Dam finite element analysis method and system based on dynamic time history method of wave theory

Abstract

The invention belongs to the field of dam flood discharge safety, and provides a dam finite element analysis method and system based on a dynamic time history method of a wave theory, and the method comprises the steps: S1, building a refined finite element model of a dam-foundation-reservoir coupling system; s2, generating a fluctuation theory artificial boundary condition acting on the external boundary of the foundation medium unit; s3, seismic oscillation input is applied to the refined finite element model; s4, solving the dynamic response of the coupling system under the seismic action by adopting a nonlinear dynamic solver in combination with a time domain integration method; and carrying out earthquake response analysis and damage evaluation on the dam based on the solved dynamic response result. According to the method, through cooperative work of all the parts, dam finite element analysis based on the dynamic time history method of the wave theory is achieved, and accurate and reliable technical support can be provided for aseismic design and safety evaluation of dam engineering.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of dam flood discharge safety, and relates to a dam finite element analysis method and system based on the dynamic time history method of wave theory. BACKGROUND

[0002] As a mature numerical calculation method, finite element analysis is widely used in the dynamic response simulation of dams under seismic load in combination with the dynamic time history method to ensure the structural safety and stable operation of the dam. The dynamic time history method can simulate the response of the structure under arbitrary time history seismic action by directly integrating the structural dynamic equation, and the finite element analysis provides a discretized structural model, which provides important technical support for the seismic performance evaluation of the dam.

[0003] Among them, the dam finite element analysis based on the dynamic time history method aims to accurately capture the propagation characteristics of seismic waves in the dam-foundation-reservoir system and the induced structural dynamic response. The key to this method is to establish a refined model that can reflect the actual engineering situation and apply representative seismic input to evaluate the stress, displacement and potential damage of the dam under complex seismic action, thereby providing a scientific basis for the seismic prevention and safe operation of the dam.

[0004] However, the existing technology still has significant deficiencies in the dam finite element analysis based on the dynamic time history method. In terms of seismic wave propagation simulation, the existing methods often fail to fully consider the complex wave field coupling effects, especially the energy dissipation and mode conversion of seismic input at different medium interfaces, resulting in limited simulation accuracy of seismic input. For the treatment of complex boundary conditions, current schemes such as the equivalent nodal force method show limitations in handling multi-angle incident seismic waves, and the setting of artificial boundaries often uses simplified models that fail to fully reflect the complex scattering and reflection phenomena in wave theory, resulting in deviations between the boundary conditions and the actual situation. Furthermore, in terms of dynamic response analysis accuracy, the existing technology relies on modal parameter corrected finite element models, which lack the ability to simulate nonlinear damage behavior of dams under strong earthquakes, making it difficult to accurately assess the damage mode and extent of the dam under extreme seismic events. SUMMARY

[0005] To solve the problems in the prior art, the application provides a dam finite element analysis method and system based on the dynamic time history method of wave theory. The existing dam flood discharge safety protection technology still has deficiencies in dynamic response analysis, early warning capability and full-process intelligent control for natural disasters such as earthquakes, and a more comprehensive solution is needed.

[0006] The application adopts the following technical solutions, including the following steps: S1, establishing a refined finite element model of a dam-foundation-reservoir coupling system, the model comprising a dam body unit, a foundation medium unit and a reservoir fluid unit, and setting a nonlinear constitutive model for the dam body unit and the foundation medium unit; S2, generating a wave theory artificial boundary condition acting on an external boundary of the foundation medium unit, the wave theory artificial boundary condition being capable of absorbing incident waves and scattered waves, thereby avoiding boundary reflection; S3, applying seismic motion input on the refined finite element model, the seismic motion input being a free field displacement time history or stress time history considering spatial correlation; S4, solving dynamic response of the coupling system under the seismic motion by using a nonlinear dynamics solver in combination with a time domain integral method, the solving process considering iterative updating of the nonlinear constitutive model; and based on the dynamic response results obtained by the solving, performing seismic response analysis and damage assessment of the dam, the analysis and assessment including judging macro damage regions according to a preset damage criterion, and quantifying cumulative damage degree of the dam body by using an energy dissipation-based damage index or a cumulative plastic strain damage index.

[0007] As preferred, the establishing a refined finite element model of a dam-foundation-reservoir coupling system comprises: discretizing the dam body into solid elements, the material constitutive model of the solid elements adopting a concrete damage plasticity model; discretizing the foundation medium into solid elements, the material constitutive model of the solid elements adopting a Mohr-Coulomb elastoplasticity model or a modified Cambridge model; and discretizing the reservoir fluid into acoustic elements, and realizing coupling effect between the dam body and the reservoir fluid by setting fluid-structure coupling surface elements.

[0008] As preferred, the generating a wave theory artificial boundary condition comprises: setting a layer of perfect matched layer along the external boundary of the foundation medium unit, the perfect matched layer making waves attenuate in the perfect matched layer by introducing a frequency-dependent attenuation function, simulating reflection-free effect of an infinite medium; or setting a refined viscoelastic artificial boundary along the external boundary of the foundation medium unit, the refined viscoelastic artificial boundary applying additional damping and stiffness related to free field response and considering medium wave impedance.

[0009] As preferred, the applying seismic motion input on the refined finite element model comprises: obtaining results of seismic site effect analysis; based on the site effect analysis results, applying spatially-correlated free field displacement time history or stress time history at a connection between the foundation medium unit and the wave theory artificial boundary condition by using a multi-point input method, the free field displacement time history or stress time history reflecting traveling wave effect and incidence angle of seismic waves by considering time difference and phase difference of seismic wave propagation at different foundation points.

[0010] As preferred, the solving the dynamic response of the coupling system under the action of the seismic motion by using a nonlinear dynamics solver in combination with a time domain integration method comprises: establishing dynamic equilibrium equations of the coupling system; performing nonlinear iteration solving by using Newton-Raphson iteration method or arc length method, and correcting stiffness matrix and force vector by iteration until convergence; and performing time step integration by using Newmark-beta method or HHT-alpha method, wherein the time step is less than one tenth of the minimum period vibration time step of the coupling system.

[0011] As preferred, the damping matrix of the dynamic equilibrium equations established by the solving process uses Rayleigh damping model, and the damping coefficients α and β are determined by the main mode frequency and damping ratio of the dam structure.

[0012] As preferred, the analysis and evaluation comprises extracting absolute displacement, relative displacement, velocity, acceleration, stress component and principal stress time history of key parts of the dam; The analysis and evaluation comprises judging macro damage area and damage initiation time based on maximum principal tensile stress criterion, maximum shear stress criterion or maximum strain criterion; and quantifying the cumulative damage degree of the dam body by using damage index based on energy dissipation or cumulative plastic strain damage index.

[0013] In another aspect, a dam finite element analysis system based on dynamic time history method of wave theory comprises: A model establishing module is configured to establish a refined finite element model of a dam-foundation-reservoir coupling system, the model comprising dam body elements, foundation medium elements and reservoir fluid elements, and the dam body elements and the foundation medium elements being provided with a nonlinear constitutive model; An artificial boundary condition generating module is configured to generate a wave theory artificial boundary condition acting on the outer boundary of the foundation medium elements, the wave theory artificial boundary condition being capable of absorbing incident waves and scattered waves and avoiding boundary reflection; A seismic motion input applying module is configured to apply a free field displacement time history or stress time history seismic motion input considering spatial correlation on the refined finite element model; A dynamic response solving module is configured to solve the dynamic response of the coupling system under the action of the seismic motion by using a nonlinear dynamics solver and a time domain integration method, the solving process considering iterative updating of the nonlinear constitutive model; and a damage evaluation module is configured to perform seismic response analysis and damage evaluation of the dam based on the dynamic response results obtained by the solving, the analysis and evaluation comprising judging macro damage area according to a preset damage criterion and quantifying the cumulative damage degree of the dam body.

[0014] Preferably, the model establishing module is specifically configured to discretize the dam body into solid elements, the material constitutive model of the solid elements adopting a concrete damaged plasticity model; discretize the foundation medium into solid elements, the material constitutive model of the solid elements adopting a Mohr-Coulomb elastoplasticity model or a modified Cambridge model; and discretize the reservoir fluid into acoustic elements, and realize the coupling between the dam body and the reservoir fluid by setting fluid-structure coupling surface elements.

[0015] Compared with the prior art, the present application has the following advantages: 1. The present application can accurately simulate the nonlinear mechanical behavior of the dam, foundation and reservoir under strong earthquake action, reflect the stiffness degradation, cracking and plastic deformation of the material, and improve the accuracy of nonlinear damage behavior analysis by establishing a refined dam-foundation-reservoir coupling finite element model.

[0016] 2. The present application uses a principle based on a perfect matched layer or a refined viscoelastic artificial boundary condition, breaks through the limitations of the traditional viscoelastic boundary on the type and angle of incident waves, realizes the reflection-free simulation of the infinite medium of the foundation, can more realistically restore the propagation, scattering and reflection effects of seismic waves in the medium, and significantly improves the accuracy of wave propagation simulation and the reliability of boundary condition processing.

[0017] 3. The present application introduces a spatially correlated free-field displacement or stress time history as the seismic input, fully considers the traveling wave effect and multi-point input characteristics of seismic waves, overcomes the defect that single base excitation cannot reflect the spatial variation of seismic motion, makes the seismic input more consistent with the actual working condition, and improves the accuracy of dynamic response analysis.

[0018] 4. The present application integrates a nonlinear dynamics solver and a time-domain integration method, and combines a Newton-Raphson iteration method or an arc length method to handle nonlinear problems, ensuring stable solution of complex nonlinear systems under seismic load, and improving the reliability of dam seismic response evaluation. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 The system flowchart of the present application. DETAILED DESCRIPTION

[0020] Example 1: As Figure 1As shown, in order to solve the deficiencies of existing flood discharge safety protection technology in dynamic response analysis, early warning capability and intelligent control of the whole process for natural disasters such as earthquakes, the present application provides a dam finite element analysis method and system based on the dynamic time history method of wave theory. This method aims to overcome the deficiencies of existing technology in simulating wave propagation, boundary condition processing and dynamic response analysis accuracy, so as to realize more accurate evaluation of the seismic response of the dam. The present application constructs a fine finite element model of the dam, foundation and reservoir coupling system, introduces and implements advanced dynamic artificial boundary conditions of wave theory, accurately applies seismic time history excitation, and performs dynamic time history analysis of the coupling system, finally evaluates the seismic response and potential nonlinear damage of the dam. This method considers the propagation, scattering and reflection effects of seismic waves in different media, optimizes the wave energy absorption ability of the boundary conditions, and improves the simulation accuracy of the nonlinear behavior of the dam under strong earthquake action.

[0021] In a first aspect, the present application provides a dam finite element analysis method based on the dynamic time history method of wave theory, which comprises the following steps: S101: constructing a finite element model of a dam, foundation and reservoir coupling system; S102: applying dynamic artificial boundary conditions based on wave theory; S103: determining and inputting seismic time history excitation; S104: performing dynamic time history analysis of the coupling system; S105: evaluating the seismic response and nonlinear damage of the dam.

[0022] In detail, S101, a finite element model of a dam, foundation and reservoir coupling system is constructed. This step is the basis for analyzing the seismic response of the dam, and its accuracy and reasonableness directly affect the reliability of subsequent dynamic analysis. When constructing the finite element model of the coupling system, the dam structure, foundation medium and reservoir water body need to be finely divided in geometry and defined in material properties.

[0023] In particular, for a dam structure, its geometric model should be accurately modeled according to the actual engineering drawings, including the dam body contour, gallery, water stop and other key features. When discretizing the finite element, three-dimensional solid elements are usually used, such as eight-node isoparametric elements or twenty-node isoparametric elements, to accurately capture the spatial behavior of the dam body. The determination of the material properties of the dam is crucial. For a concrete dam, the basic mechanical parameters such as its elastic modulus, Poisson's ratio, density, etc. need to be considered. In order to simulate the nonlinear behavior of the dam under strong earthquake action, such as concrete cracking, damage accumulation, etc., a suitable nonlinear constitutive model needs to be introduced, such as a concrete damage plasticity model. This model can describe the hardening and softening characteristics of concrete under compression and tension, as well as the damage evolution process. When applying the concrete damage plasticity model, the parameters such as the crushing strength, tensile strength, fracture energy, expansion angle of the material need to be defined and checked by experimental data. The accurate acquisition of these parameters depends on detailed material mechanics experimental data and engineering experience. For example, the compressive strength of concrete can be in the range of twenty to sixty megapascals, and the Poisson's ratio is usually between 0.15 and 0.25.

[0024] For the foundation medium, its modeling range should be large enough to avoid unnecessary influence of the finite element model boundary on wave propagation. The foundation is usually considered as an elastic or elastoplastic medium, which can be discretized by solid elements. The elastic modulus, Poisson's ratio, density, shear wave velocity and compression wave velocity of the foundation material are key parameters. In order to simulate the nonlinear behavior of the foundation under earthquake action, such as the shear softening and liquefaction effect of soil, the Mohr-Coulomb elastoplastic model or more advanced nonlinear soil constitutive model can be introduced. The parameters of these models, such as the internal friction angle, cohesion, shear dilatancy angle, yield stress, etc., need to be determined by soil tests, such as triaxial shear test, consolidation test, etc., and site investigation data. The typical value range of the foundation material parameters varies significantly according to the type of rock and soil, for example, the shear wave velocity of hard rock can reach several kilometers per second, while the shear wave velocity of soft soil is only tens of meters per second.

[0025] For the reservoir water body, it is usually modeled as a compressible, incompressible fluid. The interface between the water body and the dam body, foundation is a fluid-structure coupling interface. The water body can be discretized by acoustic elements or fluid pressure elements, such as eight-node acoustic elements. The density and sound speed of the water body are its main physical parameters. When considering the geometric range of the reservoir water body, it should be ensured that it covers a far enough distance to reasonably simulate the dynamic response of the water body. The boundary of the reservoir bottom can be set as a full reflection or partial absorption boundary, while the reservoir side is connected with the foundation model. The sound speed of water is about 1,500 meters per second at normal temperature and pressure.

[0026] In the process of model construction, the quality of meshing is crucial. Local encryption should be performed at the junction of dam, foundation and reservoir, as well as stress concentration area, to improve the calculation accuracy. The mesh size should meet the requirements of wave propagation theory, i.e. at least six to ten units per wavelength, to avoid numerical dispersion effect. Compatibility and node sharing of the mesh should be ensured between different sub-regions and different media, to realize seamless coupling analysis. For example, at the junction of dam and foundation, the displacement continuity of shared nodes should be ensured, while at the junction of dam and water, the normal displacement continuity and pressure transmission of shared nodes should be ensured.

[0027] In terms of data flow, geometric model data is imported from computer-aided design software, and material parameter data is obtained from material database or user input. Meshing is completed automatically or manually by finite element pre-processing software. After integration of all these data, a complete finite element model input file is formed for subsequent dynamic analysis program. After model construction, model checking is needed, such as unit connectivity checking, material property assignment checking, boundary condition application checking, to ensure the correctness of the model.

[0028] S102, applying dynamic artificial boundary condition based on wave theory. This step is one of the core innovations of the present application to solve the deficiency of prior art in boundary condition processing. The traditional fixed boundary or free boundary cannot accurately simulate the wave propagation characteristics of infinite foundation, which will lead to incorrect reflection of wave energy, and further affect the accuracy of dam dynamic response analysis. The present application adopts dynamic artificial boundary condition based on wave theory to effectively absorb seismic waves propagating from the internal region to the external infinite domain, avoid boundary reflection, and thus more realistically simulate the dynamic behavior of the foundation.

[0029] Specifically, the dynamic artificial boundary condition adopted by the present application is based on advanced wave theory, such as viscoelastic artificial boundary, refined local uniform artificial boundary or perfectly matched layer artificial boundary. Taking viscoelastic artificial boundary as an example, the core idea is to apply a series of parallel springs and dampers on the artificial truncated boundary of the finite element model. The stiffness and damping coefficient of these springs and dampers are determined according to the physical parameters of the foundation material and the wave propagation theory, to simulate the absorption of wave energy by the infinite foundation.

[0030] The determination process of the stiffness and damping coefficient of the viscoelastic artificial boundary includes the following sub-steps: First sub-step, determine the equivalent shear modulus and shear wave velocity of the foundation medium at the artificial boundary. This needs to consider the material properties of the foundation and the frequency characteristics of seismic motion.

[0031] Secondly, the equivalent spring stiffness at each point on the boundary is calculated according to the physical parameters of the foundation medium. For the spring stiffness along the normal direction, its value is usually related to the Young's modulus, Poisson's ratio of the foundation medium, and the shape and size of the artificial boundary. For the spring stiffness along the tangential direction, it is related to the shear modulus.

[0032] Thirdly, the equivalent damper damping coefficient at each point on the boundary is calculated according to the wave velocity of the foundation medium. For the damping coefficient along the normal direction, its value is related to the compression wave velocity and the density of the foundation. For the damping coefficient along the tangential direction, it is related to the shear wave velocity and the density of the foundation. These dampers can simulate the energy dissipation of wave motion and prevent wave reflection back to the internal region.

[0033] The equivalent normal spring stiffness coefficient of the viscoelastic artificial boundary can be represented by the following formula: .

[0034] where Kn represents the normal spring stiffness coefficient; an represents the normal stiffness correction coefficient, whose value usually ranges from one point zero to two point zero; G represents the shear modulus of the foundation medium; R represents the distance from the wave source to the artificial boundary point or the characteristic size of the artificial boundary.

[0035] The equivalent normal damping coefficient of the viscoelastic artificial boundary can be represented by the following formula: where Cn represents the normal damping coefficient; βn represents the normal damping correction coefficient, whose value usually ranges from zero point five to one point zero; ρ represents the density of the foundation medium; vp represents the compression wave velocity of the foundation medium; An represents the boundary element area related to the point.

[0036] Similarly, the tangential spring stiffness coefficient and the tangential damping coefficient can also be calculated by similar formulas, where the wave velocity is replaced by the shear wave velocity. The determination of these parameters needs to consider the frequency components of ground motion, for example, for ground motion dominated by high frequency components, the boundary parameters should be adjusted accordingly to improve the absorption effect.

[0037] In the data flow direction, the boundary node information of the finite element model constructed in step S101, together with the foundation material parameters and the characteristic parameters of the ground motion, are passed as input to the artificial boundary condition calculation module. This module calculates the equivalent spring and damper parameters for each boundary node according to the above formulas. These parameters are then integrated into the global stiffness matrix and damping matrix of the finite element model to realize the effect of dynamic absorbing boundary in dynamic analysis.

[0038] In practice, attention should be paid to the location of the artificial boundary. Generally, the artificial boundary should be placed far enough from the dam structure to ensure minimal impact on the dynamic response of the internal region. For example, the boundary distance from the structure is usually not less than two to three times the height of the dam or the thickness of the bedrock. At the same time, the shape of the boundary should be as regular as possible, such as rectangular or circular, to facilitate the calculation and application of parameters.

[0039] With this dynamic artificial boundary based on wave theory, the reflection of seismic waves at the boundary of the finite element model can be significantly reduced, allowing the seismic waves propagating from the internal region to be effectively absorbed, thus more accurately simulating the influence of an infinite foundation on the dynamic response of the dam and improving the reliability of the analysis results.

[0040] S103, determine and input the time history of seismic excitation. This step is a key input for dynamic time history analysis of the dam, and its selection and application directly affect the accuracy and representativeness of the analysis results. The selection of the time history of seismic excitation should take into full consideration the seismic risk of the site, the seismic fortification standard of the dam project, and the frequency characteristics of the seismic motion.

[0041] Specifically, the determination of the time history of seismic excitation includes the following sub-steps: First sub-step, select appropriate seismic records. These records can be actual seismic waveforms observed by seismic stations or artificially synthesized seismic waveforms based on the seismic characteristics of the site. When selecting actual seismic records, the magnitude, epicentral distance, site conditions, and duration and spectral characteristics of the seismic waveforms should be considered to match the design seismic parameters of the site where the dam is located. Usually, multiple sets, such as three, five or seven sets, of seismic records are selected for analysis to cover the uncertainty of seismic motion.

[0042] Second sub-step, baseline correction and filtering of the selected seismic records. The original seismic records may contain non-seismic signals or baseline drift, which need to be corrected to eliminate these errors. Filtering is intended to remove noise outside the frequency range of interest and ensure the physical reasonableness of the seismic motion signal. For example, high-pass filtering to remove low-frequency noise and low-pass filtering to remove high-frequency noise.

[0043] Third sub-step, scale the seismic records to the target seismic intensity level. According to the requirements of the seismic design code, adjust the peak acceleration or response spectrum of the selected seismic acceleration time history to meet the design seismic parameters, for example, by multiplying the acceleration time history by a scaling factor. This scaling factor can be determined according to the peak acceleration ratio or the root mean square ratio of the response spectrum.

[0044] There are several ways to input the seismic excitation, such as base excitation method, equivalent nodal force method or free field displacement method. In the present invention, the free field displacement method is considered, which can more realistically reflect the propagation characteristics of seismic waves in an infinite domain foundation, and the free field displacement time history is applied to the artificial boundary.

[0045] The application process of free field displacement includes the following sub-steps: The first sub-step is to calculate the free field displacement time history of each node on the artificial boundary. This usually needs to be calculated in combination with the propagation direction of the seismic wave, the speed and the geometric position of the artificial boundary relative to the wave source. For plane wave or shear wave incidence, simple geometric relationships and wave functions can be used for calculation. For more complex seismic waves, special wave field analysis tools may be needed.

[0046] The second sub-step is to apply the calculated free field displacement time history as a boundary condition to the artificial boundary nodes determined in step S102. These displacement time histories serve as driving forces to make the dam, foundation and reservoir coupled system produce dynamic responses under seismic excitation.

[0047] In terms of data flow, seismic record data is obtained from a seismic database, pre-processed and scaled to generate acceleration time history data suitable for analysis. These acceleration time history data are further calculated by wave propagation theory to obtain the free field displacement time history on the artificial boundary, and are transmitted to the finite element solver as dynamic input data. The sampling frequency of the input time history should match the time step of the finite element analysis to avoid interpolation errors. Generally, the sampling frequency should not be less than one hundred hertz.

[0048] By carefully selecting and accurately applying the seismic time history excitation, the dynamic response of the dam under specific seismic action can be truly and effectively simulated, providing reliable input for subsequent damage assessment.

[0049] S104, performing dynamic time history analysis of the coupled system. This step uses the finite element model constructed in the foregoing and the applied boundary conditions and excitations to solve the dynamic response of the dam, foundation and reservoir coupled system under seismic excitation. Dynamic time history analysis involves complex numerical calculations, including the solution of nonlinear equations and time integration.

[0050] Specifically, the dynamic time history analysis includes the following sub-steps: The first sub-step is to establish the dynamic equilibrium equation of the system. For a finite element system considering nonlinearity and damping, its dynamic equilibrium equation can be expressed as: ; where M represents the mass matrix of the system; C represents the damping matrix of the system; Kt represents the tangent stiffness matrix of the system, which will dynamically change with the nonlinear behavior of the material; 、 and U represent the node acceleration, velocity, and displacement vectors, respectively; F represents the external excitation force vector, which mainly refers to the equivalent node forces caused by ground motion and artificial boundary conditions.

[0051] Second sub-step, select a suitable numerical integration method to time-integrate the dynamic equilibrium equation. Since the dam may exhibit significant nonlinear behavior under strong earthquake action, an implicit integration method with good stability and accuracy for nonlinear problems needs to be selected, such as the Newmark-Beta method or the Generalized-Alpha method. These methods achieve accurate treatment of nonlinear terms by iteratively solving within a time step.

[0052] Taking the Newmark-Beta method as an example, the basic idea is to derive the displacement and velocity at the next time step by assuming the acceleration variation within the time step. The selection of the Newmark-Beta method parameters Beta and Gamma directly affects the stability and accuracy of the algorithm. Generally, Gamma is set to zero point five and Beta is set to zero point two five, at which time the algorithm is the constant average acceleration method, with unconditional stability and second-order accuracy.

[0053] The iterative solution process of the Newmark-Beta method includes: First subdivision step, based on the displacement, velocity, and acceleration of the current time step, predict the initial values of displacement and velocity at the next time step.

[0054] Second subdivision step, calculate the tangent stiffness matrix and internal force vector at the next time step according to the predicted displacement.

[0055] Third subdivision step, solve the nonlinear equilibrium equation using the Newton-Raphson iteration method or its variants until the convergence criterion is met. The convergence criterion is usually based on the relative error of displacement, residual force, or energy. If it does not converge, update the displacement, velocity, and acceleration, and repeat the iteration until it converges.

[0056] Fourth subdivision step, once convergence is achieved, update the displacement, velocity, and acceleration of all nodes, and proceed to the calculation of the next time step.

[0057] When dealing with nonlinear problems, to accelerate convergence and handle stiffness degradation caused by structural damage, the modified Newton-Raphson method or the arc length method can be used. The time step should be small enough to capture the high-frequency components of the ground motion and the rapid nonlinear response of the material. Generally, the time step should be less than one-tenth of the minimum period of the ground motion, for example, zero point zero zero five seconds to zero point zero two seconds.

[0058] The quality matrix and damping matrix constructed in step S101, considering structural damping such as Rayleigh damping, initial stiffness matrix, and the time history of excitation forces input in step S103, together with the parameters of the Newmark- Beta method and the time step, are passed as inputs to the finite element solver. The solver outputs the dynamic response data of each time step, such as node displacement, velocity, acceleration, element stress, strain, etc., and stores them in the result file for subsequent evaluation.

[0059] During execution, an exception handling mechanism needs to be introduced. For example, when the iteration does not converge, the system should be able to automatically adjust the time step or adopt a more robust solving strategy; when material failure or element distortion occurs, abnormal information should be recorded and the calculation may be stopped or mesh redivision may be performed. Computational resource management is also an important aspect. Dynamic time history analysis of large finite element models requires a large amount of computing power and storage space, and parallel computing and high-performance computing resources should be fully utilized.

[0060] S105, evaluate the seismic response and nonlinear damage of the dam. This step is based on the dynamic time history analysis results obtained in step S104, and the performance of the dam under seismic action is comprehensively evaluated, including macroscopic response and microscopic damage state.

[0061] Specifically, the evaluation process includes the following sub-steps: The first sub-step is to extract and analyze the dynamic response parameters of the dam. These parameters include the displacement time history, velocity time history, acceleration time history of each key point of the dam, as well as the stress time history, strain time history inside the dam. By processing these time history data through peak extraction, response spectrum analysis, Fourier transform, etc., the overall and local dynamic characteristics of the dam can be obtained. For example, analyze the maximum horizontal displacement of the dam crest, the maximum stress of the dam bottom, the maximum shear stress of the gallery, etc.

[0062] The second sub-step is to evaluate the nonlinear damage state of the dam. Based on the nonlinear constitutive model introduced in step S101, such as the concrete damage plasticity model, the damage factor of the material can be directly obtained from the analysis results. The damage factor is a scalar between zero and one, zero indicating no damage and one indicating complete damage. By visualizing the spatial distribution of the damage factor, the damage area and damage degree inside the dam can be identified. For example, the damage accumulation in the vulnerable areas such as the dam heel, dam toe, gallery periphery, etc. can be identified.

[0063] The third sub-step is to compare the analysis results with the seismic design specifications and performance objectives. According to the seismic fortification level of the dam project, compare the response indicators of the dam, such as displacement, stress, damage factor, etc., to see if they meet the corresponding performance requirements, such as normal use, basically intact, and prevent collapse, etc.

[0064] In addition to the damage factor, other damage indicators can also be used to evaluate nonlinear damage. For example, strain-based damage indicators such as maximum plastic strain; energy-based damage indicators such as cumulative hysteretic energy; or stiffness degradation-based damage indicators. These indicators reflect the damage degree of the dam from different angles.

[0065] In terms of data flow, the dynamic response result file generated by S104 step contains displacement, velocity, acceleration, stress, strain and damage factor information as input. The evaluation module reads these data through the post-processing program, performs necessary calculations and visualization. The final evaluation report and graphical output will be an important basis for engineering decision-making.

[0066] In terms of exception handling, if the evaluation result shows that the dam has serious damage or exceeds the design limit, the system should issue an alarm and suggest further detailed analysis or structural reinforcement measures. The interface of the evaluation module should support integration with decision support systems or risk assessment platforms for more comprehensive engineering risk management.

[0067] In summary, the present application combines wave theory with dynamic time history method through a systematic approach to analyze the dynamic response and nonlinear damage of the dam under seismic action with high precision, providing more reliable technical support for seismic design and safety evaluation of dam engineering.

[0068] The present application also provides a dam finite element analysis system based on the dynamic time history method of wave theory to realize the steps of the above method. The system can be configured as a general or special computer system, such as a server, workstation, personal computer or cloud computing platform, and integrated with high-performance computing units and data storage devices.

[0069] The dam finite element analysis system based on the dynamic time history method of wave theory includes: A finite element model construction unit for performing S101 step to construct a finite element model of the dam, foundation and reservoir coupled system; An artificial boundary application unit for performing S102 step to apply dynamic artificial boundary conditions based on wave theory; A seismic motion input unit for performing S103 step to determine and input seismic motion time history excitation; A dynamic time history analysis unit for performing S104 step to perform dynamic time history analysis of the coupled system; A response damage evaluation unit for performing S105 step to evaluate the seismic response and nonlinear damage of the dam.

[0070] The finite element model construction unit is mainly composed of a high-performance processor cluster, a large-capacity memory module, and a high-speed storage device. Inside this unit, there is a professional finite element pre-processing software module that is responsible for processing geometric data, material property definition, mesh generation and optimization, and the setting of coupling interfaces between different media. It can receive three-dimensional geometric model data exported from a computer-aided design system and read the physical and mechanical parameters of concrete, rock-soil, and water bodies from a material database. The output of this unit is a structured finite element model data file containing node coordinates, element connection information, material properties, initial boundary conditions, and fluid-structure coupling and soil-solid coupling interface definitions. It also contains a verification submodule that automatically performs topology checks, mesh quality assessments, and material parameter consistency checks after the model is constructed, ensuring the effectiveness and integrity of the model input.

[0071] The artificial boundary application unit is tightly coupled with the finite element model construction unit and is responsible for calculating and generating the stiffness and damping matrices of the dynamic artificial boundary based on the boundary information of the finite element model generated in step S101, combined with the material parameters of the foundation and the pre-set wave theory model. This unit contains a wave theory solver module inside, which can automatically determine the equivalent spring and damping coefficients of the viscoelastic artificial boundary based on the shear modulus, Poisson's ratio, density, shear wave speed, and compression wave speed of the foundation, as well as the geometry and position of the artificial boundary. The calculated boundary parameters are integrated into the global stiffness matrix and damping matrix of the finite element model through an interface. The output of this unit is an updated finite element model input file containing detailed parameters of the dynamic artificial boundary conditions. It also has a visualization module that can display the application range and parameter distribution of the artificial boundary, facilitating user verification.

[0072] The seismic motion input unit is responsible for the acquisition, preprocessing, and application of seismic time history data. This unit contains a seismic database interface module that can connect to external seismic databases to obtain seismic records that meet design requirements. It also contains a signal processing module for baseline correction, filtering, and scaling of original seismic data to ensure the effectiveness and applicability of the input seismic motion. In addition, the unit integrates a free wave field displacement calculation module that can calculate the free wave field displacement time history of each node on the artificial boundary based on the selected seismic wave propagation theory. These displacement time history data are loaded into the finite element model as excitation through an interface with the artificial boundary application unit.

[0073] The dynamic time history analysis unit is the core computational module of the system, composed of a high-performance parallel computing cluster and an optimized finite element solver. This unit can handle large-scale nonlinear dynamic equilibrium equations and uses advanced numerical integration algorithms such as Newmark-Beta or Generalized-Alpha methods for time integration of coupled systems. It has strong nonlinear solving capabilities, capable of handling the nonlinear behavior of concrete damage plasticity models and soil elastoplasticity models through iterative algorithms, while effectively handling the dynamic response of fluid-structure coupling interfaces. The unit also integrates adaptive time step adjustment and convergence acceleration techniques to improve computational efficiency and stability. The massive dynamic response data generated during the calculation process, such as node displacement, velocity, acceleration, element stress, strain, and damage factor, are stored and transmitted in real-time to the response damage assessment unit.

[0074] The response damage assessment unit is responsible for post-processing and visualization of the dynamic time history analysis results and performance evaluation based on the dam seismic design code. This unit contains a data analysis module that can extract key response parameters such as peak displacement, peak stress, and damage factor distribution from the result files output by the dynamic time history analysis unit. At the same time, it also integrates a visualization module that can display the deformation mode, stress distribution, and damage area of the dam in three-dimensional graphics, thereby intuitively presenting the damage condition of the dam under seismic action. The unit also has a report generation module that can automatically generate detailed evaluation reports based on pre-set evaluation standards and performance targets, including statistical analysis of various indicators, specification comparison, and damage area identification. If the evaluation results exceed the design requirements, the system will automatically issue an alarm.

[0075] The system proposed in this invention realizes the finite element analysis of dams based on the dynamic time history method of wave theory through the cooperative work of the above-mentioned units, and can provide accurate and reliable technical support for the seismic design and safety evaluation of dam projects.

Claims

1. A method for finite element analysis of a dam based on a dynamic time history method of wave theory, characterized by, The method comprises the following steps: S1, establishing a refined finite element model of a dam-foundation-reservoir coupling system, the model comprising dam body units, foundation medium units and reservoir fluid units, and setting a nonlinear constitutive model for the dam body units and the foundation medium units; S2, generating a wave theory artificial boundary condition acting on the external boundary of the foundation medium units, the wave theory artificial boundary condition being capable of absorbing incident waves and scattered waves, thereby avoiding boundary reflection; S3, applying seismic motion input on the refined finite element model, the seismic motion input being free field displacement time history or stress time history considering spatial correlation; S4, solving the dynamic response of the coupling system under the seismic motion by using a nonlinear dynamics solver in combination with a time domain integral method, the solving process considering iterative updating of the nonlinear constitutive model; and performing seismic response analysis and damage assessment of the dam based on the dynamic response results obtained by the solving, the analysis and assessment comprising judging macro damage areas according to a preset damage criterion, and quantifying the cumulative damage degree of the dam body by using an energy dissipation-based damage index or a cumulative plastic strain damage index.

2. The dam finite element analysis method based on the wave motion theory-based dynamic time history method according to claim 1, characterized in that: The establishment of the refined finite element model of the dam-foundation-reservoir coupling system comprises: discretizing the dam body into solid units, the material constitutive model of the solid units being a concrete damage plasticity model; discretizing the foundation medium into solid units, the material constitutive model of the solid units being a Mohr-Coulomb elastoplasticity model or a modified Cambridge model; and discretizing the reservoir fluid into acoustic units, and realizing the coupling effect between the dam body and the reservoir fluid by setting fluid-structure coupling surface units.

3. The dam finite element analysis method based on the wave motion theory-based dynamic time history method according to claim 1, characterized in that: The generation of the wave theory artificial boundary condition comprises: setting a layer of perfect matched layer along the external boundary of the foundation medium units, the perfect matched layer making waves attenuate in the perfect matched layer by introducing a frequency-dependent attenuation function, thereby simulating the non-reflecting effect of an infinite medium; or setting a refined viscoelastic artificial boundary along the external boundary of the foundation medium units, the refined viscoelastic artificial boundary applying additional damping and stiffness related to free field response and considering medium wave impedance.

4. The dam finite element analysis method based on the wave motion theory-based dynamic time history method according to claim 1, characterized by: The application of seismic motion input on the refined finite element model comprises: obtaining seismic site effect analysis results; based on the site effect analysis results, applying spatially correlated free field displacement time history or stress time history at the connection between the foundation medium units and the wave theory artificial boundary condition by using a multi-point input method, the free field displacement time history or stress time history reflecting the traveling wave effect and incident angle of seismic waves by considering the propagation time difference and phase difference of seismic waves at different foundation points.

5. The dam finite element analysis method based on the wave motion theory-based dynamic time history method according to claim 1, characterized by, The solving process comprises: establishing dynamic equilibrium equations of the coupled system; solving the dynamic equilibrium equations by using Newton-Raphson iteration method or arc length method to iteratively correct stiffness matrix and force vector until convergence; and performing time step integration by using Newmark-beta method or HHT-alpha method, wherein the time step is less than one tenth of the minimum period vibration time step of the coupled system.

6. The dam finite element analysis method based on the wave motion theory-based dynamic time history method according to claim 1, characterized by, The damping matrix of the dynamic equilibrium equations established by the solving process adopts Rayleigh damping model, and the damping coefficients α and β are determined by the main mode frequency and damping ratio of the dam structure.

7. The dam finite element analysis method based on the wave motion theory-based dynamic time history method according to claim 1, characterized by, The analysis and evaluation comprises extracting absolute displacement, relative displacement, velocity, acceleration, stress component and principal stress time history of key parts of the dam; The analysis and evaluation comprises judging the macro damage area and damage initiation time based on maximum principal tensile stress criterion, maximum shear stress criterion or maximum strain criterion; and quantifying the cumulative damage degree of the dam body by using damage index based on energy dissipation or cumulative plastic strain damage index.

8. A dam finite element analysis system based on a dynamic time history method of wave theory, characterized by, The method comprises: a model establishing module configured to establish a refined finite element model of a dam-foundation-reservoir coupled system, the model comprising dam body elements, foundation medium elements and reservoir fluid elements, and the dam body elements and the foundation medium elements being provided with a nonlinear constitutive model; an artificial boundary condition generating module configured to generate a wave theory artificial boundary condition acting on the external boundary of the foundation medium elements, the wave theory artificial boundary condition being capable of absorbing incident waves and scattered waves and avoiding boundary reflection; a seismic motion input applying module configured to apply a free field displacement time history or stress time history seismic motion input considering spatial correlation on the refined finite element model; a dynamic response solving module configured to solve the dynamic response of the coupled system under the action of the seismic motion by using a nonlinear dynamics solver and a time domain integration method, the solving process taking into account iterative updating of the nonlinear constitutive model; and a damage evaluation module configured to perform seismic response analysis and damage evaluation of the dam based on the dynamic response results obtained by the solving, the analysis and evaluation comprising judging a macro damage area according to a preset damage criterion and quantifying the cumulative damage degree of the dam body.

9. The system of claim 8, wherein, The model establishing module is specifically configured to: discretize the dam body into solid elements, the material constitutive model of the solid elements adopting a concrete damage plasticity model; discretize the foundation medium into solid elements, the material constitutive model of the solid elements adopting a Mohr-Coulomb elastoplasticity model or a modified Cambridge model; and discretize the reservoir fluid into acoustic elements, and realize coupling between the dam body and the reservoir fluid by setting fluid-structure coupling surface elements.

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