Three-dimensional geological model simplification method and system incorporating intensity parameters
By introducing a weighted sum of normal vector entropy and Gaussian curvature entropy, combined with intensity parameters, the problems of excessive number of nodes and insufficient simulation accuracy in the simplification of three-dimensional geological models are solved, achieving efficient model simplification and accuracy improvement.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- GUANGXI ROAD & BRIDGE ENG GRP CO LTD
- Filing Date
- 2022-10-26
- Publication Date
- 2026-06-26
Smart Images
Figure CN115619952B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of finite element analysis technology for three-dimensional geological models, and in particular to a method and system for simplifying three-dimensional geological models by incorporating strength parameters. Background Technology
[0002] In the past, due to limitations in computer technology, engineers typically analyzed geotechnical engineering problems based on columnar sections and cross-sectional information provided by surveys. With the rapid development of computer technology and the improvement of geotechnical engineering techniques, geotechnical engineers have an increasingly strong demand for three-dimensional numerical simulations of geotechnical engineering problems.
[0003] Simplification of the 3D geological model is essential in 3D numerical simulation. While both 3D geological modeling and 3D numerical simulation are 3D problems, they address different issues, leading to two distinct directions: CAD (Computer-Aided Design) and CAE (Computer-Aided Engineering). In 3D geological modeling, high model accuracy is often prioritized, with less emphasis on mesh number and type. However, 3D numerical simulation places stringent requirements on the number and type of mesh nodes. Appropriate mesh types and node counts significantly reduce computation time and improve convergence and accuracy. Therefore, when using a 3D geological model for 3D numerical simulation, simplification is necessary. The simplified model should meet the mesh requirements of 3D numerical simulation while maintaining a reasonable reduction in accuracy.
[0004] In engineering applications, 3D geological models often refer to 3D stratigraphic models. The strata in a 3D stratigraphic model are generally composed of irregular triangular meshes. This results in a large number of nodes within a relatively small geological body. Currently, there are two approaches to address the problem of a large number of nodes in the geological body mesh. The first approach is to simplify the model by utilizing the normal vector entropy and Gaussian curvature entropy at the nodes in the strata; the second approach is to reconstruct the 3D geological model. The advantage of the first approach is that it can greatly simplify the nodes on the strata, but a major drawback is that this simplification process does not consider the influence of the strength of the soil and rock materials. For strata with low soil and rock strength parameters, the number of nodes needs to be appropriately increased to ensure improved calculation accuracy in potential plastic failure zones. While using the second approach to process the 3D geological model can avoid excessive reduction of nodes in some areas during the simplification process, thus affecting the accuracy of the final analysis results, the model is reconstructed, resulting in low model fidelity and potentially significant differences from the original geological model. This patent provides an alternative algorithm to address these two approaches. Based on this algorithm, geotechnical engineers can obtain a highly accurate representation of the original geological model while greatly simplifying the number of nodes in the model, thereby further improving the accuracy of three-dimensional numerical simulation. Summary of the Invention
[0005] To address the shortcomings of the two approaches mentioned above, this invention utilizes the first law of geology to calculate the normal vector of a node, and simultaneously calculates the normal vector entropy and Gaussian curvature entropy of the grid nodes on the ground plane. It also introduces an intensity parameter to weight the corresponding entropy values, thereby optimizing the simplification method for three-dimensional geological models. This invention proposes a simplification method and system for three-dimensional geological models that incorporates an intensity parameter.
[0006] To achieve the above-mentioned objectives, the present invention provides the following technical solution:
[0007] The method for simplifying three-dimensional geological models by incorporating intensity parameters includes the following steps:
[0008] S1, Establish a three-dimensional geological model and extract each geological stratum;
[0009] S2, calculate the normal vector and normal vector entropy on all ground plane grid nodes;
[0010] S3, calculate the Gaussian curvature and Gaussian curvature entropy on all ground plane grid nodes;
[0011] S4, Introduce strength parameters, and calculate the weighted sum of the normal vector entropy and Gaussian curvature entropy at the node based on the strength parameters, wherein the strength parameters are the ratio of the shear strength at the node to the Mohr-Coulomb strength;
[0012] S5: Traverse all ground surface grid nodes, remove nodes with corresponding entropy weights and values less than a preset threshold, and obtain a simplified three-dimensional geological model.
[0013] As a preferred embodiment, the formula for calculating the weighted sum of the normal vector entropy and the Gaussian curvature entropy at the node is as follows:
[0014] H s =H n *α p +H G *α p
[0015] Among them, H s H is the weighted sum of the normal vector entropy and the Gaussian curvature entropy at node p. n H is the entropy of the normal vector at node p. G It is the Gaussian curvature entropy at node p, α p It is the strength parameter, α p This is the ratio of the shear strength at node p to the molar coulomb strength.
[0016] As a preferred option, the shear strength τ at node p j The calculation formula is:
[0017]
[0018] in, It is the maximum value of the inherent strength parameter of the rock and soil mass, c. j It is the maximum cohesion of the stratum where node p is located, and is the cohesion of the soil and rock mass. λ is the internal friction angle of the stratum where node p is located, j is the element number in the corresponding neighborhood of node p when the inherent strength parameter of the soil and rock mass reaches its maximum value, m is the total number of strata vertically downwards from the surface to node p, and λ is the internal friction angle of the stratum where node p is located. i The coefficients represent the inherent properties of the soil at node p, where i is the stratum number vertically downwards from the surface to node p, and h represents the soil's inherent properties. i Let q be the thickness of the i-th layer of soil and rock. k It is an external load, ξ k Represents node p and external load q k For the effect coefficient of this node, n is the number of units in the corresponding neighborhood of node p, and k is the index of the unit in the neighborhood of the node.
[0019] As a preferred option, the formula for calculating the molar coulomb strength at node p is:
[0020]
[0021] Among them, c p It is the cohesion of the stratum where node p is located. λ is the internal friction angle of the stratum where node p is located, m is the total number of strata extending vertically downwards from the surface to node p, and λ is the internal friction angle of the stratum where node p is located. i The coefficients represent the inherent properties of the soil at node p, where i is the stratum number vertically downwards from the surface to node p, and h represents the soil's inherent properties. i Let q be the thickness of the i-th layer of soil and rock. k It is an external load, ξ k Represents node p and external load q k For the effect coefficient of this node, n is the number of units in the corresponding neighborhood of the node, and k is the index of the unit in the neighborhood of the node.
[0022] As a preferred option, the entropy of the normal vector at node p is H. n The calculation formula is:
[0023]
[0024] Where pθ, They are respectively:
[0025]
[0026] Where θ is the unit normal vector N at node p and the average unit normal vector of the (n+1) nodes. The angle between θ and n, where n is the number of elements in the neighborhood of node p, and k is the index of the element in the neighborhood of node p. k It is the unit normal vector N in the k-th neighborhood of node p and the average unit normal vector of the (n+1)-th node. The included angle.
[0027] Based on the same concept, a three-dimensional geological model simplification system incorporating intensity parameters is also proposed, comprising at least one processor and a memory communicatively connected to the at least one processor; the memory stores instructions executable by the at least one processor, which, when executed by the at least one processor, enable the at least one processor to perform the three-dimensional geological model simplification method incorporating intensity parameters described above.
[0028] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0029] By employing a simplification method for three-dimensional geological models that incorporates strength parameters, geotechnical engineers can obtain a highly accurate representation of the original geological model while significantly reducing the number of nodes in the model, thereby further improving the accuracy of three-dimensional numerical simulations. Attached image description:
[0030] Figure 1 Here is a simplified flowchart of the three-dimensional geological model method for introducing strength parameters in Example 1;
[0031] Figure 2This is a schematic diagram of the three geological surfaces and boreholes in Example 2;
[0032] Figure 3 This is a schematic diagram of the three geological surface unit grids in Example 2;
[0033] Figure 4 This is a comparison image (including node grid) of the terrain surface before and after filtering in Example 2;
[0034] Figure 5 This is a comparison image (including node mesh) of the second face from the top in Example 2 before and after filtering;
[0035] Figure 6 This is a comparison image (including node mesh) of the third face from the top in Example 2 before and after screening. Detailed Implementation
[0036] The present invention will be further described in detail below with reference to experimental examples and specific embodiments. However, this should not be construed as limiting the scope of the above-mentioned subject matter of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.
[0037] Example 1
[0038] The flowchart of the simplified method for introducing strength parameters in three-dimensional geological models is as follows: Figure 1 As shown, it includes the following steps:
[0039] S1, Establish a three-dimensional geological model and extract each geological stratum;
[0040] S2, calculate the normal vector and normal vector entropy on all ground plane grid nodes;
[0041] S3, calculate the Gaussian curvature and Gaussian curvature entropy on all ground plane grid nodes;
[0042] S4, introduce the corresponding intensity parameters, and calculate the weighted sum of the normal vector entropy and Gaussian curvature entropy at the node based on the intensity parameters;
[0043] S5: Traverse all ground surface grid nodes, remove nodes with corresponding entropy weights and values less than a preset threshold, and obtain a simplified three-dimensional geological model.
[0044] Specifically, S1 involves using any 3D geological modeling software to create a 3D geological model of the corresponding site and extracting the surface information of the corresponding 3D geological model.
[0045] S2 specifically includes the following steps:
[0046] The extracted layer information is used to deduplicate nodes, and the boundary nodes of the model are identified and fixed (these boundary points are not included in the node simplification calculation). Based on the extracted layer element information, the specific details of the neighboring elements of a given node (the centroid of the element and the element normal vector) are calculated.
[0047] Taking a specific stratigraphic level as the analysis object, the estimated value N′ of the normal vector of a node p(x0,y0,z0) in space is obtained according to the first law of geology. N′ is a weighted sum of the normal vectors of some known elements, and its formula is:
[0048]
[0049] Where n is the number of units in the neighborhood of point p(x0,y0,z0), N i w represents the true normal vector of the i-th neighboring cell. i This represents the weight coefficient of the i-th unit.
[0050] To obtain the most accurate results possible, w i The goal is to minimize the difference between the estimated normal vector N′ at point p(x0,y0,z0) and the true normal vector N0, satisfying the following equation:
[0051] E(N-N0)=0
[0052] Simultaneously calculate the minimum variance of the difference between the estimated value N′ of the node normal vector and the true value N0, i.e.
[0053] min(σ 2 = min(Var(N′-N0))
[0054] In other words, N = N(x,y,z) at any point in space consists of the regional average c and the random deviation R(x,y,z), where the variance of the deviation is a constant.
[0055] N(x,y)=E[N(x,y,z)+R(x,y,z)]=c+R(x,y,z)
[0056] By using unbiased constraints
[0057]
[0058] And by optimizing the objective function, we can obtain the following matrix equation.
[0059]
[0060] For N i =N(x) i ,y i ,z i ), N j =N(x)j ,y j ,z j Its semivariance is:
[0061]
[0062] Where γ ij Let γ be the semivariance between the i-th and j-th neighboring points (i.e., the geometric centroids of the i-th and j-th neighboring units), where λ is a constant, and 0 in the formula represents the point to be determined. ij (j≠0) is known, γ ij (j=0) Unknown. Here, a suitable fitting function γ=f(d) is needed.
[0063] For γ ij Solve for (j=0) and substitute into the following formula.
[0064]
[0065] The above formula yields w1,…,w n Substituting these values into the following formula, we obtain the final estimated value of N′:
[0066]
[0067] The unit normal vector N of node p(x0,y0,z0) is
[0068]
[0069] The unit normal vector N of node p(x0,y0,z0) and its n neighbors is obtained by calculation. i (i = 0, 1, 2, ..., n), and obtain the average unit normal vector of the local n+1 nodes.
[0070] Calculate the unit normal vector N at node p(x0,y0,z0) and the average unit normal vector of the (n+1) nodes. The included angle θ is then used to calculate the unit normal vectors of the n nodes in the neighborhood and the average unit normal vectors of the corresponding local n+1 nodes. The included angles between them are θ1, θ2, θ3, ..., θ n Then the entropy H of the normal vector of node p(x0,y0,z0) is... n The calculation is as follows:
[0071]
[0072] Where, p θ , They are respectively:
[0073]
[0074] S3 specifically includes the following steps:
[0075] Calculate the Gaussian curvature and Gaussian curvature entropy of all grid nodes on the stratum where all nodes p(x0,y0,z0) are located:
[0076] The unit normal vector N of node p(x0,y0,z0), and the nodes p in its neighborhood k. i The unit normal vector N corresponding to (i = 1, 2, ..., n) i (i = 1, 2, ..., n). Let vector p... i Projecting -p onto the tangent plane containing point p, then along its tangent vector t i The normal curvature passing through point p is:
[0077]
[0078] Find the maximum value k among all n normal curvatures. n (t id ):
[0079]
[0080] Where t id This represents the tangent vector corresponding to the maximum value among the n normal curvatures.
[0081] Establish a coordinate system using the tangent plane containing point p.
[0082]
[0083] Then, the tangent vector t i with coordinate axes The counterclockwise angle θ i The sine and cosine values are:
[0084]
[0085]
[0086] Based on this, the final calculation method for the Gaussian curvature G at node p is as follows:
[0087]
[0088] Wherein, the coefficients a, b, and c are respectively:
[0089]
[0090]
[0091] a21 =a 12 ,
[0092]
[0093]
[0094] a = k n (t id ),
[0095] Based on this, the Gaussian curvature entropy H G The calculation is as follows:
[0096]
[0097] Where, p G , They are respectively:
[0098]
[0099] G i Represents the neighboring nodes of node p. i Gaussian curvature, G i Same as the G algorithm.
[0100] S4 specifically includes the following steps:
[0101] Introducing strength parameters, taking molar coulomb strength as an example: Where c, is the inherent strength parameter of the rock and soil mass, and c is the cohesion of the rock and soil mass. This is the internal friction angle of the soil mass. σ is a variable related to the soil mass weight γ (an inherent property of the soil mass), the depth h from the surface, the Poisson's ratio ν of the corresponding stratum (an inherent property of the soil mass), and the external load q. From the above, we can see that at node p(x0,y0,z0)... It is a quantity related to the inherent properties of the soil and rock, the height h of the node relative to the vertical ground surface, and the external load q, denoted as m is the total number of strata that descend vertically from the Earth's surface to node p, i is the stratum number descending vertically from the Earth's surface to node p, and h is the number of strata. i Let λ be the thickness of the i-th layer of soil and rock. i The coefficient of the inherent properties of the soil at node p (λ) i Approximately equal to the unit weight γ of the corresponding soil and rock layer i ), ξ k Represents node p and external load q k For the action coefficient of this node, ξ k It can be approximated as
[0102] Will Substituting the Mohr-Coulomb strength criterion The value at node p is obtained from the data.
[0103]
[0104] In the formula c p , Let p be the cohesion and internal friction angle of the stratum where node p is located.
[0105] In 3D numerical simulations of soil and rock formations, the soil and rock material strength parameters of certain strata (often referred to as bedrock) are very high. These bedrock material strength parameters are then ignored. When iterating through the strength parameters of all strata (except the bedrock), the maximum value of the soil and rock material parameters is... Replacing the soil and rock material parameters of the stratum at node p yields:
[0106]
[0107] At this point, we introduce a parameter α. p ,make:
[0108] α p =τ j / τ p
[0109] α p The shear strength τ at node p j With τ p The ratio. Let α p The weighting coefficients of the entropy values used as the weighting factors for the weighted sum of the normal vector entropy and the Gaussian curvature entropy are used to calculate the weighted sum of entropy values:
[0110] H s =H n *α p +H G *α p
[0111] Thus, the strength parameter α is introduced. p Subsequently, the coupling of the two parameters, normal vector entropy and Gaussian curvature entropy, was achieved.
[0112] S5 specifically refers to: traversing all grid nodes of the same geological layer, eliminating nodes whose entropy weighted sum (excluding boundary points) is less than a preset threshold, thereby simplifying the ground layer grid nodes by introducing intensity parameters.
[0113] Example 2
[0114] For a certain three-dimensional geological model, the ground strata are as follows: Figure 2As shown, surface 0 is the topographic surface, surface 1 is the bottom surface of the first layer, and surface 2 is the bottom surface of the second layer, which is also the top surface of the bedrock layer. The strength parameters of the first geological body are c = 15 kPa and φ = 17°, and the strength parameters of the second geological body are c = 18 kPa and φ = 20°.
[0115] The node mesh of the three faces is as follows Figure 3 As shown, from top to bottom, the number of nodes on the top surface is 6577, the number of nodes on the second surface (bottom surface of the first layer) is 6589, and the number of nodes on the third surface (bottom surface of the second layer) is 6593.
[0116] The terrain surface formed by the initial nodes and the terrain surface formed by the filtered nodes are as follows: Figure 4 As shown. For topographic surfaces, since the surface itself does not have soil or rock parameters, it is not necessary to introduce strength parameters to perform entropy value screening on the surface (i.e., α). p (1). Filtering was done directly using entropy values (threshold 2.0). The number of nodes decreased from the initial 6577 to 1395, a reduction of 78.8%.
[0117] A filtering threshold of 2.0 was set, and an algorithm was used to filter nodes. The second face, i.e., the bottom face of the first layer, reduced the number of nodes from the initial 6589 to 3769, a reduction of 42.8%. The simplified second face is shown below. Figure 5 As shown. Using the same screening threshold, the third surface, i.e., the bottom surface of the second layer, originally had 6593 nodes; after screening, only 1935 nodes remained, a reduction of 70.7%. The simplified second surface is shown below. Figure 6 As shown.
[0118] In summary, in this case study, the method of introducing strength parameters and combining them with entropy values to filter the grid nodes of the geological surfaces reduced the total number of nodes across the three geological surfaces from 19,759 to 7,099, a reduction of 64.1%. While minimizing changes to the original geological surfaces, the method also simplified the geological surfaces by incorporating strength parameters. This not only preserved the original spatial characteristics of the geological surfaces but also provided strength parameter support for subsequent grid simplification of weak layers in the soil and rock mass (i.e., minimizing the simplification of geological surface nodes related to weak layers), while significantly reducing the number of grid nodes. This provides a geological model with fewer nodes within a reasonable range for subsequent site foundation analysis or slope cut-and-fill stability analysis, saving analysis computation time and improving analysis efficiency.
[0119] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for simplifying a three-dimensional geological model by introducing strength parameters, characterized in that, Specifically, the following steps are included: S1, Establish a three-dimensional geological model and extract each geological stratum; S2, calculate the normal vector and normal vector entropy on all ground plane grid nodes; S3, calculate the Gaussian curvature and Gaussian curvature entropy on all ground plane grid nodes; S4, introduce strength parameters, and calculate the weighted sum of the normal vector entropy and Gaussian curvature entropy at the node based on the strength parameters. The strength parameters are the ratio of the shear strength to the Mohr-Coulomb strength at the node; the strength parameters are... ; ; It is a node Mohr coulomb strength, It is a node Shear strength at the point; S5, traverse all ground surface grid nodes, remove nodes with corresponding entropy weights and values less than a preset threshold, and obtain a simplified three-dimensional geological model; The formula for calculating the weighted sum of the normal vector entropy and Gaussian curvature entropy at the node is as follows: in, It is a node The weighted sum of the normal vector entropy and the Gaussian curvature entropy at a given point. It is a node The entropy of the normal vector at that point It is a node Gaussian curvature entropy at that point It is a strength parameter. For nodes The ratio of shear strength to molar coulomb strength; node shear strength The calculation formula is: in,( , () is the maximum value of the inherent strength parameter of the rock and soil mass. It is a node The maximum cohesion of the strata is the cohesion of the soil and rock mass. It is a node The internal friction angle of the stratum, When the strength parameters inherent to the soil and rock mass are taken at their maximum values, the nodes The sequence number of the corresponding neighboring unit. To reach the node vertically downwards from the ground surface The total number of strata, Representative node The inherent property coefficients of the soil. Reaching the node vertically downwards from the ground surface stratigraphic sequence number, For the first The thickness of the soil and rock layers, It is an external load. Representative node External loads Regarding the effect coefficient of this node For nodes The number of units in the corresponding neighborhood, This refers to the index of the cell within the node's neighborhood.
2. The method for simplifying a three-dimensional geological model by introducing strength parameters as described in claim 1, characterized in that, node The formula for calculating the molar coulomb strength is: in, It is a node The cohesion of the strata, It is a node The internal friction angle of the stratum, To reach the node vertically downwards from the ground surface The total number of strata, Representative node The inherent property coefficients of the soil. Reaching the node vertically downwards from the ground surface stratigraphic sequence number, For the first The thickness of the soil and rock layers, It is an external load. Representative node External loads Regarding the effect coefficient of this node This represents the number of units within the corresponding neighborhood of a node. This refers to the index of the cell within the node's neighborhood.
3. The method for simplifying a three-dimensional geological model by introducing strength parameters as described in claim 1, characterized in that, node Normal vector entropy at point The calculation formula is: in, They are respectively: in, It is a node Unit normal vector at the location and Average unit normal vector of each node The included angle, For nodes The number of units in the neighborhood, For nodes The index of the unit within the neighborhood. It is a node No. Unit normal vector within a neighborhood and Average unit normal vector of each node The included angle.
4. A simplified three-dimensional geological model system incorporating strength parameters, characterized in that, It includes at least one processor and a memory communicatively connected to the at least one processor; the memory stores instructions executable by the at least one processor, which, when executed by the at least one processor, enable the at least one processor to perform the three-dimensional geological model simplification method for introducing intensity parameters as described in any one of claims 1 to 3.