A method, system, device and medium for analyzing the seismic response of a gravity dam

Abstract

The present invention provides a method, system, device and medium for analyzing the seismic response of a gravity dam, belonging to the technical field of seismic response analysis. The method includes the following steps: setting the solid artificial boundary and the fluid artificial boundary of the foundation reservoir water of the gravity dam, and constructing a finite element model of the foundation reservoir water of the gravity dam; constructing an artificial boundary substructure model through the solid artificial boundary nodes, the fluid artificial boundary nodes, and the nodes adjacent to both; applying the displacement time history of the free wave field of the reservoir water-foundation to all the fluid artificial boundary nodes and the solid artificial boundary nodes on the upstream side of the artificial boundary substructure model, applying the displacement time history of the free wave field of the solid foundation to all the solid artificial boundary nodes on the downstream side of the artificial boundary substructure model, and performing dynamic analysis on the artificial boundary substructure model to obtain the equivalent input seismic load; inputting the equivalent input seismic load into the finite element model of the foundation reservoir water of the gravity dam to perform seismic response analysis. The present invention is more accurate in analyzing the seismic dynamic response of the gravity dam.

Description

Technical Field

[0001] The present invention belongs to the technical field of seismic response analysis, and particularly relates to a method, system, device and medium for analyzing the seismic response of a gravity dam. Background Art

[0002] In the southwestern region of China, there is abundant water energy resources, and many large dams are located here. However, the seismic intensity is high and the frequency is strong in the southwestern region, and strong earthquakes are likely to induce damage and failure of the dams. The seismic safety of the dams in the southwestern region faces severe challenges. For the seismic response problems of such open systems, the earthquake source is usually treated as an external source. A finite near-field calculation domain is intercepted, and artificial boundary conditions are set at the truncated boundary. However, introducing closed artificial boundary conditions brings a new problem: how to input the ground motion in the near-field model without affecting the absorption of scattered waves by the artificial boundary, that is, the problem of seismic wave input. Effective ground motion input is a key link to ensure the numerical simulation accuracy of the external source wave problem.

[0003] Due to the rapid development of urban underground space construction in recent decades, researchers have conducted a large number of studies on the seismic wave input method in the soil-structure interaction problem and achieved relatively rich results. Joyner and Chen completed the input of ground motion in the one-dimensional soil layer model by applying a viscous boundary at the truncated boundary of the one-dimensional model and deriving the equivalent load applicable to the artificial boundary. Clough transformed the free-field motion into an equivalent load using the foundation stiffness and applied it to the soil-structure interaction system. Wolf proposed the free-field boundary method, which realizes the seismic wave input of the soil-structure interaction system by establishing a free-field model to calculate the free-field motion and setting an absorbing boundary to absorb scattered waves. The above seismic wave input methods mainly focus on the case of vertical incidence of seismic waves. When the earthquake source is close to the engineering site, the seismic waves usually propagate obliquely upward at a certain angle. For the near-field model, the oblique incidence problem of seismic waves will cause the ground motion to change non-uniformly, which has a significant impact on the seismic response of the engineering site and the structure. The currently commonly used input methods are the wave method for ground motion input proposed by Liu Jingbo and the domain reduction method proposed by Bielak. The wave method transforms the input ground motion into an equivalent nodal load on the viscoelastic artificial boundary and combines it with the one-dimensional time-domain algorithm for free-field analysis of layered media, which can effectively solve the problem of seismic wave input in the soil-structure interaction system under oblique incidence at any angle. The domain reduction method proposes that the external excitation can be transformed into an equivalent force applied inside the model and an absorbing boundary is applied at the artificial truncated boundary, so as to realize the input method considering the earthquake source and the propagation path effect of seismic waves. In addition, based on the theory of the wave method, researchers have proposed more convenient seismic wave input methods such as the artificial boundary substructure method and the internal substructure method.

[0004] Different from the traditional soil-structure interaction system, for the hydraulic structure engineering site represented by the gravity dam-foundation-reservoir water system, due to the compressibility of water, seismic waves can propagate in the reservoir water. Due to the wave velocity difference between fluid and solid media, after the wave propagates through the solid medium and enters the fluid medium, it will propagate back and forth in the fluid medium, and complex transmission and reflection will occur at the fluid-solid coupling interface. Therefore, the seismic response analysis of the gravity dam-foundation-reservoir water system needs to consider the input problems of seismic waves in both fluid and solid media at the same time. At the same time, due to the different water levels upstream and downstream of the dam, the movement laws of the free wave fields on the upstream and downstream sides are different, and the seismic motion input is more complex.

[0005] However, for the seismic motion input of such sites at present, the fluid is usually equivalent to the additional mass moving with the solid or the hydrodynamic pressure applied to the structure. When performing seismic motion input, it is assumed that the water body is incompressible, the influence of the water body on the free field model analysis is ignored, and the reservoir water-foundation-dam interaction system is simplified to a soil-structure interaction system for seismic motion input research, resulting in a low numerical simulation accuracy of the seismic motion input, thus posing a severe challenge to the seismic safety of the dam. Summary of the Invention

[0006] In order to overcome the deficiencies of the above-mentioned existing technologies, the present invention provides a method for analyzing the seismic response of a gravity dam, including the following steps:

[0007] Set the solid artificial boundary and fluid artificial boundary of the gravity dam foundation reservoir water, and construct a finite element model of the gravity dam foundation reservoir water;

[0008] Remove the internal elements of the finite element model of the gravity dam foundation reservoir water, and construct an artificial boundary substructure model through the solid artificial boundary nodes, fluid artificial boundary nodes, and the nodes adjacent to the solid artificial boundary nodes and fluid artificial boundary nodes of the finite element model of the gravity dam foundation reservoir water;

[0009] Obtain the displacement time history of the reservoir water-foundation free wave field and the displacement time history of the solid foundation free wave field. Taking the compressional wave P-wave as the vertically incident wave and the upstream dam surface as the axis, apply the displacement time history of the reservoir water-foundation free wave field to all the fluid artificial boundary nodes and solid artificial boundary nodes on the upstream side of the artificial boundary substructure model, apply the displacement time history of the solid foundation free wave field to all the solid artificial boundary nodes on the downstream side of the artificial boundary substructure model, and perform dynamic analysis on the artificial boundary substructure model to obtain the equivalent input seismic load;

[0010] Take the equivalent input seismic load as the seismic wave vertically input into the finite element model of the gravity dam foundation reservoir water, perform dynamic analysis on all the artificial boundary nodes of the artificial boundary substructure model to obtain the extreme values of the displacement and stress of the gravity dam, and perform seismic response analysis of the gravity dam according to the extreme values of the displacement and stress of the gravity dam.

[0011] Preferably, the process for obtaining the displacement time history of the reservoir water-foundation free wave field includes the following steps:

[0012] Assume that the reservoir water medium is inviscid and compressible, and the foundation is linearly elastic, and determine the wave equations of the reservoir water medium and the foundation medium;

[0013] Determine the response characteristics of the reservoir water-foundation site under seismic waves through the wave equations, and the propagation characteristics of seismic waves in the reservoir water medium and the foundation medium. According to the medium wave theory, establish a free wave field;

[0014] Assume that the P wave is vertically incident on the reservoir water-foundation site. According to the medium wave theory, the total displacement in the solid domain is caused by the incident P wave and the reflected P wave, and the total displacement in the fluid domain is caused by the transmitted P wave and the reflected P wave at the free liquid surface. Through the seismic wave superposition principle, superimpose the total displacement in the solid domain and the total displacement in the fluid domain to obtain the displacement time history of the free wave field at any position and at any time under seismic action in the reservoir water-foundation site;

[0015] Establish the boundary conditions for the motion of the free wave field. The motion of the free wave field in the reservoir water-foundation site under seismic action satisfies the boundary conditions of stress continuity and displacement continuity. The specific boundary conditions are as follows: at the reservoir water-foundation coupling surface, the normal displacement and normal stress of the solid medium and the liquid medium are balanced, and there is no shear stress in the liquid, and the shear stress is 0. At the free liquid surface, the pressure of the liquid is 0;

[0016] According to the boundary conditions, establish the potential function amplitude relationship between each wave system, and perform Fourier transform on the displacement time history of the free wave field to obtain the frequency domain solution of the reservoir water-foundation free wave field;

[0017] Perform inverse Fourier transform on the frequency domain solution of the reservoir water-foundation free wave field to obtain the displacement-time transformation law at any position in the reservoir water-foundation site under seismic action, that is, the displacement time history of the reservoir water-foundation free wave field.

[0018] Preferably, the process for obtaining the displacement time history of the solid foundation free wave field is specifically as follows: According to the one-dimensional wave law, the total displacement of the downstream foundation site is the superposition of the incident P wave and the reflected P wave. For any position y in the foundation site, the time required for the incident P wave to reach point y is The time required for the reflected P wave to reach point y is The displacement of point y at time t is:

[0019]

[0020] where u sr is the displacement generated by the incident P wave in the solid medium, u sf is the displacement generated by the reflected P wave in the solid medium, h is the height of the foundation site, c p$v$ is the propagation wave velocity of seismic waves in the foundation, and $u_0(t)$ is the seismic wave of the input site.

[0021] Preferably, the fluid artificial boundary condition is specifically adding a damper and a mass unit at the fluid boundary nodes.

[0022] Preferably, the solid artificial boundary condition is adding a parallel spring and a damper at the solid boundary.

[0023] The present invention also provides a gravity dam seismic response analysis system, including:

[0024] A model construction module, configured to set the solid artificial boundary and the fluid artificial boundary of the gravity dam foundation reservoir water, and construct a finite element model of the gravity dam foundation reservoir water;

[0025] A substructure model construction module, configured to remove the internal elements of the finite element model of the gravity dam foundation reservoir water, and construct an artificial boundary substructure model through the solid artificial boundary nodes, the fluid artificial boundary nodes, and the nodes adjacent to the solid artificial boundary nodes and the fluid artificial boundary nodes of the finite element model of the gravity dam foundation reservoir water;

[0026] An equivalent input seismic load acquisition module, configured to acquire the time history of the displacement of the free wave field of the reservoir water - foundation and the time history of the displacement of the free wave field of the solid foundation. Taking the compressional wave P wave as the vertically incident wave, with the upstream dam surface as the axis, applying the time history of the displacement of the free wave field of the reservoir water - foundation to all the fluid artificial boundary nodes and the solid artificial boundary nodes on the upstream side of the artificial boundary substructure model, applying the time history of the displacement of the free wave field of the solid foundation to all the solid artificial boundary nodes on the downstream side of the artificial boundary substructure model, and performing dynamic analysis on the artificial boundary substructure model to obtain the equivalent input seismic load;

[0027] A seismic response analysis module, configured to take the equivalent input seismic load as the seismic wave vertically input into the finite element model of the gravity dam foundation reservoir water, perform dynamic analysis on all the artificial boundary nodes of the artificial boundary substructure model to obtain the extreme values of the displacement and stress of the gravity dam, and perform seismic response analysis of the gravity dam according to the extreme values of the displacement and stress of the gravity dam.

[0028] The present invention also provides a computer device, including a memory and a processor; the memory stores a computer program, and the processor is configured to run the computer program in the memory to execute the gravity dam seismic response analysis method.

[0029] The present invention also provides a computer - readable storage medium, the computer - readable storage medium stores a computer program, and the computer program is suitable for being loaded by a processor to execute the gravity dam seismic response analysis method.

[0030] The method, system, device and medium for analyzing the seismic response of a gravity dam provided by the present invention have the following beneficial effects:

[0031] When constructing the finite element model of the gravity dam foundation and reservoir water, the present invention introduces a fluid artificial boundary and proposes an artificial sub-boundary structure model; when inputting ground motion, considering the influence of the compressibility of the reservoir water on the ground motion input, the motion law of the free wave field of the reservoir water-foundation is deduced, and based on the artificial boundary sub-structure model, the time history of the displacement of the free wave field of the reservoir water-foundation is applied to all the fluid artificial boundary nodes and solid artificial boundary nodes on the upstream side of the artificial boundary sub-structure model, and the time history of the displacement of the free wave field of the solid foundation is applied to all the solid artificial boundary nodes on the downstream side of the artificial boundary sub-structure model, thereby improving the method for inputting ground motion of the traditional free field ground motion. This process can apply the time history of the free wave field displacement corresponding to the spatial position of the node to each node of the artificial boundary sub-structure model, and its simulation of the ground motion input for irregular sites is more accurate; by performing dynamic analysis on the artificial boundary sub-structure model, the equivalent input seismic load can be obtained. This method for inputting ground motion can effectively simulate the input of the complex wave field of the dam under the vertical incidence of P waves; by taking the equivalent input seismic load as the seismic wave and vertically inputting it into the finite element model of the gravity dam foundation and reservoir water, and analyzing the seismic response of the gravity dam, this method is more accurate for analyzing the seismic dynamic response of the gravity dam and has guiding significance for the seismic safety measures of the dam. Description of the Drawings

[0032] In order to more clearly illustrate the embodiments of the present invention and its design, the drawings required for this embodiment will be briefly introduced below. The drawings in the following description are only partial embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0033] Figure 1 It is the flowchart of the method for analyzing the seismic response of the gravity dam according to the embodiment of the present invention;

[0034] Figure 2 It is the model of the gravity dam foundation and reservoir water;

[0035] Figure 3 It is the schematic diagram of the combin40 element;

[0036] Figure 4 It is based on the artificial boundary sub-structure model, where Figure 4 (a) of Figure 4 and (b) of are the models before and after removing the internal elements of the finite element model of the gravity dam foundation and reservoir water respectively;

[0037] Figure 5 It is the schematic diagram of the reservoir water-foundation half-space, where Figure 5(a) is the free field of the upper overlying reservoir water layer and the half space, Figure 5 (b) is the free field of the downstream foundation and the half space;

[0038] Figure 6 is a schematic diagram of the free field wave system at any point on the downstream side;

[0039] Figure 7 is the foundation-reservoir free field model;

[0040] Figure 8 is the time history of the incident wave displacement;

[0041] Figure 9 is the displacement diagram of the observation point. Among them, Figure 9 (a), Figure 9 (b), and Figure 9 (c) are the time histories of the displacements at points A, B, and C respectively;

[0042] Figure 10 is the finite element model considering the input of reservoir water fluctuations;

[0043] Figure 11 is the incident seismic wave. Among them, Figure 11 (a) and Figure 11 (b) are the time history curve of the seismic wave acceleration and the time history curve of the seismic wave displacement respectively;

[0044] Figure 12 is the finite element model of the non-overflow dam section of Xiangjiaba;

[0045] Figure 13 is the result analysis diagram at the dam heel. Among them, Figure 13 (a), Figure 13 (b), Figure 13 (c), and Figure 13 (d) are the time history diagram of the vertical displacement, the time history diagram of the horizontal displacement, the horizontal stress diagram at the dam heel, and the vertical stress diagram at the dam heel respectively;

[0046] Figure 14 is the result analysis diagram at the dam crest. Among them, Figure 14 (a), Figure 14 (b), Figure 14 (c), and Figure 14 (d) are the time history diagram of the vertical displacement at the dam crest, the time history diagram of the horizontal displacement at the dam crest, the time history diagram of the horizontal stress at the dam crest, and the time history diagram of the vertical stress at the dam crest respectively. Specific implementation manner

[0047] To enable those skilled in the art to better understand the technical solution of the present invention and be able to implement it, the present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0048] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "axial", "radial", "circumferential", etc. indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the technical solution of the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation to the present invention.

[0049] In addition, the terms "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance. In the description of the present invention, it should be noted that unless otherwise clearly specified or limited, the terms "connected" and "connected" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances. In the description of the present invention, unless otherwise stated, the meaning of "plurality" is two or more, which will not be elaborated here.

[0050] Embodiment

[0051] The present invention provides a method for analyzing the seismic response of a gravity dam, specifically as Figure 1 shown, including the following steps:

[0052] Step 1: Set the solid artificial boundary and fluid artificial boundary of the foundation reservoir water of the gravity dam, and construct a finite element model of the foundation reservoir water of the gravity dam.

[0053] Different from the traditional soil-structure interaction system, the engineering site of hydraulic structures such as dams is a complex semi-infinite open system composed of bedrock-reservoir water with an overlying fluid medium on the upstream water-retaining side and bedrock on the downstream side. When intercepting a finite near-field calculation domain, in addition to setting solid artificial boundary conditions at the truncated boundary, it is also necessary to consider setting artificial boundary conditions for the fluid medium, specifically as Figure 2 shown.

[0054] For the artificial boundary conditions of fluid media, some researchers have derived stress-type displacement format fluid artificial boundaries applicable to different dimensions and given the implementation methods in finite element software. This boundary condition is realized by adding dampers and mass elements at the corresponding boundary nodes. The physical parameters of the damping-mass system under different dimensions are shown in Table 1. In ANSYS, the combin40 element can be used for simulation, and the schematic diagram of this element is as shown in Figure 3 shown, where I and J are two nodes; K1 and K2 are the stiffness coefficients of two parallel springs; GAP is the gap width; F SLIDE is the ultimate anti-sliding force; C is the damping coefficient of the damper; M is the lumped mass. When conducting numerical simulation, node I is set as the artificial boundary node, a lumped mass is added at node J, and K1, K2, F SLIDE and GAP are set to zero, and the parameters shown in Table 1 are added to the lumped mass and the damper respectively.

[0055] Table 1 Physical parameters of the damping-mass system

[0056]

[0057] In Table 1: ρ0 is the density of the fluid medium, r b is the distance from the wave source to the boundary node, is the effective influence area of the boundary node.

[0058] The solid artificial boundary condition adopts the viscoelastic artificial boundary condition, and this element consists of a parallel spring and damper. The damper is used to absorb the scattered waves of the shape, and the spring is used to simulate the recovery performance of the far-field foundation. It can be simulated by the combin14 spring element provided by ANSYS. One end is at the solid artificial boundary node, and the other end is fixed, and the corresponding material parameters are added to the spring and the damper.

[0059] Since the fluid boundary condition and the ground motion input method adopted in the present invention are derived and established with displacement, velocity, and acceleration as the basic variables, the solid and fluid media are respectively simulated by the Solid45 element and the Fluid80 element provided by the general finite element software ANSYS. The Fluid80 displacement-type acoustic fluid element can effectively simulate problems such as large sloshing of liquids. The dynamic interaction between the fluid-solid media can be realized by coupling the normal degrees of freedom of the solid and liquid nodes at the interface. When establishing the reservoir water-foundation-dam body system model, the solid medium and the fluid medium should be modeled separately, and the corresponding artificial boundary conditions should be added at the boundary nodes. Since both Fluid80 and Solid45 are three-dimensional solid elements, when establishing a two-dimensional model, a layer of elements can be established in the plane, and the out-of-plane degrees of freedom of all nodes should be constrained. At the same time, the size of the discretized grid should satisfy the formula:

[0060] Δx = αλ min , In the formula: λ min is the shortest wavelength of wave propagation in the discrete grid model, c min is the minimum wave speed in the medium, f max is the cut-off frequency of the numerical simulation of the wave problem.

[0061] Step 2: Remove the internal elements of the finite element model of the reservoir water in the gravity dam foundation, and construct an artificial boundary substructure model through the solid artificial boundary nodes, fluid artificial boundary nodes, and the nodes adjacent to the solid artificial boundary nodes and fluid artificial boundary nodes of the finite element model of the reservoir water in the gravity dam foundation.

[0062] Establish a finite element model of the reservoir water-foundation-dam body system, specifically as Figure 4 shown, Figure 4 in (a) and Figure 4 in (b) are the models before and after removing the internal elements of the finite element model of the reservoir water in the gravity dam foundation respectively, Figure 4 and (b) is the artificial boundary substructure model constructed by the solid artificial boundary nodes, fluid artificial boundary nodes, and the nodes adjacent to the solid artificial boundary nodes and fluid artificial boundary nodes of the finite element model of the reservoir water in the gravity dam foundation.

[0063] Step 3: Obtain the time history of the displacement of the free wave field of the reservoir water-foundation and the time history of the displacement of the free wave field of the solid foundation. Taking the compressional wave P-wave as the vertically incident wave and the upstream dam surface as the axis, apply the time history of the displacement of the free wave field of the reservoir water-foundation to all the fluid artificial boundary nodes and solid artificial boundary nodes on the upstream side of the artificial boundary substructure model, apply the time history of the displacement of the free wave field of the solid foundation to all the solid artificial boundary nodes on the downstream side of the artificial boundary substructure model, and conduct a dynamic analysis on the artificial boundary substructure model to obtain the equivalent input seismic load.

[0064] The composition of seismic waves is very complex, mainly divided into body waves and surface waves. Body waves include shear waves (S-waves) and compressional waves (P-waves), and surface waves include Rayleigh waves and Love waves. For seismic response analysis, the seismic source can be approximately regarded as a point source, so the elastic waves in the rock can be regarded as plane waves. Compared with plane SH waves, the propagation characteristics of plane SV waves and plane P waves are more complex, and SV waves are shear waves and do not propagate in liquid media. Therefore, in this invention, taking plane P waves as an example, the construction theory of the free field of the reservoir water-foundation under the vertical incidence of P waves is deduced, and this method can also be applied to other types of seismic waves.

[0065] The wave input method of the artificial boundary substructure model is one of the commonly used ground motion input methods proposed based on the wave method theory. This method directly obtains the equivalent input load of ground motion through dynamic analysis by establishing an artificial boundary substructure model, and has the advantages of high simulation accuracy, high operation efficiency, and convenient calculation. Currently, this method is mainly applied to the ground motion input of regular site forms that are horizontally uniform and vertically layered.

[0066] For the ground motion input of the irregular site composed of the upstream site with reservoir water and the downstream solid foundation site of hydraulic structures such as gravity dams, therefore, the present invention has made improvements, specifically: applying the free wave field displacement time history u f (y, t), u s (y, t) corresponding to the node spatial position to all nodes of the artificial boundary substructure model. Taking the upstream dam surface as the axis, applying the reservoir water-foundation free wave field displacement time history to the upstream side nodes and the solid foundation free wave field displacement time history to the downstream side nodes. As shown in Figure 4 (b), performing dynamic analysis on this substructure model to obtain the reaction force of the artificial boundary nodes, which is the equivalent input seismic load for realizing seismic wave input.

[0067] Applying the equivalent input seismic load to all artificial boundary nodes of the finite element model shown in Figure 4 (a) and performing dynamic time history calculation, thus completing the seismic wave input of the gravity dam site.

[0068] The process of obtaining the reservoir water-foundation free wave field displacement time history includes the following steps:

[0069] Assuming that the reservoir water medium is inviscid and compressible and the foundation is linearly elastic, determining the wave equations of the reservoir water medium and the foundation medium. Assuming that the foundation is linearly elastic and its stress-strain relationship satisfies the generalized Hooke's law; the reservoir water medium is inviscid and compressible, and the hydrodynamic pressure p fIt is linearly related to the spatial divergence of the displacement vector; the response characteristics of the reservoir water-foundation site under seismic waves are determined through the wave equation, and the propagation characteristics of seismic waves in the reservoir water medium and the foundation medium. (2) According to the medium wave theory, a free wave field is established. Assuming that the P-wave is vertically incident on the site, according to the medium wave theory, the total displacement in the solid domain is caused by the incident P-wave and the reflected P-wave, and the total displacement in the fluid domain is caused by the transmitted P-wave and the reflected P-wave at the free liquid surface. Through the superposition principle of seismic waves, the free field motion at any position and at any time under seismic action of the reservoir water-foundation site can be obtained, that is, the displacement time history of the free field. (3) The displacement potential function is introduced to represent the displacement time history of the free field. Since the P-wave propagates back and forth in the reservoir water layer and the law is complex, it is difficult to directly establish the free field motion equation. Therefore, a scalar potential function is introduced to represent the seismic wave to establish the free field motion equation, and the motion equation can be solved by solving the amplitude of the potential function. The scalar potential function has no curl and generates a compression wave, that is, the P-wave. The amplitude of the potential function is the amplitude of the seismic wave, is the time required for the seismic wave to propagate to the free field position y. (4) The boundary conditions of the free field motion of the site are established. The free field motion of the reservoir water-foundation site under seismic action should satisfy the boundary conditions of stress continuity and displacement continuity. At the fluid-structure coupling surface, due to the fluid-structure coupling effect, the normal displacement and normal stress of the solid medium and the liquid medium at the fluid-structure coupling surface should satisfy the equilibrium; there is no shear stress in the liquid, and the shear stress is 0; at the free liquid surface, the pressure of the liquid is 0. (5) According to the boundary conditions, the amplitude relationship of the potential function between each wave system is established. According to the stress-strain relationship of the solid medium and the relationship between the hydrodynamic pressure and displacement of the fluid medium, the relationship between the stress and pressure and displacement of the free field can be established. Therefore, substituting the displacement potential function into the boundary conditions can obtain the relationship between the amplitudes of the potential functions of each seismic wave. (6) The obtained displacement wave field is Fourier-transformed into the frequency domain to solve the amplitude of the incident P-wave potential function. The motion equation obtained in (3) is Fourier-transformed to obtain the frequency domain solution of the free wave field. The motion of the free field in the frequency domain is independent of time and only related to the amplitude and phase of the seismic wave. The amplitude of the potential function of the incident P-wave is the same as the input seismic wave u0(t) of the site, and the phase is related to y. When y is 0, the incident P-wave is the input ground motion u0(t). Let y of the incident P-wave be 0, and substituting u0(t) into the relationship of the frequency domain solution of the incident P-wave can obtain the amplitude of the incident P-wave potential function. (7) Substitute the amplitude of the incident P-wave potential function into the amplitude relationship of each wave system established in (5) to solve the amplitudes of each wave system, and obtain the frequency domain solution of the reservoir water-foundation free wave field. (8) The frequency domain solution of the reservoir water-foundation free wave field is Fourier inverse-transformed to obtain the law of displacement change with time at any position of the reservoir water-foundation site under seismic action, that is, the displacement time history of the reservoir water-foundation free wave field.

[0070] The free field of the gravity dam site can be decomposed into the free field of the reservoir water - foundation on the upstream side and the free field of the foundation on the downstream side. The free field of the half - space overlying the reservoir water layer is as shown in Figure 5 (a) of. Let the height of the reservoir water be H and the height of the foundation be h. When the height of the reservoir water H = 0, it is the free field of the foundation half - space on the downstream side, as shown in Figure 5 (b) of. When solving the free field, the free fields on both the upstream and downstream sides can be solved separately, and then the results can be superimposed to obtain the complete theoretical solution of the free field. The wave equations of the solid and fluid media are shown in Eqs. (1) and (2), where the fluid medium adopts the assumption of inviscid and compressible, and analyze the free field model as shown in Figure 5 to solve the time - domain solution of the free wave field of ground motion.

[0071]

[0072] In the formula: is the gradient operator; u is the displacement vector of the fluid particle, and the superscript “.” represents a first - order differentiation of the displacement vector u; ρ s , ρ f are the densities of the solid and fluid media respectively; λ and G are the Lame constant and shear elastic modulus of the solid medium respectively; K bulk is the bulk modulus of the fluid medium. The stress - strain relationship in the solid medium satisfies Hooke's law:

[0073]

[0074] In the formula: σ and τ are the normal stress and shear stress respectively, u represents the displacement, the subscript s represents the solid medium, and the subscripts x and y represent the x and y directions respectively.

[0075] The hydrodynamic pressure p f is linearly related to the spatial divergence of the displacement vector, that is:

[0076]

[0077] The P - wave is a compression wave. According to the wave theory of the medium, when the incident P - wave vertically enters the free field of the upstream with the overlying water layer, the incident P - wave generates a reflected P - wave and a transmitted P - wave at the fluid - solid coupling surface. The reflected P - wave is absorbed by the far - field foundation, and the transmitted P - wave generates a reflected P - wave at the free liquid surface, and so on, and the propagation law is complex. The free wave field is decomposed into the wave field of the solid domain and the wave field of the fluid domain. The free wave field of the solid domain is composed of the incident wave u sr (y, t) traveling upward and the reflected wave u sf (y, t) traveling downward; the free wave field of the fluid domain is composed of the transmitted wave u ft (y, t) traveling upward and the reflected wave u ff (y, t) traveling downward reflected by the free liquid surface.

[0078] Let the vertical incident wave be u0(t), and let the vertical displacement of the free field of the foundation be u s , and the vertical displacement of the free field of the reservoir water be u f . Then, according to the wave superposition theory, the displacement of the free field can be expressed as:

[0079] Vertical displacement of bedrock:

[0080] u s = u sr + u sf (5);

[0081] Vertical displacement of reservoir water:

[0082] u f = u ft + u ff (6);

[0083] When the incident wave is a simple harmonic wave with frequency ω, the displacement potential function can be introduced, and the above formula can be expressed as:

[0084]

[0085] In the formula, u sr is the displacement generated by the incident P-wave in the solid medium, u sf is the displacement generated by the reflected P-wave in the solid medium; u ft is the displacement generated by the transmitted P-wave in the liquid medium, u ff is the displacement generated by the reflected P-wave in the liquid medium. A sr , A sf are the amplitudes of the incident P-wave and the reflected P-wave in the solid medium respectively, A ft , A ff are the amplitudes of the transmitted P-wave and the reflected P-wave in the liquid medium, is the propagation speed of the P-wave in the solid medium, is the propagation speed of the P-wave in the liquid medium, is the unit imaginary number, t is time, and y is the vertical coordinate of the field geological point.

[0086] At the fluid-structure interface (y = 0), the boundary conditions of continuous normal displacement and balanced normal stress should be satisfied for the motion of the free wave field:

[0087]

[0088] In the formula: u represents displacement, σ represents stress, P represents pressure, the subscript s represents the solid medium, the subscript f represents the fluid medium, and the subscript y represents the y direction.

[0089] Since there is no shear stress in the liquid, there is:

[0090] τ sxy(y,t)| y＝0 = 0 (10);

[0091] In addition, at the free surface (y = H), the pressure is zero:

[0092] P f (y,t)| y＝H = 0 (11);

[0093] Taking the partial derivative of the potential function and substituting it into Eqs. (5) and (6), we get:

[0094]

[0095] For u s , u f Taking the partial derivative and substituting the boundary conditions (9) - (11) respectively, we can obtain the relationship of the amplitude:

[0096]

[0097] Where:

[0098]

[0099] Performing the Fourier transform on Eq. (12), we obtain the frequency-domain solution of the free wave field:

[0100]

[0101] Where the frequency-domain solution of the incident wave is:

[0102]

[0103] For any given input ground motion u0(t), performing the Fourier transform on it to obtain U0(ω), then we have:

[0104] U sr (y,ω)| y＝0 = U0(ω) (17);

[0105] In the formula: U sr (y,ω) is the frequency-domain solution of the incident wave, and U0(ω) is the frequency-domain solution of the input seismic wave.

[0106] From this, we can obtain:

[0107] A sr = -c p U0(ω) / (iω) (18);

[0108] Substituting (18) and (13) into Eq. (15) and then performing the inverse Fourier transform, we can obtain the time-domain solutions u s (y,t), u f(y, t), which is the time history of the displacement of the free wave field of the reservoir water - foundation

[0109]

[0110] For the free field of the downstream foundation, compared with the upstream water level, the downstream water level of the gravity dam is generally lower, and the propagation time of seismic waves in the downstream reservoir water is shorter (the wave velocity of seismic waves in the reservoir water is 1435 m / s). The downstream reservoir water has less influence on the seismic motion input. Therefore, when performing the seismic motion input on the downstream side, the site can be simplified to be treated as a solid foundation site only. Since the free liquid surface height H = 0, the model is only a half - space free field composed of a single solid medium, specifically as Figure 6 shown, and its free wave field consists of the incident P - wave u sr (y, t) traveling upward and the reflected P - wave u sf (y, t) traveling downward after reflection from the free surface. Its motion law is relatively simple, and the motion law of its free field can be directly derived in the time domain. Similarly, assuming the incident P - wave is u0(t), according to the one - dimensional wave theory, for any point y at any time t in the free field, its total motion field u s is composed of the incident wave field u sr and the reflected wave field u sf superposed, that is:

[0111]

[0112] According to Equation (20), the time - domain solution of the free field on the downstream side can be obtained. It is also possible to use the solution method derived for the upstream reservoir water - foundation, set H to 0, and solve step by step according to the above - mentioned solution steps. The time - domain solution of the solid domain obtained by calculation is taken as the analytical solution of the free wave field on the downstream side, that is, the time history of the displacement of the free wave field of the solid foundation.

[0113] To verify the applicability and calculation accuracy of the above - derived seismic motion input method, taking the problem of a half - space with an overlying water layer under vertical incidence of P - waves as an example, a finite - element model of a half - space with an overlying water layer as shown in Figure 7 is established. The length of the calculation domain is 100 m, and the heights of both the reservoir water area and the solid domain are 100 m. The solid and liquid media are simulated by Solid45 and Fluid80 respectively; the solid artificial boundary condition is simulated by combin14, and the liquid artificial boundary condition is simulated by combin40. The medium material parameters are shown in Table 2.

[0114] Table 2 Model material parameters

[0115]

[0116] Using as shown in Figure 8Perform dynamic analysis on the unit impulse compression displacement wave shown, with the pulse duration being 0.2 s. Select three locations at the bottom of the bedrock (A), the fluid-structure coupling surface (B), and the free water surface (C) respectively for comparative analysis, and the results are as Figure 9 shown, where Figure 9 (a) of Figure 9 (b) of Figure 9 and (c) of Figure 9 are the displacement time histories of points A, B, and C respectively.

[0117] Step 4: Take the equivalent input seismic load as the vertical input of seismic waves to the finite element model of the gravity dam foundation with reservoir water, perform dynamic analysis on all artificial boundary nodes of the artificial boundary substructure model, obtain the extreme values of the displacement and stress of the gravity dam, and perform seismic response analysis of the gravity dam according to the extreme values of the displacement and stress of the gravity dam.

[0118] To study the influence of wave input in the water medium on the seismic response of the gravity dam hydraulic structure. The present invention takes the Xiangjiaba Gravity Dam as the research object, selects the No. 3 non-overflow dam section on the left bank of the Xiangjiaba Dam, with the dam section height being 162 m and the normal storage water level being 158 m. The foundation is taken as 1.5 times the dam height at the upstream, downstream, and bottom, and a numerical model is established. The model is as Figure 10 shown. The dynamic response analysis of the gravity dam under the vertical incidence of seismic waves is carried out by using the method derived in the present invention (Method 1) and the input method of only inputting seismic waves in the solid medium and ignoring the wave input of the water body (Method 2) respectively. The selection of seismic waves is to generate a random ground motion with a peak acceleration of 0.2g based on the site spectrum of the Xiangjiaba Project, with parameters T1 = 0.1, Tg = 0.25, and βmax = 2, as shown in Figure 11 , where Figure 11 (a) of Figure 11 and (b) of

[0119] are the acceleration time history of the seismic wave and the displacement time history curve of the seismic wave respectively. Figure 12 The material zoning of the dam body is shown in

[0120] The Rayleigh damping model is adopted, and the damping coefficients are determined by the first two natural vibration frequencies of the model and a damping ratio of 0.1. At the same time, according to the requirements of the Seismic Design Code for Hydraulic Structures of Hydropower Projects, the standard value of the dynamic elastic modulus of the dam concrete is taken as 1.5 times the standard value of the static elastic modulus of the concrete.

[0121] Method 1 uses the free-field theory derived above and the improved input method, and Method 2 uses the solid

[0122] Table 3 Material Parameters of the Dam and the Foundation

[0123]

[0124] Based on the free-field theory, by setting the reservoir water height H to 0, it can be derived. For the earthquake ground motion input method, the artificial boundary substructure method is adopted. Similarly, only the boundary nodes and the elements enclosed by the internal nodes adjacent to them are retained by deleting the internal nodes to obtain the substructure. The time history of the solid free-field displacement corresponding to the nodes is applied to all nodes of the artificial boundary substructure for dynamic analysis. Then, the reaction force of the boundary nodes calculated by the substructure (i.e., the equivalent input load of the earthquake ground motion) is applied to the artificial boundary nodes of the complete model for dynamic calculation. The time histories of displacements and stresses at the heel and the top of the gravity dam are selected for comparative analysis, and the results are as Figure 13 and Figure 14 shown, where Figure 13 (a) of Figure 13 (b) of Figure 13 (c) of Figure 13 (d) of Figure 14 (a) of Figure 14 (b) of Figure 14 (c) of Figure 14 (d) of Figure 13 and Figure 14 are the time history diagrams of vertical displacement, horizontal displacement, horizontal stress at the heel, and vertical stress at the heel respectively;

[0125] Extract the extreme values of displacements and stresses at the heel and crest of the dam for analysis. The results are shown in Tables 4 and 5. As shown in Tables 4 and 5, the peak values obtained by the seismic motion input method (Method 1) considering the compressibility of the fluid in the present invention are all lower than those obtained by only considering the foundation input (Method 2). Among them, the peak values of the horizontal displacement and the vertical stress at the heel of the dam are the most significant. The peak value of the horizontal displacement at the heel of the dam is reduced by 31.81% compared with Method 2, and the peak value of the vertical stress is reduced by 27.19%. The peak values of the horizontal displacement and the horizontal stress at the crest of the dam are the most significant. The peak value of the horizontal displacement at the crest of the dam is reduced by 44.64% compared with Method 2, and the peak value of the horizontal stress is reduced by 24.52%. The reason for the small change in the peak value of the vertical displacement may be that the P-wave velocity adopted in the present invention is too large and the height of the reservoir water is small, resulting in a short propagation time of the wave in the reservoir water. In addition, the wave velocity of the P-wave in the reservoir water is relatively close to that in the solid, resulting in a small change in the amplitude of the reflected wave and the transmitted wave.

[0126] From the above results, it can be seen that considering the seismic motion input of the reservoir water medium has a significant impact on the seismic response analysis of gravity dams. Ignoring the influence of the compressibility of the fluid on the seismic motion input significantly overestimates the seismic response of gravity dams, indicating that it is necessary to consider the compressibility of the fluid, i.e., the wave input of the water body, in the seismic response research of gravity dams and other structures.

[0127] Table 4 Result analysis at the heel of the dam

[0128]

[0129] Table 5 Result analysis at the crest of the dam

[0130]

[0131] The seismic response analysis of hydraulic structures such as gravity dams is of great significance for the scientific planning and construction of water conservancy projects. The present invention focuses on giving a seismic motion input method considering the compressibility of the fluid for the foundation-reservoir water under seismic action from three aspects: numerical modeling method, construction method of the reservoir water-foundation free field, and improvement of the seismic load input of the artificial sub-boundary structure, and the following conclusions are obtained through the analysis of free field numerical examples:

[0132] The improved seismic motion input method of the present invention can effectively realize the seismic motion input of the complex wave field of the dam under the vertical incidence of P-waves.

[0133] By comparing the results of two different methods, it is found that the results obtained by calculating the seismic response analysis of gravity dams using the method of the present invention are lower than those obtained by the seismic motion input method ignoring the compressibility of the fluid, especially for the peak values of the horizontal displacement and the vertical stress of the dam body, which are the most significant. Ignoring the influence of the compressibility of the fluid on the seismic motion input will significantly overestimate the seismic response of gravity dams, and it is necessary to consider the wave input of the reservoir water medium.

[0134] The present invention also provides a gravity dam seismic response analysis system, including a model construction module, a substructure model construction module, an equivalent input seismic load acquisition module, and a seismic response analysis module. The model construction module is used to set the solid artificial boundary and the fluid artificial boundary of the gravity dam foundation reservoir water, and construct a finite element model of the gravity dam foundation reservoir water. The substructure model construction module is used to remove the internal elements of the finite element model of the gravity dam foundation reservoir water, and construct an artificial boundary substructure model through the solid artificial boundary nodes, the fluid artificial boundary nodes, and the nodes adjacent to the solid artificial boundary nodes and the fluid artificial boundary nodes of the finite element model of the gravity dam foundation reservoir water. The equivalent input seismic load acquisition module is used to obtain the displacement time history of the reservoir water-foundation free wave field and the displacement time history of the solid foundation free wave field. Taking the compressional wave P-wave as the vertically incident wave and the upstream dam surface as the axis, apply the displacement time history of the reservoir water-foundation free wave field to all the fluid artificial boundary nodes and the solid artificial boundary nodes on the upstream side of the artificial boundary substructure model, apply the displacement time history of the solid foundation free wave field to all the solid artificial boundary nodes on the downstream side of the artificial boundary substructure model, and perform dynamic analysis on the artificial boundary substructure model to obtain the equivalent input seismic load. The seismic response analysis module is used to vertically input the equivalent input seismic load as a seismic wave into the finite element model of the gravity dam foundation reservoir water, perform dynamic analysis on all the artificial boundary nodes of the artificial boundary substructure model, obtain the extreme values of the displacement and stress of the gravity dam, and perform seismic response analysis of the gravity dam according to the extreme values of the displacement and stress of the gravity dam.

[0135] The present invention also provides a computer device, including a memory and a processor; the memory stores a computer program, and the processor is used to run the computer program in the memory to execute the gravity dam seismic response analysis method.

[0136] The present invention also provides a computer-readable storage medium, which stores a computer program, and the computer program is suitable for being loaded by a processor to execute the gravity dam seismic response analysis method.

[0137] When constructing a finite element model of the foundation and reservoir water of a gravity dam in the present invention, acoustic fluid elements in displacement format are used to simulate the reservoir water, and fluid artificial boundaries are introduced to simulate the radiation damping effect of the far-field water body. This model can effectively consider the influence of reservoir water on the seismic response characteristics of the gravity dam. When performing ground motion input, the influence of the compressibility of the reservoir water on the ground motion input is considered, the motion of the reservoir water-foundation free field is derived, and based on the artificial boundary substructure model, the ground motion input method of the traditional free field ground motion is improved. By applying the time history of the reservoir water-foundation free wave field displacement to all fluid artificial boundary nodes and solid artificial boundary nodes on the upstream side of the artificial boundary substructure model, and applying the time history of the solid foundation free wave field displacement to all solid artificial boundary nodes on the downstream side of the artificial boundary substructure model, it is possible to apply the time history of the free wave field displacement corresponding to the spatial position of the nodes to all nodes of the artificial boundary substructure model respectively, and its simulation of ground motion input for irregular sites is more accurate. By performing dynamic analysis on the artificial boundary substructure model, the equivalent input seismic load can be obtained. This ground motion input method can effectively realize the simulation of ground motion input for the complex wave field of the dam under the vertical incidence of P waves. By using the equivalent input seismic load as the seismic wave to vertically input into the finite element model of the foundation and reservoir water of the gravity dam and performing seismic response analysis of the gravity dam, this method is more accurate for seismic dynamic response analysis of the gravity dam and has guiding significance for the seismic safety measures of the dam.

[0138] The above-described embodiments are only the preferred specific embodiments of the present invention, and the protection scope of the present invention is not limited thereto. Any simple changes or equivalent replacements of the technical solutions that can be obviously obtained by those skilled in the art within the technical scope disclosed by the present invention all belong to the protection scope of the present invention.

Claims

1. A gravity dam seismic response analysis method, characterized in that: The steps include: Set the solid artificial boundary and fluid artificial boundary of the gravity dam foundation reservoir water, and construct the finite element model of the gravity dam foundation reservoir water; The internal units of the gravity dam foundation water reservoir finite element model are removed, and an artificial boundary substructure model is constructed through the solid artificial boundary nodes, the fluid artificial boundary nodes, and the nodes adjacent to the solid artificial boundary nodes and the fluid artificial boundary nodes of the gravity dam foundation water reservoir finite element model; Obtain the reservoir water-foundation free wave field displacement time history and the solid foundation free wave field displacement time history. Take the compression wave P wave as the vertical incident wave and the upstream dam surface as the axis. Apply the reservoir water-foundation free wave field displacement time history to all fluid artificial boundary nodes and solid artificial boundary nodes on the upstream side of the artificial boundary substructure model. Apply the solid foundation free wave field displacement time history to all solid artificial boundary nodes on the downstream side of the artificial boundary substructure model. Perform dynamic analysis on the artificial boundary substructure model to obtain the equivalent input seismic load. The equivalent input seismic load is used as seismic wave vertically input into the finite element model of the gravity dam foundation reservoir. Dynamic analysis is performed on all artificial boundary nodes of the artificial boundary substructure model to obtain the displacement and stress extremes of the gravity dam. The seismic response analysis of the gravity dam is performed based on the displacement and stress extremes of the gravity dam.

2. The gravity dam seismic response analysis method according to claim 1, characterized in that: The process of acquiring the reservoir water-foundation free wave field displacement time history includes the following steps: Assuming that the reservoir water medium is inviscid and compressible and the foundation medium is elastic, determine the wave equations of the reservoir water medium and the foundation medium; The response characteristics of the reservoir water-foundation site under the action of seismic waves and the propagation characteristics of seismic waves in the reservoir water medium and the foundation medium are determined through the wave equation. Based on the medium wave theory, the free wave field is established. Assuming that the P wave is incident vertically on the reservoir-foundation site, according to the medium wave theory, the total displacement of the solid domain is caused by the incident P wave and the reflected P wave, and the total displacement of the fluid domain is caused by the transmitted P wave and the reflected P wave on the free liquid surface. Through the principle of seismic wave superposition, the total displacement of the solid domain and the total displacement of the fluid domain are superimposed to obtain the displacement time history of the free wave field at any position of the reservoir-foundation site at any time under the action of the earthquake; Establish the boundary conditions of free wave field motion. The free wave field motion of the reservoir water-foundation site under the action of earthquake meets the boundary conditions of stress continuity and displacement continuity. The boundary conditions are as follows: at the reservoir water-foundation coupling surface, the normal displacement and normal stress of the solid medium and the liquid medium are balanced, the liquid has no shear stress, the shear stress is 0, and at the free liquid surface, the pressure of the liquid is 0; According to the boundary conditions, the potential function amplitude relationship between each wave system is established to perform Fourier transform on the displacement time history of the free wave field, and the frequency domain solution of the reservoir water-foundation free wave field is obtained; The frequency domain solution of the reservoir water-foundation free wave field is inversely transformed by Fourier transform to obtain the displacement change law of any position in the reservoir water-foundation site under the action of earthquake, that is, the displacement time history of the reservoir water-foundation free wave field.

3. The gravity dam seismic response analysis method according to claim 1, characterized in that: The acquisition process of the solid foundation free wave field displacement time history is as follows: According to the one-dimensional wave law, the total displacement of the waterless foundation site on the downstream side is the superposition of the incident P wave and the reflected P wave. For any position y of the waterless foundation site on the downstream side, the time required for the incident P wave to reach point y is The time required for the reflected P wave to reach point y is The displacement of point y at time t is: In the formula, u sr is the displacement caused by the incident P wave in the solid medium, u sf is the displacement caused by the reflection of P wave by solid medium, h is the height of the foundation site, c p is the propagation velocity of seismic waves in the foundation, and u0(t) is the seismic wave at the input site.

4. The gravity dam seismic response analysis method according to claim 1, characterized in that: The fluid artificial boundary condition specifically includes adding a damper and a mass unit at the fluid boundary node.

5. The gravity dam seismic response analysis method according to claim 1, characterized in that: The solid artificial boundary condition is to add a parallel spring and a damper on the solid boundary.

6. A gravity dam seismic response analysis system, characterized in that: include: A model building module is used to set the solid artificial boundary and fluid artificial boundary of the gravity dam foundation reservoir water and build a finite element model of the gravity dam foundation reservoir water; A substructure model construction module is used to remove the internal units of the gravity dam foundation reservoir water finite element model, and to construct an artificial boundary substructure model through the solid artificial boundary nodes, the fluid artificial boundary nodes, and the nodes adjacent to the solid artificial boundary nodes and the fluid artificial boundary nodes of the gravity dam foundation reservoir water finite element model; The equivalent input seismic load acquisition module is used to obtain the reservoir water-foundation free wave field displacement time history and the solid foundation free wave field displacement time history. With the compression wave P wave as the vertical incident wave and the upstream dam surface as the axis, the reservoir water-foundation free wave field displacement time history is applied to all the fluid artificial boundary nodes and solid artificial boundary nodes on the upstream side of the artificial boundary substructure model, and the solid foundation free wave field displacement time history is applied to all the solid artificial boundary nodes on the downstream side of the artificial boundary substructure model. The artificial boundary substructure model is subjected to dynamic analysis to obtain the equivalent input seismic load; The seismic response analysis module is used to input the equivalent input seismic load as a seismic wave vertically into the finite element model of the gravity dam foundation reservoir, perform dynamic analysis on all artificial boundary nodes of the artificial boundary substructure model, obtain the displacement and stress extremes of the gravity dam, and perform seismic response analysis of the gravity dam based on the displacement and stress extremes of the gravity dam.

7. A computer device, characterized in that: It comprises a memory and a processor; the memory stores a computer program, and the processor is used to run the computer program in the memory to execute the gravity dam seismic response analysis method according to any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and the computer program is suitable for being loaded by a processor to execute the gravity dam seismic response analysis method according to any one of claims 1-5.

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