A random field modeling method for spatial variability of rock mass parameters under complex geological structures

Abstract

The present invention discloses a random field modeling method for the spatial variability of rock mass parameters under complex geological structures. First, a two-dimensional rectangular coordinate system is established. A background area is set according to the rock mass area where a random field needs to be established, and a background grid is generated; mathematical statistical features in the random field are set; a covariance matrix decomposition method is used to calculate the random field value on any background grid node; the background grid is translated to ensure that the grid area completely contains the rock mass area, and the background grid is deformed to make it present a geological structure morphology; the random field value of the rock mass unit point is calculated by inverse distance weighting; the random field composed of the rock mass unit points is processed by mean regression and standard deviation regression to obtain the final random field effect. The method described in the present invention can simulate the spatial variability of rock mass parameters under complex geological structures more realistically, and can be selected according to different geological structure types.

Description

Technical Field

[0001] The invention belongs to the technical field of rock mass structure geometric modeling, and in particular relates to a random field modeling method of rock mass parameter spatial variability under complex geological structures. Background Art

[0002] After a long period of geological action, natural rock mass has formed a variety of complex geological structures, which pose great challenges to engineering construction. Rock mass parameters have significant spatial variability due to different locations. Ignoring this characteristic can no longer meet the needs of modern complex engineering construction. The mechanical properties of natural rock mass vary with spatial position. Random field theory can help researchers understand this complexity by statistically analyzing the spatial variability of rocks. By collecting characteristic data of rock samples, such as rock mass parameters and structural characteristics, a random field model of rock mass mechanical properties can be established to reveal the distribution law of its internal structure and properties.

[0003] However, current random field construction methods, such as covariance matrix decomposition (i.e., Cholesky decomposition), KL series expansion, expanded linear optimal estimation, and fast Fourier transform, are all constructed with the autocorrelation function as the core, which can only consider the spatial position correlation between rock masses, ignoring the complex spatial correlation caused by geological structures. For example, in the paper "Bhardwaj Pandit*, GL, Sivakumar Babu. 2021. Probabilistic stability assessment of tunnel-support system considering spatial variability in weak rock mass. Computers and Geotechnics", the authors used random field modeling methods to generate isotropic correlation lengths, horizontal and vertical correlation lengths of anisotropic random fields, etc., which did not consider any geological structures in terms of their impact on tunnel performance and the damage mechanisms involved.

[0004] Common types of geological structures include parallel rock layers, synclines, anticlines, folds, faults, etc. At present, researchers have introduced rotation matrices in the autocorrelation function to realize spatial rotation anisotropy to generate random field models with fixed inclination angles, such as the paper "DING Y, ZHU G, MENG Q. 2023. GPU-Accelerated Anisotropic RandomField and Its Application in the Modeling of a Diversion Tunnel. Sustainability", and a Chinese invention patent, title: A rotational anisotropic non-stationary random field modeling method for rock and soil parameters, patent application number: 202110362390.7. However, for the combination of geological structures such as anticlines, synclines, folds and faults, there is no fully achievable random field modeling method. Therefore, it is necessary to further study and improve the existing random field methods and develop more accurate and applicable random field models that can effectively simulate and predict the above-mentioned various complex geological structures. Summary of the invention

[0005] The purpose of the present invention is to provide a random field modeling method that can realize the spatial variability of rock mass parameters under complex geological structures, so as to solve the problem that the existing random field modeling technology cannot realize the spatial variability of rock mass parameters under anticlines, synclines, folds, faults and combinations of these geological structures.

[0006] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0007] A random field modeling method for spatial variability of rock mass parameters under complex geological structures comprises the following steps:

[0008] S1: Establish a two-dimensional rectangular coordinate system XOY, set the background area according to the rock mass area where the random field needs to be established, ensure that the background area can cover the rock mass unit area, and determine the number of grid nodes on the length and width of the background area to generate the background grid;

[0009] S2: Setting the mathematical statistical characteristics in the random field, including the mean, standard deviation, autocorrelation function and correlation length of the rock mass parameters;

[0010] S3: Use the covariance matrix decomposition method to construct the correlation coefficient matrix and perform Cholesky decomposition to calculate the random field value of any background grid node;

[0011] S4: translating the background grid so that the center point of the background area coincides with the center point of the rock mass area, ensuring that the background grid area completely contains the rock mass area; then deforming the background grid to simulate the set geological structure;

[0012] S5: for any rock mass unit point, determine the position coordinates of the four background grid nodes around it, calculate the distance between the rock mass unit point and the four background grid nodes, and the random field values ​​of the four background grid nodes; then, based on the random field values ​​of the four nodes, calculate the random field value of the rock mass unit point by the inverse distance weighted method;

[0013] S6: Calculate the random field of the rock mass area, and perform mean regression and standard deviation regression processing on the random field of the rock mass area to obtain the final random field model effect.

[0014] Further optimization, in step S1, the width D of the background area D x With length D y is larger than the size corresponding to the rock mass area, ensuring that the generated background mesh can still cover the entire rock mass area after deformation in step S4; setting the width D of the background area D x The number of nodes on N x and length D y The number of nodes on N y , then the number of grid nodes in the background area D n = N x × N y .

[0015] Although the more background grid nodes are set, the more accurate the inverse distance weight assignment in the subsequent step S5. However, when the number of grid nodes is too large, especially when the number exceeds 10,000, the computational efficiency of covariance decomposition in step S3 will be greatly reduced. When encountering the situation of too many grid nodes, the book "Stochastic Finite Element Methods and Reliability: A State-of-the-Art Report" and the Chinese Invention Patent: A Rotational Anisotropic Non-Stationary Random Field Modeling Method for Geotechnical Parameters (Patent Application No.: 2021103623907) point out that the grid unit size is set to 0.1-0.2 times the correlation length in each direction. Therefore, the number of nodes on the lateral length of the set background grid N x and the number of nodes in the vertical length N y , satisfying that the lateral distance between adjacent grid nodes is ( L x / 10, L x / 5), the vertical distance is between ( L y / 10,L y / 5).

[0016] Further optimization, in step S2, the autocorrelation function is a coefficient that changes with the relative distance between any two points P and Q in the background area D, and the rock mass parameters corresponding to the two points P and Q are X i,j and X l,m The correlation will only decrease with the increase of relative distance and will approach a non-negative constant c , 0≤ c <1; autocorrelation function ρ ( X i,j , X l,m ) is shown in formula (2.1):

[0017] (2.1);

[0018] in,( x i , y j )and( x l , y m ) represent the position coordinates of points P and Q respectively, i , l ∈[1, N x ], j , m ∈[1, N y ];and △x , △y The horizontal distance and vertical distance between two points P and Q are respectively △x =| x i - x l |, △y =| y j - y m |.

[0019] L x and L y Respectively represent the horizontal and vertical correlation lengths of rock mass parameters. When the distance between points P and Q is less than the correlation length, the parameters at points P and Q will show a stronger correlation. The calculation formula is shown in (2.2):

[0020] (2.2);

[0021] Further optimization, in step S3, any background grid node P( x i , y j ) is calculated as follows:

[0022] (3.1);

[0023] in, X Is the background area D Rock mass parameters of inner grid nodes X i,j A collection of X ={ X i,j |1≤ i ≤ N x ,1≤ j ≤ N y}; RF (P) is based on the set X The generated background grid node P( x i , y j )’s random field; L The correlation coefficient matrix is ρ nn The lower triangular matrix obtained by Cholesky decomposition is ρ nn =LL T , L T yes L The transposed matrix of is a group of n A vector of numbers whose elements follow a standard normal distribution.

[0024] ρ nn is a symmetric matrix, when i=l , j=m When X i,j The distance from itself is 0, and when it is substituted into the autocorrelation function, we get ρ ( X i,j , X i,j )=1, that is, the diagonal elements of the correlation coefficient matrix are 1, then ρnn Simplified to:

[0025] (3.2)

[0026] Further optimization, in step S4, in step S4, the deformation of the background grid includes any one of spatial rotation, lateral stretching, lateral distortion and shear movement.

[0027] The geological structure morphology is set by the deformation simulation of the background grid. The specific operations are as follows:

[0028] (a) Rotate the background grid to simulate the geological structure of parallel rock layers: rotate all background grid nodes around the center of the background grid at any inclination angle.

[0029] (b) The background grid is stretched laterally to simulate the geological structure of anticline or syncline: the grid nodes of the same vertical coordinate are stretched upward or downward from the turning end, and the stretching angles of the grid nodes on both sides of the turning end are inconsistent.

[0030] (c) The background grid is distorted laterally to simulate the fold geological structure: trigonometric functions are introduced to transform the grid nodes with the same vertical coordinate from a horizontal line to a trigonometric function line.

[0031] (d) The background grid is sheared and moved to simulate the fault geological structure: the background grid is cut along the fault tangent line, and the grid nodes on both sides are moved parallel to the fault tangent line.

[0032] Among them, operations (b) and (c) will change the grid size and require correction of the relevant length. Specifically, if the horizontal distance between two grid nodes changes a times, becomes w x , then the correction process will become

[0033] w x / a More complex geological structures can be achieved by mixing and matching the above four operations, such as dip-parallel rock structures containing faults, which can be achieved by combining operations (a) and (d).

[0034] Further optimization, in step S5, the specific process of calculating the random field value of the rock mass unit point is as follows:

[0035] S5.1: For any rock mass unit point , determine the four background grid nodes around it , so that it satisfies , p ∈[1, N x], g ∈[1, N y ];

[0036] S5.2: Calculate the rock mass unit points separately The distances between the four background grid nodes A, B, C, and D are recorded as d 1 , d 2 , d 3 , d 4 ;

[0037] S5.3: Calculate the random field values ​​of the four background grid nodes according to formula (3.1) RF (A) RF (B) RF (C) and RF (D);

[0038] S5.4: Use the inverse distance weighted method to calculate the rock mass unit point The random field value of RF ( Y k ), as shown in formula (5.1):

[0039] (5.1);

[0040] in, Represents any rock mass unit point Y k The location coordinates of k =1,2… s , s Represents the number of rock mass unit points in the background area D; ,make d t = ∞, then d t Not participating RF ( Y k ), t=1,2,3,4. This step is to solve the problem of inaccurate assignment of rock mass parameters at the fault.

[0041] Further optimization, in step S6, mean regression and standard deviation regression are performed because the random field composed of rock mass unit points is obtained by distance inverse weighted calculation, and its mean and standard deviation have deviated from the sum set by the background grid random field. Mean regression and standard deviation regression must be performed to obtain the final random field effect. It is divided into two steps, as follows:

[0042] S6.1: Mean regression: First, the rock mass regional random field is calculated by formula (6.1): RF ( Y ) ; Then, the random field of the rock mass unit point after regression is obtained by formula (6.2):

[0043] (6.1);

[0044] (6.2);

[0045] in, RF ( Y k ) new for RF ( Y k ) After mean regression, at the rock mass unit point The updated value at ; RF ( Y ) new ={ RF ( Y k ) new | k =1,2… s},for RF ( Y k ) new The collection of is the rock mass regional random field after mean regression processing; is the mean value of rock mass parameters, obtained through actual detection and calculation of rock mass;

[0046] S6.2: Standard deviation regression: First, calculate from formula (6.3) RF ( Y ) new The actual standard deviation ; Then, the random field value of each rock mass unit point is calculated by formula (6.4) RF ( Y k ) new and The difference ; Finally, the random field value of each rock mass unit point after standard deviation regression processing is calculated by formula (6.5);

[0047] (6.3);

[0048] (6.4);

[0049] (6.5);

[0050] in, RF ( Y k ) final for RF ( Y k ) new After standard deviation regression processing, the rock mass unit point The updated value at ; RF ( Y ) final ={ RF ( Y k ) final | k =1,2… s},for RF ( Y k ) final The set of is the final value of the random field in the rock mass area; is the standard deviation of rock mass parameters, which is obtained through actual detection and calculation of the rock mass.

[0051] Compared with the prior art, the present invention has the following beneficial effects:

[0052] 1. The present invention simulates parallel rock layers, anticlines, synclines, folds, faults and their combined geological structures on the basis of ensuring the spatial correlation of rock mass by improving the traditional random field method, including the transformation of random field background grid and the correction of correlation length.

[0053] 2. The present invention introduces mean regression and mean square error regression to ensure that the mean and mean square error of the generated random field model are consistent with the set values. This innovation also solves the problem that the common random field approximate solution methods (such as KL series expansion method and expanded linear optimal estimation method) may cause inaccurate mean and mean square error, and provides reliable technical support for the numerical simulation of related geological structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is a flow chart of the random field modeling method of the spatial variability of rock mass parameters under complex geological structures according to the present invention;

[0055] Figure 2 is a schematic diagram of performing four deformation operations on the background grid in step S4;

[0056] Figure 3 is a schematic diagram of the weighted calculation of the random field values ​​of the rock mass unit points in step S5;

[0057] Figure 4The real and simulated images of the spatial variability of parallel rock layers;

[0058] Figure 5 The real map and simulated effect map of the spatial variability of anticline geological structure;

[0059] Figure 6 The real map and simulated effect map of the spatial variability of fold geological structures;

[0060] Figure 7 The real and simulated images of the spatial variability of horizontal fault geological structures.

[0061] Figure 8 These are the real and simulated images of the spatial variability of parallel + fault geological structures. DETAILED DESCRIPTION

[0062] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0063] Example 1: In this example, random field modeling of spatial variability is performed for parallel rock layers with a dip angle of 120°. The rock mass area is a parallel rock mass stratum in Yugou Town, Lingbi County, Suzhou, Anhui Province. The specific steps include: Figure 1 As shown:

[0064] S1: Establish a two-dimensional rectangular coordinate system XOY, set the background area according to the rock mass area where the random field needs to be established, ensure that the background area can cover the rock mass unit area, and determine the number of grid nodes on the length and width of the background area to generate the background grid.

[0065] Set the rock mass area length to 50×50 m , set the background area to 75×75 m , ensuring that the background grid can contain the rock mass area at any angle of rotation. The background grid cell size is set to 1 m ,Right now x i - x i-1 =1 m , y i - y i-1 =1 m , the number of background grid nodes is n = N x× N y =5776<10000, which meets the efficiency setting. The size of the rock mass unit is also set to 1m, so there are s =51×51=2601 rock unit points.

[0066] S2: Specify the mathematical statistical characteristics of the random field, such as the mean and standard deviation of rock mass parameters, correlation length, and select the type of autocorrelation function.

[0067] In this embodiment, the rock mass parameter is set to be the tensile strength of the rock mass.

[0068] Through preliminary exploration and calculation, the mean tensile strength of the rock mass in Yugou Town, Lingbi County, Suzhou, Anhui Province is 18.6MPa, and the mean square error is about 0.1 times the mean. The spatial variability of the tensile strength of the rock mass is a square exponential distribution, and the autocorrelation function is more suitable for this type. The rock layer is less than 2 in the vertical direction. m The correlation is higher than 2 m The correlation can be ignored, that is, the lower limit of the Gaussian autocorrelation function c = 0. The correlation is stronger in the horizontal direction, about 10 times that in the vertical direction, i.e. 20 m .

[0069] Combining the above information, we can conclude that:

[0070] ;

[0071] S3: Use the covariance matrix decomposition method to construct the correlation coefficient matrix, and perform Cholesky decomposition and other processes to calculate the arbitrary background grid node P( x i , y j )’s random field value:

[0072] ;

[0073] in, X The background area is 75×75 m The tensile strength of each element is a collection of 5776 background grid cell locations. X i,j has a location coordinate ( x i , y j ), 1≤ i ≤76 ,1≤ j ≤76; RF (P) is based on the set X The generated background grid node P( xi , y j ) of random fields; 18.6×10 6 yes RF The mean value of (P); 1.86×10 6 yes RF (P) standard deviation. L The correlation coefficient matrix is ρ nn The lower triangular matrix obtained by performing the Cholesky decomposition of the matrix is ρ nn =LL T , L T yes L The transposed matrix of ; is a vector of 5776 numbers whose elements satisfy the standard normal distribution.

[0074] ρ nn is the rock mass parameter X i,j and X l,m Bring in ρ ( X i,j , X l,m )The correlation coefficient matrix calculated by ρ nn is a symmetric matrix, when i=l , j=m When X i,j The distance from itself is 0, and when it is substituted into the autocorrelation function, we get ρ ( X i,j , X i,j )=1, that is, the diagonal elements of the correlation coefficient matrix are 1, then ρ nn Simplified to:

[0075] ;

[0076] S4: translating the background grid so that the center point of the background area coincides with the center point of the rock mass area, ensuring that the background grid area completely contains the rock mass area; then deforming the background grid to simulate the set geological structure.

[0077] The center of the background grid is (75 / 2, 75 / 2), which is moved to the center of the rock mass area (25, 25); then the background grid is rotated to simulate the parallel rock formation geological structure: all grid nodes are rotated to the center of the rock mass area, and the inclination is referenced. Figure 2 (a) in the figure.

[0078] In other embodiments, the deformation of the background grid, such as lateral stretching, lateral distortion, and shear movement, is referred to as Figure 2 (b), (c) and (d) in the figure.

[0079] S5: For any rock mass unit point, determine the position coordinates of the four background grid nodes around it, calculate the distance between the rock mass unit point and the four background grid nodes, and the random field values ​​of the four background grid nodes; then, based on the random field values ​​of the four nodes, calculate the random field value of the rock mass unit point by the inverse distance weighted method, specifically including:

[0080] S5.1: For any rock mass unit point , determine the four background grid nodes around it , so that it satisfies , p ∈[1, N x ], g ∈[1, N y ];

[0081] S5.2: Calculate the rock mass unit points separately The distances between the four background grid nodes A, B, C, and D are recorded as d 1 , d 2 , d 3 , d 4 ;

[0082] S5.3: Calculate the random field values ​​of the four background grid nodes according to formula (3.1) RF (A) RF (B) RF (C) and RF (D);

[0083] S5.4: Use the inverse distance weighted method to calculate the rock mass unit point The random field value of RF ( Y k ), as shown in formula (5.1):

[0084] (5.1);

[0085] in, Represents any rock mass unit point Y k The location coordinates ofk =1,2… s , s Represents the number of rock mass unit points in the background area D; ,make d t = ∞, then d t Not participating RF ( Y k ), t=1,2,3,4. This step is to solve the problem of inaccurate assignment of rock mass parameters at the fault. Figure 3 Taking the anticline and fault geological structure in the example, the weighted calculation of rock mass unit points The random field value at RF ( Y k ).

[0086] S6: Calculate the random field of the rock mass area, and perform mean regression and standard deviation regression processing on the random field of the rock mass area to obtain the final random field model effect, specifically:

[0087] S6.1: Mean regression: First, the rock mass regional random field is calculated by formula (6.1): RF ( Y ), and then the rock mass regional random field is calculated by formula (6.2) RF ( Y ) ; Then the random field of the rock mass unit point after regression is obtained by formula (6.3):

[0088] (6.1);

[0089] (6.2);

[0090] (6.3);

[0091] in, RF ( Y k ) new for RF ( Y k ) After mean regression, at the rock mass unit point The updated value at ; RF ( Y ) new ={ RF ( Y k ) new | k=1,2…,2601}, for RF ( Y k ) new The collection of is the rock mass regional random field after mean regression processing; is the mean value of rock mass parameters, which is obtained through actual detection and calculation of the rock mass.

[0092] S6.2: Standard deviation regression: First, calculate from formula (6.4) RF ( Y ) new The actual standard deviation ; Then, the random field value of each rock mass unit point is calculated by formula (6.5) RF ( Y k ) new and The difference ; Finally, the random field value of each rock mass unit point after standard deviation regression processing is calculated by formula (6.6);

[0093] (6.4);

[0094] (6.5);

[0095] (6.6);

[0096] in, RF ( Y k ) final for RF ( Y k ) new After standard deviation regression processing, the rock mass unit point The updated value at ; RF ( Y ) final ={ RF ( Y k ) final | k =1,2…2601}, RF ( Y k ) final A collection that satisfies the set and , which is the final value of the random field in the rock mass area.

[0097] Comparative Example 1: Figure 4 (a) is a partial cross-section of the parallel stratigraphic structure excavation from Yugou Town, Lingbi County, Suzhou, Anhui Province. Figure 4 (b) is a parallel stratigraphic structure rendering generated by the present invention based on the modeling of steps S1 to S6. Based on this comparison, it can be seen that the method of the present invention can simulate the spatial variability of rock mass parameters under parallel geological structures that are close to reality.

[0098] Example 2: Random field modeling is performed for the spatial variability of rock parameters under anticline geological structures.

[0099] In this embodiment, a rock mass area with a length and width of 50 m is set, and the rock layer contains anticline geological structure. The inclination angle of the anticline is 30° counterclockwise, and the inclination angle of the syncline is 60° clockwise. The turning point of the anticline is 0.1 area length on the right side of the area. In this embodiment, the background grid unit length is set to 1.0 m. The tensile strength of the rock mass satisfies spatial variability, with a relevant length of 20 m in the x-direction and a relevant length of 2 m in the y-direction, and the spatial distribution of the parameters still satisfies the normal distribution. The length and width of the background grid area are set to 75 m respectively. The tensile strength value of the rock mass unit point is calculated by the inverse distance weighted method, and then assigned after mean regression and variance regression. The results are as follows Figure 5 (b) in the figure. Since the syncline geological structure only needs to set the anticline dip angle to clockwise and the syncline dip angle to counterclockwise to meet the requirements, no further examples are given. The model formation process, i.e., other steps, refer to Example 1 and are not described in detail.

[0100] Comparative Example 2: Figure 5 (a) is a partial excavation section of an anticline geological structure from Yugou Town, Lingbi County, Suzhou, Anhui Province. Figure 5 (b) is an anticline geological effect map generated by the modeling of steps S1 to S6 of the present invention. Based on this comparison, it can be seen that the method of the present invention can simulate the spatial variability of rock mass parameters under an anticline geological structure that is close to the real one.

[0101] Example 3: Random field modeling is performed for the spatial variability of rock parameters under fold geological structures.

[0102] In this embodiment, the length and width of the rock mass area are set to 50 m, and the rock layer contains a folded geological structure. The difference between the peak and valley values ​​of the fold is 0.2 model length, and it consists of two peaks and troughs. In this embodiment, the background grid unit length is set to 1.0 m. The tensile strength of the rock mass satisfies the spatial variability, the relevant length in the x-direction is 30 m, the relevant length in the y-direction is 2 m, and the spatial distribution of the parameters still satisfies the normal distribution. The length and width of the background grid area are set to 75 m respectively. The tensile strength value of the rock mass unit point is calculated by the inverse distance weighted method, and then assigned after mean regression and variance regression. The results are as follows Figure 6 The model formation process, i.e., other steps, can refer to Example 1 and will not be described in detail.

[0103] Comparative Example 3: Figure 6 (a) is a fold geological structure map. Figure 6 (b) is a fold geological effect map generated by the present invention based on the modeling of steps S1 to S6. Based on this comparison, it can be seen that the method of the present invention can simulate the spatial variability of rock mass parameters under the fold geological structure close to the real one.

[0104] Example 4: Random field modeling is performed for the spatial variability of rock parameters under horizontal fault geological structures.

[0105] In this embodiment, the length and width of the rock mass area are set to 50 m, the rock layer contains a fault geological structure, and the fault dip is 60°. The center of the fault is located at 0.6 model widths of the model, and the height difference on both sides of the fault is 0.05 model lengths. In this embodiment, the background grid unit length is set to 1.0 m. The tensile strength of the rock mass satisfies spatial variability, with a relevant length of 30 m in the x-direction and a relevant length of 2 m in the y-direction, and the spatial distribution of the parameters still satisfies the normal distribution. The length and width of the initial grid area are set to 75 m respectively. The tensile strength value of the rock mass unit point is calculated by the inverse distance weighted method, and then assigned after mean regression and variance regression. The results are as follows. Figure 7 The model formation process, i.e., other steps, can refer to Example 1 and will not be described in detail.

[0106] Comparative Example 4: Figure 7 (a) is a fault geological structure diagram. Figure 7 (b) is a fault geological structure rendering generated by the present invention based on the modeling of steps S1 to S6. Based on this comparison, it can be seen that the method of the present invention can simulate the spatial variability of rock mass parameters under a horizontal fault geological structure that is close to the real one.

[0107] Example 5: Random field modeling for the spatial variability of rock parameters in parallel + fault geological structures.

[0108] In this embodiment, the length and width of the rock mass area are set to 50 m, the rock layer contains an inclined fault geological structure, the fault dip is 30°, and the rock layer dip is 165°. The center of the fault is located at 0.6 model widths of the model, and the height difference on both sides of the fault is 0.05 model lengths. In this embodiment, the background grid unit length is set to 1.0 m. The tensile strength of the rock mass satisfies spatial variability, with a relevant length of 30 m in the x-direction and a relevant length of 2 m in the y-direction, and the spatial distribution of the parameters still satisfies the normal distribution. The length and width of the initial grid area are set to 75 m respectively. The tensile strength value of the rock mass unit point is calculated by the inverse distance weighted method, and then assigned after mean regression and variance regression. The results are as follows Figure 8The model formation process, i.e., other steps, can refer to Example 1 and will not be described in detail.

[0109] Comparative Example 5: Figure 8 (a) is a parallel + fault geological structure diagram. Figure 8 (b) is a geological structure rendering including tilt and fault generated by the present invention based on the modeling of steps S1 to S6. Based on this comparison, it can be seen that the method of the present invention can simulate the spatial variability of rock mass parameters under the parallel + fault geological structure that is close to the real one.

[0110] It can be seen from comparative examples 1 to 5 that the method of the present invention can simulate the spatial variability of rock parameters under complex geological structures according to common geological structure types and corresponding related parameters, and provide technical support for the numerical simulation of related geological structures.

[0111] 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 specification 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 random field modeling method for spatial variability of rock mass parameters under complex geological structures, characterized in that: The following steps are involved: S1: Establish a two-dimensional rectangular coordinate system XOY, set the background area according to the rock mass area where the random field needs to be established, ensure that the background area can cover the rock mass unit area, and determine the number of grid nodes on the length and width of the background area to generate the background grid; S2: Setting the mathematical statistical characteristics in the random field, including the mean, standard deviation, autocorrelation function and correlation length of the rock mass parameters; S3: Use the covariance matrix decomposition method to construct the correlation coefficient matrix and perform Cholesky decomposition to calculate the random field value of any background grid node; S4: translating the background grid so that the center point of the background area coincides with the center point of the rock mass area, ensuring that the background grid area completely contains the rock mass area; then deforming the background grid to simulate the set geological structure; S5: for any rock mass unit point, determine the position coordinates of the four background grid nodes around it, calculate the distance between the rock mass unit point and the four background grid nodes, and the random field values ​​of the four background grid nodes; then, based on the random field values ​​of the four nodes, calculate the random field value of the rock mass unit point by the inverse distance weighted method; S6: Calculate the random field of the rock mass area, and perform mean regression and standard deviation regression processing on the random field of the rock mass area to obtain the final random field model effect.

2. The random field modeling method for spatial variability of rock mass parameters under complex geological structures according to claim 1 is characterized in that: In step S1, the width D of the background area D x With length D y The size is larger than the size corresponding to the rock mass area, ensuring that the generated background mesh can still cover the entire rock mass area after deformation in step S4; Set the width D of the background area D x The number of nodes on N x and length D y The number of nodes on N y , then the number of grid nodes in the background area D n = N x × N y .

3. The random field modeling method for spatial variability of rock mass parameters under complex geological structures according to claim 2 is characterized in that: In step S2, the autocorrelation function is a coefficient that changes with the relative distance between any two points P and Q in the background area D. The rock mass parameters corresponding to the two points P and Q are X i,j and X l,m The correlation will only decrease with the increase of relative distance and will approach a non-negative constant c , 0≤ c <1; autocorrelation function ρ ( X i,j , X l,m ) is shown in formula (2.1): （2.1）； in,( x i , y j )and( x l , y m ) represent the position coordinates of points P and Q respectively, i , l ∈[1, N x ], j , m ∈[1, N y ];and △x , △y The horizontal distance and vertical distance between two points P and Q are respectively, that is, △x =| x i - x l |, △y =| y j - y m |; L x and L y Respectively represent the horizontal and vertical correlation lengths of rock mass parameters. When the distance between points P and Q is less than the correlation length, the parameters at points P and Q will show a stronger correlation. The calculation formula is shown in (2.2): （2.2）。 4. The random field modeling method for spatial variability of rock mass parameters under complex geological structures according to claim 3 is characterized in that: In step S3, any background grid node P( x i , y j ) is calculated as follows: （3.1）； in, X Is the background area D Rock mass parameters of inner grid nodes X i,j A collection of X ={ X i,j |1≤ i ≤ N x ,1≤ j ≤ N y }; RF (P) is based on the set X The generated background grid node P( x i , y j )’s random field; L The correlation coefficient matrix is ρ nn The lower triangular matrix obtained by Cholesky decomposition is ρ nn =LL T , L T yes L The transposed matrix of is a group of n A vector of numbers whose elements satisfy the standard normal distribution; ρ nn is a symmetric matrix, when i=l , j=m When X i,j The distance from itself is 0, and when it is substituted into the autocorrelation function, we get ρ ( X i,j , X i,j )=1, that is, the diagonal elements of the correlation coefficient matrix are 1, then ρ nn Simplified to: （3.2）。 5. The random field modeling method for spatial variability of rock mass parameters under complex geological structures according to claim 4, characterized in that: In step S4, the deformation of the background grid includes any one of spatial rotation, lateral stretching, lateral distortion and shear movement; The geological structure morphology set by the deformation simulation of the background grid is as follows: (a) Rotate the background grid to simulate the geological structure of parallel rock layers; (b) Laterally stretching the background grid to simulate the anticline or syncline geological structure; (c) Transversely distorting the background grid to simulate the fold geological structure; (d) Shearing and moving the background grid to simulate the fault geological structure; Other more complex transformations are achieved by mixing and matching the above four operations.

6. The random field modeling method for spatial variability of rock mass parameters under complex geological structures according to claim 5, characterized in that: In step S4, when the background grid is stretched or distorted horizontally, the horizontal distance between any two grid nodes changes, and correction is required; specifically: if the horizontal distance between the two grid nodes changes a times, becomes w x , then the correction process is to turn it into w x / a .

7. The random field modeling method for spatial variability of rock mass parameters under complex geological structures according to claim 6, characterized in that: In step S5, the specific process of calculating the random field value of the rock mass unit point is as follows: S5.1: For any rock mass unit point , determine the four background grid nodes around it , so that it satisfies , p ∈[1, N x ], g ∈[1, N y ]; S5.2: Calculate the rock mass unit points separately The distances between the four background grid nodes A, B, C, and D are recorded as d 1 , d 2 , d 3 , d 4 ; S5.3: Calculate the random field values ​​of the four background grid nodes according to formula (3.1) RF (A) RF (B) RF (C) and RF (D); S5.4: Use the inverse distance weighted method to calculate the rock mass unit point The random field value of RF ( Y k ), as shown in formula (5.1): （5.1）； in, Represents any rock mass unit point Y k The location coordinates of k =1,2… s , s Represents the number of rock mass unit points in the background area D; ,make d t = ∞, then d t Not participating RF ( Y k ), t=1,2,3,4.

8. The random field modeling method for spatial variability of rock mass parameters under complex geological structures according to claim 7, characterized in that: In step S6, mean regression and standard deviation regression processing are performed on the random field of the rock mass area, and the specific steps are as follows: S6.1: Mean regression: First, the rock mass regional random field is calculated by formula (6.1): RF ( Y ) ; Then, the random field of the rock mass unit point after regression is obtained by formula (6.2): （6.1）； （6.2）； in, RF ( Y k ) new for RF ( Y k ) After mean regression, at the rock mass unit point The updated value at ; RF ( Y ) new ={ RF ( Y k ) new | k =1,2… s },for RF ( Y k ) new The collection of is the rock mass regional random field after mean regression processing; is the mean value of rock mass parameters, obtained through actual detection and calculation of rock mass; S6.2: Standard deviation regression: First, calculate from formula (6.3) RF ( Y ) new The actual standard deviation ; Then, the random field value of each rock mass unit point is calculated by formula (6.4) RF ( Y k ) new and The difference ; Finally, the random field value of each rock mass unit point after standard deviation regression processing is calculated by formula (6.5); （6.3）； （6.4）； （6.5）； in, RF ( Y k ) final for RF ( Y k ) new After standard deviation regression processing, the rock mass unit point The updated value at ; RF ( Y ) final ={ RF ( Y k ) final | k =1,2… s },for RF ( Y k ) final The set of is the final value of the random field in the rock mass area; is the standard deviation of rock mass parameters, which is obtained through actual detection and calculation of the rock mass.

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