts of the dam during filling and water impoundment.

[0013] As a numerical simulation method for dynamic large deformation of dams in earthquake liquefaction sites according to the present invention, further, based on the initial stress and according to the geographical location of the dam project, the method sets the ground motion data, including: first, setting the ground motion load according to the initial stress and the geographical location of the dam project, and using artificial viscoelastic boundaries to set the ground motion boundary conditions; then, setting the seismic waves in the simulated ground motion by combining the artificial boundaries with the equivalent nodal loads.

[0014] As a numerical simulation method for dynamic large deformation of dams in earthquake liquefaction sites according to the present invention, the method further includes inputting the seismic motion data into the finite element background mesh for dynamic analysis to obtain the dynamic deformation information of various engineering parts of the dam after the earthquake. This includes: firstly, dividing the earthquake into several time periods, and dynamically adjusting the position of the line nodes and updating the node coordinates of the dam engineering mesh elements according to the changes in the position of the model boundary line and the material partition line of each engineering part in each time period; then, mapping the deformed mesh information back to the background mesh, reconstructing the model according to the liquefaction deformation, and re-subdividing the analysis domain of the reconstructed model, remapping the mesh information on the background mesh to the re-subdivided analysis domain mesh, and repeating the dynamic analysis until the earthquake ends, obtaining the dynamic deformation information of various engineering parts of the dam after the earthquake through the final re-subdivision and mapping.

[0015] As a numerical simulation method for dynamic large deformation of dams in seismic liquefaction sites according to the present invention, the deformed mesh information is further mapped back to the background mesh, which includes: first, using a semi-analytical solution function of a scaled boundary finite element to construct a mapping equation for the associated node information of a polygonal scaled boundary finite element; then, using the mapping equation to map the deformed mesh information in the computational domain to the background mesh, wherein the deformed mesh information includes, but is not limited to: nodal pore pressure, nodal deformation, element Gaussian point stress, element Gaussian point strain, element Gaussian point pore pressure, and constitutive internal variables.

[0016] As a numerical simulation method for dynamic large deformation of dams in seismic liquefaction sites according to the present invention, further, in the mapping process, firstly, the polygonal element is pre-divided into several triangular sub-elements with the centroid of the element as the center. Based on the triangular finite element, the pore pressure Gaussian points and displacement Gaussian points of each sub-element are arranged. The parent element is constructed and an information mapping domain is created according to the distribution of Gaussian points and nodes. Then, the local coordinates of the Gaussian points in the parent element are determined, and the Gaussian point information is obtained by interpolation based on the element shape function and local coordinates.

[0017] As a numerical simulation method for dynamic large deformation of dams in earthquake liquefaction sites according to the present invention, further, in the re-meshing process, the deformable mesh elements and node information in the computational domain are mapped to the background mesh elements and nodes. Based on the earthquake liquefaction deformation increment of the dam project obtained in the current time period and the dam outline, partition line and layer line obtained in the static analysis, the mesh of the dam project is re-meshed using a meshing method based on Delaunay meshing theory, and the polygon scale boundary elements in the computational domain are updated.

[0018] As a numerical simulation method for dynamic large deformation of dams in earthquake liquefaction sites according to the present invention, further, model reconstruction based on liquefaction deformation includes: first, obtaining the deformation of each engineering part of the dam based on the pore pressure accumulated in the liquefied foundation soil caused by the earthquake load and the change of pore pressure on modulus and strength, wherein the deformation of each engineering part of the dam includes at least the sliding deformation of the dam slope to the left and right sides respectively; then, reconstructing the dam engineering structure model based on the deformation of each engineering part of the dam.

[0019] The beneficial effects of this invention are:

[0020] This invention establishes a structural model within the engineering analysis domain based on engineering conditions, subdivides the background mesh into polygonal boundary elements, sets boundary conditions and material parameters for each part of the engineering model, and performs static analysis. After the static analysis, it inputs the seismic motion, tracks the feature boundary lines and updates the coordinates at each time step, maps the deformed mesh information back to the background mesh, and then reconstructs the mesh based on liquefaction deformation. The mesh is then re-subdivided. By re-subdividing the computational domain and re-mapping the mesh information from the background mesh back to the re-subdivided engineering analysis domain mesh, this dynamic analysis step is repeated until the seismic motion process ends. Through repeated subdivision and mapping, the damage information of various parts of the project after the earthquake can be obtained, completing the dynamic large deformation analysis, improving the efficiency of seismic simulation calculations for dam projects, and facilitating the intuitive identification of seismically weak parts in the dam structure. This allows for the optimization of dam structural design, improvement of its seismic fortification level, and ensures the safety of dam facilities and personnel. Attached image description:

[0021] Figure 1 This is a schematic diagram of the numerical simulation process for the dynamic large deformation of the dam in the earthquake liquefaction site in the embodiment.

[0022] Figure 2 This is a schematic diagram of the polygonal scale boundary finite element background mesh used for the seismic large deformation analysis of the dam project in the embodiment;

[0023] Figure 3 This is a schematic diagram of the initial polygonal scale boundary finite element mesh for the static and dynamic numerical analysis of the dam in the embodiment.

[0024] Figure 4 This is a schematic diagram of the arrangement of Gaussian points for pore pressure and displacement in the polygonal scale boundary element of saturated soil in the embodiment.

[0025] Figure 5 This is a schematic diagram illustrating the relationship between the computational domain deformation elements and the background mesh elements in the embodiment.

[0026] Figure 6 This is a schematic diagram of Gaussian point mapping information at different locations in the embodiment;

[0027] Figure 7 This is a schematic diagram of the background mesh and the mesh after re-subdividing the computational domain of the dam project in the embodiment;

[0028] Figure 8 This is a schematic diagram of the polygonal scale boundary finite element mesh of the dam project after repartitioning in the embodiment. Detailed implementation method:

[0029] To make the objectives, technical solutions, and advantages of this invention clearer and more understandable, the invention will be further described in detail below with reference to the accompanying drawings and technical solutions.

[0030] For cases involving large dynamic deformation of dams due to seismic loads, see the embodiment in this case. Figure 1 As shown, a numerical simulation method for dynamic large deformation of dams in seismic liquefaction sites is provided, comprising:

[0031] S101. Establish a structural model of the dam project, and generate a background mesh for finite element analysis of earthquake large deformation by dividing the polygonal scale boundary element mesh in the structural model.

[0032] S102. Obtain the initial stress of each engineering part of the dam during the filling and water impoundment process through static analysis;

[0033] S103. Based on the initial stress, and according to the geographical location of the dam project, set the ground motion data;

[0034] S104. Based on the seismic motion data, the seismic motion is input into the finite element background mesh for dynamic analysis to obtain the dynamic deformation information of various engineering parts of the dam after the earthquake.

[0035] By simulating the entire process of soil liquefaction and seismic deformation and progressive failure of dams on seismically liquefied sites, this study aims to explore the development patterns, physical mechanisms, and influencing factors of large deformation and progressive failure of dams on seismically liquefied sites. This will facilitate the optimization of dam engineering structural design and provide a basis for seismic design by studying the reinforcement effects and mechanisms of different measures. It has important theoretical significance and engineering application value for improving and developing a seismic safety evaluation system for dams based on functional control.

[0036] As a preferred embodiment, the establishment of the dam engineering structure model further includes: first, acquiring relevant data for dam engineering modeling, and using drawing modeling line segments to describe the dam engineering morphology and calculation analysis domain, wherein the relevant data for modeling includes at least the simulation range, typical elevation, dam material analysis, and foundation layer distribution; then, performing polygon scale boundary unit meshing on the constructed model, and recording key boundary data, wherein the key boundary data includes: dam engineering outline, material partitioning lines, and stratum layering lines.

[0037] Based on the dam design drawings and provided engineering data, key modeling information including the engineering simulation range, typical elevations, dam material zoning, and foundation layer distribution is obtained. In the drawing and modeling software, the shape of the dam project and the range of the calculation and analysis domain can be described by line segments. The model is then meshed with polygonal scale boundary elements to obtain subsequent information including stress-strain model, material, seepage, and pore pressure. Key boundary information including the engineering outline, material zoning lines, and strata stratification lines is also recorded.

[0038] Furthermore, the background mesh for finite element analysis of large deformation earthquakes is generated by partitioning the polygonal scale boundary element mesh in the structural model. This includes: first, determining the calculation analysis domain of the model based on the dam engineering model; then, setting the number of segments in each line segment in the analysis domain and the densification points in the closed area, and generating the background mesh by identifying the densification points and performing mesh partitioning on the densification point locations.

[0039] Based on the engineering model, the analysis domain is determined. During the meshing process, the number of segments in each line segment of the analysis domain and the density points in closed areas can be set according to the embankment material and foundation layering. By identifying these density points, the software will mesh more densely at these locations, achieving controllability in meshing. This results in denser meshing at the interfaces and boundaries of different materials compared to other locations, facilitating detailed numerical simulations. Through the above settings and operations, the background mesh, which has been consistently used in earthquake large deformation analysis, can be generated, such as... Figure 2 As shown. Meanwhile, the background mesh in the dam engineering model is both the mesh used for the static analysis of the dam and the initial mesh for the seismic large deformation analysis. Figure 3 This is a schematic diagram of the proportional boundary mesh of the dam polygon separated from the background mesh.

[0040] As a preferred embodiment, further, the initial stress of obtaining deformation information of various engineering parts of the dam during filling and water impoundment through static analysis includes: first, preprocessing the background network, which includes: applying gravity load and water pressure load to the model, and setting the plastic deformation characteristics of the foundation material and the dam body; then, calculating and analyzing the static stress of the background mesh finite element according to the time step during the filling and water impoundment process, and outputting the initial stress data after static calculation and analysis, which includes: deformation information of stress and strain of various parts of the dam during filling and water impoundment.

[0041] Before starting static and dynamic calculations, preprocessing of the mesh can be performed: The software is used to fill, constrain, and materialize the analysis domain model, and to apply gravity and water pressure loads to the model. Based on the lithological characteristics of the foundation, the foundation is defined as a suitable material model, and the dam body is defined as a generalized plastic soil model with multiple parameters (i.e., multiple internal variables), which better reflects the deformation characteristics of the dam. After preprocessing, finite element static calculations are performed based on the total time steps used during the filling and impoundment processes. After completing the static calculations, an initial stress file is output, mainly containing deformation information such as stress and strain of various parts of the dam after the filling and impoundment processes.

[0042] Furthermore, based on the initial stress and according to the geographical location of the dam project, the ground motion data is set, including: first, setting the ground motion load according to the initial stress and the geographical location of the dam project, and setting the ground motion boundary conditions using artificial viscoelastic boundaries; then, setting the seismic waves in the simulated ground motion by combining artificial boundaries with equivalent nodal loads.

[0043] Preprocessing for dynamic analysis of large deformation of a foundation liquefaction dam under seismic loading: Based on the initial stress obtained from static calculations, appropriate seismic loads are set according to the project's geographical location, and corresponding boundary conditions are established. Artificial viscoelastic boundaries are used for the dam's boundary conditions. Seismic motion input is achieved through a combination of artificial boundaries and equivalent nodal loads. Nodes on the outer side of the elements are fully constrained, limiting both horizontal and vertical displacements. Nodes on the inner side of the elements in contact with the foundation soil elements are bound to the corresponding soil element nodes to ensure synchronous horizontal and vertical displacements under seismic loading. A suitable soil dynamic material model is selected for the foundation based on the project conditions, while the dam is defined as a generalized plastic model. Dynamic analysis is then conducted to obtain dynamic deformation information of the dam after seismic loading, such as displacement, velocity, and acceleration.

[0044] As a preferred embodiment, further, the seismic motion is input into the finite element background mesh based on the seismic motion data to obtain the dynamic deformation information of various engineering parts of the dam after the earthquake. This includes: first, dividing the earthquake into several time periods, and dynamically adjusting the position of the line nodes and updating the node coordinates of the dam engineering mesh elements according to the changes in the position of the model boundary line and the material partition line of each engineering part in each time period; then, mapping the deformed mesh information back to the background mesh, reconstructing the model according to the liquefaction deformation, and re-subdividing the analysis domain of the reconstructed model, remapping the mesh information on the background mesh to the re-subdivided analysis domain mesh, and repeating the dynamic analysis until the earthquake ends, obtaining the dynamic deformation information of various engineering parts of the dam after the earthquake through the final re-subdivision and mapping.

[0045] In the dynamic calculation process, the entire earthquake is divided into several time periods. The conservative time period can be 0.2 seconds. Due to the strong adaptability of the proportional boundary element to deformation, the time period can be increased. The positional changes of the model boundary line and material partition lines of each part are obtained based on the displacement information of the deformation. The positions of each line node are dynamically adjusted according to the positions of the boundary line and material partition lines, updating the node coordinates of the dam engineering mesh elements. Then, based on the semi-analytical characteristics of the proportional boundary element solution, and using the conventional mapping method of Gaussian points, the mapping equations of element constitutive parameters and internal variables are constructed through interpolation functions. The deformed mesh information, including nodal pore pressure, deformation, element Gaussian point stress, strain, pore pressure, and constitutive internal variables, is mapped back to the background mesh. Reconstruction is then performed based on liquefaction deformation. Seismic loads cause accumulated pore pressure in liquefiable foundation soil, reducing both modulus and strength, leading to significant deformation in various parts of the dam engineering, especially the sliding deformation of the dam slope to the left and right sides. Then, the analysis domain is re-subdivided, and the mesh information on the background mesh is remapped back to the re-subdivided engineering analysis domain mesh. This dynamic analysis step is repeated until the earthquake process ends. By repeatedly subdividing and mapping, the deformation information of various parts of the project after the earthquake can be obtained, and the dynamic large deformation analysis is completed.

[0046] Furthermore, mapping the deformed mesh information back to the background mesh includes: first, using a semi-analytical solution function of the scaled boundary finite element to construct a mapping equation for the associated node information of the polygon scaled boundary finite element; then, using the mapping equation to map the deformed mesh information in the computational domain to the background mesh. The deformed mesh information includes, but is not limited to: nodal pore pressure, nodal deformation, element Gaussian point stress, element Gaussian point strain, element Gaussian point pore pressure, and constitutive internal variables.

[0047] Throughout the dynamic calculation process, Figure 2The shape and position of the polygonal scale boundary finite element shown remain unchanged. However, after a certain period of calculation, the polygonal scale boundary finite element mesh of the dam project has deformed. The relationship between the deformed dam project scale boundary element (computation domain) and the scale boundary element of the background mesh is illustrated. Figure 5 At this point, key information of the deformed mesh within the computational domain, such as nodal pore pressure and deformation, element Gaussian point stress, strain, pore pressure, and constitutive variables, is mapped back to the background mesh. To reduce the residual error of each information mapping and ensure the effectiveness of the entire seismic large deformation analysis process, the accuracy of each information mapping needs to be ensured. This paper proposes to fully utilize the semi-analytical characteristics of the scaled boundary finite element method, combined with the concept of finite element Gaussian points, and to construct mapping equations for polygonal scaled boundary finite elements and their associated nodal information using a semi-analytical solution function of the scaled boundary finite element. This allows for high-precision mapping of the key information of the deformed mesh within the computational domain to the background mesh.

[0048] Information mapping requires the construction of corresponding interpolation functions. In this embodiment, the semi-analytical solution characteristics of the polygonal scale boundary finite element are fully utilized to solve the governing equations, obtaining the expression of the interpolation shape function and the interpolation format of the information domain. The following example illustrates the method for obtaining the pore pressure interpolation shape function.

[0049] According to the finite element theory of scaled boundaries, the pore pressure value at any point within the sectoral domain formed by the line connecting the polygonal circumferential boundary line elements and the scale center can be solved in the local coordinate system of the scaled boundary.

[0050] p(ξ,s=N p (s)p(ξ) (1)

[0051] N p (s)=[N1(s)N2(s)…N m (s)] (2)

[0052] In the formula N p (s) is the pore pressure function of the circumferential boundary element, and p(ξ) is the assumed, uniquely solvable radial pore pressure function, which can be solved by the governing equations of the steady-state seepage problem. Similarly, the pore pressure at any point of the three-dimensional polyhedral element can be solved, where N p (ξ1,ξ2) are the facet compression functions of the circumferential boundary surface, which are solved by the polygon average interpolation function. Based on the proportional boundary finite element theory framework, the governing equation of the seepage problem is expressed as (3).

[0053]

[0054] The equation is a second-order nonhomogeneous ordinary differential equation with respect to the radial coordinate ξ, where s = 2 or s = 3 represents the spatial dimension of the computational domain, i.e., a two-dimensional problem and a three-dimensional problem. The coefficient matrix, which is only related to the material permeability coefficient and the element shape, can be obtained by numerical integration sequentially along the circumferential boundary lines, and then assembled piecewise according to the degrees of freedom. f(ξ) is the boundary node flow vector. and This is the velocity transformation matrix for the boundary element.

[0055]

[0056]

[0057] When f(ξ) = 0, and matrix variable X is introduced. p (ξ), see equation (6), then the second-order nonhomogeneous differential equation in (3) can be converted into a first-order homogeneous ordinary differential equation, see equation (7).

[0058]

[0059] ξX p (ξ) ,ξ =-Z p X p (ξ) (7)

[0060] Where Q(ξ) is the internal node flow vector corresponding to p(ξ), Z p Let be the Hamiltonian matrix, expressed as (8).

[0061]

[0062] Using the eigenvalue decomposition method, for Z p Performing eigenvalue decomposition on a matrix yields the following expression for polygonal elements:

[0063]

[0064] In the formula It is a diagonal matrix whose elements are the real parts of the negative eigenvalues ​​obtained from eigenvalue decomposition, Ψ p and Ψ Q These are the transformation matrices corresponding to the pore pressure and flow modes, respectively. Based on the mathematical equation derivation, for the polygonal element, the solution to equation (3) is:

[0065]

[0066] Integral constant The pore pressure p at the circumferential boundary (ξ=1) node can be obtained. b Find:

[0067]

[0068] Substituting (11) into (10), we can obtain the expressions for the radial hole shaping function p(ξ) and the nodal flow rate Q(ξ).

[0069]

[0070] Substituting equation (12) into equation (1) yields the interpolation scheme for pore pressure, thus allowing the calculation of the pore pressure value at any point within the polygonal element domain:

[0071]

[0072] Take the right-hand side term p in the above equation b The matrix product coefficients.

[0073]

[0074] Then Φ p (ξ,s) is called the hole compression function of the polygon scale boundary finite element.

[0075] The above steps outline the solution process and expressions for the pore pressure interpolation scheme and interpolation shape functions. For information such as deformation, stress, and constitutive variables, the relevant functions can be solved by referring to the pore pressure calculation. Once the interpolation shape functions and interpolation expressions for all information are determined, information mapping can be performed.

[0076] As a preferred embodiment, further, in the mapping process, firstly, the polygonal element is pre-divided into several triangular sub-elements with the centroid of the element as the center. Based on the triangular finite element, the pressure Gaussian points and displacement Gaussian points of each sub-element are arranged. The parent element is constructed and an information mapping domain is created according to the distribution of Gaussian points and nodes. Then, the local coordinates of the Gaussian points in the parent element are determined, and the Gaussian point information is obtained by interpolation based on the element shape function and local coordinates.

[0077] To facilitate the concretization of the semi-analytical solution function, referring to the finite element method, the polygonal element is pre-divided into N triangular sub-elements centered on the element centroid. Based on the triangular finite element, the pore pressure Gaussian points and displacement (stress) Gaussian points of each sub-element are arranged (the changes of each variable are explained in the corresponding steps according to the program settings). The arrangement of pore pressure and displacement Gaussian points is as follows: Figure 4 As shown.

[0078] When performing information mapping based on the scaled boundary finite element theory, it is necessary to obtain the locations of Gaussian points and nodes as needed, as well as the distribution of Gaussian points and nodes in the information source mesh element, to construct the parent element and create a new information mapping domain. The following explanation uses Gaussian points as an example. Figure 6A schematic diagram of the information source grid mapping is used to represent Gaussian points acquiring information at different locations. If the Gaussian point to be acquired is located within a polygonal element composed of three Gaussian points in the information source grid cell, such as Gaussian point N1, then triangle O1-O2-O3 is the parent element. When the Gaussian point to be acquired is located outside O1-O2-O3, for N2, its parent element is O3-O4-O5 (composed of the Gaussian points in the information source grid cell and the Gaussian points in neighboring information source cells); for N3, its parent element is O1-O3-A (composed of the Gaussian points and nodes in the background grid cell). According to finite element theory, the inverse matrix of the shape function matrix can be used to determine the local coordinates of the Gaussian point in the parent element. The information of the Gaussian point is then obtained by interpolation based on the element shape function and local coordinates using the aforementioned theory.

[0079] After mapping the deformable mesh elements and node information within the computational domain to the background mesh elements and nodes, the dam project is re-meshed using the Delaunay meshing method based on the Delaunay meshing theory. This re-meshs the dam project with updated, better-shaped polygonal boundary elements, based on the seismic liquefaction deformation increment of the dam project obtained in the current time period and the contour lines, zoning lines, and layering lines recorded during the static calculation preparation stage. The positional relationship between the background mesh and the re-meshed mesh in the computational domain is as follows: Figure 7 As shown. Figure 8 The finite element mesh is a polygonal scale boundary of the re-divided dam project.

[0080] After obtaining the re-mesh of the dam project, the local coordinates of the Gaussian points and nodes of the re-mesh elements in the background mesh are determined using the method described above, and the interpolation parent element is determined. The Gaussian points and node information of the background mesh elements are then mapped back to the re-mesh of the dam project by mapping the deformed computational domain mesh information to the background mesh.

[0081] After mapping the background mesh information back to the re-subdivided mesh, the calculation for this period ends. Simultaneously, it is determined whether the cumulative time period for the large earthquake deformation analysis has reached the input earthquake duration. If not, the above process is repeated until the earthquake event ends, thus completing the large earthquake deformation analysis.

[0082] This proposed solution overcomes the shortcomings of existing methods, which struggle to accurately capture the dynamic deformation process of dams on seismically liquefied sites and fail to reveal the dam failure mechanism. It can simulate the dynamic deformation of dams on seismically liquefied sites with high precision and reasonable accuracy. By moving the constantly updated dam engineering mesh on the background mesh, it can simulate the entire process of foundation liquefaction, seismic deformation of the dam body, and progressive failure. It can numerically reproduce actual seismic damage phenomena, provide a basis for the seismic design of dams, and provide a reference for deformation simulation.

[0083] Unless otherwise specifically stated, the relative steps, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of the invention.

[0084] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0085] The units and method steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of each example have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations are not considered to be beyond the scope of this invention.

[0086] Those skilled in the art will understand that all or part of the steps in the above methods can be implemented by a program instructing related hardware, and the program can be stored in a computer-readable storage medium, such as a read-only memory, a disk, or an optical disk. Optionally, all or part of the steps in the above embodiments can also be implemented using one or more integrated circuits. Accordingly, each module / unit in the above embodiments can be implemented in hardware or as a software functional module. This invention is not limited to any particular combination of hardware and software.

[0087] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for numerical simulation of dynamic large deformation of embankments on liquefiable ground, characterized in that, Includes the following content: A structural model of the dam project is established, and the background mesh of the finite element method for seismic large deformation analysis is generated by dividing the polygonal scale boundary element mesh in the structural model. The initial stress of each engineering part of the dam during the filling and water impoundment process was obtained through static analysis; Ground motion data were set based on initial stress and according to the geographical location of the dam project; Based on the seismic motion data, the earthquake was divided into several time periods. Based on the finite element background mesh, the position of the line nodes was dynamically adjusted and the node coordinates of the dam engineering mesh elements were updated according to the changes in the position of the model boundary line and the material partition line of each engineering part in each time period. Then, the deformed mesh information was mapped back to the background mesh, the model was reconstructed according to the liquefaction deformation, and the analysis domain of the reconstructed model was re-subdivided. The mesh information on the background mesh was re-mapped to the re-subdivided analysis domain mesh. Through repeated dynamic analysis until the earthquake ended, the dynamic deformation information of each engineering part of the dam after the earthquake was obtained through the final re-subdivision and mapping.

2. The method of claim 1, wherein, The establishment of the dam engineering structural model includes: first, acquiring relevant data for dam engineering modeling, and using drawing modeling line segments to describe the dam engineering morphology and calculation analysis domain, wherein the relevant data for modeling includes at least the simulation range, typical elevation, dam material analysis, and foundation layer distribution; then, performing polygon scale boundary unit meshing on the constructed model, and recording key boundary data, wherein the key boundary data includes: dam engineering outline, material partition lines, and stratum layering lines.

3. The method for numerical simulation of seismic liquefaction site embankment dynamic large deformation according to claim 1 or 2, characterized in that, The background mesh for seismic large deformation analysis is generated by dividing the polygonal scale boundary element mesh in the structural model. The process includes: first, determining the calculation analysis domain of the model based on the dam engineering model; then, setting the number of segments in each line segment in the analysis domain and the densification points in the closed area, and generating the background mesh by identifying the densification points and dividing the mesh at the location of the densification points.

4. The method for numerical simulation of seismic liquefaction site embankment dynamic large deformation according to claim 1, characterized in that, The initial stress of the dam is obtained by static analysis to obtain deformation information of various engineering parts of the dam during the filling and water impoundment process. The process includes: first, preprocessing the background mesh, which includes applying gravity load and water pressure load to the model and setting the plastic deformation characteristics of the foundation material and the dam body; then, calculating and analyzing the static stress of the background mesh finite element according to the time step during the filling and water impoundment process, and outputting the initial stress data after static calculation and analysis. The initial stress data includes the deformation information of stress and strain of various parts of the dam during the filling and water impoundment process.

5. The method for numerical simulation of seismic liquefaction site embankment dynamic large deformation according to claim 1, characterized in that, Based on the initial stress and according to the geographical location of the dam project, the ground motion data is set, including: first, setting the ground motion load according to the initial stress and the geographical location of the dam project, and setting the ground motion boundary conditions using artificial viscoelastic boundaries; then, setting the seismic waves in the simulated ground motion by combining artificial boundaries with equivalent nodal loads.

6. The method for numerical simulation of seismic liquefaction site embankment dynamic large deformation according to claim 1, characterized in that, Mapping the deformed mesh information back to the background mesh involves: first, using a semi-analytical solution function of a scaled boundary finite element to construct a mapping equation for the associated node information of a polygonal scaled boundary finite element; then, using the mapping equation to map the deformed mesh information in the computational domain to the background mesh. The deformed mesh information includes, but is not limited to: nodal pore pressure, nodal deformation, element Gaussian point stress, element Gaussian point strain, element Gaussian point pore pressure, and constitutive internal variables.

7. The method of claim 1 or 6, wherein During the mapping process, firstly, the polygonal element is pre-divided into several triangular sub-elements with the centroid of the element as the center. Based on the triangular finite element, the pressure Gaussian points and displacement Gaussian points of each sub-element are arranged. The parent element is constructed and an information mapping domain is created according to the distribution of Gaussian points and nodes. Then, the local coordinates of the Gaussian points in the parent element are determined, and the Gaussian point information is obtained by interpolation based on the element shape function and local coordinates.

8. The method for numerical simulation of seismic liquefaction site embankment dynamic large deformation according to claim 1, characterized in that, In the re-meshment, the deformable mesh elements and node information in the computational domain are mapped to the background mesh elements and nodes. Based on the seismic liquefaction deformation increment of the dam project obtained in the current time period and the dam outline, partition line and layer line obtained in the static analysis, the mesh of the dam project is re-meshed using the meshing method based on Delaunay meshing theory, and the polygon scale boundary elements in the computational domain are updated.

9. The method for numerical simulation of seismic liquefaction site embankment dynamic large deformation according to claim 1, characterized in that, Model reconstruction based on liquefaction deformation includes: first, obtaining the deformation of each engineering part of the dam based on the accumulated pore pressure in the liquefied foundation soil caused by seismic load and the change of pore pressure on modulus and strength, wherein the deformation of each engineering part of the dam includes at least the sliding deformation of the dam slope to the left and right sides respectively; then, reconstructing the dam engineering structure model based on the deformation of each engineering part of the dam.

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