High arch dam deformation state fractional order numerical analysis method and module

Abstract

The invention discloses a high arch dam deformation state fractional order numerical analysis method and module, and relates to the technical field of hydraulic structure service state analysis and computational mechanics. The method comprises the following steps: establishing a high arch dam body and dam foundation fractional order rheological mechanical element model by constructing a fractional order characterization method of attenuation rheological, steady-state rheological and accelerated rheological in a three-dimensional stress state; calculating an internal stress increment, a viscoelastic strain increment, a viscoplastic strain increment and a deformation increment in a delta tn time period by adopting a front difference formula according to the stress, the viscoelastic strain, the viscoplastic strain and the deformation at the tn moment by virtue of an increment finite element method, so as to obtain the stress, the strain and the deformation at the tn + 1 moment; and repeatedly calculating to obtain the stress, strain and deformation of the high arch dam in the analysis time period. According to the method, the nonlinear rheological effect of the dam body and the dam foundation of the high arch dam is objectively described, scientific deformation property numerical value quantitative analysis is achieved, technical support is provided for safety monitoring and dangerous case early warning of the in-service high arch dam, and the method has wide application prospects and market prospects.

Description

Technical Field

[0001] The invention relates to the technical field of hydraulic structure service performance analysis and computational mechanics, and more particularly to a high arch dam deformation performance fractional-order numerical analysis method and module. Background Art

[0002] my country has abundant water resources, with a total volume of about 2.8124 trillion m 3 , accounting for about 6% of the world's total runoff resources. The theoretical reserves of river water energy in China are about 680 million kilowatts, ranking first in the world in both reserves and development capacity. Hydropower has the advantages of stable output, low pollution and renewable, and has become an important part of my country's energy structure. Since the 1950s, in order to meet the needs of flood control, power generation, irrigation, water supply, shipping, etc., my country has built more than 98,000 dams. With the in-depth promotion of hydropower development, the construction of high arch dams has achieved remarkable achievements. At present, a number of high arch dams have been completed and put into operation, such as Jinping I, Xiaowan, Xiluodu, Dagangshan, etc. These giant projects have played a vital role in my country's economic and social development.

[0003] The safe service of dams has always been widely concerned by governments and the international community, especially for high arch dams. Once a failure occurs, it will cause huge casualties and property losses downstream. Arch dam failure is a gradual process, which gradually develops from local structural failure to overall instability. If scientific and effective methods are used to monitor the operation of arch dams in real time, abnormal signs of dams are captured in time, and targeted engineering and non-engineering measures are taken, accidents may be avoided. Deformation changes are a comprehensive reflection of the changes in the structural properties of high arch dams and are an important indicator of whether the structure is normal. Many engineering cases in history have demonstrated the importance of deformation property analysis of arch dams. Malpasset Arch Dam in France has a dam height of 66m, a dam crest length of 222.7m, a dam bottom thickness of 6.78m, a thickness-to-height ratio of 0.103, and a reservoir capacity of 51 million m 3In February 1959, the dam suddenly collapsed, causing more than 500 deaths or disappearances and property losses of 30 billion francs. By comparing the deformation simulation results with the monitoring data, it was found that the deformation monitoring values ​​4 months before the dam collapse were larger than the calculated values. The radial deformation monitoring values ​​of the arch beam 8 to 10 meters away from the dam foundation had reached 12 to 16 mm, which was 2 to 2.8 times the calculated value. The deformation near the dam foundation was even greater and had long exceeded the warning value. A typical case of avoiding accidents by effectively analyzing the deformation behavior is the Zeuzil hyperbolic arch dam in Switzerland. Under normal water storage levels, the vertical deformation monitoring data showed that the dam had abnormal deformation upstream. The reservoir was then drained and the dam was inspected. It was found that there were many cracks on the upstream dam surface. After analyzing the monitoring data of the slope and reservoir settlement, it was found that the canyon where the dam site was located had sunk over a large area and the valley width had shrunk. After repair, the dam resumed normal operation. Therefore, establishing scientific theories, methods and techniques for analyzing the deformation properties of high arch dams will help engineering and technical personnel to discover hidden dangers early and avoid dam failures.

[0004] The temporal and spatial characteristics of the deformation state of high arch dams are closely related to the physical and mechanical properties of the structure. When the external load state changes, the high arch dam first undergoes instantaneous deformation. Under the continuous action of the load, due to the creep effect of the dam body and the creep effect of the dam foundation (both collectively referred to as the rheological effect), the high arch dam undergoes a time-dependent deformation that changes with time. Scientific characterization of the physical and mechanical properties of high arch dams is the premise and basis for objective quantitative analysis of the deformation state of high arch dams. The physical and mechanical properties of high arch dams include elasticity, plasticity, viscoelasticity, viscoplasticity and viscoelastic-plasticity. At present, the models describing these mechanical properties can be summarized as empirical models, component models and theoretical models. Among them, the component model has been widely used in engineering because of its simple use and clear physical meaning. The traditional component model is constructed based on the theory of integer-order calculus, and uses a series-parallel combination of basic mechanical elements such as springs, viscoelastic pots and sliders to characterize the above physical and mechanical properties. Although the classic integer-order rheological mechanics component model is convenient to use, it has certain shortcomings. For example, when the integer-order standard linear body (Hooke body and Kelvin body in series) is used to simulate the rheological test process, although the instantaneous elasticity and delayed elasticity can be characterized, the calculation results such as relaxation modulus are poorly fitted with the test data. It is difficult to well characterize the nonlinear rheological effect of high arch dams using only the integer-order rheological mechanics component model. The physical and mechanical property characterization method is an important factor that restricts the objectivity of the numerical analysis of the deformation behavior of high arch dams.

[0005] Fractional calculus is the study of calculus theory with fractional operations. In the early 19th century, mathematicians began to study the theory of fractional calculus. The research results of scientists such as Laplace and Fourier laid the theoretical foundation for fractional calculus. However, for a long time, due to the unclear physical meaning of fractional calculus and the lack of support in the application field, related research stagnated in the theoretical exploration stage. The international conference on "Fractional Calculus and Its Application" held at the University of New Haven in the United States in 1974 promoted the development of fractional calculus theory in the application field. At present, it has been successfully applied in geotechnical engineering, electromagnetism, fractals and other fields, and the advantages of this theory over classical integer calculus have gradually been discovered. So far, relevant scholars have strictly defined fractional calculus from different perspectives. Commonly used definition methods include: Riemann-Liouville definition, Caputo definition and Grunwald-Letnikov definition. In essence, fractional calculus is the extension of integer calculus to fractional order. When the order of fractional calculus is an integer, the two are consistent. And due to the characteristics of fractional calculus itself, it is related to past historical information, that is, fractional calculus has a memory function, while integer calculus does not have this function. Combining the theory of fractional calculus with the integer characterization method of rheological effect can make the physical meaning of the component model clearer, and provide an effective way to describe the nonlinear rheological behavior of high arch dams.

[0006] Existing research on fractional-order component models focuses on rheological test analysis, and there are many one-dimensional stress state models. In actual operation, high arch dams are in a three-dimensional stress state, but there are fewer studies on three-dimensional models, especially fractional-order component models that characterize the accelerated rheological effect under three-dimensional high stress state. Therefore, based on the theory of fractional calculus, it is a key problem that technicians in the field of hydraulic structure service performance analysis and computational mechanics need to solve to study the construction method of fractional-order rheological mechanical component models for the dam body and foundation of high arch dams under three-dimensional stress state, and then realize the fractional-order numerical analysis of the deformation state of high arch dams. Summary of the invention

[0007] In view of this, the present invention provides a fractional-order numerical analysis method and module for deformation properties of a high arch dam to solve the bottleneck problem existing in the background technology.

[0008] In order to achieve the above object, the present invention adopts the following technical solution.

[0009] On the one hand, a fractional-order numerical analysis method for deformation behavior of a high arch dam is provided, including:

[0010] Based on the fractional calculus theory, a fractional characterization method for each stage of rheological effect under three-dimensional stress state is constructed. Each stage includes decay rheology, steady-state rheology and accelerated rheology. On this basis, a fractional rheological mechanical element model of the high arch dam body and foundation is established.

[0011] Based on the fractional-order rheological mechanics model of the dam body and foundation, the incremental finite element method is used to perform fractional-order numerical analysis. n The stress, viscoelastic strain, viscoplastic strain and deformation at the time Δt are calculated using the pre-difference formula n The stress increment, viscoelastic strain increment, viscoplastic strain increment and deformation increment in the time period are obtained, and then t n+1 The stress, strain and deformation at each moment are calculated repeatedly to obtain the stress, strain and deformation of the high arch dam during the analysis period.

[0012] On the other hand, a fractional-order numerical analysis module for deformation behavior of high arch dams is provided, including:

[0013] The fractional-order characterization unit is designed based on a parallel structure and includes a decaying rheological characterization subunit, a steady-state rheological characterization subunit, and an accelerating rheological characterization subunit;

[0014] The model building unit is based on the parallel structure design and includes a dam body fractional-order rheological mechanics element model subunit and a dam foundation fractional-order rheological mechanics element model subunit;

[0015] The incremental calculation unit is designed based on a series-parallel structure and includes a viscoelastic strain incremental calculation subunit, a viscoplastic strain incremental calculation subunit, a deformation incremental calculation subunit and a stress incremental calculation subunit;

[0016] The visual display unit outputs results including but not limited to instantaneous deformation, time-dependent deformation, stress and strain, which are presented to operators in the form of cloud maps, contour maps, distribution maps and process lines.

[0017] It can be seen from the above technical solution that, compared with the prior art, the present invention discloses a fractional-order numerical analysis method and module for deformation behavior of high arch dams, which has the following beneficial effects:

[0018] (1) By constructing the fractional-order characterization method of decay rheology, steady-state rheology and accelerated rheology under three-dimensional stress state, the fractional-order rheological mechanical element model of the high arch dam body and foundation was established;

[0019] (2) With the help of the pre-difference formula, the recursive formulas for the viscoelastic strain increment and the viscoplastic strain increment were constructed. On this basis, the calculation method of stress, strain and deformation was proposed based on the incremental finite element method;

[0020] (3) The derivative order characterizes the relationship between the hardening and recovery effects in the rheological process of soft matter. The higher the order, the more obvious the recovery effect, and the lower the order, the more significant the hardening effect. Compared with the classical integer-order rheological element model, the fractional-order rheological element model has a clearer physical meaning.

[0021] (4) The fractional-order rheological element model not only describes the properties of Hooke bodies and Newton bodies, but also characterizes the nonlinear viscous mechanical relationship between the two, and has a wider range of representation;

[0022] (5) Since the order of fractional calculus changes continuously, it is more conducive to simulating accelerated rheology. The fractional rheological element model can achieve a better characterization of the entire rheological process with fewer parameters and simpler configuration;

[0023] (6) The present invention aims to improve the accuracy and objectivity of deformation analysis of high arch dams, provide scientific basis and technical support for safety monitoring and hazard warning of in-service high arch dams, and has a relatively broad application prospect and market. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0025] Figure 1 The fractional-order numerical analysis method and module architecture of the deformation behavior of high arch dams provided by the present invention;

[0026] Figure 2 The fractional-order rheological mechanics element model of the high arch dam body provided by the present invention;

[0027] Figure 3 A fractional-order rheological element model of a high arch dam foundation provided by the present invention;

[0028] Figure 4 The calculation process of the fractional-order numerical analysis program for deformation behavior of high arch dam provided by the present invention;

[0029] Figure 5 The finite element model of the Jiagao arch dam provided by the present invention;

[0030] Figure 6 (a) is a dam body concrete material partition diagram of the Jiagao arch dam provided by the present invention; (b) is a typical node distribution diagram of the dam body of the Jiagao arch dam provided by the present invention;

[0031] Figure 7The radial instantaneous deformation distribution law of the cantilever beam of A-type arch dam under six working conditions is shown;

[0032] Figure 8 The radial instantaneous deformation distribution law of the arch ring of the A-type arch dam under six working conditions is shown;

[0033] Fig. 9 The radial time-dependent deformation variation law of different elevation nodes of the A-type arch dam under working condition 1 provided by the present invention;

[0034] Fig.10 The radial aging deformation distribution law of the cantilever beam of the high arch dam under working condition 1 provided by the present invention;

[0035] Fig.11 The radial aging deformation distribution law of the arch ring of the dam crest of the high arch dam under the working condition 1 provided by the present invention;

[0036] Fig.12 The radial instantaneous deformation and radial aging deformation variation law of the characteristic point of the A-type arch dam under working condition 2 provided by the present invention;

[0037] Fig.13 The radial aging deformation distribution law of the cantilever beam of a high arch dam under working condition 2 provided by the present invention. DETAILED DESCRIPTION

[0038] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0039] The embodiment of the present invention discloses a fractional-order numerical analysis method for deformation behavior of a high arch dam. Figure 1 As shown, including:

[0040] Based on the fractional calculus theory, a fractional characterization method for each stage of rheological effect under three-dimensional stress state is constructed. Each stage includes decay rheology, steady-state rheology and accelerated rheology. On this basis, a fractional rheological mechanical element model of the high arch dam body and foundation is established.

[0041] Based on the fractional-order rheological mechanics model of the dam body and foundation, the incremental finite element method is used to perform fractional-order numerical analysis. n The stress, viscoelastic strain, viscoplastic strain and deformation at the time Δt are calculated using the pre-difference formula n The stress increment, viscoelastic strain increment, viscoplastic strain increment and deformation increment in the time period are obtained, and then t n+1The stress, strain and deformation at each moment are calculated repeatedly to obtain the stress, strain and deformation of the high arch dam during the analysis period.

[0042] Specifically, the fractional-order characterization method of decay rheology, steady-state rheology and accelerated rheology under three-dimensional stress state is described below.

[0043] a. Fractional-order characterization method for decay rheology under three-dimensional stress state

[0044] The elastic relationship between stress and strain of high arch dam under three-dimensional stress state is:

[0045]

[0046] Where: K is the bulk modulus that characterizes elastic deformation; G is the shear modulus that characterizes elastic deformation; σ m is the spherical stress tensor; ε m is the spherical strain tensor; S ij is the deviatoric stress tensor; e ij is the deviatoric strain tensor. The relationship between K and G and the elastic modulus E and Poisson's ratio μ are:

[0047]

[0048] Similar to the elastic case, under the three-dimensional stress state, the relationship between the viscoelastic stress and strain of the high arch dam also includes two parts: the spherical tensor relationship and the deviatoric tensor relationship. Assumptions: ① The material is isotropic; ② The volume deformation of the dam is elastic deformation, caused by the spherical stress tensor, and completed at the moment of force; ③ The rheological deformation of the dam is only caused by the deviatoric stress tensor; ④ During the rheological process, the Poisson's ratio does not change with time. Under the one-dimensional stress state, the general formula of the fractional-order element model that characterizes the viscoelastic mechanical state of the high arch dam is:

[0049]

[0050] Where: t is time; a h , b w is a constant; h=1,2,…,H and w=1,2,…,W are non-negative integers; α h , β w is a real number with coprime numerator and denominator; H and W are the number of strain terms and stress terms in the general formula respectively; σ is stress; ε is strain.

[0051]

[0052] Then formula (4) is expressed as:

[0053]

[0054] Under three-dimensional stress state, the relationship between viscoelastic stress and strain of high arch dam is expressed as:

[0055]

[0056] The first formula of formula (7) is the relationship between spherical stress and spherical strain. Since spherical stress only causes elastic deformation, {Q2}=K, {P2}=1. The second formula of formula (7) is the relationship between deviatoric stress and deviatoric strain. Since deviatoric stress causes viscoelastic deformation, {Q1} and {P1} correspond to {Q} and {P} respectively. However, it is necessary to convert all elastic moduli E in {Q} and {P} into shear elastic moduli G. The conversion formula is:

[0057]

[0058] Where: μ is Poisson's ratio.

[0059] Therefore, the axial stress σ in the decay rheological fractional characterization model under one-dimensional stress state is converted into the deviatoric stress S ij , and convert the delay modulus into the shear delay modulus, that is, the fractional-order characterization method of attenuation rheology under three-dimensional stress state is obtained.

[0060] Under three-dimensional stress state, the viscoelastic strain of fractional Kelvin body and fractional Murasaki body can be expressed as follows.

[0061] The fractional Kelvin body is:

[0062]

[0063] For hard rock, creep deformation usually occurs when the stress reaches the stress threshold. is the deviatoric stress threshold tensor for decay flow, when When , the fractional-order mountain is:

[0064]

[0065] In formulas (9) and (10): t is time; is the viscoelastic strain tensor; G1 is the shear elastic modulus characterizing the decay rheology; S ij is the deviatoric stress tensor; k is a non-negative integer variable; η1 is the viscosity coefficient that characterizes the decaying rheology; γ1 is the order that characterizes the decaying rheology; Γ is the Gamma function.

[0066] b. Fractional-order characterization method for steady-state rheology under three-dimensional stress state

[0067] remember is the deviatoric stress threshold tensor for steady-state flow. Based on the P. Perzyna hypothesis, when When , the viscoplastic strain of the fractional Bingham body is expressed as:

[0068]

[0069] Where: t is time; is the viscoplastic strain tensor; F is the yield function; Q is the plastic potential function; Φ is the flow function; σ ij is the total stress tensor; η2 is the viscosity coefficient that characterizes steady-state rheology and accelerated rheology; γ2 is the order that characterizes steady-state rheology and accelerated rheology; Γ is the Gamma function.

[0070] The yield function F adopts the Drucker-Prager yield criterion, that is:

[0071]

[0072] Where: c is the cohesion; φ is the internal friction angle; I1 is the first invariant of the stress tensor; J2 is the second invariant of the deviatoric stress tensor.

[0073] Using the associated flow law (F = Q) and the power flow function, when When , the expression of the viscoplastic strain of the fractional Bingham body under three-dimensional stress state is:

[0074]

[0075] Where: t is time; is the viscoplastic strain tensor; F is the yield function; F0 is the yield function at the initial moment; σ ij is the total stress tensor; η2 is the viscosity coefficient that characterizes steady-state rheology and accelerated rheology; γ2 is the order that characterizes steady-state rheology and accelerated rheology; m is the yield parameter; Γ is the Gamma function.

[0076] c. Accelerated rheological fractional characterization method under three-dimensional stress state

[0077] When the accumulated viscoplastic strain reaches a threshold, the fractional Bingham body It changes in the form of an exponential function f(t), and the expression is:

[0078]

[0079] Where: t is time; η2 is the viscosity coefficient that characterizes steady-state rheology and accelerated rheology; γ2 is the order that characterizes steady-state rheology and accelerated rheology; α2 is the acceleration parameter. The viscoplastic strain rate increases, and the accelerated rheological stage is entered. The equivalent viscoplastic strain is introduced. Its expression is:

[0080]

[0081] Where: is the viscoplastic strain tensor.

[0082] remember To calculate the equivalent viscoplastic strain when accelerated flow occurs, use formula (15) to calculate the corresponding Determined by rheological test. When , under the three-dimensional stress state, the viscoplastic strain of the variable parameter fractional Bingham body is expressed as:

[0083]

[0084] Where: t is time; is the viscoplastic strain tensor; F is the yield function; F0 is the yield function at the initial moment; η2 is the viscosity coefficient that characterizes steady-state rheology and accelerated rheology; γ2 is the order that characterizes steady-state rheology and accelerated rheology; k is a non-negative integer variable; m is the yield parameter; Γ is the Gamma function; σ ij is the total stress tensor; α2 is the acceleration parameter; t s To accelerate the time when rheology occurs.

[0085] Specifically, based on the fractional-order characterization method of decay rheology, steady-state rheology and accelerated rheology under three-dimensional stress state, the fractional-order rheological mechanical element model of the high arch dam body and foundation is given below.

[0086] The dam model is as follows Figure 2 The configuration shown is expressed as:

[0087]

[0088] The dam foundation model is as follows Figure 3 The configuration shown is expressed as:

[0089]

[0090] In formulas (17) and (18), t is time; σ ij is the total stress tensor; ε ij is the total strain tensor; σ m is the spherical stress tensor; S ij is the deviatoric stress tensor; δ ij is the Kronecker symbol. When i=j, δ ij =1, otherwise δ ij =0; is the deviatoric stress threshold tensor for decaying rheology; K is the bulk modulus characterizing elastic deformation; G is the shear elastic modulus characterizing elastic deformation; G1 is the shear elastic modulus characterizing decaying rheology; η1 is the viscosity coefficient characterizing decaying rheology; η2 is the viscosity coefficient characterizing steady-state rheology and accelerated rheology; γ1 is the order characterizing decaying rheology; γ2 is the order characterizing steady-state rheology and accelerated rheology; k is a non-negative integer variable; m is the yield parameter; is the deviatoric stress threshold tensor for steady-state flow; Γ is the Gamma function; is the equivalent viscoplastic strain; is the equivalent viscoplastic strain when accelerated flow occurs; F is the yield function; F0 is the yield function at the initial moment; α2 is the acceleration parameter; t s To accelerate the time when rheology occurs.

[0091] Specifically, based on the fractional-order rheological element model of the dam body and foundation and with the help of the incremental finite element principle, a method for implementing the fractional-order numerical analysis of the deformation properties of high arch dams is given below.

[0092] Note n The load at the moment is {R} n ;t n The total stress at the moment is {σ ij} n ;t n The viscoelastic strain at time The viscoplastic strain at time tn is The deformation at time tn is {U} n ; The total strain increment during the Δtn period is {Δε ij} n ; Δt n The instantaneous strain increment during the time period is Δt n The viscoelastic strain increment during the time period is Δt n The viscoplastic strain increment during the time period is Δt n The deformation increment during the time period is {ΔU} n ; Δt n The total stress increment during the time period is {Δσ ij} n . The following gives t n+1 Moment stress {σ ij} n+1 , viscoelastic strain Viscoplastic strain and deformation {U} n+1 The calculation method of .

[0093] The present invention adopts the front difference formula to construct the viscous strain increment With time increment Δt n The recursive relationship between n During the time period, the viscous strain increment is expressed as:

[0094]

[0095] Where: is the viscous strain increment; t n The viscous strain rate at time .

[0096] a. Calculation of viscoelastic strain increment

[0097] Taking the fractional Kelvin body as an example, the fractional Murasaki body is similar to it. Taking the derivative of the time t in the decay rheological fractional expression under one-dimensional stress state, combined with equation (19), we can get Δt n The expression of the fractional Kelvin viscoelastic strain increment in the time period is:

[0098]

[0099] Where: t n for a certain moment; is Δt under one-dimensional stress state n The viscoelastic strain increment during the time period; E1 is the elastic modulus that characterizes the decay rheology; σ n t n The axial stress at the moment; k is a non-negative integer variable; η1 is the viscosity coefficient that characterizes the decaying rheology; γ1 is the order that characterizes the decaying rheology; Γ is the Gamma function.

[0100] Under three-dimensional stress state, Δt n Viscoelastic strain increment of fractional Kelvin body in time period It is expressed as:

[0101]

[0102] Where: t n for a certain moment; = Δt n The viscoelastic strain increment during the time period; μ is Poisson's ratio; is the Poisson's ratio matrix; k is a non-negative integer variable; {S ij} n t n The deviatoric stress at the moment; η1 is the viscosity coefficient that characterizes the decaying rheology; γ1 is the order that characterizes the decaying rheology; G1 is the shear elastic modulus that characterizes the decaying rheology; Γ is the Gamma function.

[0103] b. Calculate the viscoplastic strain increment

[0104] By differentiating the time t in the fractional Bingham body expression under three-dimensional stress state, the expression of viscoplastic strain rate is obtained as follows:

[0105]

[0106] So Δt n The viscoplastic strain increment of the fractional-order Bingham body during the time period is:

[0107]

[0108] By taking the derivative of the time t in the viscoplastic strain expression of the variable parameter fractional Bingham body, the expression of the viscoplastic strain rate is obtained as follows:

[0109]

[0110] Then Δt n Fractional Bingham viscoplastic strain increment within a time period for:

[0111]

[0112] In formulas (22) to (25): t n for a certain moment; t n The viscoplastic strain rate at time t; = Δt n The viscoplastic strain increment within the time period; F is the yield function; F0 is the yield function at the initial moment; η2 is the viscosity coefficient that characterizes steady-state rheology and accelerated rheology; γ2 is the order that characterizes steady-state rheology and accelerated rheology; k is a non-negative integer variable; m is the yield parameter; Γ is the Gamma function; {σ ij} n t n The total stress at the moment; α2 is the acceleration parameter; t s To accelerate the time when rheology occurs.

[0113] Solution The key is to calculate It breaks down into:

[0114]

[0115] In formula (26):

[0116]

[0117]

[0118] In equations (26) to (29), I1 is the first invariant of the stress tensor; J2 and J3 are the second and third invariants of the deviatoric stress tensor, respectively; S xx , S yy , S zz , S xy , S yz and S zx are the components of the deviatoric stress tensor; {σ ij} n is the total stress at time tn.

[0119] For the Drucker-Prager yield criterion, C1=α2, C2=1 and C3=0 exist. Substituting equations (27) to (29) into equation (26), we obtain:

[0120]

[0121] Where: F is the yield function; α2 is the acceleration parameter; I1 is the first invariant of the stress tensor; J2 is the second invariant of the deviatoric stress tensor; {σ ij} n t n The total stress at time; {X} and {Y} are constant matrices.

[0122] {X} and {Y} are represented as:

[0123]

[0124]

[0125] c. Calculate the deformation increment {ΔU} within the Δtn period n and tn +1 The transformation of time +1

[0126] According to elasticity theory, Δt n During the period, the stress increment of the high arch dam {Δσ ij} n Expressed as:

[0127]

[0128] Where: {D} is the elasticity matrix; {Δσ ij} n = Δt n Total stress increment during the time period; = Δt n The elastic strain increment during a period of time.

[0129] The total strain increment {Δε ij} nInclude instantaneous strain increment Viscoelastic strain increment and viscoplastic strain increment satisfy:

[0130]

[0131] Substituting formula (34) into formula (33), we obtain:

[0132]

[0133] According to the principle of virtual work, the incremental balance equation after the structure is discretized is:

[0134]

[0135] Where: {B} n is the geometric matrix in the Δtn period; {ΔR} n is the external load increment within the Δtn period; {Δσ ij} n = Δt n The total stress increment in the time period. Substituting equation (35) into equation (36), the viscoelastic-plastic finite element incremental equilibrium equation is expressed as:

[0136] {K}{ΔU} n ={ΔR} n +{ΔR ve} n +{ΔR vp} n (37)

[0137] Where: {K} is the overall stiffness matrix; {ΔU} n = Δt n The deformation increment matrix within the time period; {ΔR ve} n = Δt n Viscoelastic strain increment within a period of time The corresponding equivalent node load increment; {ΔR vp} n is the viscoplastic strain increment during the Δtn period The corresponding equivalent nodal load increment; {ΔR} n is the external load increment within the period Δtn.

[0138] {K}, {ΔR ve} n and {ΔR vp} n The expressions are:

[0139]

[0140] In formulas (38) to (40): {B} n = Δt n The geometric matrix in the time period; {D} is the elasticity matrix; = Δt n The viscoelastic strain increment during the time period; = Δt n The viscoplastic strain increment within the time period. The integration objects of equations (38) to (40) are all elements, elements in the viscoelastic state, and elements in the viscoplastic state, respectively.

[0141] Calculate the deformation increment {ΔU} of the high arch dam within the Δtn period n ,Right now:

[0142] {ΔU}n={K}- 1 ({ΔR}n+{ΔRve}n+{ΔRvp}n)(41)

[0143] This gives tn +1 The deformation value of the high arch dam at time {U} n+1 ,Right now:

[0144] {U} n+1 ={U} n +{ΔU} n (42)

[0145] In formulas (41) and (42): {ΔR ve} n is the viscoelastic strain increment during the Δtn period The corresponding equivalent node load increment; {ΔR vp} n is the viscoplastic strain increment during the Δtn period The corresponding equivalent nodal load increment; {ΔR} n = Δt n The external load increment during the time period; {K} is the overall stiffness matrix; {U} n is the deformation at time tn.

[0146] d. Calculate Δt n The total stress increment {Δσ ij} n and t n+1 The total stress {σ ij} n+1

[0147] Calculate Δt according to formula (33): n The total stress increment of the high arch dam during the period {Δσ ij} n , then t n+1 The total stress {σij} n+1 Expressed as:

[0148] {σ ij} n+1 ={σ ij} n +{Δσ ij} n (43)

[0149] Where: {σ ij} n is the total stress at time tn.

[0150] Through the above analysis steps, we can calculate {Δσ ij} n , and {ΔU} n , combined with {σ ij} n , and{U} n , we can conclude that {σ ij} n+1 , and{U} n+1 , repeatedly calculate the stress, strain and deformation of the high arch dam during the analysis period, thereby realizing the scientific quantitative analysis of the rheological effect and deformation properties of the high arch dam body and foundation.

[0151] The calculation process of the fractional-order numerical analysis program for deformation behavior of high arch dams is as follows: Figure 4 shown.

[0152] Specifically, based on the above method, a fractional-order numerical analysis module for deformation behavior of high arch dam is provided below. Figure 1 As shown, including:

[0153] The fractional-order characterization unit is designed based on a parallel structure and includes a decaying rheological characterization subunit, a steady-state rheological characterization subunit, and an accelerating rheological characterization subunit;

[0154] The model building unit is based on the parallel structure design and includes a dam body fractional-order rheological mechanics element model subunit and a dam foundation fractional-order rheological mechanics element model subunit;

[0155] The incremental calculation unit is designed based on a series-parallel structure and includes a viscoelastic strain incremental calculation subunit, a viscoplastic strain incremental calculation subunit, a deformation incremental calculation subunit and a stress incremental calculation subunit;

[0156] The visual display unit outputs results including but not limited to instantaneous deformation, time-dependent deformation, stress and strain, which are presented to operators in the form of cloud maps, contour maps, distribution maps and process lines.

[0157] An embodiment is introduced below to further illustrate the method of the present invention.

[0158] The Jiagao Arch Dam is a concrete hyperbolic arch dam, a large (1) type project, with a permanent main hydraulic structure of Class 1, a dam crest elevation of 1885m, a maximum dam height of 305m, a dam crest width of 16m, a dam crest centerline arc length of 552.23m, a maximum span of 480m, a minimum foundation elevation of 1580m, and a dam bottom thickness of 63m. The river valley has a width-to-height ratio of 1.57, and the river valley is a typical deep "V" shape. The normal water level is 1880m, the dead water level is 1800m, and the reservoir capacity below the normal water level is 7.76 billion m 3 , regulating reservoir capacity 4.91 billion m 3 On October 23, 2009, the first dam section 14 (elevation 1580-1581.5m) began to be poured, and the entire dam was sealed in December 2013. After completion, the 3D finite element model of the dam is as follows: Figure 5 As shown, the dam body concrete material division is as follows Figure 6 As shown in (a), the typical node distribution of the cantilever beam and the dam top arch ring is as follows: Figure 6 (b) as shown.

[0159] In the fractional numerical analysis, the design values ​​of the elastic-plastic physical and mechanical parameters of the dam body and dam foundation of Jiagao Arch Dam are shown in Table 1. The delay modulus of the dam body concrete is taken as E1 = 70 GPa, and the viscosity coefficient is taken as η1 = 2×10 3 GPa·d,η2=1.5×10 4 GPa·d, the orders γ1 and γ2 are taken as 0.7 and 0.8 respectively, and the attenuation flow stress threshold Taken as 0.15 times of the instantaneous strength of concrete, the viscoplastic parameter It is taken as 0.8 times of the instantaneous strength of concrete, and the parameter α2 is taken as 0.003h -1 The delayed modulus of the dam foundation rock mass is taken as E1 = 50 GPa, and the viscosity coefficient is taken as η1 = 3 × 10 3 GPa·d,η2=1.5×10 4 GPa·d, the orders γ1 and γ2 are taken as 0.7 and 0.8 respectively, and the attenuation flow stress threshold Taken as 0.15 times of the instantaneous strength of the rock mass, the viscoplastic parameter It is taken as 0.8 times of the instantaneous strength of the rock mass, and the parameter α2 is taken as 0.003h -1 .

[0160] Table 1 Design values ​​of elastic-plastic physical and mechanical parameters of Jiagao arch dam

[0161]

[0162] During the construction process, the main loads borne by the high arch dam include: water pressure, temperature load and deadweight. Before the arch grouting, all the loads are borne by the cantilever beam. After the arch grouting, the loads are jointly borne by the arch-beam system. The loads of the unsealed grouting parts are still borne by the cantilever beam. The process of pouring the dam body concrete, sealing the arch in stages and storing water in stages of the A-Gao arch dam is relatively complicated, and this example is simplified to a certain extent. Since the A-Gao arch dam was fully sealed in December 2013, the relevant analysis of the present invention is based on January 1, 2014 as the starting date. At this time, the reservoir water level is about 1840m. It is assumed that the casting elevation of the A-Gao arch dam is the same as the arch sealing elevation. Starting from the foundation elevation (about 1580m), the deadweight of the dam body and the reservoir water pressure before the water level of 1840m are applied in 5 levels. The loading process is shown in Table 2, and the calculated stress field is used as the initial stress field.

[0163] Table 2 Casting, arch sealing and water storage elevation of A high arch dam

[0164]

[0165] a. Law of instantaneous deformation change

[0166] Taking six typical working conditions as examples, the instantaneous deformation change law of Grade A arch dam is analyzed below. The calculation conditions are: dead water level, dead water level + maximum temperature rise, dead water level + maximum temperature drop, normal water storage level, normal water storage level + maximum temperature rise, normal water storage level + maximum temperature drop. Figure 7 The radial instantaneous deformation distribution law of the cantilever beam of the A-type arch dam under six calculation conditions is shown in Figure 2. Figure 6 (b) Figure 8 The radial instantaneous deformation distribution law of the arch ring of the Jiagao arch dam under six calculation conditions is presented, and the following conclusions are drawn:

[0167] (1) The upper and middle parts of the A-type arch dam, especially the middle part of the dam crest, are more sensitive to changes in load conditions than other parts because they are less constrained by the dam foundation and the bank slope. For example, when the upstream water level changes from 1800m to 1880m, the calculated radial instantaneous deformation value of the cantilever beam top node (node ​​number 9561) changes from -7.63mm to 34.94mm, and the deformation increases by 42.57mm downstream, while the calculated radial instantaneous deformation value of the node with an elevation of 1630m (node ​​number 9498) changes from 11.27mm to 21.65mm, and the deformation increases by 10.38mm downstream. In the same process, the calculated radial instantaneous deformation value of the node in the middle of the dam crest arch ring (node ​​number 10484) changes from -7.66mm to 39.47mm, and the deformation increases by 47.13mm downstream, while the calculated radial instantaneous deformation value of the node near the left slope of the dam crest arch ring (node ​​number 9683) changes from -4.71mm to -0.87mm, and the deformation increases by 3.84mm downstream.

[0168] (2) The effect of temperature load on the instantaneous deformation of the dam can be summarized as follows: when the temperature rises, the dam deforms relatively upstream; when the temperature decreases, the dam deforms relatively downstream. For example, when the upstream water level is 1880 m, the radial instantaneous deformation of the cantilever beam top node (node ​​number 9561) is calculated to be 34.94 mm. When the temperature load reaches the maximum temperature rise condition, the radial instantaneous deformation of the node is calculated to be 17.04 mm, which is 17.9 mm relatively upstream. When the temperature load reaches the maximum temperature drop condition, the radial instantaneous deformation of the node is calculated to be 52.83 mm, which is 17.89 mm relatively downstream.

[0169] (3) The effect of water pressure load on the instantaneous deformation of the dam can be summarized as follows: when the water level rises, the dam body deforms downstream; when the water level drops, the dam body deforms less downstream or deforms upstream. For example, when the upstream water level is 1800 m, the radial instantaneous deformation of the cantilever beam top node (node ​​number 9561) is calculated to be -7.63 mm. When the water level reaches 1880 m, the radial instantaneous deformation of the node is calculated to be 34.94 mm. That is, in the process of the water level rising from 1800 m to 1880 m, the cantilever beam top deformed 42.57 mm downstream.

[0170] b. Changes of deformation over time

[0171] Taking the following two working conditions as examples, the time-dependent deformation variation law of Jiagao arch dam is calculated and analyzed.

[0172] Condition 1: With 1 day (unit: d) as the time interval and 2 m as the unit, the reservoir water level is loaded from 1840 m to the normal water level of 1880 m in 21 steps, and then the reservoir water level is maintained at 1880 m until the 300th day. The reservoir water load application method is shown in Table 3. The reservoir water level change process is as follows Fig. 9 Indicated by the double-dotted line.

[0173] Table 3 Reservoir water load application method (condition 1)

[0174]

[0175] Fig. 9 The radial time-dependent deformation variation law of the characteristic points at different elevations of the A-type arch dam is shown in Figure 2. Fig.10 The radial time-dependent deformation distribution law of the cantilever beam of the high arch dam is shown in Figure 1. The positions of the characteristic points and the cantilever beam are shown in Figure 2. Figure 6 (b) Fig.11 The radial time-dependent deformation distribution law of the arch ring of the dam crest is shown in Figure 1 (for ease of description, the upstream nodes of the dam crest arch ring are numbered 1 to 53 from the left bank to the right bank), and the following conclusions are drawn:

[0176] (1) Under the continuous action of reservoir water load, the radial time-dependent deformation of Jiagao arch dam develops rapidly in the early stage of water storage, and gradually converges in the later stage. By the 300th day of the calculation period, the radial time-dependent deformation convergence value of the node at the elevation of 1885m of the cantilever beam (node ​​number is 9561) is 4.77mm; the radial time-dependent deformation convergence value of the node at the elevation of 1800m of the cantilever beam (node ​​number is 9533) is 4.65mm; the radial time-dependent deformation convergence value of the node at the elevation of 1750m of the cantilever beam is 4.65mm. The radial time-dependent deformation convergence value of the node at the cantilever beam with an elevation of 1720m (node ​​number 9519) is 4.26mm; the radial time-dependent deformation convergence value of the node at the cantilever beam with an elevation of 1660m (node ​​number 9507) is 2.61mm; the radial time-dependent deformation convergence value of the node at the cantilever beam with an elevation of 1600m (node ​​number 9506) is 0.98mm.

[0177] (2) The radial deformation distribution of the cantilever beam of the A-type high arch dam is closely related to the reservoir water load. When the reservoir water level is low, the radial deformation of the middle part of the cantilever beam is large. By the 10th day, the maximum radial deformation of the cantilever beam is 0.34 mm, which occurs at the elevation of 1720 m of the cantilever beam (node ​​number is 9519). When the reservoir water level is high, the radial deformation of the upper part of the cantilever beam is large. By the 300th day, the maximum radial deformation of the cantilever beam is 4.77 mm, which occurs at the elevation of 1880 m of the top of the cantilever beam (node ​​number is 9561).

[0178] (3) The radial time-dependent deformation of the left bank of the middle part of the dam crest arch ring of the Jiagao arch dam is relatively large. By the 300th day of the calculation period, the radial time-dependent deformation of the 10484th node of the dam crest arch ring is 5.49 mm. Due to the constraints of the mountains on both sides, the radial time-dependent deformation of the parts close to the slope is relatively small. The radial time-dependent deformation of the 9600th node on the left slope is only 0.68 mm.

[0179] Condition 2: The reservoir water level changes according to the water storage process from January 1, 2014 (the first day) to March 31, 2015 (the 455th day), the time interval is 1 day, the reservoir water load is applied as shown in Table 4, and the reservoir water level change process is as follows: Fig.12 Indicated by the double-dotted line.

[0180] Table 4 Reservoir water load application method (condition 2)

[0181]

[0182] Fig.12 The radial instantaneous deformation and radial time-dependent deformation variation law of the characteristic point of Jiagao arch dam (elevation 1750m, node number 9528) are shown in Figure 1. Fig.13 The radial time-dependent deformation distribution law of the cantilever beam of the high arch dam is shown in Figure 1. The positions of the characteristic points and the cantilever beam are shown in Figure 2. Figure 6As shown in (b), the following conclusions are drawn:

[0183] (1) The radial instantaneous deformation of the 1750m elevation node (node ​​number 9528) of the cantilever beam of the Jiagao arch dam is significantly affected by the reservoir water level. When the reservoir water level rises, the node deforms downstream, and when the reservoir water level drops, the node deforms upstream. The radial time-dependent deformation of the node shows a nonlinear change characteristic, which develops rapidly in the early stage of water storage and gradually converges in the later stage. At the end of the calculation period, the radial time-dependent deformation of the node is 2.82 mm. The radial time-dependent deformation of this period is fitted by c1θ+c2lnθ. The fitting results are shown in Fig.12 The single-dash line in the middle shows a fitted complex correlation coefficient of 0.976, and coefficients c1 and c2 are 0.2735 and 0.9346, respectively.

[0184] (2) The radial time-dependent deformation distribution of the cantilever beam of the Jiagao arch dam is closely related to the reservoir water load. When the reservoir water level is low, the radial time-dependent deformation of the middle part of the cantilever beam is large. For example, on the 150th day (February 19, 2014), the maximum radial time-dependent deformation of the cantilever beam is 0.81 mm, which occurs at an elevation of 1690 m (node ​​number 9526). On the 200th day (July 19, 2014), the maximum radial time-dependent deformation of the cantilever beam is 1.14 mm, which occurs at an elevation of 1720 m (node ​​number 9519). From the 250th day to the 380th day (October 27, 2014 to February 4, 2015), the reservoir water level was relatively high, fluctuating around the normal water storage level of 1880m. The radial aging deformation of the upper part of the cantilever beam was relatively large, and the radial aging deformation values ​​were close from the elevation of 1800m to the dam top. On the 380th day, the maximum radial aging deformation of the cantilever beam was 2.78mm, occurring at the cantilever beam top elevation of 1885m (node ​​number 9561).

[0185] This example is based on the fractional-order numerical analysis method and module of the deformation properties of high arch dams, and analyzes the radial instantaneous deformation and radial time-dependent deformation variation law of high arch dam A. The calculation results generally reflect the actual situation, thus verifying the feasibility of the present invention.

[0186] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0187] Thus, the present invention will not be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A fractional-order numerical analysis method for deformation behavior of high arch dams, characterized in that: include: Based on the fractional calculus theory, a fractional characterization method for each stage of rheological effect under three-dimensional stress state is constructed. Each stage includes decay rheology, steady-state rheology and accelerated rheology. On this basis, a fractional rheological mechanical element model of the high arch dam body and foundation is established. Based on the fractional-order rheological mechanics model of the dam body and foundation, the incremental finite element method is used to perform fractional-order numerical analysis. n The stress, viscoelastic strain, viscoplastic strain and deformation at the time Δt are calculated using the pre-difference formula n The stress increment, viscoelastic strain increment, viscoplastic strain increment and deformation increment in the time period are obtained, and then t n+1 The stress, strain and deformation at each moment are calculated repeatedly to obtain the stress, strain and deformation of the high arch dam during the analysis period.

2. A fractional-order numerical analysis method for deformation behavior of a high arch dam according to claim 1, characterized in that: Fractional Kelvin body and fractional Murasaki body are used to characterize the attenuation rheological effect. Under three-dimensional stress state, the fractional Kelvin body viscoelastic strain is expressed as: remember is the deviatoric stress threshold tensor for decay flow, when When , under the three-dimensional stress state, the fractional-order village mountain viscoelastic strain is expressed as: Where: t is time; is the viscoelastic strain tensor; G1 is the shear elastic modulus characterizing the decay rheology; S ij is the deviatoric stress tensor; k is a non-negative integer variable; η1 is the viscosity coefficient that characterizes the decaying rheology; γ1 is the order that characterizes the decaying rheology; Γ is the Gamma function.

3. A fractional-order numerical analysis method for deformation behavior of a high arch dam according to claim 1, characterized in that: Fractional Bingham bodies are used to characterize steady-state rheological processes; remember is the deviatoric stress threshold tensor for steady-state flow, when When , under the three-dimensional stress state, the expression of the viscoplastic strain of the fractional Bingham body is: Where: t is time; is the viscoplastic strain tensor; F is the yield function; F0 is the yield function at the initial moment; σ ij is the total stress tensor; η2 is the viscosity coefficient that characterizes steady-state rheology and accelerated rheology; γ2 is the order that characterizes steady-state rheology and accelerated rheology; Γ is the Gamma function; and m is the yield parameter.

4. A fractional-order numerical analysis method for deformation behavior of a high arch dam according to claim 1, characterized in that: Using variable parameter fractional Bingham body to characterize the accelerated rheological process; When the accumulated viscoplastic strain reaches a threshold, the fractional Bingham body It changes in the form of an exponential function f(t), and the expression is: along with The viscoplastic strain rate increases, and the accelerated rheological stage is entered. The equivalent viscoplastic strain is introduced. The expression is: remember To accelerate the equivalent viscoplastic strain when rheology occurs, When , under the three-dimensional stress state, the viscoplastic strain of the variable parameter fractional Bingham body is expressed as: Where: t is time; is the viscoplastic strain tensor; F is the yield function; F0 is the yield function at the initial moment; σ ij is the total stress tensor; η2 is the viscosity coefficient that characterizes steady-state rheology and accelerated rheology; γ2 is the order that characterizes steady-state rheology and accelerated rheology; α2 is the acceleration parameter; t s is the time when accelerated flow occurs; Γ is the Gamma function; k is a non-negative integer variable; m is the yield parameter.

5. A fractional-order numerical analysis method for deformation behavior of a high arch dam according to claim 3 or 4, characterized in that: The yield function F adopts the Drucker-Prager criterion; The yield function F of the Drucker-Prager criterion is expressed as: Where: c is the cohesion; φ is the internal friction angle; I1 is the first invariant of the stress tensor; J2 is the second invariant of the deviatoric stress tensor.

6. A fractional-order numerical analysis method for deformation behavior of a high arch dam according to claim 1, characterized in that: The expression of the fractional-order rheological element model of the dam body is: The expression of the fractional-order rheological element model of the dam foundation is: Where: t is time; σ ij is the total stress tensor; ε ij is the total strain tensor; σ m is the spherical stress tensor; S ij is the deviatoric stress tensor; δ ij is the Kronecker symbol. When i=j, δ ij =1, otherwise δ ij =0; is the deviatoric stress threshold tensor for decaying rheology; K is the bulk modulus characterizing elastic deformation; G is the shear elastic modulus characterizing elastic deformation; G1 is the shear elastic modulus characterizing decaying rheology; η1 is the viscosity coefficient characterizing decaying rheology; η2 is the viscosity coefficient that characterizes steady-state rheology and accelerated rheology; γ1 is the order that characterizes decay rheology; γ2 is the order that characterizes steady-state rheology and accelerated rheology; k is a non-negative integer variable; m is the yield parameter; is the deviatoric stress threshold tensor for steady-state flow; Γ is the Gamma function; is the equivalent viscoplastic strain; is the equivalent viscoplastic strain when accelerated flow occurs; F is the yield function; F0 is the yield function at the initial moment; α2 is the acceleration parameter; t s To accelerate the time when rheology occurs.

7. A fractional-order numerical analysis method for deformation behavior of a high arch dam according to claim 1, characterized in that: The incremental finite element method is used to calculate t n+1 Stress, strain and deformation at each moment; In Δt n During the time period, the viscoelastic strain increment of the fractional Kelvin body is expressed as: Where: t n for a certain moment; = Δt n The viscoelastic strain increment during the time period; μ is Poisson's ratio; is the Poisson's ratio matrix; k is a non-negative integer variable; {S ij } n t n Deviatoric stress at a moment; η1 is the viscosity coefficient that characterizes the decay rheology; γ1 is the order that characterizes the decay rheology; G1 is the shear elastic modulus that characterizes the decay rheology; Γ is the Gamma function; In Δt n During the time period, the viscoplastic strain increment of the fractional Bingham body is expressed as: In Δt n During the time period, the viscoplastic strain increment of the variable parameter fractional Bingham body is expressed as: Where: t n for a certain moment; = Δt n The viscoplastic strain increment within the time period; F is the yield function; F0 is the yield function at the initial moment; η2 is the viscosity coefficient that characterizes steady-state rheology and accelerated rheology; γ2 is the order that characterizes steady-state rheology and accelerated rheology; k is a non-negative integer variable; m is the yield parameter; Γ is the Gamma function; {σ ij } n t n The total stress at the moment; α2 is the acceleration parameter; t s To accelerate the time when rheology occurs; Deformation increment {ΔU} within Δtn period n and tn +1 The deformation value at the moment {U} n+1 The calculation formula is: {ΔU}n={K}- 1 ({ΔR}n+{ΔRve}n+{ΔRvp}n) {U} n+1 ={U} n +{ΔU} n Where: {K} is the overall stiffness matrix; {ΔR ve } n = Δt n Viscoelastic strain increment within a period The corresponding equivalent node load increment; {ΔR vp } n is the viscoplastic strain increment during the Δtn period The corresponding equivalent nodal load increment; {ΔR} n is the external load increment within the period of Δtn; {U} n is the deformation value at time tn; Δt n The stress increment {Δσ ij } n and t n+1 Moment stress {σ ij } n+1 The calculation formula is: {s} ij } n+1 ={σ ij } n +{Ds ij } n Where: is the elastic strain increment; {D} is the elasticity matrix; {σ ij } n t n The total stress at time.

8. A fractional-order numerical analysis method for deformation behavior of a high arch dam according to claim 7, characterized in that: Fractional Bingham body and variable parameter fractional Bingham body viscoplastic strain increment expression The calculation formula is: Where: F is the yield function; {σ ij } n t n The total stress at the moment; α2 is the acceleration parameter; I1 is the first invariant of the stress tensor; J2 is the second invariant of the deviatoric stress tensor; and is a constant matrix.

9. A fractional-order numerical analysis module for deformation behavior of high arch dams, characterized in that: A method for fractional-order numerical analysis of deformation behavior of a high arch dam according to any one of claims 1 to 8 is applied, comprising: The fractional-order characterization unit is designed based on a parallel structure and includes a decaying rheological characterization subunit, a steady-state rheological characterization subunit, and an accelerating rheological characterization subunit; The model building unit is based on the parallel structure design and includes a dam body fractional-order rheological mechanics element model subunit and a dam foundation fractional-order rheological mechanics element model subunit; The incremental calculation unit is designed based on a series-parallel structure and includes a viscoelastic strain incremental calculation subunit, a viscoplastic strain incremental calculation subunit, a deformation incremental calculation subunit and a stress incremental calculation subunit; The visual display unit outputs results including but not limited to instantaneous deformation, time-dependent deformation, stress and strain, which are presented to operators in the form of cloud maps, contour maps, distribution maps and process lines.

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