A method for identifying and extracting potential sliding surfaces of slopes using three-dimensional numerical simulation analysis

Abstract

The present invention relates to a method for identifying and extracting potential sliding surfaces of slopes under three-dimensional numerical simulation analysis, and belongs to the field of traffic slope engineering. The present invention does not need to introduce strength reduction technology and does not limit the shear strength criterion of rock and soil. After obtaining the slope stress field by numerical simulation calculation, the potential sliding surface of the three-dimensional slope can be efficiently, automatically and intelligently identified and extracted. The obtained potential sliding surface conforms to the shear failure mechanism of the slope and can effectively show the actual failure form of the three-dimensional slope under real scenes. The present invention first determines the sliding boundary line of the three-dimensional potential sliding surface, and then extracts the discrete points of the three-dimensional potential sliding surface within this range, so as to facilitate the intelligent identification and extraction of the three-dimensional potential sliding surface. The present invention has the characteristics of wide application range, high efficiency, small deviation, strong versatility, good effect, low cost, etc., and has automation and intelligent features. It can provide a strong scientific basis for the prediction of the potential instability range of the slope and the determination of the reinforcement area in actual engineering.

Description

Technical Field

[0001] The invention belongs to the field of traffic slope engineering, and in particular relates to a method for identifying and extracting potential sliding surfaces of slopes based on three-dimensional numerical simulation analysis. Background Art

[0002] Landslides are a common geological disaster, especially in mountainous or rainy areas. They are extremely destructive and harmful, causing casualties, property loss, traffic disruptions, damage to water conservancy projects, and ecological damage. To minimize losses or prevent landslides, it is essential to accurately identify the most potentially dangerous sliding surface on the slope.

[0003] Accurately determining the most potentially dangerous sliding surface on a slope has the following benefits. First, disaster prevention and mitigation measures can be taken in advance, such as building protective projects, reinforcing slopes, and evacuating personnel, thereby reducing losses and casualties caused by landslides. Second, based on the determined most potentially dangerous sliding surface on the slope, the project design can be optimized, and appropriate construction methods and support measures can be selected to further improve the safety and stability of the project. In addition, the potential sliding surface analysis results can also be used to establish a slope monitoring and early warning system to monitor slope deformation and displacement in real time, issue early warning information in a timely manner, and ensure the safety of people and property.

[0004] Currently, the determination of the potential sliding surface of a slope is generally simplified as a two-dimensional problem. However, in actual engineering, the slope failure body is often a spatial combination of multiple rock and soil masses, and the failure surface presents a complex spatial geometry. At the same time, the external forces exerted on the failure body itself are often asymmetric. Therefore, considering these spatial complexities, the potential sliding surface of the slope should not be simplified as a two-dimensional problem but should be analyzed in three dimensions.

[0005] Existing methods for determining the potential sliding surface of three-dimensional slopes primarily include theoretical analysis, numerical simulation, and on-site monitoring. Theoretical analysis methods primarily employ the limit equilibrium method, based on the rigid body limit equilibrium theory. This method presupposes a sliding surface pattern, such as spherical, wedge-shaped, cylindrical, planar, wedge-shaped, or irregular. A corresponding size range is then set for the sliding surface of the pre-assumed pattern. The method then searches for the minimum slope safety factor, and through multiple iterative calculations, ultimately determines the most dangerous sliding surface of the slope. Numerical simulation methods establish a numerical slope model based on the actual slope geometry and reasonable physical and mechanical parameters. Numerical calculations are then used to obtain the slope stress, strain, and displacement fields to determine whether the slope is experiencing instability. Strength reduction techniques are often employed during the numerical calculation process to gradually reduce the shear strength of the rock mass, thereby forcing the slope to shear failure. The potential sliding surface of the slope is then determined based on the connected shear strain plastic zone at the time of shear failure. The on-site monitoring method determines the layout range and location of slope surface and deep deformation monitoring points based on the acquired slope geological conditions, rock and soil properties, and historical landslide situations. Then, by regularly collecting slope surface and deep deformation data and based on the incremental change relationship between the slope surface and deep deformation over time, the potential sliding range of the slope is roughly determined, and early warning of slope landslide disasters is issued accordingly.

[0006] Existing methods for determining potential sliding surfaces on slopes often simplify three-dimensional problems into two-dimensional ones for analysis, failing to account for the spatial complexity of the actual potential sliding surface. Furthermore, among the aforementioned methods for determining potential sliding surfaces on three-dimensional slopes, theoretical analysis methods require pre-established assumptions about sliding surface patterns, which may not align with actual conditions. Furthermore, the limit equilibrium method, the most widely used in actual engineering, primarily restricts the shear strength criterion for geotechnical materials to the linear MC strength criterion, making it difficult to obtain reliable results for slope stability analysis under complex conditions. While numerical simulation methods offer advantages such as high accuracy, wide applicability, dynamic analysis, and multi-field coupling, they incorporate strength reduction techniques, resulting in slope stress fields that are not realistic after strength parameter reduction in numerical analysis. Consequently, the inferred potential sliding surface is also not the actual potential sliding surface. Furthermore, multiple criteria exist for identifying slope instability in numerical analysis, and the calculation results differ between different criteria. On-site monitoring methods can roughly determine the shape and location of the potential sliding surface of a slope based on actual monitoring data. However, the accuracy of determining the potential sliding surface of a slope is closely related to the density of monitoring points. To obtain a more accurate potential sliding surface, a larger number of monitoring points and corresponding monitoring components are required, which leads to an increase in corresponding labor and monitoring costs. In addition, the reliability, durability, and accuracy of the monitoring components also restrict the accuracy of the potential sliding surface identification of the slope.

[0007] Invention patent CN202210223672.3 discloses a method for determining the three-dimensional anti-sliding safety factor using micro-disturbance displacement isosurfaces, including using the existing continuous numerical simulation platform to establish a geomechanical model of a slope with complex stratum distribution, using the classic Mohr-Coulomb criterion to calculate the slope stress field, applying a small parameter perturbation to induce displacement of the slope after equilibrium, and then using the displacement isosurface as a potential sliding surface to search for and calculate the safety factor. Multiple displacement surfaces attempt to obtain the minimum safety factor and the sliding surface on which they are located, thereby obtaining the global minimum safety factor and potential sliding surface. The entire calculation method is simple and reasonable, with strong logic, and can accurately reflect the three-dimensional safety factor and sliding surface of the slope. The evaluation of slope stability is more in line with reality, and has important reference significance for the calculation of slope safety factors and the determination of treatment plans in the geotechnical field. That is, this invention patent uses micro-perturbation displacement isosurfaces to establish the relationship between the three-dimensional slope anti-sliding safety factor and the micro-perturbation displacement, and determines the most appropriate control displacement value and its three-dimensional potential sliding surface based on the minimum three-dimensional slope anti-sliding safety factor. However, the implementation of this patent is based on the premise that the displacement values of all parts of the three-dimensional potential sliding surface are equal. This premise does not necessarily conform to the actual situation. For example, in the process of quantitative change to qualitative change of slope displacement in the push-type or traction-type landslide, the displacement of the rear end of the slope potential sliding surface is usually greater than the front end, while in the case of the latter, the displacement of the front end of the slope potential sliding surface is greater than the rear end. Therefore, there will be a certain difference between the three-dimensional potential sliding surface identified by this invention patent and the actual sliding surface. In addition, when identifying the three-dimensional potential sliding surface, this invention patent needs to continuously try micro-perturbation displacements and repeat the three-dimensional sliding surface extraction and three-dimensional slope anti-sliding safety factor calculation until the most appropriate control displacement value is found, which makes the entire calculation process more cumbersome and computationally inefficient. At the same time, in addition to the classical Mohr-Coulomb criterion, this invention patent has not yet been able to make it applicable to general nonlinear strength criteria.

[0008] Invention patent CN202311865958.2 discloses a method, medium, and equipment for automatically retrieving the dynamic sliding surface of a slope based on the finite element-discrete element coupling method (FDEM). This retrieval method is applicable to the retrieval of two-dimensional and three-dimensional slope sliding surfaces. The method includes: meshing the slope body with a triangular mesh; inserting quadrilateral joint units on the boundaries of the triangular units; calculating the equivalent unbalanced force of the nodes; updating the node positions; deriving displacement field data; completing node classification based on the k-means clustering algorithm; extracting the boundary points of the sliding bed and the landslide body based on the Alpha Shapes algorithm; performing Boolean operations on the above point set to obtain scattered points near the separation surface; and fitting a smooth sliding surface based on the above scattered points. The device, medium, and equipment can be used to implement this method. It can provide theoretical support for reducing geological disasters related to landslides. That is to say, this invention patent utilizes the characteristic that the displacement of the nodes on the landslide body is much larger than the displacement of the nodes on the sliding bed, and distinguishes the nodes on the landslide body and the nodes on the sliding bed based on the k-means clustering algorithm, and thereby identifies and extracts the potential sliding surface of the slope. However, the necessary prerequisite is that the slope reaches destruction or is in a critical state. Therefore, this invention patent is not suitable for the extraction and identification of the potential sliding surface of the slope in a stable state. Therefore, the scope of application of this patent is limited.

[0009] As construction projects move into challenging mountainous areas, slope engineering design and construction become increasingly complex. Timely and effective landslide prevention and control are crucial, and the need to accurately identify potential sliding surfaces on slopes has become urgent. To meet this requirement, a method for accurately determining potential sliding surfaces on slopes in three dimensions is needed, characterized by wide applicability, high efficiency, minimal deviation, strong versatility, good results, and low cost, along with automated and intelligent features. In other words, a new method for identifying and extracting potential sliding surfaces on slopes using three-dimensional numerical simulation analysis is needed. Summary of the Invention

[0010] Therefore, the present invention provides a method for identifying and extracting potential sliding surfaces of slopes using three-dimensional numerical simulation analysis, the method comprising the following steps:

[0011] S1. Establish a three-dimensional slope numerical calculation model, perform numerical calculations, obtain initial ground stress, and extract information of each numerical unit in the numerical model;

[0012] S2. Calculate the local safety factor of each numerical unit in the numerical model;

[0013] S3, determining the surface numerical units of the model, and sorting the surface numerical units according to the size of the local safety factor;

[0014] S4. The numerical unit on the slope surface with the smallest local safety factor is used as the starting unit where the sliding boundary line is located, and the numerical units on the slope surface where the sliding boundary line is located are gradually identified using the adjacent advancement method;

[0015] S5, extracting the center points of the numerical units on the slope surface where the sliding boundary line is located, and connecting them in sequence, thereby determining the sliding boundary line of the three-dimensional potential sliding surface;

[0016] S6. Take the sliding boundary line of the three-dimensional potential sliding surface as the control range, determine the vertical and horizontal grid points on the xy plane within this control range, draw vertical lines through these grid points, and use the series of equally divided points on the vertical lines and the local safety factors of the corresponding numerical units to extract the discrete points s of the three-dimensional potential sliding surface. ij ;

[0017] S7, using the concave characteristics of the three-dimensional potential sliding surface, the three-dimensional potential sliding surface discrete points s ij Correct the vertical position of

[0018] S8, the corrected three-dimensional potential sliding surface discrete points s ij The three-dimensional potential sliding surface is obtained by connecting in sequence along the vertical and horizontal network lines.

[0019] In a specific embodiment, step S2 specifically includes the following steps:

[0020] S2-1. Let the general expression of the shear strength criterion of rock and soil be τ f =f(σ), where σ is the normal stress on the action surface, τ f is the shear strength on the action surface;

[0021] S2-2. Based on the Mohr stress circle reflecting the stress state of the numerical unit, determine the range of the normal stress σ on the surface of the numerical unit in different directions as [σ3, σ1], and obtain the shear stress on the surface of the numerical unit in different directions under the corresponding normal stress as τ = [(σ1–σ)(σ–σ3)] 1 / 2 ; Among them, σ1 is the major principal stress and σ3 is the minor principal stress;

[0022] S2-3. Combined with the shear strength criterion of rock and soil, calculate the shear strength on the surface in different directions under the corresponding normal stress as τ f =f(σ);

[0023] S2-4. Calculate the shear strength τ on the action surface according to the definition of safety factor f The ratio k to the shear stress τ s , and k s =f(σ) / [(σ1–σ)(σ–σ3)] 1 / 2 ;

[0024] S2-5. When the normal stress σ is in the interval [σ3, σ1], use the mathematical extreme value method to solve k s The minimum value of

[0025] S2-6, let k s The minimum value of min(k s ), which is the local safety factor F of the numerical unit s_Local , thus obtaining the local safety factor of the numerical unit as F s_Local =min(k s ).

[0026] In a specific embodiment, the slope meets the generalized nonlinear HB strength criterion, and in step S2, the shear strength calculation formula of the rock and soil mass is:

[0027]

[0028] Among them, m b is the material constant, s is the parameter reflecting the degree of rock mass fragmentation, α is a constant related to the rock mass structure and surface conditions, is the instantaneous internal friction angle of the rock mass.

[0029] In a specific embodiment, in step S2, the parameter m b , s, α and The calculation formulas are:

[0030]

[0031] α=0.5+(1 / 6)×[exp(–GSI / 15)–exp(–20 / 3)]

[0032]

[0033] Among them, GSI is the geological strength index, σ c is the uniaxial compressive strength of intact rock, m i is the material constant of intact rock, and D is the disturbance factor of the rock mass.

[0034] In a specific embodiment, step S3 includes the following steps:

[0035] S3-1. Obtain the surface layer number and the surface group in the numerical model. The numerical model divides the surface layer into six surface groups: upper side, lower side, east side, west side, south side, and north side according to the direction of the surface layer's outer normal. The boundary surface is divided into five of the surface groups: lower side, east side, west side, south side, and north side.

[0036] S3-2, extracting the nodes, node numbers and node coordinates contained in the surface layer;

[0037] S3-3, exclude the boundary surface according to the artificially set boundary conditions; among them, for the boundary surface of the lower side group, the node coordinates on the surface are all equal to the lower boundary coordinate z in the z-axis direction of the numerical model below Based on this, when considering the calculation accuracy of the model, the z-axis coordinates of the nodes on the surface are located at [z below –0.001, z below +0.001] are excluded from the surface layer; the boundary surfaces of the east, west, south, and north side groups are also excluded from the surface layer in the same way;

[0038] S3-4. Based on the number of the surface composed of the numerical unit, the numerical unit is traversed to determine whether the surface composed of the numerical unit belongs to the mid-slope surface of the surface layer, and then the numerical unit matching the mid-slope surface of the surface layer is found, and the surface numerical unit is further determined.

[0039] In a specific embodiment, steps S4 to S5 include the following steps:

[0040] S5-1. Sort the numerical units on the slope surface from small to large according to the magnitude of their local safety factors, and then determine the numerical unit on the slope surface with the smallest local safety factor, and use it as the starting unit for the sliding boundary line.

[0041] S5-2. Obtain the adjacent slope surface numerical units of the starting unit, compare the local safety factors of these adjacent slope surface numerical units, and use the slope surface numerical unit with the smallest local safety factor as the second unit where the sliding boundary line is located;

[0042] S5-3. Determine the unknown unit where the next sliding boundary line is located from the known unit where the previous sliding boundary line is located, wherein the known unit where the previous sliding boundary line is located and the unknown unit where the next sliding boundary line is located are adjacent numerical units (this is condition one); and the angle between the line connecting the center point of the known unit where the previous sliding boundary line is located and the center point of the unknown unit where the next sliding boundary line is located, and the line connecting the center point of the known unit where the previous sliding boundary line is located and the center point of the known unit where the previous sliding boundary line is located, projected on the xy plane, is in the range of [–90°, 90°] (this is condition two); on this basis, the unknown unit where the next sliding boundary line is located is the one with the smallest local safety factor among the numerical units on the slope surface that meets the above two conditions;

[0043] S5-4, determining whether the unknown cell where the next sliding boundary line is located is an adjacent cell of the starting cell where the sliding boundary line is located; if so, stopping the identification of the numerical cell on the slope surface where the sliding boundary line is located; otherwise, repeating step S5-3;

[0044] S5-5. Extract the center points of the numerical units on the slope surface where the sliding boundary line is located, and connect them in sequence to determine the sliding boundary line of the three-dimensional potential sliding surface.

[0045] In a specific embodiment, in steps S4 to S5, the principle for determining adjacent numerical units of a slope surface numerical unit is to use a certain slope surface numerical unit as a target unit, compare the target unit with other slope surface numerical units to see whether they have common vertices, and then determine whether the slope surface numerical unit is its adjacent numerical unit. The specific operation steps for determining the adjacent numerical units of the slope surface numerical unit include:

[0046] S5-3-1. Take a certain slope surface numerical unit as the target unit and obtain the node number information of each unit vertex;

[0047] S5-3-2, traverse the slope surface numerical units, and extract the node number information of each vertex of other slope surface numerical units outside the target unit;

[0048] S5-3-3, comparing the node number information of each vertex of the unit to be determined and the target unit;

[0049] S5-3-4. If the node numbers of one or more vertices of the unit to be determined and the target unit overlap, then the unit to be determined is an adjacent numerical unit of the target unit.

[0050] In a specific embodiment, in step S7, specifically, the three-dimensional potential sliding surface is cut using longitudinal and transverse vertical planes to obtain two-dimensional slicing curves of the three-dimensional potential sliding surface on these vertical planes. Then, the vertical positions of the discrete points of the three-dimensional potential sliding surface are corrected using the increasing tangent slope of the two-dimensional slicing curve under the concave feature of the three-dimensional potential sliding surface. At the same time, through repeated corrections in sequence and multiple rounds, the final vertical positions of the discrete points of the three-dimensional potential sliding surface are obtained while completely ensuring the increasing tangent slope of the two-dimensional slicing curve.

[0051] In a specific embodiment, the software FLAC 3D Perform three-dimensional numerical simulation analysis.

[0052] The advantages of the invention are that this method does not require the introduction of strength reduction technology and does not limit the shear strength criterion of the rock and soil. After obtaining the slope stress field through numerical simulation calculation, the three-dimensional slope potential sliding surface can be automatically identified and extracted. The obtained potential sliding surface conforms to the slope shear failure mechanism and can effectively show the actual failure form of the three-dimensional slope in a real scene. At the same time, the sliding boundary line of the three-dimensional potential sliding surface is first determined, and then the three-dimensional potential sliding surface discrete points are extracted within this range. This method is conducive to the intelligent identification and extraction of the three-dimensional potential sliding surface. Therefore, the present invention has the characteristics of wide application range, high efficiency, small deviation, strong versatility, good effect, low cost, etc., and has automation and intelligent features. It can provide a strong scientific basis for the prediction of the potential instability range of the slope and the determination of the reinforcement area in actual engineering.

[0053] Furthermore, compared to the prior art CN202311865958.2, the present invention can identify and extract the potential sliding surface of a slope based on the shear failure mechanism, without requiring the displacement of nodes on the landslide body to be significantly greater than that of nodes on the sliding bed. Therefore, the present invention has a wider scope of application. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 This is a schematic diagram of the three-dimensional slope numerical model of the present invention.

[0055] Figure 2 This is a schematic diagram of the numerical unit stress analysis in the present invention.

[0056] Figure 3 This is a flow chart for calculating the local safety factor of a numerical unit according to the present invention.

[0057] Figure 4 It is a schematic diagram of the boundary of the three-dimensional slope numerical model of the present invention and the vertical and horizontal network lines on the xy plane.

[0058] Figure 5 This is a schematic diagram for determining the numerical unit of the slope surface layer of the present invention.

[0059] Figure 6 This is a cloud diagram of the local safety factor distribution of the surface numerical unit of the present invention.

[0060] Figure 7 Schematic diagram of the method for determining the sliding boundary line of a three-dimensional potential sliding surface according to the present invention.

[0061] Figure 8 This is a schematic diagram of the sliding boundary line of the three-dimensional potential sliding surface of the present invention.

[0062] Figure 9 This is a schematic diagram of identifying adjacent units of a numerical unit on the slope surface according to the present invention.

[0063] Figure 10 is the three-dimensional potential sliding surface discrete point s of the present inventionij Schematic diagram of spatial position recognition.

[0064] Figure 11 This is a schematic diagram for identifying the numerical unit where the point ijk is located in the present invention.

[0065] Figure 12 Schematic diagram of the longitudinal vertical plane j and the transverse vertical plane i in the three-dimensional potential sliding surface of the present invention.

[0066] Figure 13 is the three-dimensional potential sliding surface discrete point s of the present invention ij Schematic diagram of vertical position correction on the longitudinal plane j.

[0067] Figure 14 is the three-dimensional potential sliding surface discrete point s of the present invention ij Schematic diagram of vertical position correction on the horizontal and vertical plane i.

[0068] Figure 15 This is a flowchart for the implementation of identifying and extracting potential sliding surfaces of slopes in three-dimensional numerical simulation calculations of the present invention.

[0069] In the figure: 1. 3D slope numerical model; 2. Numerical unit; 3. Major principal stress action surface; 4. Minor principal stress action surface; 5. Shear stress on the action surface in different directions in the numerical unit; 6. Normal stress on the action surface in different directions in the numerical unit; 7. Horizontal network line; 8. Vertical network line; 9. Grid point ij; 10. Projection range of the numerical unit in the numerical model on the xy plane; 11. Boundary surface; 12. Slope surface; 13. Slope surface numerical unit; 14. Starting unit where the sliding boundary line is located; 15. The first unit where the sliding boundary line is located two units; 16. The unit before the known unit where the sliding boundary line is located; 17. The known unit where the sliding boundary line is located; 18. The unknown unit where the sliding boundary line is located; 19. The sliding boundary line; 20. The target unit; 21. The adjacent numerical unit; 22. The unit vertex; 23. The control range of the sliding boundary line; 24. The numerical unit of the slope surface inside the sliding boundary line; 25. The numerical unit of the slope surface on the sliding boundary line; 26. Point ijk; 27. The numerical unit corresponding to point ijk; 28. The discrete point s of the three-dimensional potential sliding surface ij ; 29, to be determined point; 30, numerical unit side; 31, side vertex; 32, spatial geometry; 33, three-dimensional potential sliding surface; 34, vertical plane j; 35, horizontal plane i; 36, existing three-dimensional potential sliding surface discrete point s ij 37. The vertical position of the corrected three-dimensional potential sliding surface discrete point s ij vertical position. DETAILED DESCRIPTION

[0070] In order to solve the above technical method problems, the present invention designs a method for identifying and extracting potential sliding surfaces of slopes in three-dimensional numerical simulation calculations. This method obtains the slope stress field through numerical simulation. Based on the shear strength criterion of the rock and soil mass, the local safety factor of each numerical unit is calculated using the stress information of the numerical unit in the numerical model and the Mohr stress circle reflecting the stress state of the numerical unit. Then, the slope surface numerical unit is extracted from the numerical units, and the slope surface numerical unit with the smallest local safety factor is used as the starting unit where the sliding boundary of the three-dimensional potential sliding surface is located. The slope surface numerical unit where the sliding boundary is located is then gradually identified using the adjacent advancement method to determine the sliding boundary of the three-dimensional potential sliding surface. Furthermore, the sliding boundary of the three-dimensional potential sliding surface is used as the control range. The vertical and horizontal grid points and their vertical lines within this control range are used, and the vertical lines of the vertical and horizontal grid points and the local safety factors of the corresponding numerical units are combined to extract the discrete points of the three-dimensional potential sliding surface. Based on this, the vertical position of the discrete points of the three-dimensional potential sliding surface is corrected by applying the concave characteristics of the three-dimensional potential sliding surface. Finally, the corrected three-dimensional potential sliding surface discrete points are connected in sequence along the vertical and horizontal grid lines to obtain the three-dimensional potential sliding surface.

[0071] The specific implementation process and calculation method are as follows:

[0072] (1) Figure 1 As shown in Figure 1, according to the actual slope morphology, geological conditions and physical and mechanical parameters of the rock and soil layer, a corresponding three-dimensional slope numerical model is established. Combined with numerical simulation software, numerical analysis is carried out to obtain the slope stress field and extract the information of each numerical unit in the numerical model, including number information, coordinate information (such as unit center coordinates and unit vertex coordinates), volume of the numerical unit, side area and stress information (such as major principal stress σ1, minor principal stress σ3 and normal stress σ along the vertical direction). z )wait.

[0073] (2) Figure 2 As shown in the figure, taking any numerical unit as an example, the major principal stress σ1 and minor principal stress σ3 of the numerical unit are obtained by numerical simulation, and a stress analysis diagram of the numerical unit is drawn. In the stress analysis diagram of the numerical unit, OA is the minor principal stress action surface, and the force on it is the minor principal stress σ3. OB is the major principal stress action surface, and the force on it is the major principal stress σ1. Among them, the minor principal stress action surface OA and the major principal stress action surface OB are perpendicular to each other. OT is the action surface in different directions in the numerical unit, and the angle between it and the minor principal stress action surface OA is α (0°≤α≤90°), and the forces on OT are normal stress σ and shear stress τ.

[0074] (3) Figure 2As shown in the figure, based on the stress analysis of any numerical unit, the Moore stress circle reflecting the stress state of the numerical unit is obtained, and the Moore stress circle is drawn in the normal stress and shear stress rectangular coordinate systems, which is consistent with the actual stress analysis diagram. In the Moore stress circle, OA represents the action surface of the minor principal stress, OB represents the action surface of the major principal stress, and OT represents the action surface in different directions in the numerical unit, where O is the center point of the Moore stress circle, point A and point B correspond to the minor principal stress σ3 and the major principal stress σ1, respectively, and the stress corresponding to point T is σ and τ. Given that the angle in the Moore stress circle model is twice that in the actual stress analysis model, ∠AOT=2α in the Moore stress circle.

[0075] (4) Figure 2 As shown in Figure 1, based on the Moore stress circle that reflects the stress state of the numerical unit, when α varies in the range of 0° to 90°, it can be seen that the value range of the normal stress σ on the surface of the numerical unit in different directions is [σ3, σ1]. At the same time, in the Moore stress circle, according to the spatial geometric relationship of the triangle OTE, it can be obtained that τ = [(σ1–σ)(σ–σ3)] 1 / 2 , where point E is the intersection of the vertical line through point T and the normal stress axis.

[0076] (5) Figure 3 As shown in the figure, based on the selected rock and soil shear strength criterion, the stress information of the numerical unit is applied to calculate the local safety factor of each numerical unit in the numerical model. The specific implementation steps are as follows: ① Let the general expression of the rock and soil shear strength criterion be τ f =f(σ), where σ is the normal stress on the action surface, τ f is the shear strength on the action surface; ② Based on the Mohr stress circle reflecting the stress state of the numerical unit, the range of the normal stress σ on the action surface in different directions in the numerical unit is determined to be [σ3, σ1], and the shear stress on the action surface in different directions under the corresponding normal stress in the numerical unit is obtained as τ = [(σ1–σ)(σ–σ3)] 1 / 2 ; ③ Combined with the shear strength criterion of rock and soil, the shear strength on the surface in different directions under the corresponding normal stress is calculated as τ f =f(σ); ④ According to the definition of safety factor, calculate the shear strength τ on the action surface f The ratio k to the shear stress τ s , and k s =f(σ) / [(σ1–σ)(σ–σ3)] 1 / 2 ⑤ When the normal stress σ is in the interval [σ3, σ1], use the mathematical extreme value method to solve k s The minimum value of; ⑥ Let k s The minimum value of min(k s ), which is the local safety factor F of the numerical unit s_Local , thus obtaining the local safety factor of the numerical unit as Fs_Local =min(k s ).

[0077] (6) Figure 4 As shown in the figure, the xyz axis coordinate system is established with the longitudinal direction of the three-dimensional slope as the x-axis direction, the transverse direction as the y-axis direction and the vertical direction as the z-axis direction. The front and rear boundary coordinates of the three-dimensional numerical model in the x-axis direction are x and z, respectively. front and x back , the left and right boundary coordinates in the y-axis direction are y left and y right , the lower and upper boundary coordinates in the z-axis direction are z below and z above At the same time, a vertical and horizontal grid is drawn on the xy plane, where in the range [x front , x back ] Draw horizontal network lines parallel to the y-axis direction at equal intervals, and number them from 0 to n according to the x-axis coordinate size of the horizontal network lines. For the i-th horizontal network line, its x-axis coordinate is x front +i×(x back -x front ) / n, in the range [y left ,y right ] Draw longitudinal network lines parallel to the x-axis at equal intervals within the grid, and number them from 0 to m according to their y-axis coordinates. For the jth longitudinal network line, its y-axis coordinate is y right +j×(y left -y right ) / m, for the grid point ij, it is the intersection of the i-th horizontal network line and the j-th vertical network line. Correspondingly, the coordinates of the grid point ij are (x front +i×(x back -x front ) / n,y right +j×(y left -y right ) / m), it should be noted that the vertical and horizontal grid sizes should be slightly smaller than the numerical unit sizes in the numerical model, so as to ensure that the numerical units in the numerical model have grid points within the projection range on the xy plane.

[0078] (7) Figure 5As shown in the figure, in the numerical unit, there is a side surface belonging to a unique numerical unit, and this side surface is in the surface layer of the numerical model, so it is called the surface layer. The surface layer includes the slope surface and the boundary surface. Different from the slope surface coming from the natural form of the slope, the boundary surface is set artificially according to the needs of numerical analysis. That is to say, the boundary surface is self-defined and can be excluded from the surface layer according to the set boundary conditions. Here, the slope surface numerical unit is set to be a numerical unit containing the slope surface. Then, the slope surface is extracted by obtaining the surface layer in the numerical model and excluding the boundary surface. Then, the slope surface numerical unit is determined according to the matching between the slope surface and the numerical unit. The specific implementation steps are as follows: ① Get the surface layer number and the surface group in the numerical model. For example, the numerical model divides the surface layer into 6 surface groups according to the direction of the outer normal of the surface layer, namely, the upper side, lower side, east side, west side, south side, and north side. Among them, the boundary surface is divided into the 5 surface groups of the lower side, east side, west side, south side, and north side. Among them, the lower side in the surface group corresponds to Figure 5 The lower side of the numerical model corresponds to the middle side of the face group Figure 5 The back side of the numerical model corresponds to the west side of the face group Figure 5 The front side of the numerical model corresponds to the south side of the face group Figure 5 On the right side of the numerical model, the north side of the face group corresponds to Figure 5 The left side of the numerical model; ② Extract the nodes, node numbers and node coordinates contained in the surface layer; ③ Exclude the boundary surface according to the artificially set boundary conditions. For example, for the boundary surface of the lower side group, the node coordinates on the surface are all equal to the lower boundary coordinate z in the z-axis direction of the numerical model. below Based on this, when considering the calculation accuracy of the model, the z-axis coordinates of the nodes on the surface can be located at [z below –0.001, z below +0.001] are excluded from the surface layer. The boundary surfaces of the east, west, south, north and other surface groups can be excluded from the surface layer in the same way; ④ Based on the number of the surface composed of the numerical unit, the numerical unit is traversed to determine whether the surface composed of the numerical unit belongs to the mid-slope surface of the surface layer, and then the numerical unit that matches the mid-slope surface of the surface layer is found, and the surface layer numerical unit is further determined.

[0079] (8) Figures 6 to 8As shown, the sliding boundary line of the three-dimensional potential sliding surface is the intersection line of the three-dimensional potential sliding surface and the slope surface. It is a closed curve and controls the spatial range of the three-dimensional potential sliding surface. The slope surface numerical unit with the smallest local safety factor can be used as the starting unit, and the slope surface numerical units where the sliding boundary line is located can be gradually identified by the adjacent advancement method, and the sliding boundary line of the three-dimensional potential sliding surface can be determined. The specific implementation steps are as follows: ① In the slope surface numerical units, the slope surface numerical units are sorted from small to large according to the size relationship of the local safety factors of the numerical units, and then the slope surface numerical unit with the smallest local safety factor is determined, and it is used as the starting unit where the sliding boundary line is located; ② The adjacent slope surface numerical units of the starting unit are obtained, and the local safety factors of these adjacent slope surface numerical units are compared, and the slope surface numerical unit with the smallest local safety factor is used as the second unit where the sliding boundary line is located; ③ The unknown unit where the next sliding boundary line is located is determined by the known unit where the previous sliding boundary line is located, and its In the method, the known unit where the previous sliding boundary line is located and the unknown unit where the next sliding boundary line is located are adjacent numerical units (condition 1), and the angle between the line connecting the center point of the known unit where the previous sliding boundary line is located and the center point of the unknown unit where the next sliding boundary line is located, as well as the line connecting the center point of the known unit where the previous sliding boundary line is located and the center point of the known unit where the previous sliding boundary line is located, is in the range of [-90°, 90°] on the xy plane (condition 2). On this basis, the unknown unit where the next sliding boundary line is located is the one with the smallest local safety factor among the numerical units on the slope surface that meet the above two conditions; ④ determine whether the unknown unit where the next sliding boundary line is located is an adjacent unit of the starting unit where the sliding boundary line is located. If so, stop identifying the numerical units on the slope surface where the sliding boundary line is located. Otherwise, repeat step ③; ⑤ extract the center point positions of the numerical units on the slope surface where the sliding boundary line is located, and connect them in sequence to determine the sliding boundary line of the three-dimensional potential sliding surface.

[0080] (9) Figure 9 As shown in Figure 2, the principle for determining adjacent numerical units of a slope surface numerical unit is to take a certain slope surface numerical unit as the target unit and compare whether the target unit has common vertices with other slope surface numerical units (referred to as the units to be determined), thereby determining whether the slope surface numerical unit is its adjacent numerical unit. The specific operation steps are as follows: ① Take a certain slope surface numerical unit as the target unit and obtain the node number information of each unit vertex; ② Traverse the slope surface numerical units and extract the node number information of each vertex of other slope surface numerical units (i.e., the units to be determined) outside the target unit; ③ Compare the node number information of each vertex of the unit to be determined and the target unit; ④ If the node number of one or more vertices of the unit to be determined and the target unit coincide, then the unit to be determined is an adjacent numerical unit of the target unit.

[0081] (10) Figure 10 As shown in the figure, the sliding boundary line of the three-dimensional potential sliding surface is used as the control range, the vertical and horizontal grid areas where the xy plane projection of the sliding boundary line of the three-dimensional potential sliding surface is located are determined, and it is identified whether the grid points in the area are located in the sliding boundary line control range of the three-dimensional potential sliding surface. For the grid points in this control range, a vertical line is drawn through the grid points, and the z-axis coordinate on the vertical line of the grid point is taken as the z below As the starting point, the vertical line is divided into multiple segments according to a certain spacing Δz, and a series of equally divided points on the vertical line of the grid point is obtained. As for the spacing Δz, its value range is 0.1m~1.0m, and the value is determined according to the numerical unit size. If the numerical unit size is small, a small value is taken, otherwise a large value is taken. Taking the grid point ij as an example, the point on its vertical line is k, and it is named point ijk, then the coordinates of point ijk are (x front +i×(x back -x front ) / n,y right +j×(y left -y right ) / m,z below +kΔz), where z below ≤z below +kΔz≤z above and 0≤k≤Int[(z above -z below ) / Δz], Int is the rounding function, further, the numerical unit where the point ijk is located is determined, if it is in a certain numerical unit, the local safety factor of the numerical unit is used as the local safety factor of the point ijk, it should be noted that the numerical unit corresponding to the point ijk cannot be the numerical unit of the slope surface inside the sliding boundary line, but can be the numerical unit of the slope surface on the sliding boundary line, if the point ijk has no corresponding numerical unit, then a very large number (such as 1000) can be taken as the local safety factor of the point ijk, further, the local safety factors of a series of equally divided points on the vertical line of the grid point ij (i.e., point ijk) are compared, and the point corresponding to the minimum value of the local safety factor is taken as the discrete point of the three-dimensional potential sliding surface on the vertical line of the grid point ij, which is named as the three-dimensional potential sliding surface discrete point s ij Therefore, according to this processing method, the sliding surface discrete points on the vertical line of the grid point within the control range of the sliding boundary line of the three-dimensional potential sliding surface can be obtained. The specific implementation steps are as follows: ① Based on the center point position of the slope surface numerical unit where the sliding boundary line is extracted in sequence, the sliding boundary line discrete points arranged in order are obtained, and these discrete points are connected in sequence to obtain the spatial sliding boundary line. Further, the spatial sliding boundary line is projected onto the xy plane; ② The x and y axis coordinates of the discrete points of the sliding boundary line are extracted, and the minimum x axis coordinate of the discrete points of the sliding boundary line is found from them. min and the maximum value x maxAnd the minimum value y of the y-axis coordinate min and the maximum value y max Based on this, the horizontal network line number interval within the sliding boundary line control range in the vertical and horizontal grids on the xy plane is obtained as [i min ,i max ] and the vertical network line number interval is [j min ,j max ], where i min =Int[(x min -x front ) / (x back -x front )],i max =Int[(x max -x front ) / (x back -x front )],j min =Int[(y min -y right ) / (y left -y right )],j max =Int[(y max -y right ) / (y left -y right )]; ③ In the horizontal network line number interval [i min ,i max ] and vertical network line number interval [j min ,j max ] in the vertical and horizontal grids formed by the initial grid point ij, the initial grid point ij is located at i=i min and j = j min④ According to the x and y axis coordinates of the grid point ij, determine whether it is located within the projection of the sliding boundary line on the xy plane. The specific judgment method is to use the linear interpolation method to obtain the lower and upper intersection points where the longitudinal network line passing through the grid point ij intersects with the projection of the sliding boundary line on the xy plane (or the left and right intersection points where the transverse network line passing through the grid point ij intersects with the projection of the sliding boundary line on the xy plane), and compare the x axis coordinates of the grid point ij with the lower and upper intersection points (or the y axis coordinates of the grid point ij with the left and right intersection points). If the grid point ij If the x-axis coordinate of the grid point ij is outside the intersection of the lower and upper sides (or the y-axis coordinate of the grid point ij is outside the intersection of the left and right sides), it indicates that the grid point ij is not located within the projection of the sliding boundary line on the xy plane. At this time, jump to step ⑦. If it is within the intersection of the lower and upper sides (or within the intersection of the left and right sides), it indicates that it is located within the projection of the sliding boundary line on the xy plane. At this time, draw a vertical line through the grid point ij, and then divide the vertical line into segments according to the spacing Δz, and obtain a series of equally divided points k on the vertical line, where the starting point of the division is located on this vertical line with the z-axis coordinate z below The point and the end point are located on this vertical line with a z-axis coordinate close to but not exceeding z above point, then 0≤k≤Int[(z above -z below ) / Δz]; ⑤ For the vertical line passing through the grid point ij, traverse the equally divided points k on it and name them as points ijk. Further evaluate the numerical unit where the point ijk is located, and assign the corresponding numerical unit number and local safety factor to the point ijk. If there is no corresponding numerical unit or the corresponding numerical unit is a slope surface numerical unit inside the sliding boundary line, the local safety factor will be set to a maximum number (such as 1000) and assigned to the point ijk; ⑥ For the vertical line passing through the grid point ij, sort the local safety factors of the series of equally divided points on it from small to large. If there is a unique minimum value, the point corresponding to the minimum value is the three-dimensional potential sliding surface discrete point s on the vertical line passing through the grid point ij ij , and assign the coordinates of this point to the three-dimensional potential sliding surface discrete point s ij If there are multiple identical minimum values and these points correspond to the same numerical unit, the x and y axis coordinates of the grid point ij are assigned as the three-dimensional potential sliding surface discrete point s ij The x- and y-axis coordinates of the minimum value are assigned as the z-axis coordinate of the center point of the numerical unit corresponding to the minimum value as the three-dimensional sliding surface discrete point s ij If there are multiple identical minimum values and these points do not completely correspond to the same numerical unit, the x and y coordinates of the grid point ij are assigned as the three-dimensional potential sliding surface discrete point s ij The x- and y-axis coordinates of the three-dimensional sliding surface are obtained by extracting the z-axis coordinates of the center points of the numerical units corresponding to the minimum value, and assigning the minimum value of the z-axis coordinates as the discrete point s of the three-dimensional sliding surface.ij z-axis coordinate; ⑦If i≤i max and j <j max When j=j+1, repeat steps ④ to ⑥. If i max and j = j max When i=i+1 and j=j min , and repeat steps ④ to ⑥, if i=i max and j = j max ⑧ Obtain the three-dimensional potential sliding surface discrete points s on the vertical line of all grid points ij within the projection of the sliding boundary line on the xy plane ij , where the three-dimensional potential slip surface discrete points s ij The coordinates of (x i ,y j , z ij ), and x i =x front +i×(x back -x front ) / n、y i =y right +j×(y left -y right ) / m and z ij Determined by step ⑥.

[0082] (11) Figure 11 As shown in FIG, the principle for determining the numerical unit where the series of equally divided points k (i.e., points ijk) on the vertical line of the grid point ij is located is to connect the point to be determined with the vertex on the side surface of a certain numerical unit to form a spatial geometric body, and when the points are connected with the vertices on each side surface respectively, multiple spatial geometric bodies will be obtained. If the sum of the volumes of these spatial geometric bodies is equal to the volume of the numerical unit, then this point is located in the numerical unit. The specific implementation steps are as follows: ① Obtain the volume of the numerical unit and the side surface of the numerical unit and its vertex number and coordinates, and extract the side surface area of the numerical unit and the coordinates of the center point; ② Select any 4 points from the vertices and center point on a certain side surface of the numerical unit, and use this The coordinates of the four points determine the functional formula of the side surface of this space, and then, the distance calculation formula from the point to the spatial surface is applied to solve the vertical distance from the potential sliding surface point to the side surface of the numerical unit; ③ Based on the vertical distance from the point to be determined to the side surface of the numerical unit and the area of the side surface of the numerical unit, the volume of the spatial geometric body formed by connecting the point to be determined with the vertices on each side surface of the selected numerical unit and the sum of the volumes are calculated; ④ All numerical units are traversed, and it is determined whether the sum of the volumes of the spatial geometric bodies formed by connecting the point to be determined with the vertices on each side surface of the selected numerical unit is equal to the volume of the numerical unit. If the two are equal, the numerical unit where the point to be determined is located is obtained.

[0083] (12) Figures 12 to 14 ​As shown in the figure, the three-dimensional potential sliding surface should be a concave surface. In order to ensure the concave characteristics of the three-dimensional potential sliding surface, the vertical and horizontal network lines on the xy plane within the control range of the sliding boundary line are used to stretch them in the vertical direction to derive vertical planes passing through the vertical and horizontal network lines. These vertical planes are used to cut the three-dimensional potential sliding surface, and the two-dimensional slice curves of the three-dimensional potential sliding surface on these vertical planes can be obtained. Then, the increasing slope of the tangent of the two-dimensional slice curve under the concave characteristics of the three-dimensional potential sliding surface is used to correct the discrete points s of the three-dimensional potential sliding surface. ij At the same time, through repeated corrections in sequence and multiple rounds, the three-dimensional potential sliding surface discrete point s is obtained under the premise of fully ensuring the increasing slope of the tangent of the two-dimensional slice curve. ij The final vertical position of the sliding boundary line is determined by the following specific steps: ① On the xy plane within the control range of the sliding boundary line, select the jth longitudinal network line, and j=j min , stretch this longitudinal network line in the vertical direction to form a vertical plane (called vertical plane j), then the vertical plane j will cut the three-dimensional potential sliding surface, and the two-dimensional slice curve of the three-dimensional potential sliding surface on the vertical plane j can be obtained. At the same time, the discrete points s of the three-dimensional potential sliding surface ij (i min ≤i≤i max , and is located within the lower and upper intersection points of the projections of the corresponding longitudinal network line and the sliding boundary line on the xy plane) will be located in the vertical plane; ② In the vertical plane j, according to the increasing slope of the tangent of the two-dimensional slice curve in the three-dimensional potential sliding surface, the discrete point s of the three-dimensional potential sliding surface is corrected ij The vertical position of the three-dimensional potential slip surface discrete point s ij The vertical position correction of i is carried out in order from small to large, and the three-dimensional potential sliding surface discrete point s after correction ij The vertical position of the existing three-dimensional potential sliding surface discrete point s is immediately replaced ij The vertical position of the sliding surface is represented by the discrete point s ij For example, let it be compared with the previous sliding surface discrete point s (i-1)j The inclination angle of the connecting line in the horizontal direction is α x_ij (can be obtained based on the known discrete point coordinates), let the sliding surface discrete point s (i-1)j and its previous sliding surface discrete point s (i-2)j The inclination angle of the connecting line in the horizontal direction is α x_(i-1)j , then α should be satisfied x_ij ≥α x_(i-1)j Otherwise, let α x_ij =α x_(i-1)j , and use this to discrete points s on the three-dimensional potential sliding surface ij Correct its vertical position while keeping the x and y axis coordinates unchanged, that is, the z axis coordinate z ij ③If j <jmax When , set j = j + 1, and repeat step ②; ④ on the xy plane within the control range of the sliding boundary line, select the i-th horizontal network line, and i = i min , stretch this horizontal network line in the vertical direction to form a vertical plane (called horizontal vertical plane i), then the horizontal vertical plane i will cut the three-dimensional potential sliding surface, and the two-dimensional slice curve of the three-dimensional potential sliding surface on the horizontal vertical plane i can be obtained. At the same time, the discrete points s of the three-dimensional potential sliding surface ij (j min ≤j≤j max , and is within the left and right intersection points of the projections of the corresponding horizontal network line and the sliding boundary line on the xy plane) will be located in the horizontal and vertical planes; ⑤ In the horizontal and vertical planes i, according to the increasing slope of the tangent of the two-dimensional slice curve in the three-dimensional potential sliding surface, the discrete points s of the three-dimensional potential sliding surface are corrected ij The vertical position of the three-dimensional potential slip surface discrete point s ij The vertical position correction of j is carried out in order from small to large, and the three-dimensional potential sliding surface discrete point s after correction ij The vertical position of the existing three-dimensional potential sliding surface discrete point s is immediately replaced ij The vertical position of the sliding surface is represented by the discrete point s ij For example, let it be compared with the previous sliding surface discrete point s i(j-1) The inclination angle of the connecting line in the horizontal direction is α y_ij (can be obtained based on the known discrete point coordinates), let the sliding surface discrete point s i(j-1) and its previous sliding surface discrete point s i(j-2) The inclination angle of the connecting line in the horizontal direction is α y_i(j-1) , then α should be satisfied y_ij ≥α y_i(j-1) Otherwise, let α y_ij =α y_i(j-1) , and use this to discrete points s on the three-dimensional potential sliding surface ij Correct its vertical position while keeping the x and y axis coordinates unchanged, that is, the z axis coordinate z ij ;⑥if i min When , let i = i + 1 and repeat step ⑤; ⑦ repeat steps ① to ⑥ until there is no need to discrete the three-dimensional potential sliding surface point s ij When the vertical position of the two-dimensional slice curve is corrected, the tangent slope of the two-dimensional slice curve can be automatically guaranteed; ⑧ Output the corrected three-dimensional potential sliding surface discrete point s ij .

[0084] (13) Figure 15 ​As shown in Figure 1, the implementation process of identifying and extracting the potential sliding surface of the slope in the three-dimensional numerical simulation calculation is as follows: ① Establish a three-dimensional numerical calculation model of the slope, carry out numerical calculations, obtain the initial ground stress, and extract the information of each numerical unit in the numerical model; ② Calculate the local safety factor of each numerical unit in the numerical model; ③ Determine the surface numerical units of the model and sort the surface numerical units according to the size of the local safety factor; ④ The surface numerical unit of the slope with the smallest local safety factor is used as the starting unit where the sliding boundary line is located, and the surface numerical units of the slope where the sliding boundary line is located are gradually identified by using the adjacent advancement method; ⑤ Extract the center point position of the surface numerical unit of the slope where the sliding boundary line is located, and connect them in sequence to determine the sliding boundary line of the three-dimensional potential sliding surface; ⑥ Take the sliding boundary line of the three-dimensional potential sliding surface as the control range, determine the vertical and horizontal grid points on the xy plane within this control range, draw vertical lines through these grid points, and use the series of equally divided points on the vertical lines and the local safety factors of the corresponding numerical units to extract the discrete points s of the three-dimensional potential sliding surface. ij ⑦ Apply the concave characteristics of the three-dimensional potential sliding surface to the discrete points s ij ⑧ The corrected three-dimensional potential sliding surface discrete point s ij The three-dimensional potential sliding surface is obtained by connecting in sequence along the vertical and horizontal network lines.

[0085] The characteristics of the local safety factor solution of the present invention are: applying numerical simulation calculation technology to obtain the slope stress field, and on the basis of selecting the shear strength criterion of the rock and soil mass, combining the stress information of the numerical unit in the numerical model and the Moore stress circle reflecting the stress state of the numerical unit, solving the local safety factor of the numerical unit. This method can utilize the powerful calculation function of the existing numerical simulation software and its favorable conditions for restoring the actual stress field of the slope under the real scene. At the same time, compared with the introduction of the strength reduction technology to solve the slope safety factor, the local safety factor solution does not change the actual stress state of the slope, and the local safety factor solution does not depend on the specific rock and soil mass shear strength criterion, making it highly versatile.

[0086] The potential sliding surface identification and extraction method of the present invention is characterized by: using the slope surface numerical unit with the minimum local safety factor as the starting unit where the sliding boundary line of the three-dimensional potential sliding surface is located, and gradually identifying the slope surface numerical units where the sliding boundary line is located using an adjacent advancement method to determine the sliding boundary line of the three-dimensional potential sliding surface. On this basis, the sliding boundary line of the three-dimensional potential sliding surface is used as a control range, and the vertical and horizontal grid points within this control range and the equally divided points on the vertical line are used to extract the three-dimensional potential sliding surface discrete points. This method constrains the extraction of the three-dimensional potential sliding surface discrete points to a valid range, making the extraction of the three-dimensional potential sliding surface discrete points simple and universal, and easy to control the accuracy, thereby facilitating the efficient, automated and intelligent identification and extraction of potential sliding surfaces. At the same time, the identified potential sliding surface points are fully matched with the numerical units in the numerical model and are based on the minimum local safety factor, which is consistent with the slope shear failure mechanism. In addition, the vertical position of the potential sliding surface discrete points is also controlled by the concave characteristics of the potential sliding surface, thereby ensuring the rationality of the identified and extracted potential sliding surface.

[0087] Example

[0088] A kind of Figures 1 to 15 The method for identifying and extracting potential sliding surfaces in slopes using three-dimensional numerical simulations is shown. Due to complex geological conditions and low rock and soil strength, the slopes of an open-pit mine present a significant risk of landslide. To accurately predict the potential range of slope instability and identify reinforcement areas, this method for identifying and extracting potential sliding surfaces in three-dimensional numerical simulations was introduced and applied. It successfully defined the potential range of slope landslides and provided technical support for the effective implementation of reinforcement measures. The specific steps are as follows:

[0089] (1) According to the requirements of the Code for Geotechnical Engineering Investigation (GB50021-2001), the open-pit mine slope was surveyed and tested to obtain the three-dimensional slope surface shape within the analysis area; specifically, its longitudinal width is 150m, the transverse length is 200m, and the slope height H = 27.4m; and the stratigraphic data and the corresponding rock and soil strength parameters within the analysis area were obtained; specifically, the rock and soil were severely weathered and cracked and obeyed the generalized nonlinear HB strength criterion, with specific strength parameters of GSI = 25.0, σ c =40MPa,m i =0.833 and D = 0.8; where GSI is the geological strength index, σ c is the uniaxial compressive strength of intact rock, m i is the material constant of intact rock, and D is the disturbance factor of rock mass;

[0090] (2) According to the actual slope shape of the three-dimensional slope, a corresponding three-dimensional slope numerical model is established in the numerical simulation software. At the same time, the corresponding rock and soil layer parameters and their strength parameters are assigned, and the corresponding model boundary constraints are set;

[0091] (3) Carry out numerical calculations and extract the information of each numerical unit in the numerical model, including number information, coordinate information (such as unit center coordinates and unit vertex coordinates), volume, side area and stress information of the numerical unit (such as major principal stress σ1, minor principal stress σ3 and normal stress σ along the vertical direction). z )wait;

[0092] (4) Calculate the local safety factor F of each numerical unit in the numerical model s_Local , where the calculation formula for the shear strength of rock and soil under the generalized nonlinear HB strength criterion is: Parameter m b , s, α and The calculation formulas are α = 0.5 + (1 / 6) × [exp(–GSI / 15) – exp(–20 / 3)] and Among them, m b is the material constant, s is the parameter reflecting the degree of rock mass fragmentation, α is a constant related to the rock mass structure and surface conditions, is the instantaneous internal friction angle of the rock mass;

[0093] (5) Obtain the front and rear boundary coordinates of the three-dimensional slope numerical model in the x-axis direction, respectively. front = 0.0m and x back =150.0m, the left and right boundary coordinates in the y-axis direction are y right =0.0m and y left = 200.0m, the coordinates of the lower and upper boundaries in the z-axis direction are z below = 0.0m and z above =107.4m, where the ground surface height is 27.4m and the underground depth is 80m. At the same time, a vertical and horizontal grid is drawn on the xy plane, where in the range [x front , x back ] draw horizontal grid lines parallel to the y-axis direction at equal intervals, and number them from 0 to n (n=18) according to the x-axis coordinate size of the horizontal grid lines. right ,y left ] Draw longitudinal grid lines parallel to the x-axis at equal intervals within the grid, and number them from 0 to m (m=19) according to their y-axis coordinates;

[0094] (6) Using FLAC software 3DThe commands "gp.isgroup()" and "gp.pos()" are used to extract the nodes, node numbers and node coordinates contained in each surface layer. Then, all non-surface layers are eliminated according to the node coordinate characteristics of the non-surface layers to obtain the surface layer of the slope numerical model.

[0095] (7) By traversing the unit and using the software FLAC 3D The command “zone.face.isgroup()” is used to identify and extract all the slope surface numerical units corresponding to the surface layer;

[0096] (8) In the numerical units of the slope surface, the numerical units are sorted according to the size relationship of the local safety factors of the numerical units. The numerical unit of the slope surface with the smallest local safety factor is used as the starting unit of the sliding boundary line of the three-dimensional potential sliding surface. Then, the numerical units of the slope surface where the sliding boundary line is located are gradually identified by the adjacent advancement method. Subsequently, the center point positions of the numerical units of the slope surface where the sliding boundary line is located are extracted and connected in sequence to determine the sliding boundary line of the three-dimensional potential sliding surface.

[0097] (9) Extract the x-axis and y-axis coordinates of the discrete points of the sliding boundary line, and find the minimum x-axis coordinate of the discrete points of the sliding boundary line. min =26.25m and maximum value x max =138.75m and the minimum value of the y-axis coordinate y min =12.00m and maximum value y max =183.00m. Based on this, the horizontal network line number interval within the control range of the sliding boundary line in the vertical and horizontal grids on the xy plane is obtained as [3, 17] and the vertical network line number interval is [1, 18]. Then, the sliding boundary line of the three-dimensional potential sliding surface is used as the control range. For the grid points within this control range, a vertical line is drawn through the grid points, and the z-axis coordinate of the vertical line of the grid point is taken as the z below As the starting point, the vertical line is divided into multiple segments according to a certain spacing Δz, where Δz is taken as 1m. Then, a series of equally divided points on the vertical line of the grid point are obtained. Then, by identifying the numerical unit where the equally divided point on the vertical line is located, the value of the local safety factor of the corresponding numerical unit is assigned to this equally divided point. Furthermore, based on the size relationship of the local safety factors of the series of equally divided points on the vertical line, the three-dimensional potential slip surface discrete points on the vertical line of the grid point within the control range of the sliding boundary line are determined;

[0098] (10) Using longitudinal and transverse vertical planes to cut the three-dimensional potential sliding surface, a two-dimensional slicing curve of the three-dimensional potential sliding surface on these vertical planes is obtained. Then, using the increasing property of the tangent slope of the two-dimensional slicing curve under the concave feature of the three-dimensional potential sliding surface, the vertical position of the discrete point of the three-dimensional potential sliding surface is corrected. At the same time, through sequential and multiple rounds of repeated corrections, the final vertical position of the discrete point of the three-dimensional potential sliding surface is obtained under the premise of fully ensuring the increasing property of the tangent slope of the two-dimensional slicing curve;

[0099] (11) The three-dimensional potential sliding surface discrete points after correction are connected in sequence along the longitudinal and transverse network lines to obtain the three-dimensional potential sliding surface. The distribution range of the three-dimensional potential sliding surface of the slope in the longitudinal direction (i.e., the x-axis direction) is 26.25m~138.75m, and the distribution range in the transverse direction (i.e., the y-axis direction) is 12.00m~183.00m. The maximum sliding depth is 33.5m, and the projected area of the sliding perimeter on the xy plane is 2.27×10 4 m 2 , and the volume of the three-dimensional potential sliding body is 2.85×10 5 m 3 .

[0100] In summary, the present invention relates to a method for identifying and extracting potential sliding surfaces of slopes under three-dimensional numerical simulation analysis. The present invention does not need to introduce strength reduction technology and does not limit the shear strength criterion of rock and soil. After obtaining the slope stress field by numerical simulation calculation, the potential sliding surface of the three-dimensional slope can be efficiently, automatically and intelligently identified and extracted. The obtained potential sliding surface conforms to the shear failure mechanism of the slope and can effectively show the actual failure form of the three-dimensional slope in the real scene. The present invention first determines the sliding boundary line of the three-dimensional potential sliding surface, and then extracts the discrete points of the three-dimensional potential sliding surface within this range, so as to facilitate the intelligent identification and extraction of the three-dimensional potential sliding surface. The present invention has the characteristics of wide application range, high efficiency, small deviation, strong versatility, good effect, low cost, etc., and has automation and intelligent features. It can provide a strong scientific basis for the prediction of the potential instability range of the slope and the determination of the reinforcement area in actual engineering.

[0101] It will be easily understood by those skilled in the art that 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 in the scope of protection of the present invention.

Claims

1. A method for identifying and extracting potential sliding surfaces of slopes using three-dimensional numerical simulation analysis, characterized in that: The method comprises the following steps: S1. Establish a three-dimensional slope numerical calculation model, perform numerical calculations, obtain initial ground stress, and extract information of each numerical unit in the numerical model; S2. Calculate the local safety factor of each numerical unit in the numerical model; S3, determining the surface numerical units of the model, and sorting the surface numerical units according to the size of the local safety factor; S4. The numerical unit on the slope surface with the smallest local safety factor is used as the starting unit where the sliding boundary line is located, and the numerical units on the slope surface where the sliding boundary line is located are gradually identified using the adjacent advancement method; S5, extracting the center points of the numerical units on the slope surface where the sliding boundary line is located, and connecting them in sequence, thereby determining the sliding boundary line of the three-dimensional potential sliding surface; S6. Take the sliding boundary line of the three-dimensional potential sliding surface as the control range, determine the vertical and horizontal grid points on the xy plane within this control range, draw vertical lines through these grid points, and use the series of equally divided points on the vertical lines and the local safety factors of the corresponding numerical units to extract the discrete points s of the three-dimensional potential sliding surface. ij ; S7, using the concave characteristics of the three-dimensional potential sliding surface, the three-dimensional potential sliding surface discrete points s ij Correct the vertical position of S8, the corrected three-dimensional potential sliding surface discrete points s ij The three-dimensional potential sliding surface is obtained by connecting in sequence along the vertical and horizontal network lines.

2. The method for identifying and extracting potential sliding surfaces of slopes using three-dimensional numerical simulation analysis according to claim 1 is characterized in that: Step S2 specifically includes the following steps: S2-1. Let the general expression of the shear strength criterion of rock and soil be τ f =f(σ), where σ is the normal stress on the action surface, τ f is the shear strength on the action surface; S2-2. Based on the Mohr stress circle reflecting the stress state of the numerical unit, determine the range of the normal stress σ on the surface of the numerical unit in different directions as [σ3, σ1], and obtain the shear stress on the surface of the numerical unit in different directions under the corresponding normal stress as τ = [(σ1–σ)(σ–σ3)] 1 / 2 ; Among them, σ1 is the major principal stress and σ3 is the minor principal stress; S2-3. Combined with the shear strength criterion of rock and soil, calculate the shear strength on the surface in different directions under the corresponding normal stress as τ f =f(σ); S2-4. Calculate the shear strength τ on the action surface according to the definition of safety factor f The ratio k to the shear stress τ s , and k s =f(σ) / [(σ1–σ)(σ–σ3)] 1 / 2 ; S2-5. When the normal stress σ is in the interval [σ3, σ1], use the mathematical extreme value method to solve k s The minimum value of S2-6, let k s The minimum value of min(k s ), which is the local safety factor F of the numerical unit s_Local , thus obtaining the local safety factor of the numerical unit as F s_Local =min(k s ).

3. The method for identifying and extracting potential sliding surfaces of slopes using three-dimensional numerical simulation analysis according to claim 2 is characterized in that: The slope complies with the generalized nonlinear HB strength criterion, and in step S2, the shear strength calculation formula of the rock and soil mass is: Among them, m b is the material constant, s is the parameter reflecting the degree of rock mass fragmentation, α is a constant related to the rock mass structure and surface conditions, is the instantaneous internal friction angle of the rock mass.

4. The method for identifying and extracting potential sliding surfaces of slopes using three-dimensional numerical simulation analysis according to claim 3 is characterized in that: In step S2, the parameter m b , s, α and The calculation formulas are: α=0.5+(1 / 6)×[exp(–GSI / 15)–exp(–20 / 3)] Among them, GSI is the geological strength index, σ c is the uniaxial compressive strength of intact rock, m i is the material constant of intact rock, and D is the disturbance factor of the rock mass.

5. The method for identifying and extracting potential sliding surfaces of slopes using three-dimensional numerical simulation analysis according to claim 1 is characterized in that: Step S3 includes the following steps: S3-1. Obtain the surface layer number and the surface group in the numerical model. The numerical model divides the surface layer into six surface groups: upper side, lower side, east side, west side, south side, and north side according to the direction of the surface layer's outer normal. The boundary surface is divided into five of the surface groups: lower side, east side, west side, south side, and north side. S3-2, extracting the nodes, node numbers and node coordinates contained in the surface layer; S3-3, exclude the boundary surface according to the artificially set boundary conditions; among them, for the boundary surface of the lower side group, the node coordinates on the surface are all equal to the lower boundary coordinate z in the z-axis direction of the numerical model below Based on this, when considering the calculation accuracy of the model, the z-axis coordinates of the nodes on the surface are located at [z below –0.001, z below +0.001] are excluded from the surface layer; the boundary surfaces of the east, west, south, and north side groups are also excluded from the surface layer in the same way; S3-4. Based on the number of the surface composed of the numerical unit, the numerical unit is traversed to determine whether the surface composed of the numerical unit belongs to the mid-slope surface of the surface layer, and then the numerical unit matching the mid-slope surface of the surface layer is found, and the surface numerical unit is further determined.

6. The method for identifying and extracting potential sliding surfaces of slopes using three-dimensional numerical simulation analysis according to claim 1 is characterized in that: Steps S4 to S5 include the following steps: S5-1. Sort the numerical units on the slope surface from small to large according to the magnitude of their local safety factors, and then determine the numerical unit on the slope surface with the smallest local safety factor, and use it as the starting unit for the sliding boundary line. S5-2. Obtain the adjacent slope surface numerical units of the starting unit, compare the local safety factors of these adjacent slope surface numerical units, and use the slope surface numerical unit with the smallest local safety factor as the second unit where the sliding boundary line is located; S5-3. Determine the unknown unit where the next sliding boundary line is located from the known unit where the previous sliding boundary line is located, wherein the known unit where the previous sliding boundary line is located and the unknown unit where the next sliding boundary line is located are adjacent numerical units (this is condition one); and the angle between the line connecting the center point of the known unit where the previous sliding boundary line is located and the center point of the unknown unit where the next sliding boundary line is located, and the line connecting the center point of the known unit where the previous sliding boundary line is located and the center point of the known unit where the previous sliding boundary line is located, projected on the xy plane, is in the range of [–90°, 90°] (this is condition two); on this basis, the unknown unit where the next sliding boundary line is located is the one with the smallest local safety factor among the numerical units on the slope surface that meets the above two conditions; S5-4, determining whether the unknown cell where the next sliding boundary line is located is an adjacent cell of the starting cell where the sliding boundary line is located; if so, stopping the identification of the numerical cell on the slope surface where the sliding boundary line is located; otherwise, repeating step S5-3; S5-5. Extract the center points of the numerical units on the slope surface where the sliding boundary line is located, and connect them in sequence to determine the sliding boundary line of the three-dimensional potential sliding surface.

7. The method for identifying and extracting potential sliding surfaces of slopes using three-dimensional numerical simulation analysis according to claim 6 is characterized in that: In steps S4 to S5, the principle for determining adjacent numerical units of a slope surface numerical unit is to take a certain slope surface numerical unit as a target unit and compare whether the target unit has a common vertex with other slope surface numerical units, which are also referred to as units to be determined, to determine whether the slope surface numerical unit is an adjacent numerical unit. The specific steps for determining the adjacent numerical units of the slope surface numerical unit include: S5-3-1. Take a certain slope surface numerical unit as the target unit and obtain the node number information of each unit vertex; S5-3-2, traverse the slope surface numerical units, and extract the node number information of each vertex of other slope surface numerical units outside the target unit; S5-3-3, comparing the node number information of each vertex of the unit to be determined and the target unit; S5-3-4. If the node numbers of one or more vertices of the unit to be determined and the target unit overlap, then the unit to be determined is an adjacent numerical unit of the target unit.

8. The method for identifying and extracting potential sliding surfaces of slopes using three-dimensional numerical simulation analysis according to claim 1 is characterized in that: In step S7, specifically, the three-dimensional potential sliding surface is cut using longitudinal and transverse vertical planes to obtain two-dimensional slicing curves of the three-dimensional potential sliding surface on these vertical planes. Then, the vertical positions of the discrete points of the three-dimensional potential sliding surface are corrected using the increasing tangent slope of the two-dimensional slicing curve under the concave feature of the three-dimensional potential sliding surface. At the same time, through sequential and multiple rounds of repeated corrections, the final vertical positions of the discrete points of the three-dimensional potential sliding surface are obtained while fully ensuring the increasing tangent slope of the two-dimensional slicing curve.

9. The method for identifying and extracting potential sliding surfaces of slopes by simulation analysis according to any one of claims 1 to 8, characterized in that: Using FLAC software 3D Perform three-dimensional numerical simulation analysis.

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