Method for identifying and extracting potential sliding surface of side slope under three-dimensional numerical simulation analysis

Abstract

The invention relates to a method for identifying and extracting a potential sliding surface of a side slope under three-dimensional numerical simulation analysis, and belongs to the field of traffic side slope engineering. According to the method, a strength reduction technology does not need to be introduced, a rock-soil body shear strength criterion is not limited, after the slope stress field is obtained through numerical simulation calculation, the three-dimensional slope potential sliding surface can be efficiently, automatically and intelligently recognized and extracted, the obtained potential sliding surface conforms to a slope shear failure mechanism, and the method is suitable for large-scale popularization and application. The actual damage form of the three-dimensional slope in a real scene can be effectively displayed; according to the method, the sliding circumference boundary line of the three-dimensional potential sliding surface is determined firstly, and then the discrete points of the three-dimensional potential sliding surface are extracted within the range, so that intelligent identification and extraction of the three-dimensional potential sliding surface are facilitated. The method has the advantages of being wide in application range, high in efficiency, small in deviation, high in universality, good in effect, low in cost and the like, has the automatic and intelligent characteristics, and can provide a powerful scientific basis for slope potential instability range prediction and reinforcement area determination 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 under three-dimensional numerical simulation analysis. Background Art

[0002] Landslide is a common geological disaster, especially in mountainous or rainy areas, which is extremely destructive and harmful, such as causing casualties, property losses, traffic interruptions, damage to water conservancy projects, ecological environment damage, etc. In order to reduce the losses caused by landslide disasters or avoid them as much as possible, it is very necessary to accurately determine the most potentially dangerous sliding surface of the slope.

[0003] Accurately determining the most potentially dangerous sliding surface on the slope has the following effects. First, disaster prevention and mitigation measures can be taken in advance, such as building protective projects, reinforcing slopes, evacuating personnel, etc., thereby reducing the losses and casualties caused by landslides. Second, based on the determined most potentially dangerous sliding surface on the slope, the engineering design plan 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, using the results of potential sliding surface analysis, a slope monitoring and early warning system can be established to monitor the deformation and displacement of the slope in real time, and to issue early warning information in a timely manner to ensure the safety of personnel and property.

[0004] At present, the determination of the potential sliding surface of the 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 bodies, and the failure surface presents a complex spatial geometric shape. At the same time, the external force borne by the failure body itself is also mostly 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] The existing methods for determining the potential sliding surface of three-dimensional slopes mainly include theoretical analysis methods, numerical simulation methods and on-site monitoring methods. Theoretical analysis methods mainly include the limit equilibrium method based on the rigid body limit equilibrium theory. This method requires the pre-assumption of sliding surface modes, such as spherical, wedge-shaped, cylindrical, plane, wedge-shaped or irregular sliding surfaces, etc. Then, the corresponding size range is set for the sliding surface of the pre-assumed mode, and then, with the goal of searching for the minimum value of the slope safety factor, the most dangerous sliding surface of the slope is finally determined through multiple iterative calculations. The numerical simulation method establishes a slope numerical model based on the actual geometric shape of the slope and reasonable physical and mechanical parameters, and uses numerical calculations to obtain the slope stress, strain and displacement fields to determine whether the slope is unstable and damaged. In the numerical calculation process, strength reduction technology is usually introduced to gradually reduce the shear strength of the rock and soil body, thereby forcing the slope to shear failure. Then, the potential sliding surface of the slope is determined based on the connected shear strain plastic zone during 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 characteristics, 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] In the existing methods for determining the potential sliding surface of slopes, three-dimensional problems are often simplified into two-dimensional problems for analysis, which cannot consider the spatial complexity of the actual potential sliding surface. At the same time, in the above-mentioned methods for determining the potential sliding surface of three-dimensional slopes, the theoretical analysis method needs to assume the sliding surface mode in advance, which may not be consistent with the actual situation. In addition, the limit equilibrium method, which is the most widely used in actual engineering, mainly limits the shear strength criterion of rock and soil to the linear MC strength criterion, making it difficult to obtain reliable results of slope stability analysis under complex conditions. Although the numerical simulation method has the advantages of high accuracy, wide application range, dynamic analysis and multi-field coupling, the numerical simulation method introduces strength reduction technology, resulting in the slope stress field after the strength parameter reduction in the numerical analysis is not the actual stress field, and the potential sliding surface inferred is not the actual potential sliding surface. In addition, there are multiple criteria for slope instability identification in numerical analysis, and there are calculation result deviations between different criteria. The on-site monitoring method can roughly determine the shape and position of the potential sliding surface of the slope based on the actual monitoring data. However, the accuracy of determining the potential sliding surface of the slope is closely related to the density of the 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 the corresponding labor and monitoring costs. In addition, the reliability, durability and accuracy of the monitoring components also restrict the accuracy of the identification of the potential sliding surface of the slope.

[0007] Invention patent CN202210223672.3 discloses a method for determining a three-dimensional anti-sliding safety factor using micro-disturbance displacement isosurfaces, including using an existing continuous numerical simulation platform to establish a geomechanical model of a slope with complex strata distribution, and using the classic Moore-Coulomb criterion to calculate the slope stress field. After balancing, a tiny parameter perturbation is applied to induce displacement of the slope, and then the displacement isosurface is used 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 the 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 rock and soil boundary. That is to say, the invention patent uses the perturbation displacement isosurface to establish the relationship between the three-dimensional slope anti-sliding safety factor and the perturbation displacement, and determines the most appropriate control displacement value and its three-dimensional potential sliding surface according to the minimum three-dimensional slope anti-sliding safety factor. However, the premise for the implementation of the patent is that the displacement values ​​of each part on the three-dimensional potential sliding surface are equal. This premise does not necessarily conform to the actual situation. For example, in the case of push-type or traction landslides, in the process of the slope displacement from quantitative change to qualitative change, the displacement of the rear end of the potential sliding surface of the slope is usually greater than the front end, while in the case of the latter, the displacement of the front end of the potential sliding surface of the slope is greater than the rear end. Therefore, there will be a certain difference between the three-dimensional potential sliding surface identified by the invention patent and the actual sliding surface. In addition, when identifying the three-dimensional potential sliding surface, the invention patent needs to continuously try the perturbation displacement, and repeat the three-dimensional sliding surface extraction and the 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 the calculation efficiency is low. At the same time, in addition to the classical Moore-Coulomb criterion, the invention patent has not been able to make it applicable to general nonlinear strength criteria.

[0008] Invention patent CN202311865958.2 discloses an automatic retrieval method, medium and equipment for the dynamic sliding surface of a slope based on the finite element-discrete element coupling method (FDEM). The retrieval method is suitable for 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; 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, its 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 engineering construction moves towards dangerous mountainous areas, slope engineering design and construction become more complicated, and the task of timely and effective landslide prevention and control is very urgent. The need to accurately determine the potential sliding surface of the slope has become very urgent. In order to meet this requirement, it is necessary to find a three-dimensional slope potential sliding surface accurate determination method with the characteristics of wide application range, high efficiency, small deviation, strong versatility, good effect, low cost, and automatic and intelligent features. In other words, this field needs a new method for identifying and extracting the potential sliding surface of the slope under three-dimensional numerical simulation analysis. Summary of the invention

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

[0011] S1. Establish a three-dimensional slope numerical calculation model, carry out numerical calculation, obtain initial geostress, 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 of the slope surface with the smallest local safety factor is taken as the starting unit where the sliding boundary line is located, and the numerical unit of the slope surface where the sliding boundary line is located is gradually identified by using the adjacent advancement method;

[0015] S5, extracting the center point positions of the numerical units on the slope surface where the sliding boundary line is located, and connecting them in sequence, so as to determine 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 The vertical position of

[0018] S8, the corrected three-dimensional potential sliding surface discrete points s ij The vertical and horizontal network lines are connected in sequence to obtain a three-dimensional potential sliding surface.

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

[0020] S2-1. Let the general expression of 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, the range of the normal stress σ on the surface acting in different directions in the numerical unit is determined to be [σ3, σ1], and the shear stress on the surface acting in different directions under the corresponding normal stress in the numerical unit is obtained 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, the shear strength on the surface in different directions under the corresponding normal stress is calculated 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 of 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 implementation, 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 a material constant, s is a parameter reflecting the degree of rock mass fragmentation, and 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 implementation, 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 implementation, step S3 includes the following steps:

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

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

[0037] S3-3, exclude boundary surfaces according to artificially set boundary conditions; among them, for the boundary surfaces of the lower side surface group, the node coordinates on the surface are equal to the lower boundary coordinates 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 excluded from the surface layer in the same way;

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

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

[0040] S5-1. In the numerical units on the slope surface, the numerical units on the slope surface are sorted from small to large according to the size relationship of the local safety factors of the numerical units, and then the numerical unit on the slope surface with the smallest local safety factor is determined, and it is used as the starting unit where the sliding boundary line is located;

[0041] S5-2, obtaining the adjacent slope surface numerical units of the starting unit, comparing the local safety factors of these adjacent slope surface numerical units, and taking 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, which 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 and the center point of the known unit where the previous sliding boundary line is located is in the range of [–90°, 90°], which is condition two; on this basis, the unknown unit where the next sliding boundary line is located is determined to be the one with the smallest local safety factor among the numerical units on the slope surface that meet the above two conditions;

[0043] S5-4, judging 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, stopping the identification of the numerical unit of the slope surface where the sliding boundary line is located; otherwise, repeating step S5-3;

[0044] S5-5. 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.

[0045] In a specific implementation, in steps S4 to S5, the principle for determining the adjacent numerical units of the slope surface numerical unit is to take a certain slope surface numerical unit as the target unit, and to 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 its adjacent numerical unit; and the specific operation steps for determining the adjacent numerical units of the slope surface numerical unit include:

[0046] S5-3-1, taking a certain slope surface numerical unit as the target unit, obtaining 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 implementation, 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, and then, the vertical positions of 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 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 implementation, using the software FLAC 3D Conduct three-dimensional numerical simulation analysis.

[0052] The advantages of the invention of this article are: this method 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 automatically 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. At the same time, the sliding boundary line of the three-dimensional potential sliding surface is first determined, and then the discrete points of the three-dimensional potential sliding surface 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 the characteristics of automation and intelligence, which 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] In addition, compared with the prior art CN202311865958.2, the present invention can identify and extract the potential sliding surface of the slope based on the shear failure mechanism of the slope, and does not require that the displacement of the nodes on the landslide body must be much greater than the nodes on the sliding bed. Therefore, the scope of application of the present invention is wider. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0055] Figure 2 It 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 the numerical unit of 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 The figure is a schematic diagram for determining the numerical unit of the slope surface layer according to the present invention.

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

[0060] Figure 7 It is a 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 It is a schematic diagram of the sliding boundary line of the three-dimensional potential sliding surface of the present invention.

[0062] Fig. 9 It is a schematic diagram of identifying adjacent units of the numerical unit of the slope surface layer of the present invention.

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

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

[0065] Fig.12 It is a 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] Fig.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] Fig.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] Fig.15 The present invention provides a flowchart for the implementation of identifying and extracting potential sliding surfaces of slopes in three-dimensional numerical simulation calculations.

[0069] In the figure: 1. Three-dimensional slope numerical model; 2. Numerical unit; 3. Large principal stress action surface; 4. Small 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. Transverse network line; 8. Longitudinal network line; 9. Grid point ij; 10. Projection range of the numerical unit on the xy plane in the numerical model; 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 previous unit of 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, the point ijk; 27, the numerical unit corresponding to the point ijk; 28, the discrete point s of the three-dimensional potential sliding surface ij ; 29, points to be determined; 30, side of numerical unit; 31, vertex on side; 32, spatial geometric body; 33, three-dimensional potential sliding surface; 34, vertical plane j; 35, horizontal plane i; 36, discrete points s of existing three-dimensional potential sliding surface ij 37. 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. The method obtains the slope stress field by carrying out numerical simulation calculations, and then, on the basis of selecting the shear strength criterion of rock and soil, uses the stress information of the numerical unit in the numerical model and the Mohr stress circle reflecting the stress state of the numerical unit to solve the local safety factor of each numerical unit. Then, the surface numerical unit of the slope is extracted from the numerical unit, and the surface numerical unit of the slope with the smallest local safety factor is used as the starting unit where the sliding boundary line of the three-dimensional potential sliding surface is located. Then, the surface numerical unit of the slope where the sliding boundary line is located is gradually identified by the adjacent advancement method, thereby determining the sliding boundary line of the three-dimensional potential sliding surface. Further, the sliding boundary line of the three-dimensional potential sliding surface is used as the control range, and 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. On this basis, the concave characteristics of the three-dimensional potential sliding surface are used to correct the vertical positions of the discrete points of the three-dimensional potential sliding surface. Finally, the corrected three-dimensional potential sliding surface discrete points are connected in sequence according to the directions of 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, the corresponding three-dimensional slope numerical model is established, and 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 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, taking any numerical unit as an example, the major principal stress σ1 and minor principal stress σ3 of the numerical unit are calculated 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; wherein the minor principal stress action surface OA and the major principal stress action surface OB are perpendicular to each other; OT is an 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, 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 system, 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. In view of the fact 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 the figure, based on the Moore stress circle reflecting the stress state of the numerical unit, when α changes in the range of 0° to 90°, it can be known 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 numerical unit stress information 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 value 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 of 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 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 front and x back , the left and right boundary coordinates in the y-axis direction are y left and right , the coordinates of the lower and upper boundaries 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 grid lines parallel to the y-axis direction at equal intervals, and number them from 0 to n according to their x-axis coordinates. For the i-th horizontal grid line, its x-axis coordinate is x front +i×(x back -x front ) / n, in the range [y left ,y right ] Draw longitudinal grid lines parallel to the x-axis at equal intervals in the inner part, and number them from 0 to m according to their y-axis coordinates. For the jth longitudinal grid 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 the 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 as 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 six surface groups according to the direction of the outer normal of the surface layer, namely, the upper side, the lower side, the east side, the west side, the south side, and the north side. Among them, the boundary surface is divided into five surface groups, namely, the lower side, the east side, the west side, the south side, and the 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, the west side of the face group corresponds to Figure 5 The front side of the numerical model, the south side of the face group corresponds to 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 matching the mid-slope surface of the surface layer is found, and the surface numerical unit is further determined.

[0079] (8) Figure 6 to Figure 8As shown in the figure, 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 of the slope. 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 unit 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 by this. The specific implementation steps are as follows: ① In the slope surface numerical unit, the slope surface numerical unit is sorted from small to large according to the size relationship of the local safety factor of the numerical unit, 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 , 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 one), and the angle between 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 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 interval of [-90°, 90°] (condition two). On this basis, the unknown unit where the next sliding boundary line is located is determined to be 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) Fig. 9 As shown in FIG, the principle for determining the adjacent numerical units of the slope surface numerical unit is to take a certain slope surface numerical unit as the target unit, and to determine whether the target unit has common vertices with other slope surface numerical units (referred to as the units to be determined), and then determine 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 numbers of one or more vertices of the unit to be determined and the target unit coincide, then the unit to be determined is the adjacent numerical unit of the target unit.

[0081] (10) Fig.10 As shown in the figure, the sliding boundary line of the three-dimensional potential sliding surface is taken 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 control range of the sliding boundary line 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, 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 located on the vertical line of the grid point ij, and it 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 points 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 central 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 value x of the 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 the vertical network line number interval [j min , j max ], 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 lower and upper intersection points (or the y-axis coordinate of the grid point ij is outside the left and right intersection points), 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 lower and upper intersection points (or within the left and right intersection points), it indicates that it is located within the projection of the sliding boundary line on the xy plane. At this time, a vertical line is made through the grid point ij. Then, the vertical line is segmented at a spacing of Δz, and a series of equally divided points k on the vertical line are obtained, wherein the starting point of the division is located on this vertical line with a z-axis coordinate of 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 accordingly, 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 numerical unit of the slope surface inside the sliding boundary line, the local safety factor will be set to a very large 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 values, 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 , then j = j + 1, and 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 lines of all grid points ij in the projection of the sliding boundary line on the xy plane ij , where the three-dimensional potential sliding 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) Fig.11 As shown in FIG. 1 , the principle for determining the numerical unit where the series of equally divided points k (i.e., point 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 numerical unit to form a spatial geometric body, and when the points are connected to 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 the point is located in the numerical unit. The specific implementation steps are as follows: ① Obtain the volume of the numerical unit and the number and coordinates of the side surface of the numerical unit and its vertices, and extract the area of ​​the side surface of the numerical unit and the coordinates of the center point; ② Select any 4 points from the vertices and the center point on a side surface of the numerical unit, and use this ③ The coordinates of the four points determine the function 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 obtained vertical distance from the point to be determined to the side surface of the numerical unit and the side surface area of ​​the numerical unit, calculate the volume of the spatial geometric body formed by the point to be determined and the vertices on each side surface of the selected numerical unit and its sum; ④ Traverse all numerical units and determine whether the sum of the volumes of the spatial geometric bodies formed by the point to be determined and 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) Figure 12 to Figure 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 sequential and multiple rounds of repeated corrections, the three-dimensional potential sliding surface discrete points s are obtained under the premise of fully ensuring the increasing slope of the tangent line of the two-dimensional slice curve. ij The final vertical position of the sliding boundary line is determined by the following specific implementation 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 longitudinal vertical plane; ② In the longitudinal vertical plane j, according to the increasing slope of the tangent line 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 potential sliding surface is 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 discrete points s ij Take it as an 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 With 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 , let 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 three-dimensional potential sliding surface discrete point s ij (j min ≤j≤j max , and is within the left and right intersections 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 potential sliding surface is 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 discrete points s ij Take it as an 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) With 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 , then set i = i + 1 and repeat step ⑤; ⑦ repeat steps ① to ⑥ until there is no need to discretize the three-dimensional potential sliding surface points 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 ensured;⑧ Output the corrected three-dimensional potential sliding surface discrete point s ij .

[0084] (13) Fig.15 ​As shown in the figure, 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 slope numerical calculation model, carry out numerical calculation, 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 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, make vertical lines through these grid points, and use the series of equally divided points on the vertical line 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 vertical and horizontal network lines are connected in sequence to obtain a three-dimensional potential sliding surface.

[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 in 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, which makes it have strong versatility.

[0086] The characteristics of the potential sliding surface identification and extraction of the present invention are: taking 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 unit where the sliding boundary line is located by using the adjacent advancement method, so as to determine the sliding boundary line of the three-dimensional potential sliding surface. On this basis, taking the sliding boundary line of the three-dimensional potential sliding surface as the control range, and using the vertical and horizontal grid points within the control range and the equally divided points on the vertical line to extract the three-dimensional potential sliding surface discrete points, this method constrains the extraction of the three-dimensional potential sliding surface discrete points within an effective range, and makes 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 the potential sliding surface. At the same time, the identified potential sliding surface points are completely matched with the numerical units in the numerical model, and are based on the minimum local safety factor, which conforms to the shear failure mechanism of the slope. 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 Figure 1 to Figure 15 The method for identifying and extracting potential sliding surfaces of slopes in three-dimensional numerical simulation calculations is shown. Due to the complex geological conditions and low rock and soil strength of a certain open-pit mine slope, there is a great risk of landslide. In order to accurately predict the potential instability range of the slope and determine the reinforcement area, the method for identifying and extracting potential sliding surfaces of slopes in three-dimensional numerical simulation calculations invented in this paper 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 operations 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 on site to obtain the three-dimensional slope surface shape in the analysis area; specifically, its longitudinal width is 150m, the transverse length is 200m, and the slope height is H=27.4m; and the stratigraphic data and corresponding rock and soil strength parameters in the analysis area were obtained; specifically, the rock and soil were severely weathered and cracked and obeyed the generalized nonlinear HB strength criterion, and the specific strength parameters were 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 the 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 a material constant, s is a parameter reflecting the degree of rock mass fragmentation, and 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) The coordinates of the front and rear boundaries of the three-dimensional slope numerical model in the x-axis direction are x 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 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 direction at equal intervals, 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, and the surface layer of the slope numerical model is obtained.

[0095] (7) By traversing the units 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, and 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, so as 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 on the sliding boundary line, and find the minimum x-axis coordinate of the discrete points on 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 in the sliding boundary line control range of 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 taken as the control range. For the grid points within this control range, vertical lines are drawn through the grid points, and the z-axis coordinates of the vertical lines of the grid points are taken as 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, and 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 the equally divided point. Further, 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 sliding 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, obtain the two-dimensional slicing curves of the three-dimensional potential sliding surface on these vertical planes, and then, using the increasing property of the tangent slope of the two-dimensional slicing curve under the concave characteristics of the three-dimensional potential sliding surface, correct the vertical position of the discrete points of the three-dimensional potential sliding surface. At the same time, through sequential and multiple rounds of repeated corrections, under the premise of completely ensuring the increasing property of the tangent slope of the two-dimensional slicing curve, the final vertical position of the discrete points of the three-dimensional potential sliding surface is obtained;

[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 26.25 m to 138.75 m, and the distribution range in the transverse direction (i.e., the y-axis direction) is 12.00 m to 183.00 m. The maximum sliding depth is 33.5 m, and the projection area of ​​the sliding contour 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 realize 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 the characteristics of automation and intelligence, which 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 protection scope of the present invention.

Claims

1. A method for identifying and extracting potential sliding surfaces of slopes under three-dimensional numerical simulation analysis, characterized in that: The method comprises the following steps: S1. Establish a three-dimensional slope numerical calculation model, carry out numerical calculation, obtain initial geostress, 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 of the slope surface with the smallest local safety factor is taken as the starting unit where the sliding boundary line is located, and the numerical unit of the slope surface where the sliding boundary line is located is gradually identified by using the adjacent advancement method; S5, extracting the center point positions of the numerical units on the slope surface where the sliding boundary line is located, and connecting them in sequence, so as to determine 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 The vertical position of S8, the corrected three-dimensional potential sliding surface discrete points s ij The vertical and horizontal network lines are connected in sequence to obtain a three-dimensional potential sliding surface.

2. The method for identifying and extracting potential sliding surfaces of slopes under 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 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, the range of the normal stress σ on the surface acting in different directions in the numerical unit is determined to be [σ3, σ1], and the shear stress on the surface acting in different directions under the corresponding normal stress in the numerical unit is obtained 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, the shear strength on the surface in different directions under the corresponding normal stress is calculated 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 of 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 under three-dimensional numerical simulation analysis according to claim 2 is characterized in that: 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: Among them, m b is a material constant, s is a parameter reflecting the degree of rock mass fragmentation, and 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 under three-dimensional numerical simulation analysis according to claim 3 is characterized in that: In step S2, 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 under 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, wherein the numerical model divides the surface layer into six surface groups, namely, upper side, lower side, east side, west side, south side, and north side, according to the direction of the outer normal of the surface layer, wherein the boundary surface is divided into five surface groups, namely, lower side, east side, west side, south side, and north side; S3-2, extract the nodes, node numbers and node coordinates contained in the table layer; S3-3, exclude boundary surfaces according to artificially set boundary conditions; among them, for the boundary surfaces of the lower side surface group, the node coordinates on the surface are equal to the lower boundary coordinates 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 excluded from the surface layer in the same way; S3-4. Based on the number of the surface composed of the numerical units, the numerical units are traversed to determine whether the surface composed of the numerical units belongs to the mid-slope surface of the surface layer, and then the numerical units matching the mid-slope surface of the surface layer are found, and the surface numerical units are further determined.

6. The method for identifying and extracting potential sliding surfaces of slopes under three-dimensional numerical simulation analysis according to claim 1 is characterized in that: Steps S4 to S5 include the following steps: S5-1. In the numerical units on the slope surface, the numerical units on the slope surface are sorted from small to large according to the size relationship of the local safety factors of the numerical units, and then the numerical unit on the slope surface with the smallest local safety factor is determined, and it is used as the starting unit where the sliding boundary line is located; S5-2, obtaining the adjacent slope surface numerical units of the starting unit, comparing the local safety factors of these adjacent slope surface numerical units, and taking 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, which 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 and the center point of the known unit where the previous sliding boundary line is located is in the range of [–90°, 90°], which is condition two; on this basis, the unknown unit where the next sliding boundary line is located is determined to be the one with the smallest local safety factor among the numerical units on the slope surface that meet the above two conditions; S5-4, judging 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, stopping the identification of the numerical unit of the slope surface where the sliding boundary line is located; otherwise, repeating step S5-3; S5-5. 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.

7. The method for identifying and extracting potential sliding surfaces of slopes under three-dimensional numerical simulation analysis according to claim 6 is characterized in that: In steps S4 to S5, the principle for determining the adjacent numerical units of the slope surface numerical unit is to take a certain slope surface numerical unit as the target unit, and to compare whether the target unit has a common vertex with other slope surface numerical units, which are also called units to be determined, 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: S5-3-1, taking a certain slope surface numerical unit as the target unit, obtaining 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 under 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 by longitudinal and transverse vertical planes to obtain the two-dimensional slicing curves of the three-dimensional potential sliding surface on these vertical planes, and then, the vertical positions of the discrete points of the three-dimensional potential sliding surface are corrected by utilizing 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 Conduct three-dimensional numerical simulation analysis.

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