Method for realizing continuous-discontinuous soil-rock mixture and spatial variability thereof based on multiple random fields

Abstract

The application discloses a method for realizing continuous-discontinuous soil-rock mixture and spatial variability thereof based on multiple random fields, which comprises the following steps of defining the spatial range of the soil-rock mixture, dividing the soil-rock mixture into continuous and discontinuous regions, carrying out grid division, and inserting joints in the discontinuous region; setting a mathematical characteristic quantity of a random field, constructing a covariance matrix and decomposing the covariance matrix to obtain random field values of each grid cell; determining the number of rock cells according to the rock content, sorting the random field values in ascending order, distributing the random field values to the grid cells, and distinguishing the grid cells on both sides of the joint to divide the joint into three categories; respectively counting the two and three random field parameter characteristics of the rock and soil, and generating corresponding random field values; and taking the average value of the grid cells on both sides of the joint cell as the random field value of the joint cell to realize the spatial variability of the joint cell. The application can efficiently generate a soil-rock mixture model conforming to the actual situation and considers the spatial variability of each material.

Description

Technical Field

[0001] The present invention belongs to the technical field of geological structure geometric modeling research, and specifically relates to a method for realizing continuous-discontinuous soil-rock mixture and its spatial variability based on multiple random fields. Background Art

[0002] Soil-rock mixtures, composed of complex structures such as irregular rocks, soil, and soil-rock interfaces, are widespread in both natural and engineering environments and significantly impact the safety and feasibility of many engineering activities. For example, in mining and tunneling, accurately modeling the behavior of soil-rock mixtures is crucial for engineering design and disaster prevention. With the rapid development of computer simulation technology, numerical simulation has gradually become an effective alternative to traditional engineering testing. However, efficiently simulating the spatial distribution and variability of soil-rock mixtures remains a challenge in current engineering research.

[0003] Traditional modeling methods typically divide soil and rock masses into discrete volume units proportionally. This process requires independent modeling for each soil-rock mixture, including volume fraction, rock mass shape, and soil structure. In large-scale engineering projects, this approach is not only labor-intensive but also prone to errors. For example, the model in the paper "Chen Dongfang. Risk Analysis of Layered Rock Cavern Instability Based on Random Finite Differences [D]. Northeastern University, 2016" requires the design of nearly 100 independent models for different combinations of volume fractions and rock mass inclinations, which undoubtedly increases the difficulty and workload of modeling.

[0004] In addition, traditional modeling methods have poor flexibility and adaptability. Many studies simplify the shape of rock blocks during the modeling process. For example, in the paper "J. Li, B. Wang, P. Pan, H. Chen, D. Wang, P. Chen, Failure analysis of soil-rock mixture slopes using coupled MPM-DEM method, Computers and Geotechnics 169 (2024) 106226.", all rock blocks are simplified to standard circles, which is quite different from the shape of rock blocks in actual engineering. In order to be closer to the actual shape, it may be necessary to increase the number of edges of each block, resulting in the division of more computational units, increasing the complexity and time of the calculation, as described in "L. Zhao, N. Qiao, D. Huang, S. Zuo, Z. Zhang, Numerical investigation of the failure mechanisms of soil–rock mixture slopes by material point method, Computers and Geotechnics 150 (2022) 104898." Although this refined modeling can improve accuracy, its computational efficiency is low and it is difficult to meet the needs of large-scale simulation.

[0005] Furthermore, many current studies of soil-rock mixtures assume that the soil and rock are homogeneous materials, ignoring the spatial variability of these materials. In reality, the physical properties of soil-rock mixtures, such as strength, stiffness, and permeability, exhibit spatial variability, a characteristic that significantly influences their mechanical behavior. Ignoring this variability can lead to significant deviations between simulation results and actual conditions, compromising the accuracy and reliability of engineering decisions. Summary of the Invention

[0006] The purpose of the present invention is to provide a method for realizing continuous-discontinuous soil-rock mixture and its spatial variability based on multiple random fields, so as to solve the problems of repeated modeling, poor flexibility and adaptability of modeling methods in the numerical simulation of soil-rock mixture in the existing technology; at the same time, the spatial variability of soil-rock mixture is taken into account to make it closer to reality; in addition, the division of continuous-discontinuous areas provides reference significance for various numerical simulation methods, such as finite element, finite difference, discontinuous analysis, etc.

[0007] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0008] The method for realizing continuous-discontinuous soil-rock mixture and its spatial variability based on multiple random fields includes the following steps:

[0009] S1: Define the spatial extent of the soil-rock mixture, divide it into continuous and discontinuous areas, and perform grid division based on the scale characteristics of the geological body, and insert joints into the grid of the discontinuous area;

[0010] S2: Generate the first random field to achieve soil-rock two-phase and soil-rock-joint three-phase distribution, including:

[0011] S2.1: Set the mathematical characteristics and autocorrelation function of the first random field, construct the covariance matrix, select the appropriate method for decomposition, and obtain the random field value of each grid cell;

[0012] S2.2: Determine the number of rock units based on rock content, sort the random field values ​​in ascending order, and record the index of the grid unit corresponding to each value in ascending order;

[0013] S2.3: Set the grid cells at both ends of the random field corresponding to the maximum and minimum values ​​to rock until the number of rock cells is reached. Then, determine the types of grid cells on both sides of the joint and classify the joints into three types: rock-rock, soil-soil, and rock-soil.

[0014] S3: Generate the second and third random fields to achieve the spatial variability of soil, rock and joints, including:

[0015] S3.1: Statistically analyze the second and third random field parameter characteristics and autocorrelation function types of the corresponding rocks and soils, and select the appropriate decomposition method based on the size of the covariance to generate rock unit random fields and joint unit random fields to realize the spatial variability of soil and rock materials;

[0016] S3.2: Set the joint random field value to the average of the random field values ​​of the grid cells on both sides to achieve spatial variability of the joints and obtain the final soil-rock mixture model.

[0017] Further optimization is performed in step S1. The spatial extent of the model is defined, i.e., the boundary of the soil-rock mixture is selected. This is usually determined based on the characteristics of the actual geological region to ensure that the size and shape of the model can cover the study area. The selection of the grid size needs to be determined based on the scale characteristics of the geological body being studied. Larger geological bodies may require larger grid units, and vice versa. This is because the grid size affects the number of grids within the spatial range, and an excessive number leads to lower efficiency. The key parts of the model are divided into discontinuous areas, i.e., joint units are inserted between the grid units in this area, because the discontinuous model can better reflect the mechanical response of the key parts. The grid unit set Mesh = {Mesh(i)|1≤i≤m}, Joint = {Joint(j)|1≤j≤n} is obtained, where m and n represent the number of grids and the number of joints, respectively.

[0018] Further optimization, in step S2.1, the main steps of generating the first random field are as follows:

[0019] S2.1.1: Set the mathematical characteristics of the first random field, including mean μ, coefficient of variation Cov, and horizontal correlation length θ x Vertical correlation length θ y ; The autocorrelation function ρ(Δx,Δy) is usually specified as exponential (Exp) or square exponential (SExp), and the corresponding formulas for the two types are shown in (2.1) and (2.2) respectively:

[0020]

[0021] Among them, the coefficient of variation Cov is the ratio of the random field mean μ to the mean square error σ, that is, μ / σ; the correlation length θ x and θ y They represent the scope of strong correlation of the random field in the horizontal and vertical directions, respectively, which affects the size distribution of rock blocks in the subsequent soil-rock mixture; Δx and Δy represent the horizontal and vertical distances between any two points in the model space, and in the model they are set as the distance between any two grid cells.

[0022] S2.1.2: Construct the covariance matrix Cor_M: Each element Cor_M(i,j) inside the matrix is ​​the result of substituting the mesh units Mesh(i) and Mesh(j) in the model into the autocorrelation function formula (2.1) or (2.2), 1≤i,j≤m, as shown in formulas (2.3) and (2.4) respectively:

[0023]

[0024]

[0025] Among them, x i and x j Respectively represent the horizontal coordinates of the i-th grid cell Mesh(i) and the j-th grid cell Mesh(j), y i and y j They represent the vertical coordinates of the i-th mesh cell Mesh(i) and the j-th mesh cell Mesh(j) respectively.

[0026] S2.1.3: The size of the covariance matrix Cor_M is m*m. When the matrix size is too large, the traditional lower triangular matrix decomposition will be too inefficient. Therefore, it is necessary to select different decomposition methods according to the size of m to obtain the random field value. The classification is as follows:

[0027] When m≤5000, the random field is generated using formula (2.5):

[0028] RF(X)=μ(1+Cov*Lχ)(2.5)

[0029] When m>5000, the random field is approximated by the Karhunen-Loeve (KL) series expansion method, as shown in formula (2.6):

[0030]

[0031] In formula (2.5), L is the lower triangular matrix obtained by decomposing the covariance matrix Cor_M, that is, Cor_M = LL T ,L T is the transposed matrix of L; χ is a normally distributed array with length m, mean 0, and standard deviation 1; in formula (2.6), Q is the truncation term, and the size of Q affects the accuracy of the random field; λ p and φ p (X) is the larger value of the eigenvalues ​​of Cor_M and the corresponding eigenfunction, that is, after all eigenvalues ​​are sorted in descending order, the λ and the corresponding φ(X) with an index greater than Q are ignored; X is the coordinate set of all grid cells in the model, that is, X={X i =(x i ,y i )|1≤i≤m}; RF(X) is the set of random field values ​​generated at each grid cell point, that is, RF(X)={RF(X i )|1≤i≤m}.

[0032] Further optimization, in step S2.2, determining the number of rock units and sorting the random field is divided into two steps:

[0033] S2.2.1: Based on the rock content RBP, 0 ≤ RBP ≤ 100%, determine the number of rock units Rock_num, calculated using formula (2.7):

[0034] Rock_num≈Round(RBP*m)(2.7)

[0035] Among them, Round() is to find the nearest integer of a number, satisfying the rounding principle;

[0036] S2.2.2: Sort the random field values ​​in ascending order using formula (2.8):

[0037] index=Sort(RF(X)) (2.8)

[0038] Where, Sort() is the ascending arrangement of the original array, and the returned index is the index set of the sorted random field, each index sequence index{i'} satisfies 1≤i'≤m, and each index sequence index{i'} corresponds to a grid unit Mesh(index{i'}). The Round() and Sort() have mature algorithms in existing programming software such as Matlab and Python, and will not be expanded.

[0039] Further optimization, in the step S2.3, the soil-rock two-phase classification and joint three-phase classification of the grid unit are realized, including the following steps:

[0040] S2.3.1: This step realizes the soil-rock two-phase classification. After the ascending arrangement of RF(X), the maximum and minimum values are distributed at both ends, so i' is 1 and m respectively, and index{1} and index{m} correspond to the grid unit indexes with the maximum and minimum random field values respectively. First, the grid units with the maximum and minimum random field values are set as rock, and then the grid units with the second maximum and second minimum random field values are set as rock, and so on. This process continues until the number of allocated rock units reaches the pre-set Rock_num.

[0041] This step is summarized as counting the grid indexes corresponding to the random field values at both ends, and sequentially setting them as rock units. According to the sorting rule, it is realized by formula (2.9):

[0042]

[0043] S2.3.2: This step realizes the joint three-phase classification. Since the joint is inserted between two grids, the grid units corresponding to Mesh(index{a}) and Mesh(index{b}) on both sides of each joint unit Joint(j) (1≤j≤n) are counted, and 1≤a,b≤m. The soil-rock types of the two grid units are determined, and then the joint is divided into three types: rock-rock, soil-soil, and rock-soil. The rule is shown in formula (2.10):

[0044]

[0045] Further optimization, in the step S3.1, the random field of the rock unit and the soil unit is generated; the spatial variability distribution of soil and rock is realized, which is divided into the following two steps:

[0046] S3.1.1: The characteristic quantities of the second random field are counted, i.e. the mean value μ of the rock unit properties in the region r , the coefficient of variation Cov r , the correlation length θ rx and θ ry, and specify the type of rock autocorrelation function ρ(Δx,Δy), construct the covariance matrix, and decompose it to obtain the rock unit random field. The calculation formula (3.1) is as follows:

[0047]

[0048] Among them, X r is the location coordinate of the rock mass unit, L r It's X r Substitute ρ(Δx,Δy) to obtain the lower triangular matrix of the covariance matrix decomposition, χ r Is a normally distributed array with length Rock_num, mean 0, and standard deviation 1; rp and φ rp (X r ) is the larger value of the eigenvalues ​​of its covariance matrix and the corresponding characteristic function, that is, after all eigenvalues ​​are arranged in descending order, the index is greater than λ of Q rp and the corresponding φ rp (X r ) is ignored.

[0049] S3.1.2: Statistical characteristic of the third random field, i.e., the mean μ of the soil unit properties in the region s , Coefficient of variation Cov s , correlation length θ sx and θ sy , and specify the type of rock autocorrelation function ρ(Δx,Δy), construct the covariance matrix, and decompose it to obtain the soil unit random field. The calculation formula (3.2) is as follows:

[0050]

[0051] Among them, X s is the position coordinate of the soil unit, L s It's X s Substitute ρ(Δx,Δy) to obtain the lower triangular matrix of the covariance matrix decomposition, χ s is a normally distributed array with a length of m-Rock_num, a mean of 0, and a standard deviation of 1; sp and φ sp (X s ) is the larger value of the eigenvalues ​​of its covariance matrix and the corresponding characteristic function, that is, after all eigenvalues ​​are arranged in descending order, the index is greater than λ of Q sp and the corresponding φ sp (X s ) is ignored.

[0052] Further optimization, in step S3.2, the joint random field value is directly set to the average random field value of the grid units on both sides. This is mainly because the joint is inserted between the grids on both sides and acts as a discontinuous interface. The spatial variability of this interface is mainly affected by the spatial variability of the grids on both sides. There is no need to set a separate random field to achieve the spatial variability of the joint.

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] By introducing a multiple random field approach, the present invention successfully achieves the generation of continuous and discontinuous soil-rock mixtures, taking into account the spatial variation of internal elements. Specifically, the soil and stone are first classified in ascending order through the first random field, and the discontinuous areas are divided into three types: jointed rock-rock, soil-soil, and stone-soil. Then, the second and third random fields simulate the spatial variability of rock and soil, respectively. Finally, the spatial variability of joints is obtained by averaging the spatial variability of adjacent grid cells. This method is different from the traditional soil-rock mixture modeling method, which usually requires separate modeling of soil, stone, and block shapes with different volume fractions, which is labor-intensive and inefficient. The present invention greatly improves the modeling efficiency by introducing multiple random fields. At the same time, this method can more realistically reflect the spatial variability of each part and is more in line with actual conditions. In addition, by classifying continuous and discontinuous areas, this method can better adapt to various numerical simulation technologies and provide a reliable soil-rock mixture generation solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 Flowchart of the method for realizing continuous-discontinuous soil-rock mixture and its spatial variability based on multiple random fields;

[0056] Figure 2 This is a schematic diagram of the spatial modeling scope of Example 1;

[0057] Figure 3 The model of the mesh after segmentation and the inserted joints in Example 1;

[0058] Figure 4 The soil-rock two-phase classification model of Example 1;

[0059] Figure 5 The joint two-phase classification model of Example 1;

[0060] Figure 6 This is the effect diagram of soil and rock spatial variability in Example 1;

[0061] Figure 7 This is the final effect diagram of Example 1;

[0062] Figure 8 This is a real CT scan image;

[0063] Figure 9 This is the final effect diagram of Example 2;

[0064] Figure 10 This is the final effect diagram of Example 3;

[0065] Figure 11 This is a real photo of the rock-soil mixture. DETAILED DESCRIPTION

[0066] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0067] Example 1:

[0068] In this embodiment, for a continuous-discontinuous soil-rock mixture model with a volume fraction of 40% and considering spatial variability, a method for realizing a continuous-discontinuous soil-rock mixture and its spatial variability based on multiple random fields includes the following steps:

[0069] S1: Define the spatial extent of the soil-rock mixture, divide it into continuous and discontinuous areas, and perform grid division based on the scale characteristics of the geological body, and insert joints into the grid of the discontinuous area;

[0070] In this embodiment, a soil-rock mixture slope geometric model is established, and the slope shape and size are as follows: Figure 2 As shown in the figure, the size of the rock blocks inside the slope varies from 0.3m to 10m, so the grid size is set to 0.3m for meshing. The area near the slope sliding surface is set as a discontinuous area, and joints are inserted between adjacent grid cells to facilitate better analysis of slope sliding and rupture in subsequent simulations. The resulting grid cell set Mesh = {Mesh(i)|1≤i≤7422} and the joint cell set Joint = {Joint(j)|1≤j≤5903} are obtained, where 7422 and 5903 represent the number of grids and the number of joints, respectively. The grid and joints are shown as follows: Figure 3 As shown, the white lines are inserted between the grid cells as joints, and the joint insertion area is a discontinuous area; the blue part is a continuous area.

[0071] S2: Generate the first random field to achieve soil-rock two-phase and soil-rock-joint three-phase distribution, including:

[0072] S2.1: Set the mathematical characteristics and autocorrelation function of the first random field, construct the covariance matrix, select the appropriate method for decomposition, and obtain the random field value of each grid cell. The specific steps include the following:

[0073] S2.1.1: The results of the first random field are only used to generate soil-rock mixtures. Changes in the mean and coefficient of variation will not affect the random sorting results. Therefore, these two characteristic quantities can be specified manually. Set the mean μ = 1.0 and the coefficient of variation Cov = 0.1. The correlation length is half of the maximum size of the rock, so the horizontal correlation length θ x =5m, vertical correlation length θ y =5m; the autocorrelation function ρ(Δx, Δy) is specified as a square exponential type, as shown in (2.2):

[0074]

[0075] S2.1.2: Construct the covariance matrix Cor_M: Each element Cor_M(i,j) inside the matrix is ​​the result of substituting the mesh units Mesh(i) and Mesh(j) in the model into the autocorrelation function formula (2.2), as shown in formula (2.4), 1≤i,j≤7422:

[0076]

[0077] Wherein, x_i and x_j represent the horizontal coordinates of the i-th mesh cell Mesh(i) and the j-th mesh cell Mesh(j), respectively, and y_i and y_j represent the vertical coordinates of the i-th mesh cell Mesh(i) and the j-th mesh cell Mesh(j), respectively.

[0078] S2.1.3: The size of the covariance matrix Cor_M is 7422*7422. At this time, the matrix size is too large, and the matrix decomposition cannot use the traditional lower triangular matrix decomposition, which will be too inefficient. However, 7422>5000, so the random field uses the Karhunen-Loeve (KL) series expansion method for approximation, as shown in formula (2.6):

[0079]

[0080] In formula (2.5), L is the lower triangular matrix obtained by decomposing the covariance matrix Cor_M, that is, Cor_M = LL T ,L Tis the transposed matrix of L; χ is a normally distributed array with a length of 7422, a mean of 0, and a standard deviation of 1; in formula (2.6), the size of the truncation term affects the accuracy of the random field. Chen Dongfang. Risk analysis of instability of layered rock caverns based on random finite differences [D]. Northeastern University, 2016. points out that a truncation term of 20 can fully meet the requirements; λ p and φ p (X) is the larger value and corresponding characteristic function among the eigenvalues ​​of Cor_M, that is, after all eigenvalues ​​are sorted in descending order, the λ with an index greater than Q and the corresponding φ(X) are ignored; X is the coordinate set of all grid cells in the model, that is, X={X i =(x i ,y i )|1≤i≤7422}; RF(X) is the set of random field values ​​generated at each grid cell point, that is, RF(X)={RF(X i )|1≤i≤7422}.

[0081] S2.2: Determine the number of rock units based on rock content, sort the random field values ​​in ascending order, and record the index of the grid unit corresponding to each value in ascending order;

[0082] S2.2.1: The rock content of the area is statistically determined to be 40%. The number of rock units Rock_num is determined and calculated using formula (2.7):

[0083] Rock_num≈Round(40%*7422)=Round(2968.8)=2969(2.7)

[0084] Among them, Round() is to find the nearest integer of a number, satisfying the rounding principle.

[0085] S3S2.2.2: Random field values ​​are sorted in ascending order using formula (2.8)

[0086] index=Sort(RF(X))(2.8)

[0087] Among them, Sort() arranges the random field values ​​in ascending order, index is the sorted random field index set, and each index number index{i′}, 1≤i′≤7422, corresponds to a mesh unit Mesh(index{i′}); Round() and Sort() have mature algorithms in existing programming software such as Matlab and Python, so they will not be elaborated on here.

[0088] S2.3: Set the grid cells at both ends of the random field's maximum and minimum values ​​to rock until the number of rock cells is reached. Then, identify the types of grid cells on both sides of the joint and classify the joints into three types: rock-rock, soil-soil, and rock-soil. This achieves two-phase classification of soil and rock in grid cells and three-phase classification of joints. Follow these steps:

[0089] S2.3.1: This step implements the soil-rock two-phase classification. After RF(X) is sorted in ascending order, its maximum and minimum values ​​are distributed at both ends. First, the grid cells with the largest and smallest random field values ​​are set as rocks. Then, the grid cells with the second largest and second smallest random field values ​​are set as rocks. This process continues until the number of assigned rock units reaches the preset number of 2969. This step can be summarized as counting the grid indices corresponding to the random field values ​​at both ends and setting them as rock units in turn. According to the sorting rule, this can be achieved by the following formula (2.9):

[0090]

[0091] The soil-rock two-phase classification is achieved as follows Figure 4 As shown, the blue area is soil and the red area is rock.

[0092] S2.3.2: This step implements the three-phase classification of joints. Since joints are inserted between two meshes, the corresponding Mesh(index{a}) and Mesh(index{b}), 1≤a,b≤7422, of the mesh units on both sides of each joint unit Joint(j) (1≤j≤5906) are counted to determine the soil-rock type of the mesh units on both sides. The joints are then divided into three types: rock-rock, soil-soil, and rock-soil. The rules are shown in formula (2.10):

[0093]

[0094] The three-phase classification of joints is achieved as follows Figure 5 As shown, the black lines are soil-soil joints, the green lines are rock-rock joints, and the white lines are soil-rock joints.

[0095] S3: Statistical analysis of the corresponding second and third random field parameter characteristics and autocorrelation function types for rock and soil, and select a decomposition method based on the size of the covariance to generate rock unit random fields and joint unit random fields to achieve spatial variability of soil and rock materials. Specifically, it includes:

[0096] In S3.1, random fields of rock units and soil units are generated; the spatial variability distribution of soil and rock is realized in the following two steps:

[0097] S3.1.1: Statistics of the characteristic quantities of the second random field show that the tensile strength of rock presents spatial variability, and its mean μr =2.1GPa, coefficient of variation Cov r =0.2, correlation length θ rx =10m,θ ry =5m, the rock autocorrelation function ρ(Δx, Δy) type, construct the covariance matrix, and the number of rock units Rock_num = 2969 ≤ 5000. Therefore, direct decomposition can be used, and the obtained random field is as shown in calculation formula (3.1):

[0098] RF(X r )=2.1*(1+0.2*L r χ r )(3.1)

[0099] Among them, X r is the location coordinate of the rock mass unit, L r It's X r Substitute ρ(Δx,Δy) to obtain the lower triangular matrix of the covariance matrix decomposition, χ r It is a normally distributed array with a length of 2969, a mean of 0, and a standard deviation of 1;

[0100] S3.1.2: Statistics of the characteristic quantities of the third random field show that the shear strength of the soil presents spatial variability, and its mean μ s =15.3MPa, coefficient of variation Cov s =0.1, correlation length θ rx =30m,θ ry =10m, the rock autocorrelation function ρ(Δx, Δy) type, construct the covariance matrix, and the number of soil units m-Rock_num=4453≤5000. Therefore, direct decomposition can be used, and the obtained random field is as shown in calculation formula (3.2):

[0101] RF(X s )=15.3(1+0.1*L r χ r )(3.2)

[0102] Among them, X s is the position coordinate of the soil unit, L s It's X s Substitute ρ(Δx,Δy) to obtain the lower triangular matrix of the covariance matrix decomposition, χ s It is a normally distributed array with a length of 4453, a mean of 0, and a standard deviation of 1;

[0103] Spatial variability of tensile strength of soil-rock mixtures Figure 6 shown

[0104] S3.2: The joint random field value is directly set to the average of the random field values ​​of the grid cells on both sides to achieve spatial variability of the joints and obtain the final soil-rock mixture model.

[0105] The final effect of the continuous-discontinuous soil-rock mixture model considering spatial variability in this case is as follows Figure 7 Comparative Example 1:

[0106] Attachment Figure 8 The image is from the paper "Y.Wu, J.Yan, Y.Zhang, Y.Kong, Z.Song, Combination of digital image processing and random generation in modeling soil-rock mixture slopes for post-failure analyses by material point method, Computers and Geotechnics 165(2024)105886". Figure 4 is the soil-rock mixture model of the present invention, and the two have high similarity. Figure 7 This is the final effect diagram of the present invention based on steps S1 to S3. Based on this comparison, it can be seen that the present invention can generate a soil-rock mixture model that takes into account spatial variability.

[0107] Example 2:

[0108] In this embodiment, for a continuous-discontinuous soil-rock mixture model with a volume fraction of 20% and considering spatial variability, a method for realizing a continuous-discontinuous soil-rock mixture and its spatial variability is based on multiple random fields. The same mixture slope geometric model as in the case of Example 1 is used, such as Figure 2 As shown, no re-modeling is required. Therefore, the mesh unit and joint unit set is still Mesh = {Mesh(i)|1≤i≤7422}, Joint = {Joint(j)|1≤j≤5903}, 7422 and 5903 represent the number of meshes and the number of joints respectively; the mesh and joint display is still as Figure 3 The first random field generation is consistent with Example 1, with a volume fraction RBP = 20%, and the number of rock mass units is determined as follows:

[0109] Rock_num≈Round(20%*7422)=1484(3.1)

[0110] Sort the random field values, determine the corresponding grid index, and determine the grid unit according to formula 4.1:

[0111]

[0112] The classification of joints is based on Formula 4.2:

[0113]

[0114] The characteristic value of the second random field is the same as that in Example 1, and the obtained random field is calculated as shown in Formula 5.1:

[0115] RF(X r )=2.1*(1+0.2*L r χ r )(5.1)

[0116] Among them, X r is the location coordinate of the rock mass unit, L r It's X r Substitute ρ(Δx,Δy) to obtain the lower triangular matrix of the covariance matrix decomposition, χ r It is a normally distributed array with a length of 1484, a mean of 0, and a standard deviation of 1;

[0117] The characteristic value of the third random field is the same as that in Example 1, and the obtained random field is calculated as shown in Formula 5.2:

[0118] RF(X s )=15.3(1+0.1*L r χ r )(5.2)

[0119] Among them, X r is the location coordinate of the rock mass unit, L r It's X r Substitute ρ(Δx,Δy) to obtain the lower triangular matrix of the covariance matrix decomposition, χ r It is a normally distributed array with a length of 1484, a mean of 0, and a standard deviation of 1;

[0120] Among them, X s is the position coordinate of the soil unit, L s It's X s Substitute ρ(Δx,Δy) to obtain the lower triangular matrix of the covariance matrix decomposition, χ s It is a normally distributed array with a length of 5938, a mean of 0, and a standard deviation of 1;

[0121] The random field value of the joint is set as the average value of the random field values ​​of the grid cells on both sides to obtain the final soil-rock mixture model.

[0122] The final effect of the continuous-discontinuous soil-rock mixture model considering spatial variability in this case is as follows Figure 9 shown.

[0123] Comparative Example 2:

[0124] The final effect of comparative example 1 Figure 7 The final effect of Example 2 Figure 9 It can be seen that this patent can generate soil-rock mixture models with different block stone contents without the need for re-modeling, saving modeling time and eliminating the impact of grid changes in numerical simulation.

[0125] Example 3:

[0126] In this embodiment, a continuous-discontinuous rock-soil mixture model with a volume fraction of 50% and considering spatial variability is used to implement a method for continuous-discontinuous soil-rock mixture and its spatial variability based on multiple random fields. The same mixture slope geometric model as in Example 1 is used, such as Figure 2 As shown, no further modeling is required. The rock masses inside the slope are layered, with vertical dimensions ranging from 0.3m to 10m and lateral dimensions ranging from 0.3m to 2m. The correlation length is half of the maximum dimension of the rock, so the lateral correlation length θ x =5m, vertical correlation length θ y = 1m; therefore, the mesh unit and joint unit set is still Mesh = {Mesh(i)|1≤i≤7422}, Joint = {Joint(j)|1≤j≤5903}, 7422 and 5903 represent the number of meshes and the number of joints respectively; the mesh and joint display is still as Figure 3 The first random field generation is consistent with Example 1, with a volume fraction RBP = 50%, and the number of rock mass units is determined as follows:

[0127] Rock_num≈Round(50%*7422)=3711(3.1)

[0128] Sort the random field values, determine the corresponding grid index, and determine the grid unit according to formula 4.1:

[0129]

[0130] The classification of joints is based on Formula 4.2:

[0131]

[0132] The characteristic value of the second random field is the same as that in Example 1, and the obtained random field is calculated as shown in Formula 5.1:

[0133] RF(X r )=2.1*(1+0.2*L r χ r )(5.1)

[0134] Among them, X ris the location coordinate of the rock mass unit, L r It's X r Substitute ρ(Δx,Δy) to obtain the lower triangular matrix of the covariance matrix decomposition, χ r It is a normally distributed array with a length of 1484, a mean of 0, and a standard deviation of 1;

[0135] The characteristic value of the third random field is the same as that in Example 1, and the obtained random field is calculated as shown in Formula 5.2:

[0136] RF(X s )=15.3(1+0.1*L r χ r )(5.2)

[0137] Among them, X r is the location coordinate of the rock mass unit, L r It's X r Substitute ρ(Δx,Δy) to obtain the lower triangular matrix of the covariance matrix decomposition, χ r It is a normally distributed array with a length of 3711, a mean of 0, and a standard deviation of 1;

[0138] Among them, X s is the position coordinate of the soil unit, L s It's X s Substitute ρ(Δx,Δy) to obtain the lower triangular matrix of the covariance matrix decomposition, χ s It is a normally distributed array with a length of 3711, a mean of 0, and a standard deviation of 1;

[0139] The random field value of the joint is set as the average value of the random field values ​​of the grid cells on both sides to obtain the final soil-rock mixture model.

[0140] The final effect of the continuous-discontinuous rock-soil mixture model considering spatial variability is as follows Figure 10 Comparative Example 3:

[0141] Attachment Figure 11 The paper "Y.Liu, H.Xiao, K.Yao, J.Hu, H.Wei, Rock-soil slopestability analysis by two-phase random media and finite elements, GeoscienceFrontiers 9(6)(2018)1649-1655" is a real rock-soil mixture model. Figure 10This is the final rendering of the present invention based on steps S1 to S3, and the two have a high degree of similarity. Based on this comparison, it can be seen that the present invention can also generate a continuous-discontinuous rock-soil mixture model with different horizontal and vertical dimensions considering spatial variability.

[0142] The above descriptions are merely embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention's description and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A method for realizing continuous-discontinuous soil-rock mixture and its spatial variability based on multiple random fields, characterized by: The following steps are involved: S1: Define the spatial extent of the soil-rock mixture, divide it into continuous and discontinuous areas, and perform grid division based on the scale characteristics of the geological body, inserting joints into the grid of the discontinuous area; S2: Generate the first random field to achieve soil-rock two-phase and soil-rock-joint three-phase distribution, including: S2.1: Set the mathematical characteristics and autocorrelation function of the first random field, construct the covariance matrix, select the appropriate method for decomposition, and obtain the random field value of each grid cell; S2.2: Determine the number of rock units based on rock content, sort the random field values ​​in ascending order, and record the index of the grid unit corresponding to each value in ascending order; S2.3: Set the grid cells at the two ends of the joint corresponding to the maximum and minimum values ​​of the random field as rock. Then set the grid cells with the second largest and second smallest random field values ​​as rock. Repeat this process until the number of rock cells is reached. Then, determine the type of grid cells on both sides of the joint and classify the joint into three types: rock-rock, soil-soil, and rock-soil. S3: Generate the second and third random fields to achieve the spatial variability of soil, rock and joints, including: S3.1: Statistically analyze the second and third random field parameter characteristics and autocorrelation function types of the corresponding rocks and soils, and select the appropriate decomposition method based on the size of the covariance to generate rock unit random fields and joint unit random fields to realize the spatial variability of soil and rock materials; S3.2: Set the joint random field value to the average of the random field values ​​of the grid cells on both sides to achieve spatial variability of the joints and obtain the final soil-rock mixture model.

2. The method for realizing continuous-discontinuous soil-rock mixture and its spatial variability based on multiple random fields according to claim 1, characterized in that: In step S1, the spatial range of the model is defined, that is, the boundary of the soil-rock mixture is selected to ensure that the size and shape of the model can cover the study area; The key parts of the model are divided into discontinuous areas, that is, joint units are inserted between the mesh units at this location, and the mesh unit set Mesh = {Mesh(i)|1≤i≤m}, Joint = {Joint(j)|1≤j≤n} is obtained, where m and n represent the number of meshes and the number of joints, respectively.

3. The method for realizing continuous-discontinuous soil-rock mixture and its spatial variability based on multiple random fields according to claim 2, characterized in that: In step S2.1, the steps for generating the first random field are as follows: S2.1.1: Set the mathematical characteristics of the first random field, including mean μ, coefficient of variation Cov, and horizontal correlation length θ x Vertical correlation length θ y The autocorrelation function ρ(Δx, Δy) is specified as exponential or square exponential. The corresponding formulas for the two types are shown in (2.1) and (2.2) respectively: Among them, the coefficient of variation Cov is the ratio of the random field mean μ to the mean square error σ, that is, μ / σ; the correlation length θ x and θ y Respectively represent the scope of strong correlation of random fields in the horizontal and vertical directions, which affect the size distribution of rock blocks in the subsequent soil-rock mixture; Δx and Δy represent the horizontal and vertical distances between any two points in the model space, and in the model they are set as the distance between any two grid cells; S2.1.2: Construct the covariance matrix Cor_M: Each element Cor_M(i,j) inside the matrix is ​​the result of substituting the mesh units Mesh(i) and Mesh(j) in the model into the autocorrelation function formula (2.1) or (2.2), 1≤i,j≤m, as shown in formulas (2.3) and (2.4) respectively: Among them, x i and x j Respectively represent the horizontal coordinates of the i-th grid cell Mesh(i) and the j-th grid cell Mesh(j), y i and y j Represent the ordinates of the i-th mesh cell Mesh(i) and the j-th mesh cell Mesh(j) respectively; S2.1.3: The size of the covariance matrix Cor_M is m*m. Depending on the size of m, different decomposition methods are selected to obtain random field values. The classification is as follows: When m≤5000, the random field is generated using formula (2.5): RF(X)=μ(1+Cov*Lχ)(2.5) When m>5000, the random field is approximated by the Karhunen-Loeve (KL) series expansion method, as shown in formula (2.6): In formula (2.5), L is the lower triangular matrix obtained by decomposing the covariance matrix Cor_M, that is, Cor_M = LL T ,L T is the transposed matrix of L; χ is a normal distribution array with length m, mean 0, and standard deviation 1; in formula (2.6), Q is the truncation term, λ p and φ p (X) are the larger value and corresponding characteristic function of the eigenvalues ​​of Cor_M, that is, after all eigenvalues ​​are sorted in descending order, the λ and corresponding φ(X) with an index greater than Q are ignored; X is the coordinate set of all grid cells in the model, that is, X={X i =(x i ,y i )|1≤i≤m}; RF(X) is the set of random field values ​​generated at each grid cell point, that is, RF(X)={RF(X i )|1≤i≤m}.

4. The method for realizing continuous-discontinuous soil-rock mixture and its spatial variability based on multiple random fields according to claim 3, characterized in that: In step S2.2, determining the number of rock units and sorting the random field is divided into two steps: S2.2.1: Based on the rock content RBP, determine the number of rock units Rock_num, 0 ≤ RBP ≤ 100%, calculated using formula (2.7): Rock_num≈Round(RBP*m)(2.7) Among them, Round() is to find the nearest integer of a number, satisfying the rounding principle; S2.2.2: Sort the random field values ​​in ascending order using formula (2.8): index=Sort(RF(X))(2.8) Among them, Sort() arranges the original array in ascending order, and the returned index is the sorted random field index set. Each index number index{i ′ },1≤i ′ ≤m, corresponding to a mesh unit Mesh(index{i ′ }).

5. The method for realizing continuous-discontinuous soil-rock mixture and its spatial variability based on multiple random fields according to claim 4, characterized in that: In step S2.3, the grid unit soil-rock two-phase classification and joint three-phase classification are implemented, including the following steps: S2.3.1: Realize soil-rock two-phase classification: After RF(X) is arranged in ascending order, its maximum and minimum values ​​are distributed at both ends, so i ′ If index{1} and index{m} are 1 and m respectively, then index{1} and index{m} correspond to the indices of the grid cells with the largest and smallest random field values, respectively. First, the grid cells with the largest and smallest random field values ​​are set as rocks. Then, the grid cells with the second largest and second smallest random field values ​​are set as rocks. This process continues until the number of allocated rock cells reaches the preset Rock_num. This step can be summarized as counting the grid indices corresponding to the random field values ​​at both ends, setting them as rock mass units in turn, and implementing them according to the sorting rules using formula (2.9): S2.3.2: Implement three-phase classification of joints: Count the corresponding Mesh(index{a}) and Mesh(index{b}), 1≤a, b≤m, of the mesh units on both sides of each joint unit Joint(j)(1≤j≤n), and determine the soil-rock type of the mesh units on both sides. Then, classify the joints into three types: rock-rock, soil-soil, and rock-soil. The rules are shown in formula (2.10):

6. The method for realizing continuous-discontinuous soil-rock mixture and its spatial variability based on multiple random fields according to claim 5, characterized in that: In step S3.1, random fields of rock units and soil units are generated; and spatial variability distribution of soil and rock is achieved, which is divided into the following two steps: S3.1.1: Statistical characteristic of the second random field, i.e., the mean μ of the rock mass unit properties in the region r , Coefficient of variation Cov r , correlation length θ rx and θ ry , and specify the type of rock autocorrelation function ρ(Δx,Δy), construct the covariance matrix, and decompose it to obtain the rock unit random field. The calculation formula (3.1) is as follows: Among them, X r is the location coordinate of the rock mass unit, L r It's X r Substitute ρ(Δx,Δy) to obtain the lower triangular matrix of the covariance matrix decomposition, χ r Is a normally distributed array with length Rock_num, mean 0, and standard deviation 1; rp and φ rp (X r ) is the larger value of the eigenvalues ​​of its covariance matrix and the corresponding characteristic function, that is, after all eigenvalues ​​are arranged in descending order, the index is greater than λ of Q rp and the corresponding φ rp (X r ) is ignored; S3.1.2: Statistical characteristic of the third random field, i.e., the mean μ of the soil unit properties in the region s , Coefficient of variation Cov s , correlation length θ sx and θ sy , and specify the type of rock autocorrelation function ρ(Δx,Δy), construct the covariance matrix, and decompose it to obtain the soil unit random field. The calculation formula (3.2) is as follows: Among them, X s is the position coordinate of the soil unit, L s It's X s Substitute ρ(Δx,Δy) to obtain the lower triangular matrix of the covariance matrix decomposition, χ s is a normally distributed array with a length of m-Rock_num, a mean of 0, and a standard deviation of 1; sp and φ sp (X s ) is the larger value of the eigenvalues ​​of its covariance matrix and the corresponding characteristic function, that is, after all eigenvalues ​​are arranged in descending order, the index is greater than λ of Q sp and the corresponding φ sp (X s ) is ignored.

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