Three-dimensional random field simulation method, system, device and storage medium for large reservoir bank slope rock and soil parameters based on domain independence

Abstract

The present invention discloses a method, system, device, and storage medium for simulating three-dimensional random fields of rock and soil parameters of large-scale reservoir bank slopes based on domain independence, and belongs to the technical field of reservoir bank slope risk analysis. The method includes constructing a three-dimensional finite element model of a target reservoir bank slope; obtaining probability information of the three-dimensional random field of the rock and soil parameters of the target reservoir bank slope; constructing a regular three-dimensional random field domain of the target reservoir bank slope, and dividing the regular three-dimensional random field domain into multiple regular three-dimensional random field subdomains; constructing a generalized stiffness matrix, and calculating the eigenvalues ​​and eigenfunctions of the three-dimensional random field based on the generalized stiffness matrix; obtaining the unit midpoints of the three-dimensional finite element model of the target reservoir bank slope, and combining the eigenvalues ​​and eigenfunctions of the three-dimensional random field to simulate and generate a three-dimensional random field of the rock and soil parameters of the target reservoir bank slope. The present invention can simulate large-scale and irregular three-dimensional random fields of rock and soil parameters of reservoir bank slopes, which is conducive to exploring the influence of spatial variability of rock and soil parameters on the stability of reservoir bank slopes.

Description

Technical Field

[0001] The present invention belongs to the technical field of reservoir bank slope risk analysis, and specifically relates to a three-dimensional random field simulation method, system, device and storage medium for large reservoir bank slope rock and soil parameters based on domain independence. Background Art

[0002] Landslides on reservoir bank slopes pose a significant threat to human life and property. Therefore, reliability analysis and risk assessment of reservoir bank slopes are crucial for water conservancy and hydropower projects. However, natural rock and soil exhibit significant spatial variations under environmental and geological influences, known as spatial variability. Numerous studies have shown that this spatial variability significantly influences the failure modes and landslide consequences of reservoir bank slopes.

[0003] Random field theory is often used to describe the spatial variability of geotechnical masses. It assumes that geotechnical parameters are both spatially correlated and similar. The definition of a random field typically includes a marginal distribution function and an autocorrelation function. The key to implementing a random field lies in converting the infinite-dimensional autocorrelation function into a finite-dimensional autocorrelation coefficient matrix to meet the practical needs of water conservancy and hydropower projects. Commonly used random field discretization methods include point series expansion methods. Among these series expansion methods, the Karhunen-Loève series expansion method (KL expansion method) has broad application prospects due to its biorthogonal properties, which allows it to encapsulate three-dimensional random field information into deterministic characteristic pairs.

[0004] However, the Karhunen-Loève series expansion method requires the calculation of a six-dimensional second-kind Fredholm integral equation involving the autocorrelation function of a three-dimensional random field. As the scale of the reservoir bank slope increases, the computational cost and memory requirements of the second-kind Fredholm integral equation increase dramatically. Furthermore, the irregular morphology of the reservoir bank slope makes traditional techniques quite cumbersome when dealing with three-dimensional random fields in irregular domains. These challenges limit the application of the Karhunen-Loève series expansion method to the three-dimensional random fields of geotechnical parameters in large-scale and irregular reservoir bank slopes, yet the realization of three-dimensional random fields is crucial for the design, construction, and maintenance of reservoir bank slopes.

[0005] Therefore, it is urgent to develop a simulation method for the three-dimensional random field of rock and soil parameters in large reservoir bank slopes in water conservancy and hydropower projects to solve the important problems currently faced. Summary of the Invention

[0006] The purpose of the present invention is to overcome the shortcomings of the existing technology and provide a three-dimensional random field simulation method, system, device and storage medium for rock and soil parameters of large-scale reservoir bank slopes based on domain independence. The method can effectively simulate the three-dimensional random field of rock and soil parameters in large-scale and irregular reservoir bank slopes, which helps to deeply explore the impact of spatial variability of rock and soil parameters on the stability of reservoir bank slopes.

[0007] The present invention provides the following technical solutions:

[0008] In a first aspect, a method for simulating three-dimensional random field parameters of rock and soil mass of a large reservoir bank slope based on domain independence is provided, comprising: constructing a three-dimensional finite element model of a target reservoir bank slope based on pre-acquired three-dimensional information based on the target reservoir bank slope;

[0009] Obtain the probability information of the three-dimensional random field of the rock and soil parameters of the target reservoir bank slope;

[0010] Based on the three-dimensional finite element model, a regular three-dimensional random field of the target reservoir bank slope is constructed, and the regular three-dimensional random field is divided into a plurality of regular three-dimensional random field subdomains;

[0011] According to the probability information of the three-dimensional random field of the rock and soil mass parameters of the target reservoir bank slope and the regular three-dimensional random field subdomain, a generalized stiffness matrix is ​​constructed, and the eigenvalues ​​and eigenfunctions of the three-dimensional random field are calculated according to the generalized stiffness matrix;

[0012] The unit midpoints of the three-dimensional finite element model of the target reservoir bank slope are obtained, and the three-dimensional random field of the rock and soil parameters of the target reservoir bank slope is simulated and generated by combining the eigenvalues ​​and eigenfunctions of the three-dimensional random field.

[0013] As an optional technical solution of the present invention, the probability information of the three-dimensional random field of the rock and soil parameters of the target reservoir bank slope includes the mean function , standard deviation function , autocorrelation function and probability distribution types; wherein the probability distribution types include lognormal distribution, extreme value type I distribution, and Weibull distribution.

[0014] As an optional technical solution of the present invention, the three-dimensional finite element model is used to construct a regular three-dimensional random field of the target reservoir bank slope, including: identifying the outermost boundary of the target reservoir bank slope, the outermost boundary including the minimum value in the x direction and maximum value , the minimum value in the y direction and maximum value and the minimum value in the z direction and maximum value ;

[0015] A regular three-dimensional random field of the target reservoir bank slope is constructed based on the outermost boundary of the target reservoir bank slope. , expressed as:

[0016] Ω = [ x min , x max ] ⊗ [ y min , y max ] ⊗ [ z min , z max ] ;

[0017] in, Represents the tensor product symbol.

[0018] As an optional technical solution of the present invention, the step of dividing the regular three-dimensional random field into a plurality of regular three-dimensional random field sub-fields comprises: dividing the regular three-dimensional random field into a plurality of regular three-dimensional random field sub-fields; Divide into multiple non-overlapping regular three-dimensional random field subdomains , expressed as;

[0019] Ω ( k ) = [ x min ( k ) , x max ( k ) ] ⊗ [ y min ( k ) , y max ( k ) ] ⊗ [ z min ( k ) , z max ( k ) ] ;

[0020] Where k represents the kth regular three-dimensional random field subdomain , k = 1, 2, ..., K, K represents a regular three-dimensional random field subdomain The total number of and Represent regular three-dimensional random field subdomains The minimum and maximum values ​​in the x direction, and Represent regular three-dimensional random field subdomains The minimum and maximum values ​​in the y direction, and Represent regular three-dimensional random field subdomains The minimum and maximum values ​​in the z direction.

[0021] As an optional technical solution of the present invention, the generalized stiffness matrix is ​​constructed based on the probability information of the three-dimensional random field of the rock and soil parameters of the target bank slope and the regular three-dimensional random field subdomain, including: calculating the elements of the local generalized stiffness matrix , expressed as:

[0022] ;

[0023] Where s represents the kth regular three-dimensional random field subdomain The sequence number of the basis function, s = 1,2,..., , Representing a regular three-dimensional random field subdomain The total number of basis functions in , t represents the lth regular three-dimensional random field subdomain The serial number of the basis function in t = 1,2,..., , Representing a regular three-dimensional random field subdomain The total number of basis functions in , Representing a regular three-dimensional random field subdomain The sth basis function in , Representing a regular three-dimensional random field subdomain The tth basis function in , represents the autocorrelation function;

[0024] The regular three-dimensional random field subdomain The sth basis function in Expressed as:

[0025] g s ( k ) ( x ) = [ ( 2 q x ( k ) + 1 2 a x ( k ) ) 1 / 2 J q x ( k ) ( x − T x ( k ) a x ( k ) ) ] [ ( 2 q y ( k ) + 1 2 a y ( k ) ) 1 / 2 J q y ( k ) ( y − T y ( k ) a y ( k ) ) ] [ ( 2 q z ( k ) + 1 2 a z ( k ) ) 1 / 2 J q z ( k ) ( z − T z ( k ) a z ( k ) ) ] ;

[0026] in, 、 and Represent regular three-dimensional random field subdomains One-dimensional Legendre orthogonal polynomials in the x-, y-, and z-directions, 、 and Represent regular three-dimensional random field subdomains The degree of the one-dimensional Legendre orthogonal polynomial in the x-, y-, and z-directions, 、 and Represent regular three-dimensional random field subdomains The scaling factors in the x, y, and z directions, 、 and Represent regular three-dimensional random field subdomains The translation coefficients in the x, y, and z directions, where x, y, and z represent regular three-dimensional random field subdomains, respectively. The coordinate values ​​of any point x in the x-direction, y-direction and z-direction, 、 and Represent regular three-dimensional random field subdomains Any other point x ’ Coordinate values ​​in the x-, y-, and z-directions;

[0027] Based on the elements of the local generalized stiffness matrix Get the local generalized stiffness matrix , expressed as:

[0028] A ( kl ) = [ A 11 ( kl ) A 12 ( kl ) ⋯ A 1 N ( l ) ( kl ) A 21 ( kl ) A 22 ( kl ) ⋯ A 2 N ( l ) ( kl ) ⋮ ⋮ ⋱ ⋮ A N ( k ) 1 ( kl ) A N ( k ) 2 ( kl ) ⋯ A N ( k ) N ( l ) ( kl ) ] ;

[0029] Based on the local generalized stiffness matrix Get the generalized stiffness matrix , expressed as:

[0030] A = [ A ( 11 ) A ( 12 ) ⋯ A ( 1 K ) A ( 21 ) A ( 22 ) ⋯ A ( 2 K ) ⋮ ⋮ ⋱ ⋮ A ( K 1 ) A ( K 2 ) ⋯ A ( KK ) ] .

[0031] As an optional technical solution of the present invention, the calculation of the eigenvalues ​​and eigenfunctions of the three-dimensional random field according to the generalized stiffness matrix includes: solving the generalized stiffness matrix The eigenvalue of and eigenvectors , d j = [ d j ( 1 ) , d j ( 1 ) , ⋯ , d j ( k ) , ⋯ , d j ( K ) ] T , where T represents the matrix transpose, represents the kth eigenvector subvector, j represents the jth eigenvector, j = 1, 2, ..., N, N represents a regular three-dimensional random field The total number of basis functions in is expressed as:

[0032] ;

[0033] Where k represents the kth regular three-dimensional random field subdomain , k = 1, 2, ..., K, K represents a regular three-dimensional random field subdomain the total number of;

[0034] The generalized stiffness matrix The eigenvalue of and eigenvectors According to the characteristic value Arrange them in descending order, and the eigenvalues ​​after sorting are counted as , the eigenvector is counted as ;

[0035] The generalized stiffness matrix The first M eigenvalues ​​after arrangement As the eigenvalues ​​of a three-dimensional random field , i=1, 2, ..., M;

[0036] The characteristic function of the three-dimensional random field Expressed as:

[0037] ;

[0038] in, Represents the sorted feature vector Subvector of The sth element in represents the indicator function, when hour, = 1, otherwise, = 0.

[0039] As an optional technical solution of the present invention, the three-dimensional random field is combined with the characteristic value and characteristic function of the three-dimensional random field to simulate and generate the three-dimensional random field of the rock and soil parameters of the target reservoir bank slope, including: generating a standard normal distribution three-dimensional random field based on the unit midpoint of the three-dimensional finite element model of the target reservoir bank slope , expressed as:

[0040] ;

[0041] in, represents the midpoint of the element of the three-dimensional finite element model of the target reservoir bank slope, e=1, 2, ..., E, E represents the total number of elements, represents a random sample from a standard normal distribution;

[0042] The standard normal distribution three-dimensional random field Mapping into three-dimensional random field of rock and soil parameters , expressed as:

[0043] H ( x mid e ) = F − 1 [ Φ ( H D ( x mid e ) ) ] ;

[0044] in, F − 1 [ · ] Represents the inverse cumulative distribution function, which is based on the mean function , standard deviation function and the probability distribution type is obtained, Represents the cumulative distribution function of the standard normal distribution.

[0045] In a second aspect, a three-dimensional random field simulation system for rock and soil parameters of a large-scale reservoir bank slope based on domain independence is provided, comprising: a model construction module for constructing a three-dimensional finite element model of a target reservoir bank slope based on pre-acquired three-dimensional information based on the target reservoir bank slope;

[0046] An information acquisition module is used to obtain the probability information of the three-dimensional random field of the rock and soil parameters of the target reservoir bank slope;

[0047] A random field construction module is used to construct a regular three-dimensional random field of the target reservoir bank slope based on the three-dimensional finite element model, and divide the regular three-dimensional random field into a plurality of regular three-dimensional random field subdomains;

[0048] A characteristic calculation module is used to construct a generalized stiffness matrix based on the probability information of the three-dimensional random field of the rock and soil parameters of the target bank slope and the regular three-dimensional random field subdomain, and calculate the eigenvalues ​​and characteristic functions of the three-dimensional random field based on the generalized stiffness matrix;

[0049] The simulation generation module is used to obtain the unit midpoints of the three-dimensional finite element model of the target reservoir bank slope, and simulate and generate the three-dimensional random field of the rock and soil parameters of the target reservoir bank slope by combining the eigenvalues ​​and characteristic functions of the three-dimensional random field.

[0050] In a third aspect, a three-dimensional random field simulation device for large-scale reservoir bank slope rock and soil parameters based on domain independence is provided, including a processor and a storage medium;

[0051] The storage medium is used to store instructions;

[0052] The processor is used to operate according to the instructions to execute the steps of the three-dimensional random field simulation method for large-scale reservoir bank slope rock and soil parameters based on domain independence in the first aspect.

[0053] In a fourth aspect, a computer-readable storage medium is provided, on which a computer program is stored, characterized in that when the program is executed by a processor, the steps of the three-dimensional random field simulation method of large reservoir bank slope rock and soil parameters based on domain independence as described in the first aspect are implemented.

[0054] Compared with the prior art, the present invention has the following beneficial effects:

[0055] The domain-independence-based three-dimensional random field simulation method for rock and soil parameters of large-scale reservoir bank slopes provided by the present invention utilizes the principle of random field independence of the Karhunen-Loève series expansion method to convert irregular reservoir bank slopes into regular three-dimensional random fields, and further divide them into regular three-dimensional random field subdomains. At the same time, the regular three-dimensional random field subdomains are used to realize the gradual assembly of generalized stiffness matrices, thereby effectively simulating the three-dimensional random fields of rock and soil parameters in large-scale and irregular reservoir bank slopes, which helps to deeply explore the influence of spatial variability of rock and soil parameters on the stability of reservoir bank slopes, and has strong practical application value in water conservancy and hydropower projects. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 Flowchart of a three-dimensional random field simulation method for large-scale reservoir bank slope rock and soil parameters based on domain independence in an embodiment of the present invention;

[0057] Figure 2 1. It is a model and unit division diagram of the reservoir bank slope in an embodiment of the present invention;

[0058] Figure 3 is a regular three-dimensional random field map of the outermost boundary of the reservoir bank slope in an embodiment of the present invention;

[0059] Figure 4 is a division diagram of a regular three-dimensional random field subdomain in an embodiment of the present invention;

[0060] Figure 5is a graph of eigenvalues ​​of items 1-100 of a three-dimensional random field in an embodiment of the present invention;

[0061] Figure 6 is a characteristic function graph of items 1-3 of the three-dimensional random field in an embodiment of the present invention;

[0062] Figure 7 is a characteristic function graph of items 4-6 of the three-dimensional random field in an embodiment of the present invention;

[0063] Figure 8 3 are sample graphs of three-dimensional random fields of cohesion in an embodiment of the present invention. DETAILED DESCRIPTION

[0064] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention.

[0065] Example 1

[0066] This embodiment provides a three-dimensional random field simulation method for large-scale reservoir bank slope rock and soil parameters based on domain independence. Figure 1 As shown, the method includes the following steps:

[0067] Step 1: Construct a three-dimensional finite element model of the target reservoir bank slope based on the pre-acquired three-dimensional information of the target reservoir bank slope.

[0068] In this embodiment, the three-dimensional finite element model of the target reservoir bank slope is modeled using ABAQUS. Figure 2 As shown in the figure, the lengths of the three-dimensional finite element model in the x-, y-, and z-directions are 50 m, 30 m, and 150 m, respectively, and the total volume of the model is 150,000 m 3 , divided into 261,030 units

[0069] Step 2: Obtain the probability information of the three-dimensional random field of the rock and soil parameters of the target reservoir bank slope.

[0070] Specifically, the probability information of the three-dimensional random field of the target reservoir bank slope rock and soil parameters includes the mean function , standard deviation function , autocorrelation function and probability distribution types; wherein the probability distribution types include lognormal distribution, extreme value type I distribution, and Weibull distribution.

[0071] In this embodiment, the rock and soil parameter is cohesion, and the probability information of the three-dimensional random field of cohesion includes the mean function =20kPa, standard deviation function =3kPa.

[0072] Autocorrelation function Using a separable square exponential form, it is expressed as:

[0073] ρ ( x , x ′ ) = exp [ − π ( x − x ′ δ x ) 2 ] exp [ − π ( y − y ′ δ y ) 2 ] exp [ − π ( z − z ′ δ z ) 2 ] ;

[0074] Where x, y, and z represent the coordinate values ​​of any point x in the three-dimensional random field of cohesion in the x, y, and z directions, respectively. 、 and represents any other point x in the three-dimensional random field of cohesion ’ The coordinate values ​​in the x, y, and z directions, , and Represent the fluctuation range in the x-direction, y-direction and z-direction respectively.

[0075] The probability distribution type adopts lognormal distribution.

[0076] Step 3: Based on the three-dimensional finite element model, a regular three-dimensional random field of the target reservoir bank slope is constructed, and the regular three-dimensional random field is divided into multiple regular three-dimensional random field subdomains.

[0077] 3.1. Identify the outermost boundary of the target reservoir bank slope.

[0078] In this embodiment, the outermost boundary of the target reservoir bank slope includes the minimum value in the x direction. =0m and maximum =50m, minimum value in the y direction =0m and maximum =30m and the minimum value in the z direction =0m and maximum =150m.

[0079] 3.2, such as Figure 3 As shown, a regular three-dimensional random field of the target reservoir bank slope is constructed based on the outermost boundary of the target reservoir bank slope. , expressed as:

[0080] Ω = [ x min , x max ] ⊗ [ y min , y max ] ⊗ [ z min , z max ] ;

[0081] in, Represents the tensor product symbol.

[0082] 3.3. The regular three-dimensional random field Divide into multiple non-overlapping regular three-dimensional random field subdomains , expressed as;

[0083] Ω ( k ) = [ x min ( k ) , x max ( k ) ] ⊗ [ y min ( k ) , y max ( k ) ] ⊗ [ z min ( k ) , z max ( k ) ] ;

[0084] Where k represents the kth regular three-dimensional random field subdomain , k = 1, 2, ..., K, K represents a regular three-dimensional random field subdomain The total number of and Represent regular three-dimensional random field subdomains The minimum and maximum values ​​in the x direction, and Represent regular three-dimensional random field subdomains The minimum and maximum values ​​in the y direction, and Represent regular three-dimensional random field subdomains The minimum and maximum values ​​in the z direction.

[0085] In this embodiment, if Figure 4 As shown, the x-direction, y-direction, and z-direction are equally divided into 4, 4, and 4 parts, respectively, for a total of 64 regular three-dimensional random field subdomains.

[0086] Step 4: Based on the probability information of the three-dimensional random field of the target bank slope rock and soil parameters and the regular three-dimensional random field subdomain, a generalized stiffness matrix is ​​constructed, and the eigenvalues ​​and eigenfunctions of the three-dimensional random field are calculated based on the generalized stiffness matrix.

[0087] 4.1. Calculating the elements of the local generalized stiffness matrix , expressed as:

[0088] ;

[0089] Where s represents the kth regular three-dimensional random field subdomain The sequence number of the basis function, s = 1,2,..., , Representing a regular three-dimensional random field subdomain The total number of basis functions in , t represents the lth regular three-dimensional random field subdomain The serial number of the basis function in t = 1,2,..., , Representing a regular three-dimensional random field subdomain The total number of basis functions in , Representing a regular three-dimensional random field subdomain The sth basis function in , Representing a regular three-dimensional random field subdomain The tth basis function in , represents the autocorrelation function.

[0090] The regular three-dimensional random field subdomain The sth basis function in Expressed as:

[0091] g s ( k ) ( x ) = [ ( 2 q x ( k ) + 1 2 a x ( k ) ) 1 / 2 J q x ( k ) ( x − T x ( k ) a x ( k ) ) ] [ ( 2 q y ( k ) + 1 2 a y ( k ) ) 1 / 2 J q y ( k ) ( y − T y ( k ) a y ( k ) ) ] [ ( 2 q z ( k ) + 1 2 a z ( k ) ) 1 / 2 J q z ( k ) ( z − T z ( k ) a z ( k ) ) ] ;

[0092] in, 、 and Represent regular three-dimensional random field subdomains One-dimensional Legendre orthogonal polynomials in the x-, y-, and z-directions, 、 and Represent regular three-dimensional random field subdomains The degree of the one-dimensional Legendre orthogonal polynomial in the x-, y-, and z-directions, 、 and Represent regular three-dimensional random field subdomains The scaling factors in the x, y, and z directions, 、 and Represent regular three-dimensional random field subdomains The translation coefficients in the x, y, and z directions, where x, y, and z represent regular three-dimensional random field subdomains, respectively. The coordinate values ​​of any point x in the x-direction, y-direction and z-direction, 、 and Represent regular three-dimensional random field subdomains Any other point x ’ Coordinate values ​​in the x-, y-, and z-directions.

[0093] 4.2. Elements based on the local generalized stiffness matrix Get the local generalized stiffness matrix , expressed as:

[0094] A ( kl ) = [ A 11 ( kl ) A 12 ( kl ) ⋯ A 1 N ( l ) ( kl ) A 21 ( kl ) A 22 ( kl ) ⋯ A 2 N ( l ) ( kl ) ⋮ ⋮ ⋱ ⋮ A N ( k ) 1 ( kl ) A N ( k ) 2 ( kl ) ⋯ A N ( k ) N ( l ) ( kl ) ] .

[0095] 4.3 Based on the local generalized stiffness matrix Get the generalized stiffness matrix , expressed as:

[0096] A = [ A ( 11 ) A ( 12 ) ⋯ A ( 1 K ) A ( 21 ) A ( 22 ) ⋯ A ( 2 K ) ⋮ ⋮ ⋱ ⋮ A ( K 1 ) A ( K 2 ) ⋯ A ( KK ) ] .

[0097] In this embodiment, the maximum degree of the one-dimensional Legendre orthogonal polynomials in all regular three-dimensional random field subdomains is set to 8, then the regular three-dimensional random field domain The total number of basis functions in =165, generalized stiffness matrix The dimensions are 10560×10560.

[0098] 4.4. Calculate the eigenvalues ​​and eigenfunctions of three-dimensional random fields.

[0099] (1) Solve the generalized stiffness matrix The eigenvalue of and eigenvectors , d j = [ d j ( 1 ) , d j ( 1 ) , ⋯ , d j ( k ) , ⋯ , d j ( K ) ] T , where T represents the matrix transpose, represents the kth eigenvector subvector, j represents the jth eigenvector, j = 1, 2, ..., N, N represents a regular three-dimensional random field The total number of basis functions in is expressed as:

[0100] ;

[0101] Where k represents the kth regular three-dimensional random field subdomain , k = 1, 2, ..., K, K represents a regular three-dimensional random field subdomain The total number of .

[0102] (2) The generalized stiffness matrix The eigenvalue of and eigenvectors According to the characteristic value Arrange them in descending order, and the eigenvalues ​​after sorting are counted as , the eigenvector is counted as .

[0103] (3) The generalized stiffness matrix The first M eigenvalues ​​after arrangement As the eigenvalues ​​of a three-dimensional random field , i = 1, 2, ..., M;

[0104] The characteristic function of the three-dimensional random field Expressed as:

[0105] ;

[0106] in, Represents the sorted feature vector Subvector of The sth element in represents the indicator function, when hour, = 1, otherwise, = 0.

[0107] In this embodiment, the three-dimensional random field The number of basis functions in N = 10560. Figure 5 As shown, the number of expanded items M is set to 100. This embodiment provides the calculation result diagram of the characteristic functions of items 1 to 6, as shown in FIG. Figure 6-7 shown.

[0108] Step 5: Obtain the unit midpoints of the three-dimensional finite element model of the target reservoir bank slope, and simulate and generate the three-dimensional random field of the rock and soil parameters of the target reservoir bank slope by combining the eigenvalues ​​and characteristic functions of the three-dimensional random field.

[0109] 5.1. Obtain the unit midpoints of the three-dimensional finite element model of the target reservoir bank slope.

[0110] 5.2. Generate a standard normal distribution three-dimensional random field based on the unit midpoint of the three-dimensional finite element model of the target reservoir bank slope , expressed as:

[0111] ;

[0112] in, represents the midpoint of the element of the three-dimensional finite element model of the target reservoir bank slope, e=1, 2, ..., E, E represents the total number of elements, Represents a random sample from the standard normal distribution.

[0113] In this embodiment, the number of units E = 261030.

[0114] 5.3. The standard normal distribution three-dimensional random field Mapping into three-dimensional random field of rock and soil parameters , expressed as:

[0115] H ( x mid e ) = F − 1 [ Φ ( H D ( x mid e ) ) ] ;

[0116] in, F − 1 [ · ] Represents the inverse cumulative distribution function, which is based on the mean function , standard deviation function and the probability distribution type is obtained, Represents the cumulative distribution function of the standard normal distribution.

[0117] like Figure 8As shown in Figure 1, this embodiment provides three samples of a three-dimensional cohesion random field. In the generated three-dimensional cohesion random field, high-strength and low-strength soils are alternately distributed. This feature truly reflects the complex spatial distribution of rock and soil parameters in the reservoir bank slope.

[0118] Example 2

[0119] This embodiment provides a three-dimensional random field simulation system for large-scale reservoir bank slope rock and soil parameters based on domain independence, including:

[0120] The model building module is used to build a three-dimensional finite element model of the target library bank slope based on the pre-acquired three-dimensional information of the target library bank slope.

[0121] The information acquisition module is used to obtain the probability information of the three-dimensional random field of the rock and soil parameters of the target reservoir bank slope.

[0122] The random field construction module is used to construct a regular three-dimensional random field of the target reservoir bank slope based on the three-dimensional finite element model, and divide the regular three-dimensional random field into multiple regular three-dimensional random field subdomains.

[0123] The characteristic calculation module is used to construct a generalized stiffness matrix based on the probability information of the three-dimensional random field of the rock and soil parameters of the target bank slope and the regular three-dimensional random field subdomain, and calculate the eigenvalues ​​and characteristic functions of the three-dimensional random field based on the generalized stiffness matrix.

[0124] The simulation generation module is used to obtain the unit midpoints of the three-dimensional finite element model of the target reservoir bank slope, and simulate and generate the three-dimensional random field of the rock and soil parameters of the target reservoir bank slope by combining the eigenvalues ​​and characteristic functions of the three-dimensional random field.

[0125] Example 3

[0126] This embodiment provides a three-dimensional random field simulation device for large-scale reservoir bank slope rock and soil parameters based on domain independence, including a processor and a storage medium; the storage medium is used to store instructions; the processor is used to operate according to the instructions to execute the steps of the three-dimensional random field simulation method for large-scale reservoir bank slope rock and soil parameters based on domain independence described in Example 1.

[0127] Example 4

[0128] This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the steps of the three-dimensional random field simulation method for large-scale reservoir bank slope rock and soil parameters based on domain independence described in Example 1 are implemented.

[0129] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0130] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0131] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0132] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The steps for the function specified in one or more boxes.

[0133] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A three-dimensional random field simulation method for large-scale reservoir bank slope rock and soil parameters based on domain independence, characterized by: include: Constructing a three-dimensional finite element model of the target reservoir bank slope based on pre-acquired three-dimensional information of the target reservoir bank slope; Obtain the probability information of the three-dimensional random field of the rock and soil parameters of the target reservoir bank slope; Based on the three-dimensional finite element model, a regular three-dimensional random field of the target reservoir bank slope is constructed, and the regular three-dimensional random field is divided into a plurality of regular three-dimensional random field subdomains; According to the probability information of the three-dimensional random field of the rock and soil mass parameters of the target reservoir bank slope and the regular three-dimensional random field subdomain, a generalized stiffness matrix is ​​constructed, and the eigenvalues ​​and eigenfunctions of the three-dimensional random field are calculated according to the generalized stiffness matrix; Obtaining the unit midpoints of the three-dimensional finite element model of the target reservoir bank slope, and simulating and generating a three-dimensional random field of rock and soil parameters of the target reservoir bank slope by combining the eigenvalues ​​and eigenfunctions of the three-dimensional random field; The generalized stiffness matrix is ​​constructed based on the probability information of the three-dimensional random field of the rock and soil parameters of the target reservoir bank slope and the regular three-dimensional random field subdomain, including: Compute elements of the local generalized stiffness matrix , expressed as: ； Where s represents the kth regular three-dimensional random field subdomain The sequence number of the basis function, s = 1,2,..., , Representing a regular three-dimensional random field subdomain The total number of basis functions in , t represents the lth regular three-dimensional random field subdomain The serial number of the basis function in t = 1,2,..., , Representing a regular three-dimensional random field subdomain The total number of basis functions in , Representing a regular three-dimensional random field subdomain The sth basis function in , Representing a regular three-dimensional random field subdomain The tth basis function in , represents the autocorrelation function; The regular three-dimensional random field subdomain The sth basis function in Expressed as: ； in, 、 and Represent regular three-dimensional random field subdomains One-dimensional Legendre orthogonal polynomials in the x-, y-, and z-directions, 、 and Represent regular three-dimensional random field subdomains The degree of the one-dimensional Legendre orthogonal polynomial in the x-, y-, and z-directions, 、 and Represent regular three-dimensional random field subdomains The scaling factors in the x, y, and z directions, 、 and Represent regular three-dimensional random field subdomains The translation coefficients in the x, y, and z directions, where x, y, and z represent regular three-dimensional random field subdomains, respectively. The coordinate values ​​of any point p in the x, y and z directions, 、 and Represent regular three-dimensional random field subdomains Any other point p ’ Coordinate values ​​in the x-, y-, and z-directions; Based on the elements of the local generalized stiffness matrix Get the local generalized stiffness matrix , expressed as: ； Based on the local generalized stiffness matrix Get the generalized stiffness matrix , expressed as: 。 2. The three-dimensional random field simulation method for large-scale reservoir bank slope rock and soil parameters based on domain independence according to claim 1 is characterized in that: The probability information of the three-dimensional random field of the rock and soil parameters of the target reservoir bank slope includes the mean function , standard deviation function , autocorrelation function and probability distribution types; wherein the probability distribution types include lognormal distribution, extreme value type I distribution, and Weibull distribution.

3. The three-dimensional random field simulation method for large-scale reservoir bank slope rock and soil parameters based on domain independence according to claim 1 is characterized in that: The method of constructing a regular three-dimensional random field of the target reservoir bank slope based on the three-dimensional finite element model includes: Identify the outermost boundary of the target reservoir bank slope, which includes the minimum value in the x direction and maximum value , the minimum value in the y direction and maximum value and the minimum value in the z direction and maximum value ; A regular three-dimensional random field of the target reservoir bank slope is constructed based on the outermost boundary of the target reservoir bank slope. , expressed as: ； in, Represents the tensor product symbol.

4. The three-dimensional random field simulation method for large-scale reservoir bank slope rock and soil parameters based on domain independence according to claim 3 is characterized in that: The step of dividing the regular three-dimensional random field into a plurality of regular three-dimensional random field sub-fields comprises: The regular three-dimensional random field Divide into multiple non-overlapping regular three-dimensional random field subdomains , expressed as; ； Where k represents the kth regular three-dimensional random field subdomain , k = 1, 2, ..., K, K represents a regular three-dimensional random field subdomain The total number of and Represent regular three-dimensional random field subdomains The minimum and maximum values ​​in the x direction, and Represent regular three-dimensional random field subdomains The minimum and maximum values ​​in the y direction, and Represent regular three-dimensional random field subdomains The minimum and maximum values ​​in the z direction.

5. The three-dimensional random field simulation method for large-scale reservoir bank slope rock and soil parameters based on domain independence according to claim 1 is characterized in that: The calculating of the eigenvalues ​​and eigenfunctions of the three-dimensional random field according to the generalized stiffness matrix includes: Solve the generalized stiffness matrix The eigenvalue of and eigenvectors , , where T represents the matrix transpose, represents the kth eigenvector subvector, j represents the jth eigenvector, j = 1, 2, ..., N, N represents a regular three-dimensional random field The total number of basis functions in is expressed as: ； Where k represents the kth regular three-dimensional random field subdomain , k = 1, 2, ..., K, K represents a regular three-dimensional random field subdomain the total number of; The generalized stiffness matrix The eigenvalue of and eigenvectors According to the characteristic value Arrange them in descending order, and the eigenvalues ​​after sorting are counted as , the eigenvector is counted as ; The generalized stiffness matrix The first M eigenvalues ​​after arrangement As the eigenvalues ​​of a three-dimensional random field , i = 1,2, ..., M; The characteristic function of the three-dimensional random field Expressed as: ； in, Represents the sorted feature vector Subvector of The sth element in represents the indicator function, when hour, = 1, otherwise, = 0.

6. The three-dimensional random field simulation method for large-scale reservoir bank slope rock and soil parameters based on domain independence according to claim 5 is characterized in that: The method of combining the eigenvalues ​​and eigenfunctions of the three-dimensional random field to simulate and generate the three-dimensional random field of the rock and soil parameters of the target reservoir bank slope includes: A standard normal distribution three-dimensional random field is generated based on the unit midpoint of the three-dimensional finite element model of the target reservoir bank slope. , expressed as: ； in, represents the midpoint of the element of the three-dimensional finite element model of the target reservoir bank slope, e=1, 2, ..., E, E represents the total number of elements, represents a random sample from a standard normal distribution; The standard normal distribution three-dimensional random field Mapping into three-dimensional random field of rock and soil parameters , expressed as: ； in, Represents the inverse cumulative distribution function, which is based on the mean function , standard deviation function and the probability distribution type is obtained, Represents the cumulative distribution function of the standard normal distribution.

7. A three-dimensional random field simulation system for large-scale reservoir bank slope rock and soil parameters based on domain independence, characterized by: The method for simulating three-dimensional random fields of rock and soil parameters of large-scale reservoir bank slopes based on domain independence as described in any one of claims 1 to 6 comprises: A model building module is used to build a three-dimensional finite element model of the target bank slope based on the pre-acquired three-dimensional information of the target bank slope; An information acquisition module is used to obtain the probability information of the three-dimensional random field of the rock and soil parameters of the target reservoir bank slope; A random field construction module is used to construct a regular three-dimensional random field of the target reservoir bank slope based on the three-dimensional finite element model, and divide the regular three-dimensional random field into a plurality of regular three-dimensional random field subdomains; A characteristic calculation module is used to construct a generalized stiffness matrix based on the probability information of the three-dimensional random field of the rock and soil parameters of the target bank slope and the regular three-dimensional random field subdomain, and calculate the eigenvalues ​​and characteristic functions of the three-dimensional random field based on the generalized stiffness matrix; The simulation generation module is used to obtain the unit midpoints of the three-dimensional finite element model of the target reservoir bank slope, and simulate and generate the three-dimensional random field of the rock and soil parameters of the target reservoir bank slope by combining the eigenvalues ​​and characteristic functions of the three-dimensional random field.

8. A three-dimensional random field simulation device for large-scale reservoir bank slope rock and soil parameters based on domain independence, characterized in that: including processors and storage media; The storage medium is used to store instructions; The processor is used to operate according to the instructions to execute the steps of the three-dimensional random field simulation method of large reservoir bank slope rock and soil parameters based on domain independence as described in any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the three-dimensional random field simulation method of large-scale reservoir bank slope rock and soil parameters based on domain independence as described in any one of claims 1 to 6 are implemented.

Images