Method for simulating three-dimensional spatial variability of earth-rock dam foundation based on discontinuous galerkin method

Abstract

The application relates to the field of water conservancy and hydropower engineering, and particularly discloses a soil-rock dam foundation three-dimensional space variability simulation method based on an intermittent Galerkin method, which comprises the following steps: establishing a geometric model of a soil-rock dam foundation; determining probability distribution information of a three-dimensional random field of soil parameters; dividing the three-dimensional random field domain of the soil parameters into three-dimensional random field subdomains; creating base functions in the three-dimensional random field subdomains and assembling a generalized stiffness matrix; calculating eigenvalues and eigenfunctions of an autocorrelation function; extracting standard normal distribution samples and simulating the three-dimensional random field of the soil parameters. The three-dimensional random field domain is divided into a plurality of subdomains, and independent base functions are constructed in each subdomain, so that the independence between the base functions in the subdomains is ensured. The numerical instability of high-order polynomials is eliminated, the assembly format of the generalized stiffness matrix is simplified, and the three-dimensional random field with large scale and high resolution can be generated.

Description

Technical Field

[0001] This application relates to the field of water conservancy and hydropower engineering, and in particular to a method for simulating the three-dimensional spatial variability of earth-rock dam foundations based on the discontinuous Galerkin method. Background Technology

[0002] Soil and rock materials undergo complex geological processes such as weathering, transportation, deposition, tectonics, and magmatism, exhibiting significant spatial variability. This spatial variability profoundly affects the seepage and settlement performance of earth-rock dams, thereby impacting the accuracy of reliability analysis and risk assessment results. To deeply investigate the influence of soil spatial variability on earth-rock dams, one of the most effective methods is to model it as a three-dimensional random field, thus more accurately describing its spatial distribution and variation patterns.

[0003] The core objective of realizing a random field in the foundation of an earth-rock dam is to construct a three-dimensional random field model that meets accuracy requirements with the fewest possible random variables. This process must ensure the accuracy of the random field while reducing the number of random variables to improve computational efficiency and practicality. Currently, there are many random field discretization methods, with point discretization, average discretization, and series expansion being the three most commonly used categories. Among them, the series expansion method has attracted much attention because it is not limited by the number of random field domain elements and can flexibly handle large-scale, high-resolution three-dimensional random field problems. This application focuses on the application of the Karhunen-Loève series expansion method in hydraulic engineering, which requires the fewest random variables to realize the random field with respect to global variance error.

[0004] The implementation of the Karhunen-Loève series expansion method requires solving the second kind of Fredholm integral equation, where the kernel is the autocorrelation function of the three-dimensional random field. However, as the scale of the three-dimensional random field in the foundation of an earth-rock dam increases, the computational cost and memory requirements for solving this integral equation also increase dramatically, making traditional finite element Galerkin techniques and polynomial Galerkin techniques inadequate. Therefore, these traditional techniques mainly focus on one- and two-dimensional random field problems in hydraulic engineering, while solving large-scale three-dimensional random field problems remains challenging. Therefore, efficient and accurate simulation of the three-dimensional spatial variability of earth-rock dam foundations provides more reliable theoretical support and technical assurance for the design, construction, and maintenance of earth-rock dams, and this is one of the important problems that urgently need to be solved in hydraulic engineering. Summary of the Invention

[0005] To address the challenge of large-scale, high-resolution three-dimensional random field simulation in water conservancy and hydropower projects, this application provides a method for simulating the three-dimensional spatial variability of earth-rock dam foundations based on the discontinuous Galerkin method.

[0006] The method for simulating the three-dimensional spatial variability of earth-rock dam foundation based on the discontinuous Galerkin method provided in this application adopts the following technical solution:

[0007] A method for simulating the three-dimensional spatial variability of earth-rock dam foundations based on the discontinuous Galerkin method includes the following steps:

[0008] Establish a geometric model of the earth-rock dam foundation;

[0009] Determine the probability distribution information of the three-dimensional random field of soil parameters;

[0010] The three-dimensional random field domain for dividing soil parameters is a three-dimensional random field subdomain;

[0011] Create basis functions in a three-dimensional random field subdomain and assemble the generalized stiffness matrix;

[0012] Calculate the eigenvalues ​​and eigenfunctions of the autocorrelation function;

[0013] We extract standard normal distribution samples and simulate a three-dimensional random field of soil parameters.

[0014] Furthermore, the geometric model of the earth-rock dam foundation includes the length, width, and height of the earth-rock dam foundation.

[0015] Furthermore, the probability distribution information of the three-dimensional random field of soil parameters includes the probability distribution type, mean function μ(x), standard deviation function σ(x), and autocorrelation function ρ(x,x'), wherein the probability distribution type includes normal distribution and log-normal distribution.

[0016] Furthermore, the specific method for dividing the three-dimensional random field domain of soil parameters into three-dimensional random field subdomains is as follows:

[0017] First, the expression for calculating the three-dimensional random field Ω is:

[0018]

[0019] Where, x min and x max Let y be the minimum and maximum values ​​in the x-direction of a three-dimensional random field Ω. min and y max Let z be the minimum and maximum values ​​in the y-direction of a three-dimensional random field Ω. min and z max Let be the minimum and maximum values ​​in the z-direction of the three-dimensional random field Ω. The symbol for tensor product;

[0020] Then, the three-dimensional random field domain Ω is divided into non-overlapping three-dimensional random field subdomains Ω. (k) :

[0021]

[0022] Where k is the three-dimensional random field subdomain Ω (k)The sequence number, k = 1, 2, ..., K; K is the subdomain Ω of the three-dimensional random field. (k) Quantity;

[0023] Finally, the three-dimensional random field subdomain Ω (k) The calculation expression is:

[0024]

[0025] Where, x min (k) and x max (k) For a three-dimensional random field subdomain Ω (k) Minimum and maximum values ​​in the x-direction, y min (k) and y max (k) For a three-dimensional random field subdomain Ω (k) Minimum and maximum values ​​in the y-direction, z min (k) and z max (k) For a three-dimensional random field subdomain Ω (k) The minimum and maximum values ​​in the z-direction.

[0026] Furthermore, the calculation expression for the basis functions in the three-dimensional random field subdomain is as follows:

[0027]

[0028] in, and These are three-dimensional random field subdomains Ω (k) The one-dimensional Legendre orthogonal polynomial in the x, y, and z directions, q x (k) q y (k) and q z (k) These are three-dimensional random field subdomains Ω (k) The degree of the one-dimensional Legendre orthogonal polynomial in the x, y, and z directions; a x (k) a y (k) and a z (k) These are three-dimensional random field subdomains Ω (k) Scaling factors in the x, y, and z directions, T x (k) T y (k) and T z (k) These are three-dimensional random field subdomains Ω(k) The translation coefficients in the x, y, and z directions, where s is the subdomain of the three-dimensional random field Ω. (k) The basis function indices are s = 1, 2, ..., N. (k) N (k) For a three-dimensional random field subdomain Ω (k) The number of basis functions in the dataset.

[0029] Furthermore, the specific method for assembling the generalized stiffness matrix is ​​as follows:

[0030] First, assemble the three-dimensional random field subdomain Ω. (k) The three-dimensional auxiliary integrator vector B s (k) Its calculation expression is:

[0031]

[0032] Among them, B xs (k) B ys (k) and B zs (k) These are three-dimensional random field subdomains Ω (k) The one-dimensional auxiliary integrator vectors in the x, y, and z directions are calculated as follows:

[0033]

[0034]

[0035] in, and These are three-dimensional random field subdomains Ω (k) Gauss-Legendre integration node vectors in the x, y, and z directions. and These are three-dimensional random field subdomains Ω (k) Gauss-Legendre integral weight diagonal matrices in the x, y, and z directions;

[0036] Secondly, assemble the three-dimensional random field subdomain Ω (k) The three-dimensional auxiliary integral submatrix B (k) ,

[0037] Then, assemble the three-dimensional auxiliary integral matrix B in the three-dimensional random field Ω, B = diag([B (1) B (2) …B (k) …B (K)]), where diag(·) represents converting a vector into a diagonal matrix;

[0038] Next, assemble the autocorrelation matrix R at the integration points, R = [R (kl) ], where R (kl) The autocorrelation submatrix of the integration nodes is obtained by transforming the three-dimensional random field subdomain Ω. (k) The three-dimensional integral nodes are substituted into the autocorrelation function to calculate the three-dimensional random field subdomain Ω. (k) 3D integral nodes The three-dimensional random field subdomain Ω (k) One-dimensional integration nodes in the x, y, and z directions and Obtained through tensor calculations. and The calculation expression is as follows:

[0039]

[0040] Finally, assemble the generalized stiffness matrix A, A = B. T RB, where the superscript "T" represents matrix transpose.

[0041] Furthermore, the specific method for calculating the eigenvalues ​​and eigenfunctions of the autocorrelation function is as follows:

[0042] First, establish the standard eigenvalue problem AD = DΛ, where Λ is the diagonal matrix of eigenvalues, Λ = diag([λ1λ2…λ)). N ]), D is the eigenvector matrix, D = [D1] (k) D2 (k) ,…,D (k) ,…,D (K) ], D (k) For a three-dimensional random field subdomain Ω (k) The eigenvector submatrix in the matrix, where N is the number of basis functions in the three-dimensional random field Ω, is calculated as follows:

[0043]

[0044] Then, the eigenvalue diagonal matrix Λ and the eigenvector matrix are solved using MATLAB's "eig" function, where the first M diagonal elements of the eigenvalue diagonal matrix Λ are the eigenvalues ​​λ of the autocorrelation function. j j is the index of the expanded term, j = 1, 2, ..., M; M is the number of expanded terms;

[0045] Finally, the characteristic function φ j The expression for calculating (x) is:

[0046]

[0047] Among them, D sj (k) For a three-dimensional random field subdomain Ω (k) The eigenvector submatrix D in (k) The element in the s-th row and j-th column, I (k) For a three-dimensional random field subdomain Ω (k) The indicator function, when x∈Ω (k) I (k) =1, otherwise, I (k) =0.

[0048] Furthermore, the calculation expression for the three-dimensional random field of soil parameters is as follows:

[0049]

[0050] Among them, F -1 (·) is the inverse function of the cumulative distribution, Φ(·) is the cumulative distribution function of the standard normal distribution, and ξ j It is a random sample that follows a standard normal distribution.

[0051] This application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements a method for simulating the three-dimensional spatial variability of earth-rock dam foundation based on the discontinuous Galerkin method.

[0052] This application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements a method for simulating the three-dimensional spatial variability of earth-rock dam foundations based on the discontinuous Galerkin method.

[0053] In summary, this application includes the following beneficial technical effects:

[0054] This application provides a method for simulating the three-dimensional spatial variability of earth-rock dam foundations based on discontinuous Galerkin techniques, aiming to solve the challenge of large-scale, high-resolution three-dimensional random field simulation in water conservancy and hydropower engineering. This technique divides the three-dimensional random field into several subdomains and constructs independent basis functions within each subdomain, ensuring the independence of basis functions between subdomains. This avoids directly applying high-order polynomials in large-scale, high-resolution three-dimensional random fields, thus eliminating the risk of numerical instability. Simultaneously, the independence of basis functions simplifies the assembly process of the generalized stiffness matrix, improving assembly convenience. After obtaining eigenvalues ​​and eigenfunctions, this technique can rapidly generate large-scale, high-resolution three-dimensional random fields, applicable to any type of autocorrelation function. The advantages of this technique contribute to a deeper exploration of the impact of the three-dimensional spatial variability of soil parameters on earth-rock dams and risk assessment, further demonstrating its practical value in water conservancy and hydropower engineering. Attached Figure Description

[0055] Figure 1 This is a flowchart of a method for simulating the three-dimensional spatial variability of earth-rock dam foundations based on discontinuous Galerkin technology, provided in an embodiment of this application.

[0056] Figure 2 This is a model diagram of an earth-rock dam in an embodiment of this application;

[0057] Figure 3 This is a three-dimensional random field partitioning diagram in the embodiments of this application;

[0058] Figure 4 These are the first 500 feature values ​​in the embodiments of this application;

[0059] Figure 5 These are the slice diagrams of the 1st, 10th, 20th, 30th, 40th and 50th feature functions in the embodiments of this application;

[0060] Figure 6 These are sample diagrams of six three-dimensional random fields of elastic modulus in the embodiments of this application. Detailed Implementation

[0061] The following is in conjunction with the appendix Figure 1-6 This application will be described in further detail.

[0062] This application discloses a method for simulating the three-dimensional spatial variability of earth-rock dam foundations based on the discontinuous Galerkin method. (Refer to...) Figure 1 The method for simulating the three-dimensional spatial variability of earth-rock dam foundations based on the discontinuous Galerkin method includes the following steps:

[0063] S100. Establish the geometric model of the earth-rock dam foundation;

[0064] In this embodiment of the application, a model diagram of an earth-rock dam is shown below. Figure 2 The earth-rock dam foundation is 220m long, 200m wide, and 60m high, with a volume of 2,640,000 m³. 3 The foundation of the earth-rock dam is a three-dimensional random field, with the x, y, and z directions divided into 110, 100, and 60 parts respectively, totaling 660,000 elements.

[0065] S200. Determine the probability distribution information of the three-dimensional random field of soil parameters;

[0066] In this embodiment, the soil parameter is the elastic modulus, and the probability distribution information of the three-dimensional random field of the elastic modulus includes the probability distribution type, the mean function μ(x), the standard deviation function σ(x), and the autocorrelation function ρ(x,x'); wherein, the probability distribution type is a log-normal distribution, the mean function μ(x) = 40 MPa, the standard deviation function σ(x) = 15 MPa, and the expression of the autocorrelation function ρ(x,x') is:

[0067]

[0068] Where, δ x =80m, δ y =60m and δ z =10m represents the fluctuation range in the x, y, and z directions, respectively.

[0069] S300, the three-dimensional random field domain for dividing soil parameters is a three-dimensional random field subdomain;

[0070] The calculation expressions for S310 and the three-dimensional random field Ω are as follows:

[0071]

[0072] Where, x min and x max Let y be the minimum and maximum values ​​in the x-direction of a three-dimensional random field Ω. min and y max Let z be the minimum and maximum values ​​in the y-direction of a three-dimensional random field Ω. min and z max Let be the minimum and maximum values ​​in the z-direction of the three-dimensional random field Ω. The symbol for tensor product;

[0073] S320. Divide the three-dimensional random field Ω into non-overlapping three-dimensional random field subfields Ω (k) :

[0074]

[0075] Where k is the three-dimensional random field subdomain Ω (k) The sequence number, k = 1, 2, ..., K; K is the subdomain Ω of the three-dimensional random field. (k) Quantity;

[0076] S330, Three-dimensional random field subdomain Ω (k) The calculation expression is:

[0077]

[0078] Where, x min (k) and x max (k) For a three-dimensional random field subdomain Ω (k) Minimum and maximum values ​​in the x-direction, y min (k) and y max (k) For a three-dimensional random field subdomain Ω (k) Minimum and maximum values ​​in the y-direction, zmin (k) and z max (k) For a three-dimensional random field subdomain Ω (k) The minimum and maximum values ​​in the z-direction.

[0079] In this embodiment of the application, the three-dimensional random field partitioning is described in [reference needed]. Figure 3 The x, y, and z directions are divided into 6, 6, and 6 parts respectively, totaling 216 three-dimensional random field subdomains.

[0080] S400: Create basis functions in a three-dimensional random field subdomain and assemble the generalized stiffness matrix;

[0081] S410, The calculation expression for the basis functions in the three-dimensional random field subdomain is as follows:

[0082]

[0083] in, and These are three-dimensional random field subdomains Ω (k) The one-dimensional Legendre orthogonal polynomial in the x, y, and z directions, q x (k) q y (k) and q z (k) These are three-dimensional random field subdomains Ω (k) The degree of the one-dimensional Legendre orthogonal polynomial in the x, y, and z directions; a x (k) a y (k) and a z (k) These are three-dimensional random field subdomains Ω (k) Scaling factors in the x, y, and z directions, T x (k) T y (k) and T z (k) These are three-dimensional random field subdomains Ω (k) The translation coefficients in the x, y, and z directions, where s is the subdomain of the three-dimensional random field Ω. (k) The basis function indices are s = 1, 2, ..., N. (k) N (k) For a three-dimensional random field subdomain Ω (k) The number of basis functions in the dataset.

[0084] S420, The specific method for assembling the generalized stiffness matrix is ​​as follows:

[0085] S421, Assemble a three-dimensional random field subdomain Ω (k) The three-dimensional auxiliary integrator vector B s (k) Its calculation expression is:

[0086]

[0087] Among them, B xs (k) B ys (k) and B zs (k) These are three-dimensional random field subdomains Ω (k) The one-dimensional auxiliary integrator vectors in the x, y, and z directions are calculated as follows:

[0088]

[0089] in, and These are three-dimensional random field subdomains Ω (k) Gauss-Legendre integration node vectors in the x, y, and z directions. and These are three-dimensional random field subdomains Ω (k) Gauss-Legendre integral weight diagonal matrices in the x, y, and z directions;

[0090] S422, Assemble a three-dimensional random field subdomain Ω (k) The three-dimensional auxiliary integral submatrix B (k) ,

[0091] S423. Assemble the three-dimensional auxiliary integral matrix B in the three-dimensional random field Ω, B = diag([B (1) B (2) …B (k) …B (K) ]), where diag(·) represents converting a vector into a diagonal matrix;

[0092] S424. Assemble the autocorrelation matrix R at the integration points, R = [R (kl) ], where R (kl) The autocorrelation submatrix of the integration nodes is obtained by transforming the three-dimensional random field subdomain Ω. (k) The three-dimensional integral nodes are substituted into the autocorrelation function to calculate the three-dimensional random field subdomain Ω. (k) 3D integral nodes The three-dimensional random field subdomain Ω (k) One-dimensional integration nodes in the x, y, and z directions and Obtained through tensor calculations. and The calculation expression is as follows:

[0093]

[0094] S425. Assemble the generalized stiffness matrix A, A = B T RB, where the superscript "T" represents matrix transpose.

[0095] In this embodiment of the application, the highest degree of the three-dimensional Legendre orthogonal polynomials in all three-dimensional random field subdomains is set to 4. Therefore, the three-dimensional random field subdomain Ω... (k) The number of basis functions N (k) =35, and the dimensions of the assembled generalized stiffness matrix A are 7560×7560.

[0096] S500, Calculate the eigenvalues ​​and eigenfunctions of the autocorrelation function;

[0097] S510. Establish the standard eigenvalue problem AD = DΛ, where Λ is the diagonal matrix of eigenvalues, Λ = diag([λ1λ2…λ)). N ]), D is the eigenvector matrix, D = [D1] (k) D2 (k) ,…,D (k) ,…,D (K) ], D (k) For a three-dimensional random field subdomain Ω (k) The eigenvector submatrix in the matrix, where N is the number of basis functions in the three-dimensional random field Ω, is calculated as follows:

[0098]

[0099] S520. Use MATLAB's "eig" function to solve for the eigenvalue diagonal matrix Λ and the eigenvector matrix, where the first M diagonal elements of the eigenvalue diagonal matrix Λ are the eigenvalues ​​λ of the autocorrelation function. j j is the index of the expanded term, j = 1, 2, ..., M; M is the number of expanded terms;

[0100] S530, Characteristic Function φ j The expression for calculating (x) is:

[0101]

[0102] Among them, D sj (k) For a three-dimensional random field subdomain Ω (k) The eigenvector submatrix D in (k)The element in the s-th row and j-th column, I (k) For a three-dimensional random field subdomain Ω (k) The indicator function; when x∈Ω (k) I (k) =1, otherwise, I (k) =0.

[0103] In this embodiment, the number of basis functions in the three-dimensional random field Ω is N = 7560, and the calculation results of the first 500 eigenvalues ​​are shown below. Figure 4 The calculation results for the 1st, 10th, 20th, 30th, 40th, and 50th characteristic functions are shown in [the table]. Figure 5 As the number of expanded terms increases, the eigenvalues ​​gradually decrease, and the volatility of the eigenfunction gradually increases.

[0104] S600: Extract standard normal distribution samples and simulate a three-dimensional random field of soil parameters;

[0105] The calculation expression for the three-dimensional random field of soil parameters is as follows:

[0106]

[0107] Among them, F -1 (·) is the inverse function of the cumulative distribution, Φ(·) is the cumulative distribution function of the standard normal distribution, and ξ j It is a random sample that follows a standard normal distribution.

[0108] In this embodiment of the application, the six elastic modulus three-dimensional random field samples are shown below. Figure 6 .

[0109] Combination Figure 6 It can be seen that the variability of the three-dimensional random field of elastic modulus is more significant in the vertical direction than in the horizontal direction. For such a large-scale, high-resolution three-dimensional random field problem, this application divides the three-dimensional random field domain into several subdomains and constructs independent basis functions in each subdomain. This allows for accurate simulation of the three-dimensional random field using only fourth-order polynomials, eliminating the risk of numerical instability associated with traditional methods employing higher-order polynomials. Simultaneously, the independence of the basis functions simplifies the assembly process of the generalized stiffness matrix, improving assembly convenience. After obtaining the eigenvalues ​​and eigenfunctions, this technique can rapidly generate large-scale, high-resolution three-dimensional random fields, applicable to arbitrarily complex types of autocorrelation functions. This invention is crucial for in-depth research into the impact of the three-dimensional spatial variability of soil parameters on earth-rock dams and risk assessment, and has significant practical value in water conservancy and hydropower engineering.

[0110] This application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the above-mentioned method for simulating the three-dimensional spatial variability of earth-rock dam foundation based on the discontinuous Galerkin method.

[0111] This application also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the above-described method for simulating the three-dimensional spatial variability of earth-rock dam foundations based on the discontinuous Galerkin method.

[0112] The above are all preferred embodiments of this application, and are not intended to limit the scope of protection of this application. Therefore, all equivalent changes made in accordance with the structure, shape and principle of this application should be covered within the scope of protection of this application.

Claims

1. A method for simulating three-dimensional spatial variability of a dam foundation of an earth-rockfill dam based on an interrupted Galerkin method, characterized in that: The method comprises the following steps: establishing a geometric model of the earth-rock dam foundation; determining probability distribution information of a three-dimensional random field of soil parameters; dividing the three-dimensional random field domain of the soil parameters into three-dimensional random field subdomains; creating a base function in the three-dimensional random field subdomain and assembling a generalized stiffness matrix; calculating eigenvalues and eigenfunctions of the autocorrelation function; extracting a standard normal distribution sample and simulating the three-dimensional random field of the soil parameters; wherein the specific method of assembling the generalized stiffness matrix is: First, the three-dimensional auxiliary integration sub-vector in the three-dimensional random field sub-domain Ω (k) B s (k) with the computational expression​ where is the tensor product symbol, B xs (k) , B ys (k) and B zs (k) are one-dimensional auxiliary integration subvectors in the directions (k) x , y and z , respectively, with the computational expressions​ in, u x (k)* , u y (k)* and u z (k)* These are three-dimensional random field subdomains Ω (k) middle x direction, y direction and z Gauss-Legendre integration node vectors in the direction, w x (k)* , w y (k)* and w z (k)* These are three-dimensional random field subdomains Ω (k) middle x direction, y direction and z The Gauss-Legendre integral weight diagonal matrix in the direction, , and These are three-dimensional random field subdomains Ω (k) middle x direction, y direction and z One-dimensional Legendre orthogonal polynomial in the direction, q x (k) , q y (k) and q z (k) These are three-dimensional random field subdomains Ω (k) middle x direction, y direction and z Degree of a one-dimensional Legendre orthogonal polynomial in a direction; a x (k) , a y (k) and a z (k) These are three-dimensional random field subdomains Ω (k) middle x direction, y direction and z Scaling factor in direction, s For a three-dimensional random field subdomain Ω (k) the number of basis functions in Ω s = 1, 2,..., N (k) ; N (k) the number of basis functions in Ω (k) the number of basis functions in Ω Second, the three-dimensional auxiliary integral sub-matrix in the three-dimensional random field sub-domain Ω (k) is assembled B (k) , B (k) = [ B 1 (k) , B 2 (k) ,…, B s (k) ,…, ]; Then, assemble the three-dimensional auxiliary integration matrix in the three-dimensional random field domain Ω B , B = diag([ B (1) B (2) … B (k) … B (K) ]), wherein diag(·) represents converting a vector into a diagonal matrix; Next, the autocorrelation matrix of the integration points is assembled. R , R = [ R (kl) ],in R (kl) The autocorrelation submatrix of the integration nodes is obtained by transforming the three-dimensional random field subdomain Ω. (k) The three-dimensional integral nodes are substituted into the autocorrelation function to calculate the three-dimensional random field subdomain Ω. (k) 3D integral nodes x 3D (k)* The three-dimensional random field subdomain Ω (k) middle x direction, y direction and z One-dimensional integral nodes in the direction x 1D (k)* , y 1D (k)* and z 1D (k)* Obtained through tensor calculations. x 1D (k)* , y 1D (k)* and z 1D (k)* The calculation expression is as follows: wherein T x (k) , T y (k) and T z (k) are translation coefficients in the direction of the (k) x direction, y direction and z direction, respectively, of a three-dimensional random field subdomain​ Finally, the assembled generalized stiffness matrix A , A = B T RB where the superscript "T" represents matrix transposition.

2. The method according to claim 1, wherein the method is characterized by: The geometric model of the earth-rock dam foundation comprises length, width and height of the earth-rock dam foundation.

3. The method according to claim 1, wherein the method is characterized by: The probability distribution information of the three-dimensional random field of the soil body parameter includes a probability distribution type, a mean function μ ( x ), a standard deviation function σ ( x ), and an autocorrelation function ρ ( x , x' ). The probability distribution type includes a normal distribution and a lognormal distribution.

4. The method according to claim 1, wherein the method is characterized by: The specific method of dividing the three-dimensional random field domain of the soil parameters into three-dimensional random field subdomains is: First, the calculation expression of the three-dimensional random field domain Ω is: wherein x min and x max are the minimum and maximum values of the gradient of the function f in the direction x , y min and y max are the minimum and maximum values of the gradient of the function f in the direction y , z min and z max are the minimum and maximum values of the gradient of the function f in the direction z , is the tensor product symbol; Then, the three-dimensional random field domain Ω is divided into three-dimensional random field subdomains Ω (k) : in, k For a three-dimensional random field subdomain Ω (k) The serial number, k = 1, 2,…, K ; K For a three-dimensional random field subdomain Ω (k) Quantity; Finally, the calculation expression of the three-dimensional random field sub-domain Ω (k) is: in, x min (k) and x max (k) For a three-dimensional random field subdomain Ω (k) middle x Minimum and maximum values ​​in the direction, y min (k) and y max (k) For a three-dimensional random field subdomain Ω (k) middle y Minimum and maximum values ​​in the direction, z min (k) and z max (k) For a three-dimensional random field subdomain Ω (k) middle z Minimum and maximum values ​​of the direction.

5. The method according to claim 1, wherein the method is characterized by: The calculation expression of the base function in the three-dimensional random field subdomain is: 。 6. The method according to claim 1, wherein the method is characterized by: The specific method of calculating the eigenvalues and eigenfunctions of the autocorrelation function is: First, establish the standard eigenvalue problem. AD = DΛ ,in Λ It is an eigenvalue diagonal matrix. Λ = diag([ λ 1 λ 2… λ N ]), D The eigenvector matrix, D = [ D 1 (k) , D 2 (k) ,…, D (k) ,…, D (K) ], D (k) For a three-dimensional random field subdomain Ω (k) The eigenvector submatrix in N Let Ω be the number of basis functions in the three-dimensional random field Ω, and its calculation expression is: Then, the eigenvalue diagonal matrix and the eigenvector matrix are solved by using the "eig" function of MATLAB, wherein the first p diagonal elements of the eigenvalue diagonal matrix Λ are the eigenvalues of the autocorrelation function Λ M λ j , j is the serial number of the expansion term, j = 1, 2, …, M ; M is the number of expansion terms;​​ Finally, the characteristic function j ( x ) is given by the expression wherein D sj (k) is the eigenvector matrix of the second order tensor (k) in the three-dimensional random field subdomain Ω D (k) is the element of the first s row and the second j column of the second order tensor I (k) is the indicator function of the three-dimensional random field subdomain Ω (k) when x ∈ Ω (k) , I (k) = 1, otherwise, I (k) = 0.

7. The method according to claim 1, wherein the method is characterized by: The calculation expression of the three-dimensional random field of the soil parameters is: wherein F -1 (·) is the inverse cumulative distribution function, Φ (·) is the cumulative distribution function of the standard normal distribution, ξ j is a random sample from the standard normal distribution.

8. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that: The processor executes the program to realize the three-dimensional spatial variability simulation method of the earth-rock dam foundation based on the discontinuous Galerkin method according to any one of claims 1-7.

9. A computer readable storage medium having stored thereon a computer program, characterized in that: The computer program is executed by the processor to realize the three-dimensional spatial variability simulation method of the earth-rock dam foundation based on the discontinuous Galerkin method according to any one of claims 1-7.

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