Gravity dam earthquake response analysis method, system, equipment and medium

Abstract

The invention provides a gravity dam earthquake response analysis method, system, equipment and medium, and belongs to the technical field of earthquake response analys.The method comprises the following steps that a solid artificial boundary and a fluid artificial boundary of gravity dam foundation reservoir water are set, and a gravity dam foundation reservoir water finite element model is constructed; constructing an artificial boundary substructure model through solid artificial boundary nodes, fluid artificial boundary nodes and nodes adjacent to the solid artificial boundary nodes and the fluid artificial boundary nodes; a reservoir water-foundation free wave field displacement time history is applied to all fluid artificial boundary nodes and solid artificial boundary nodes on the upstream side of the artificial boundary substructure model, and a solid foundation free wave field displacement time history is applied to all solid artificial boundary nodes on the downstream side of the artificial boundary substructure model; performing dynamic analysis on the artificial boundary substructure model to obtain an equivalent input seismic load; and inputting the equivalent input earthquake load into the gravity dam foundation reservoir water finite element model, and carrying out earthquake response analysis. The gravity dam earthquake dynamic response analysis is more accurate.

Description

Technical Field

[0001] The present invention belongs to the technical field of earthquake response analysis, and in particular relates to a gravity dam earthquake response analysis method, system, equipment and medium. Background Art

[0002] my country's southwest region is rich in hydropower resources, and many large dams are located here. However, the earthquake intensity and frequency in the southwest region are high, and strong earthquakes can easily induce damage to dams. The seismic safety of dams in the southwest region faces severe challenges. For seismic response problems of such open systems, the seismic source is usually treated as an external source. A limited near-field calculation domain is intercepted, and artificial boundary conditions are set at the truncation boundary. However, the introduction of closed artificial boundary conditions brings a new problem: how to realize the input of seismic motion in the near-field model without affecting the absorption of scattered waves by the artificial boundary, that is, the seismic wave input problem. Effective seismic motion input is the key link to ensure the accuracy of numerical simulation of external source wave problems.

[0003] Due to the rapid development of urban underground space construction in recent decades, researchers have conducted a lot of research on the seismic wave input method in soil-structure interaction problems and achieved relatively fruitful results. Joyner and Chen completed the input of seismic motion in a one-dimensional soil layer model by applying a viscous boundary at the truncation boundary of the one-dimensional model and deriving an equivalent load suitable for the artificial boundary. Clough used the foundation stiffness to convert the free field motion into an equivalent load and applied it to the soil-structure interaction system. Wolf proposed a 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 are mainly aimed at the case of vertical incidence of seismic waves. When the earthquake source is close to the engineering site, the seismic wave usually propagates upward at a certain angle. For the near-field model, the oblique incidence of seismic waves will cause the seismic ground motion to show non-uniform changes, which will have a significant impact on the seismic response of the engineering site and the structure. The commonly used input methods are the wave method of seismic motion input proposed by Liu Jingbo and the domain reduction method proposed by Bielak. The wave method converts input seismic motion into equivalent nodal loads on viscoelastic artificial boundaries. Combined with the one-dimensional time domain algorithm for free field analysis of layered media, it can effectively solve the input problem of seismic waves in soil-structure interaction systems under arbitrary angles of oblique incidence. The domain reduction method proposes that external excitation can be converted into equivalent forces applied inside the model and absorbing boundaries can be applied at artificial truncation boundaries, thereby realizing an input method that takes into account the effects of the seismic source and the propagation path of seismic waves. In addition, based on the theory of the wave method, researchers have proposed simpler seismic wave input methods such as artificial boundary substructures and internal substructure methods.

[0004] Unlike the traditional soil-structure interaction system, for hydraulic structure engineering sites represented by the gravity dam-foundation-reservoir water system, due to the compressibility of the water body, seismic waves can be relayed in the reservoir water. Due to the difference in wave velocity between the fluid and solid media, after the wave is transmitted into the fluid medium through the solid 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 of seismic waves in the fluid and solid media at the same time. At the same time, due to the different water levels upstream and downstream of the dam body, the motion laws of the free wave field on the upstream and downstream sides are different, and the seismic input is more complicated.

[0005] However, for the current seismic input of such sites, the fluid is usually equivalent to the additional mass moving with the solid or the dynamic water pressure applied to the structure. When conducting seismic input, it is assumed that the water body is incompressible, and the influence of the water body on the free field model analysis is ignored. The reservoir water-foundation-dam body interaction system is simplified to a soil-structure interaction system for seismic input research, resulting in low numerical simulation accuracy of seismic input, which poses severe challenges to the seismic safety of the dam. Summary of the invention

[0006] In order to overcome the above-mentioned deficiencies in the prior art, the present invention provides a gravity dam seismic response analysis method, comprising the following steps:

[0007] 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;

[0008] 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;

[0009] 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.

[0010] 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.

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

[0012] 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;

[0013] 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.

[0014] 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;

[0015] 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;

[0016] 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;

[0017] 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.

[0018] Preferably, 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 downstream foundation site is the superposition of the incident P wave and the reflected P wave. For any position y of 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] 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 speed of seismic waves in the foundation, u0 (t) is the seismic wave of the input site.

[0021] Preferably, the fluid artificial boundary condition is specifically to add a damper and a mass unit at the fluid boundary node.

[0022] Preferably, the solid artificial boundary condition is to add a spring and a damper in parallel on the solid boundary.

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

[0024] 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;

[0025] 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;

[0026] 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;

[0027] 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.

[0028] The present invention also provides a computer device, comprising 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.

[0029] The present invention also provides a computer-readable storage medium, wherein 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 gravity dam seismic response analysis method, system, device and medium provided by the present invention have the following beneficial effects:

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

[0032] In order to more clearly illustrate the embodiment of the present invention and its design scheme, the following briefly introduces the drawings required for this embodiment. The drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0033] Figure 1 is a flow chart of a gravity dam seismic response analysis method according to an embodiment of the present invention;

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

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

[0036] Figure 4 is a model based on artificial boundary substructure, where Figure 4 (a) and Figure 4 (b) are the models before and after removing the internal units of the gravity dam foundation reservoir finite element model;

[0037] Figure 5 This is a schematic diagram of the reservoir water-foundation half space, where: Figure 5 (a) is the free field in the half space of the overlying reservoir water layer, Figure 5(b) is the free space of the foundation half space on the downstream side;

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

[0039] Figure 7 It is the free field model of foundation reservoir water;

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

[0041] Fig. 9 is the displacement map of the observation point, where Fig. 9 (a) Fig. 9 (b) and Fig. 9 (c) are the displacement time histories of points A, B and C respectively;

[0042] Fig.10 To consider the reservoir water fluctuation input, the finite element model was developed;

[0043] Fig.11 is the incident seismic wave, where Fig.11 (a) and Fig.11 (b) are the time history curves of seismic wave acceleration and seismic wave displacement respectively;

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

[0045] Fig.13 This is the result analysis diagram of the dam heel, where: Fig.13 (a) Fig.13 (b) Fig.13 (c) and Fig.13 (d) are vertical displacement time history diagram, horizontal displacement time history diagram, dam heel horizontal stress diagram and dam heel vertical stress diagram respectively;

[0046] Fig.14 This is the result analysis diagram of the dam top, where: Fig.14 (a) Fig.14 (b) Fig.14 (c) and Fig.14 (d) are the time history diagram of vertical displacement at the dam crest, the time history diagram of horizontal displacement at the dam crest, the time history diagram of horizontal stress at the dam crest and the time history diagram of vertical stress at the dam crest. DETAILED DESCRIPTION

[0047] In order to enable those skilled in the art to better understand the technical solution of the present invention and implement it, the present invention is 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 scope of protection of the present invention.

[0048] In the description of the present invention, it is to be understood that the terms “center”, “longitudinal”, “lateral”, “length”, “width”, “thickness”, “up”, “down”, “front”, “back”, “left”, “right”, “vertical”, “horizontal”, “top”, “bottom”, “inside”, “outside”, “axial”, “radial”, “circumferential”, etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing the technical solutions of the present invention and simplifying the description, and do not indicate or imply 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 on the present invention.

[0049] In addition, the terms "first", "second", etc. are used for descriptive purposes only and are not to 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 a direct connection or an indirect connection through an intermediate medium. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to the specific circumstances. In the description of the present invention, unless otherwise specified, "plurality" means two or more, which will not be described in detail here.

[0050] Example

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

[0052] Step 1: 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.

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

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

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

[0056]

[0057] In Table 1: 0 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 viscoelastic artificial boundary condition, and the unit 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 remote foundation. It can be simulated by the combin14 spring unit provided by ANSYS, with one end on the solid artificial boundary node and the other end fixed. The corresponding material parameters are added to the spring and damper.

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

[0060] Δx=αλ min , Where: 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 cutoff frequency for numerical simulation of wave problems.

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

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

[0063] Step 3: 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, and 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.

[0064] The components of seismic waves are very complex, mainly divided into body waves and surface waves. Body waves include shear waves (S waves) and compression waves (P waves), and surface waves include Rayleigh waves and Love waves. For earthquake response analysis, the seismic source can be approximately regarded as a point source, so the elastic fluctuations 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 complicated, and SV waves are shear waves and do not propagate in liquid media. Therefore, the present invention takes plane P waves as an example to derive the construction theory of reservoir water-foundation free field under vertical incidence of P waves. 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 seismic input methods based on the wave method theory. This method directly obtains the equivalent input load of seismic motion by establishing an artificial boundary substructure model for dynamic analysis. It has the advantages of high simulation accuracy, high operation efficiency and convenient calculation. At present, this method is mainly used for seismic input in the form of regular sites with uniform lateral and vertical stratification.

[0066] The semi-space free field of hydraulic structures such as gravity dams is an irregular field composed of the upstream reservoir water field and the downstream solid foundation field. Therefore, the present invention has made improvements, specifically: the free wave field displacement time history u corresponding to the spatial position of the node is applied to all nodes of the artificial boundary substructure model. f (y, t), u s (y, t), with the upstream dam surface as the axis, the upstream nodes are applied with the reservoir water-foundation free wave field displacement time history, and the downstream nodes are applied with the solid foundation free wave field displacement time history, as shown in Figure 4 As shown in (b), a dynamic analysis is performed on the 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] For example Figure 4 Equivalent input seismic loads are applied to all artificial boundary nodes of the finite element model shown in (a), and dynamic time history calculation is performed, 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, determine the wave equations of the reservoir water medium and the foundation medium. Assuming that the foundation is linearly elastic, its stress-strain relationship satisfies the generalized Hooke's law; the reservoir water medium is inviscid and compressible, and the fluid hydrodynamic pressure p f It is linearly related to the spatial divergence of the displacement vector; 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 by the wave equation. (2) According to the medium wave theory, a free wave field is established. Assuming that the P wave is incident vertically into the 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 free field motion of any position at any time in the reservoir water-foundation site under the action of an earthquake 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 produces a compression wave, that is, a 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 y position of the free field. (4) Establish the boundary conditions for the free field motion of the site. The free field motion of the reservoir water-foundation site under the action of earthquake should satisfy the boundary conditions of stress continuity and displacement continuity. At the fluid-solid coupling surface, due to the fluid-solid coupling effect, the normal displacement and normal stress of the solid medium and the liquid medium at the fluid-solid coupling surface should satisfy 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) Establish the potential function amplitude relationship between each wave system based on the boundary conditions. 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 of the free field and the displacement can be established. Therefore, by substituting the displacement potential function into the boundary conditions, the relationship between the amplitudes of the potential functions of each seismic wave can be obtained. (6) Convert the obtained displacement wave field into the frequency domain by Fourier transform, and solve the amplitude of the incident P wave potential function. The motion equation obtained by (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 has nothing to do with time and is 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 u 0 (t) is the same, and the phase is related to y. When y is 0, the incident P wave is the input ground motion u 0 (t). Let y of the incident P wave be 0, and u 0 (t) Substitute the frequency domain solution of the incident P wave into the relationship of the incident P wave potential function to 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 amplitude of each wave system and obtain the frequency domain solution of the reservoir water-foundation free wave field. (8) Perform an inverse Fourier transform on the frequency domain solution of the reservoir water-foundation free wave field to obtain the time-varying law of displacement at any position of the reservoir water-foundation site under the action of an earthquake, 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 upstream reservoir water-foundation free field and the downstream foundation free field. The free field of the semi-space of the overlying reservoir water layer is as follows: Figure 5 As shown in (a). Assume that the reservoir water height is H and the foundation height is h. When the reservoir water height H = 0, it is the free field of the downstream foundation half space, as shown in Figure 5 As shown in (b), 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 free field theoretical solution. The wave equations of solid and fluid media are shown in equations (1) and (2), where the fluid medium adopts the inviscid compressible assumption. The analysis is as follows Figure 5 The free field model shown is used to solve the time domain solution of the seismic free wave field.

[0071]

[0072] Where: is the gradient operator; u is the displacement vector of the fluid particle, and the superscript “.” represents the first differentiation of the displacement vector u; ρ s , 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 the generalized Hooke's law:

[0073]

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

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

[0076]

[0077] P waves are compression waves. According to the wave theory of media, when the incident P wave is incident vertically into the free field of the upstream overlying water layer, it will generate reflected P waves and transmitted P waves at the fluid-solid coupling surface. The reflected P wave is absorbed by the distant foundation, while the transmitted P wave will generate reflected P waves at the free liquid surface. This cycle repeats and the propagation law is complex. The free wave field is decomposed into the solid domain wave field and the fluid domain wave field. The free wave field in the solid domain is composed of the upward incident wave u sr (y, t) and the downward reflected wave u sf (y, t) composition; the upward transmission wave u of the free wave field in the fluid domain ft (y, t) and the downward wave u reflected from the free surface ff (y, t) composition.

[0078] Let the vertical incident wave be u 0 (t), let the vertical displacement of the foundation free field be u s , the vertical displacement of the reservoir water free field is u f , then according to the wave superposition theory, the free field displacement 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 frequency is a simple harmonic wave of 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 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; u ft is the displacement caused by the liquid medium transmitting the P wave, u ff A is the displacement caused by the reflection of P wave by liquid medium. sr , A sf are the amplitudes of the incident P wave and the reflected P wave in the solid medium, A ft , A ff is the amplitude of the transmitted P wave and reflected P wave of the liquid medium, is the propagation speed of P waves in solid media, is the propagation speed of P wave in liquid medium, is a unit imaginary number, t is time, and y is the vertical coordinate of the field geological point.

[0086] The free wave field motion at the fluid-solid coupling interface (y = 0) should meet the boundary conditions of normal displacement continuity and normal stress equilibrium:

[0087]

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

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

[0090] τ sxy (y,t)| y＝0 =0 (10);

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

[0092] P f (y,t)| y＝H =0 (11);

[0093] Partially differentiate the potential function and substitute it into equations (5) and (6) to obtain:

[0094]

[0095] To u s 、u f By taking partial differentials and substituting them into boundary conditions (9) to (11), we can obtain the relationship between amplitudes:

[0096]

[0097] in:

[0098]

[0099] Perform Fourier transform on equation (12) to obtain the frequency domain solution of the free wave field:

[0100]

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

[0102]

[0103] For any given input ground motion u 0 (t), perform Fourier transform on it and get U 0 (ω), then:

[0104] U sr (y,ω)| y＝0 =U 0 (ω) (17);

[0105] Where: U sr (y,ω) is the frequency domain solution of the incident wave, U 0 (ω) is the frequency domain solution of the input seismic wave.

[0106] From this we can conclude that:

[0107] A sr =-c p U 0 (ω) / (iω) (18);

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

[0109]

[0110] For the free field of the downstream foundation, the water level downstream of the gravity dam is generally lower than the upstream water level, and the propagation time of seismic waves in the downstream reservoir water is shorter (the wave speed of seismic waves in the reservoir water is 1435m / s), and the downstream reservoir water has little effect on the seismic input. Therefore, when performing the seismic input on the downstream side, the site can be simplified to a solid foundation site treatment 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, Figure 6As shown, the free wave field is composed of the upward incident P wave u sr (y, t) and the downgoing P wave u reflected by the free surface sf (y, t), the motion law is relatively simple, and its free field motion law can be directly deduced in the time domain. Similarly, assuming that the incident P wave is u 0 (t), according to the one-dimensional wave theory, the total motion field u of a point y at any position in the free field at any time t s By the incident wave field u sr and the reflected wave field u sf Superposition, that is:

[0111]

[0112] The time domain solution of the free field on the downstream side can be obtained according to formula (20). Alternatively, the solution method derived from the reservoir water-foundation on the upstream side can be adopted, H is set to 0, and the above solution steps are followed in sequence to obtain the analytical solution of the free wave field on the downstream side, that is, the displacement time history of the free wave field of the solid foundation.

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

[0114] Table 2 Model material parameters

[0115]

[0116] Use as Figure 8 The unit pulse compression displacement wave shown in the figure is used for dynamic analysis, and the pulse duration is 0.2s. The bedrock bottom (A), fluid-solid coupling surface (B), and free liquid surface (C) are selected for comparative analysis. The results are shown in Fig. 9 As shown, Fig. 9 (a) Fig. 9 (b) and Fig. 9 (c) are the displacement time histories of points A, B and C respectively. Fig. 9It shows that the results calculated by the method of the present invention are very close to the theoretical solution, proving that this method can effectively realize the seismic wave input of the flooded site. When considering the seismic input of reservoir water and foundation at the same time, the law of model displacement change is more complicated, and the displacement time history presents a fluctuation form with gradually decreasing amplitude. The energy exchange at the fluid-solid coupling surface of the model under the action of earthquake may be the main reason for this result. Due to the difference in the propagation speed of elastic waves in the fluid and solid media, the P wave is transmitted and reflected at the coupling interface when it is vertically incident, and the reservoir water and the foundation exchange energy. After the wave is transmitted into the fluid medium through the solid medium, it propagates back and forth in the fluid medium and gradually attenuates, causing the model displacement to fluctuate and gradually decrease.

[0117] Step 4: 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.

[0118] In order to study the influence of wave input in water medium on the seismic response of gravity dam hydraulic structure, this paper takes Xiangjiaba gravity dam as the research object, selects Xiangjiaba left bank non-overflow dam section 3#, the dam section height is 162m, the normal water storage level is 158m, the foundation is 1.5 times the dam height at the upstream and downstream and bottom, and establishes a numerical model. The model is as follows Fig.10 As shown. The dynamic response analysis of the gravity dam under vertical incidence of seismic waves was carried out by using the method derived from the present invention (method one) and the input method of only solid medium input seismic waves and ignoring the wave input of water body (method two). The selection of seismic waves is based on the site spectrum of Xiangjiaba project to generate a random seismic motion with a peak acceleration of 0.2g. The parameters are T1=0.1, Tg=0.25, βmax=2, see Fig.11 ,in, Fig.11 (a) and Fig.11 (b) are the seismic wave acceleration time history curves and seismic wave displacement time history curves respectively.

[0119] Material division of the dam body is shown in Fig.12 The material parameters of each area of ​​the dam and the foundation are shown in Table 3.

[0120] The Rayleigh damping model is adopted, and the damping coefficient is determined by the first two natural frequencies of the model and the 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 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, while method 2 uses the solid ground

[0122] Table 3 Parameters of dam body and foundation materials

[0123]

[0124] Based on the free field theory, the reservoir water height H is set to 0 to derive the result. The seismic input method uses the artificial boundary substructure method. The internal nodes are deleted and only the units surrounded by the boundary nodes and the internal nodes adjacent to them are retained to obtain the substructure. The solid free field displacement time history corresponding to the nodes is applied to all nodes of the artificial boundary substructure for dynamic analysis. Then, the reaction force of the boundary node calculated by the substructure (i.e., the equivalent input load of seismic motion) is applied to the artificial boundary nodes of the complete model for dynamic calculation. The displacement time history and stress time history at the heel and the crest of the gravity dam are selected for comparative analysis. The results are as follows: Fig.13 and Fig.14 As shown, Fig.13 (a) Fig.13 (b) Fig.13 (c) and Fig.13 (d) are vertical displacement time history diagram, horizontal displacement time history diagram, dam heel horizontal stress diagram and dam heel vertical stress diagram respectively; Fig.14 (a) Fig.14 (b) Fig.14 (c) and Fig.14 (d) are the time history diagram of vertical displacement at the dam crest, the time history diagram of horizontal displacement at the dam crest, the time history diagram of horizontal stress at the dam crest and the time history diagram of vertical stress at the dam crest. Fig.13 and Fig.14 It can be seen that the waveforms and amplitudes of the displacement time history and stress time history at the dam heel and dam crest calculated by the method of the present invention and the method without considering the reservoir water earthquake input are quite different. The results show that the consideration of the compressibility of reservoir water and the fluctuation in reservoir water in the earthquake wave input method has a great influence on the displacement and stress response of the gravity dam.

[0125] The displacement and stress extremes at the dam heel and dam crest were extracted for analysis, and the results are shown in Tables 4 and 5. As shown in Tables 4 and 5, the peak values ​​obtained by the earthquake input method (method one) considering the compressibility of fluid using the method of the present invention are lower than the peak values ​​under the consideration of foundation input (method two). Among them, the horizontal displacement peak value and vertical stress peak value at the dam heel are the most significant. The horizontal displacement peak value at the dam heel is reduced by 31.81% and the vertical stress peak value is reduced by 27.19% compared with method two. The horizontal displacement peak value and horizontal stress peak value at the dam crest are the most significant. The horizontal displacement peak value at the dam crest is reduced by 44.64% and the horizontal stress peak value is reduced by 24.52% compared with method two. The reason for the small change in the vertical displacement peak value may be that the P wave velocity used in the present invention is too large, and the height of the reservoir water is small, which makes the propagation time of the wave in the reservoir water shorter. In addition, the velocity of the P wave in the reservoir water is close to the velocity in the solid, which makes the amplitude change of the reflected wave and the transmitted wave not large.

[0126] From the above results, it can be seen that considering the seismic input of the reservoir water medium has a significant impact on the seismic response analysis of the gravity dam. Not considering the effect of fluid compressibility on the seismic input will obviously overestimate the seismic response of the gravity dam. This shows that it is necessary to consider the fluid compressibility, that is, the wave input of the water body, in the seismic response study of gravity dams.

[0127] Table 4 Analysis of results at dam heel

[0128]

[0129] Table 5 Analysis of results at dam top

[0130]

[0131] Seismic response analysis of hydraulic structures such as gravity dams is of great significance for the scientific planning and construction of water conservancy projects. This paper focuses on the three aspects of numerical modeling method, reservoir water-foundation free field construction method and improved seismic load input of artificial sub-boundary structure to provide a foundation-reservoir water seismic input method considering fluid compressibility under earthquake action, and obtains the following conclusions through free field numerical example analysis:

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

[0133] By comparing the results of the two different methods, it is found that the results of the gravity dam seismic response analysis calculated by the method of the present invention are lower than those of the seismic input method that ignores the compressibility of the fluid, especially for the horizontal displacement peak and vertical stress peak of the dam body. Not considering the impact of fluid compressibility on seismic input will significantly overestimate the seismic response of the gravity dam, and it is necessary to consider the fluctuation input of the reservoir water medium.

[0134] The present invention also provides a gravity dam seismic response analysis system, comprising 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 units 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 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 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 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 vertically input the equivalent input seismic load as a seismic wave into the finite element model of the gravity dam foundation reservoir water, and to perform dynamic analysis 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.

[0135] The present invention also provides a computer device, comprising 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. The computer program is suitable for being loaded by a processor to execute the gravity dam seismic response analysis method.

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

[0138] The embodiments described above are only preferred specific implementation modes 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 any technician familiar with the field within the technical scope disclosed in the present invention 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.

Images