A method for identifying and extracting potential slip surfaces of slopes in two-dimensional numerical simulations

Abstract

The present invention relates to a method for identifying and extracting potential sliding surfaces of slopes in two-dimensional numerical simulation calculations, belonging to the field of traffic slope engineering. Based on the positional relationship of the numerical units on the surface layer of the slope with the smallest and the second smallest local safety factors, the identified boundary position of the potential sliding surface is defined as the lower or upper edge boundary position of the potential sliding surface; finally, the potential sliding points identified and extracted are sequentially connected to obtain the potential sliding surface of the two-dimensional slope. The present invention does not need to introduce the strength reduction technology and does not limit the shear strength criterion of rock and soil masses, can automatically and intelligently identify and extract the potential sliding surface of the two-dimensional slope, the obtained potential sliding surface conforms to the shear failure mechanism of the slope, and can effectively show the actual failure form of the two-dimensional slope in the real scene; it has the characteristics of wide application range, high precision, good versatility, good effect, low cost, etc., and is used to provide a strong scientific basis for predicting the potential instability range of slopes and determining the reinforcement area in practical engineering.

Description

Technical Field

[0001] The present invention belongs to the field of traffic slope engineering, and particularly relates to a method for identifying and extracting potential sliding surfaces of slopes in two-dimensional numerical simulation calculations. Background Art

[0002] Landslides are common natural disasters, and the losses caused by them every year are quite huge. In order to reduce the losses caused by landslide disasters or avoid landslide disasters as much as possible, it is very necessary to accurately determine the potential sliding surfaces of slopes.

[0003] After determining the potential sliding surface of the slope, on the one hand, the specific position and shape of the potential sliding surface can be obtained, which can be used to guide engineering design and construction optimization, and provide a prerequisite for selecting appropriate support structures and reinforcement measures, so as to ensure the effectiveness and economy of engineering reinforcement measures. On the other hand, the layout range of slope displacement monitoring equipment can be determined, which can be used to monitor the deformation of the slope in real time, and provide an information basis for taking emergency measures and accurate early warning of landslide disasters.

[0004] The existing methods for determining the potential sliding surface of slopes mainly include theoretical analysis methods, numerical simulation methods and field monitoring methods. Theoretical analysis methods include the limit equilibrium method based on the rigid body limit equilibrium theory and the limit analysis method based on the plastic mechanics theory. For both the limit equilibrium method and the limit analysis method, it is necessary to pre-assume the slip surface mode (such as the former is the circular arc slip surface mode and the latter is the logarithmic spiral slip surface mode), and then establish the slope safety factor calculation formula according to their respective theories (such as the former makes reasonable assumptions about the acting point or magnitude of the inter-slice force and applies the mechanical equilibrium condition, and the latter applies the functional balance relationship of the sliding body). Based on this, after setting the corresponding size range for the pre-assumed mode of the slip surface, the minimum value of the slope safety factor can be used as the search target to determine the potential sliding surface of the slope. The numerical simulation method establishes a slope numerical model according to the actual geometric shape of the slope and reasonable physical and mechanical parameters, and uses numerical calculations to obtain the stress, strain and displacement fields of the slope to judge whether the slope has undergone instability failure. During the numerical calculation process, the strength reduction technique is usually introduced to gradually reduce the shear strength of the rock and soil mass, thereby forcing the slope to undergo shear failure, and then the potential sliding surface of the slope is determined according to the connected shear strain plastic zone at the time of shear failure. The field monitoring method determines the layout range and position of the surface and deep deformation monitoring points of the slope based on the obtained slope geological conditions, rock and soil characteristics and historical landslide conditions, and then regularly collects the surface and deep deformation data of the slope, and roughly determines the potential sliding range of the slope according to the incremental change relationship between the surface and deep deformation of the slope over time, and at the same time issues early warnings for slope collapse disasters accordingly.

[0005] Among the above several methods for determining potential slip surfaces of slopes, the theoretical analysis method needs to assume the slip surface mode in advance, which may not conform to the actual situation. Moreover, the limit equilibrium method, which is the most widely used in practical engineering applications, mainly limits the shear strength criterion of rock and soil masses to the linear M-C strength criterion, making it difficult to obtain reliable results for slope stability analysis under complex conditions. The limit analysis method needs to introduce the strength reduction technology and use the reduced slip surface strength parameters as the control parameters for the slip surface shape, resulting in a certain degree of distortion of the potential slip surface obtained. Although the numerical simulation method has the advantages of high precision, wide application range, dynamic analysis, and multi-field coupling, the numerical simulation method also introduces the strength reduction technology, resulting in the fact that the slope stress field after the strength parameters are reduced in the numerical analysis is not the actual stress field, and thus the inferred potential slip surface is not the actual potential slip surface. In addition, there are multiple criteria for identifying slope instability in numerical analysis, and there are calculation result deviations between different criteria. The field monitoring method can roughly determine the shape and position of the potential slip surface of the slope based on actual monitoring data. However, the determination accuracy of the potential slip surface of the slope is closely related to the density of monitoring points. To obtain a more accurate potential slip surface, a large number of monitoring points and corresponding monitoring components are required, resulting in 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 discrimination of the potential slip surface of the slope.

[0006] Chinese invention patent CN201910211393.3 discloses a slope stability analysis system based on the dynamic strength reduction DDA method. To consider the problem of non-uniform damage of rock mass structural planes in real situations, this system proposes to dynamically reduce the shear strength parameters c and of the block structural planes with a displacement change not less than the threshold. In the program calculation, the shear strength parameters of the block structural planes are reduced only for the structural planes that meet the displacement change requirements according to the relationship between the relative displacement change of the blocks and the threshold every certain time step (10,000 steps, each time step is 0.001 s). The reduction coefficient starts from 1.000 and increases by 0.001 in turn until a sharp deformation occurs. At this time, its value is the safety factor of the slope sliding surface. The dangerous area rock mass of the slope can be peeled off in advance according to the retrieved position of the sliding surface, which has strong practicability and contributes a new means for the multi-slip surface stability analysis and treatment of slopes. This invention patent uses the DDA method and applies the dynamic strength reduction technology to achieve the numerical analysis of slope stability. However, since this invention patent introduces the strength reduction technology, the slope stress field after the strength parameters are reduced in the numerical analysis is not the actual stress field, and further, the inferred potential slip surface of the slope is not the actual slope slip surface. In addition, this patent does not clearly state how to use numerical means to extract and identify the potential slip surface of the slope. Therefore, this invention patent still has deficiencies in implementation accuracy and effect.

[0007] Chinese Invention Patent CN202210520129.X discloses a non-circular slope sliding surface search method based on an improved wolf pack algorithm, which includes the following steps: establishing a numerical model and extracting the basic information of the numerical model; classifying the cells according to the unit material numbers and drawing the slope image in layers; setting the areas on the slope surface within a certain range of the slope top and slope foot in the slope image as the possible activity ranges of the alpha wolves and the beta wolves; the alpha wolves, beta wolves, and scout wolves move around with a fixed step length to jointly form a wolf pack combination and determine the stress information of each point on the path; calculating the sliding force and anti-sliding force between two adjacent wolves according to the stress information, defining the fitness of the wolf pack as the reciprocal of the safety factor, and taking the spline curve with the maximum fitness value as the optimal spline curve. The invention can make up for the defect that the assumption of the circular sliding surface does not conform to the actual situation, quickly and accurately determine the position of the slope sliding surface and calculate the safety factor. Specifically, the invention patent applies the improved wolf pack algorithm to search for the potential non-circular sliding surface of the slope. During the search for the potential sliding surface, the sliding surface is divided into three segments, and the curves of each sliding surface segment are assumed to be smooth and continuous cubic spline curves. Based on this, the slope safety factor is solved according to the stress information of each sliding surface segment and the shear strength criterion of the rock and soil mass. At the same time, the potential sliding surface corresponding to the minimum value of the slope safety factor is taken as the search target. Therefore, the invention patent does not satisfy that each part of the sliding surface conforms to the slope shear failure mechanism, resulting in a difference between the potential sliding surface of the slope determined by the search of the invention patent and the actual slope sliding surface; in addition, the acquisition of the stress information of each sliding surface segment also needs to apply machine learning methods, which further increases the complexity of the implementation of the patent and greatly reduces the practicability of the patent.

[0008] As engineering construction advances towards difficult mountainous areas, the design and construction of slope engineering become more complex. The task of preventing and controlling landslides in a timely and effective manner is very urgent, and the need to accurately determine the potential sliding surface of the slope becomes extremely urgent. To meet this requirement, a method for determining the potential sliding surface criterion of the slope with characteristics such as a wide application range, high accuracy, good generality, excellent effect, and automation and intelligence is needed.

[0009] That is to say, a new method for identifying and extracting the potential sliding surface of the slope in two-dimensional numerical simulation calculations is needed in this field. Summary of the Invention

[0010] Therefore, the present invention provides a method for identifying and extracting the potential sliding surface of the slope in two-dimensional numerical simulation calculations, and the method includes the following steps:

[0011] Step S1: Establish a two-dimensional slope numerical calculation model, conduct numerical calculations, and extract the information of each numerical unit in the numerical model;

[0012] Step S2: Calculate the local safety factor of each numerical unit in the numerical model, and obtain the angle α between the most unfavorable shear direction and the horizontal plane direction of each numerical unit critical ;

[0013] Step S3: Determine the numerical unit on the surface layer of the slope with the minimum local safety factor, and based on the positional relationship between the numerical unit on the surface layer of the slope with the minimum local safety factor and the numerical unit on the surface layer of the slope with the second minimum local safety factor, determine whether the determined numerical unit on the surface layer of the slope is the lower edge boundary position or the upper edge boundary position of the potential slip surface;

[0014] Step S4: Take the center point of the determined numerical unit on the surface layer of the slope as the starting point for identifying and extracting the potential slip surface, and let the coordinates of this center point be (x0, z0);

[0015] Step S5: Apply the piecewise step-by-step identification method to solve the position of the next unknown potential slip point i based on the previous known potential slip point i–1. The specific calculation formula is x i = x i–1 + Δd × cosα i–1 and z i = z i–1 + Δd × sinα i–1 ; where α i–1 is the angle between the most unfavorable shear direction and the horizontal plane direction of the numerical unit where point i–1 is located; and if the determined numerical unit on the surface layer of the slope is the lower edge boundary position of the potential slip surface, then take Δd as a positive value; otherwise, take Δd as a negative value;

[0016] where, (x i–1 , z i–1 ) are the coordinates of the previous known potential slip point i–1, (x i , z i ) are the coordinates of the next unknown potential slip point, Δd is the length of the segmented slip surface, and α i–1 is the angle between the most unfavorable shear direction and the horizontal plane direction of the numerical unit where point i–1 is located;

[0017] Step S6: Calculate the sum of the volumes of the spatial geometric bodies formed by connecting the potential slip point i to the vertices on each side surface in each numerical unit, and determine the numerical unit where the potential slip point i is located based on the equality of this sum of volumes and the volume of a certain numerical unit;

[0018] Step S7: Judge whether the potential slip point exceeds the slope surface according to whether the potential slip point is located on a certain numerical unit; if the potential slip point i exceeds the slope surface, stop the identification and extraction of the potential slip surface; otherwise, repeat Step S5 to Step S6;

[0019] Step S8: Connect the identified and extracted potential slip points in sequence to obtain the two-dimensional potential slip surface of the slope.

[0020] In a specific implementation, step S2 specifically includes the following steps:

[0021] Step 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;

[0022] Step S2-2: Based on the Mohr stress circle reflecting the stress state of the numerical unit, determine the value range of the normal stress σ on the surface acting in different directions in the numerical unit as [σ3, σ1], and obtain the shear stress on the surface acting in different directions under the corresponding normal stress in the numerical unit as τ = [(σ1–σ)(σ–σ3)] 1 / 2 ; Among them, σ3 is the minor principal stress of the numerical unit, and σ1 is the major principal stress of the numerical unit;

[0023] Step 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);

[0024] Step S2-4: Calculate the shear strength τ on the action surface according to the safety factor definition f The ratio k of shear stress τ s , and k s =f(σ) / [(σ1–σ)(σ–σ3)] 1 / 2 ;

[0025] Step 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 s ), which is the local safety factor F of the numerical unit s_Local , that is, F s_Local =min(k s );

[0026] Step S2-6: The most unfavorable shear direction based on the numerical unit is k s The direction of the action surface corresponding to the minimum value is taken. The relationship between the normal stress σ and the angle α on the action surface in different directions in the numerical unit is σ=(σ3+σ1) / 2–[(σ1–σ3) / 2]cos2α. The angle between the most unfavorable shear direction of the numerical unit and the direction of the small principal stress action surface is solved as α k =(1 / 2)×arcos{[(σ3+σ1)–2σ k ] / (σ1–σ3)}, where σ k k s The normal stress on the corresponding action surface when the minimum value is taken;

[0027] Step S2-7: Solve for the angle α between the horizontal plane and the plane of action of the minor principal stress using the relationship σ = (σ3 + σ1) / 2 – [(σ1 – σ3) / 2]cos2α z = (1 / 2)×arcos{[(σ3 + σ1) – 2σ z / (σ1 – σ3)}; σ z is the normal stress in the vertical direction of this numerical unit;

[0028] Step S2-8: Based on the angle between the most unfavorable shear direction of the numerical unit and the direction of the plane of action of the minor principal stress, and the angle between the horizontal plane and the plane of action of the minor principal stress, it is deduced that the angle between the most unfavorable shear direction and the horizontal plane direction is α critical = α z – α k , where when α critical is greater than 0, the angular direction is counterclockwise, and vice versa it is clockwise.

[0029] In a specific embodiment, the slope conforms to the generalized non-linear H-B strength criterion, and in step S2, the calculation formula for the shear strength of the rock and soil mass is:

[0030]

[0031] where m b is a material constant, s is a parameter reflecting the degree of rock mass fragmentation, α is a constant related to the rock mass structure form and the surface conditions of the structural plane, is the instantaneous internal friction angle of the rock mass.

[0032] In a specific embodiment, in step S2, the calculation formulas for the parameters m b , s, α and are respectively:

[0033]

[0034] α = 0.5 + (1 / 6)×[exp(–GSI / 15) – exp(–20 / 3)]

[0035]

[0036] 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.

[0037] In a specific embodiment, in step S5, after the coordinates (x0, z0) of the center point are extracted, extend upward along its sliding trend, and the length of each extension is Δd, where Δd is taken as 0.1 - 0.5 m. Furthermore, apply a segmented step-by-step identification method to solve for the position of the next unknown potential sliding point i based on the previous known potential sliding point i - 1; and in order to satisfy the concave feature of the sliding surface, α i–1 should satisfy α i–1 ≥α i–2 ; otherwise, if α i–1 <α i–2 , then let α i–1 =α i–2 .

[0038] In a specific embodiment, use the software FLAC 3D for numerical simulation analysis.

[0039] The advantages of the present invention are as follows: The method provided by the present invention does not need to introduce the strength reduction technology and does not limit the shear strength criterion of rock and soil masses. After obtaining the slope stress field by numerical simulation calculation, it can automatically identify and extract the potential sliding surface of the two-dimensional slope. The obtained potential sliding surface conforms to the slope shear failure mechanism and can effectively show the actual failure form of the two-dimensional slope in the real scene; at the same time, the segmented step-by-step identification method can better control the fineness of the identification and extraction of the potential sliding surface, which is conducive to realizing the intelligent identification and extraction of the two-dimensional potential sliding surface. Therefore, the present invention has the characteristics of wide application range, high precision, good generality, good effect, low cost, etc., and has the characteristics of automation and intelligence, which can provide a strong scientific basis for predicting the potential instability range of slopes and determining the reinforcement area in practical engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a schematic diagram of the two-dimensional slope numerical model of the present invention.

[0041] Figure 2 It is a schematic diagram of the stress analysis of the numerical unit in the present invention.

[0042] Figure 3 It is a flowchart of the implementation of the calculation of the local safety factor of the numerical unit and the determination of the most unfavorable shear direction in the present invention.

[0043] Figure 4 It is a schematic diagram of the determination of the surface numerical unit of the slope in the present invention.

[0044] Figure 5 It is a schematic diagram of the determination of the boundary position below or above the potential sliding surface in the present invention.

[0045] Figure 6 It is a schematic diagram of the segmented step-by-step identification of the trend and position of the potential sliding surface in the present invention.

[0046] Figure 7 Schematic diagram for determining the numerical unit where the sliding point of the present invention is located.

[0047] Figure 8 Schematic diagram for identifying the sliding point of the present invention exceeding the slope surface.

[0048] Figure 9 Flow chart for identifying and extracting the potential sliding surface of the slope in the two-dimensional numerical simulation calculation of the present invention.

[0049] In the figure: 1. Two-dimensional slope numerical model; 2. Numerical unit; 3. Plane of minor principal stress; 4. Plane of major principal stress; 5. Horizontal plane; 6. Normal stress on different-direction planes in the numerical unit; 7. Shear stress on different-direction planes in the numerical unit; 8. Slope surface; 9. Boundary surface; 10. Numerical units on the slope surface layer; 11. Numerical unit on the slope surface layer with the minimum local safety factor; 12. Numerical unit on the slope surface layer with the second minimum local safety factor; 13. Center point of the numerical unit; 14. Starting point of the potential sliding surface; 15. Previous known potential sliding point; 16. Next unknown potential sliding point; 17. Trend of the sliding surface; 18. Length of the sliding surface; 19. Side surface of the numerical unit; 20. Upper vertex of the side surface of the numerical unit; 21. Potential sliding point to be determined; 22. Spatial geometric body; 23. Sliding point exceeding the slope surface; 24. Potential sliding surface. Detailed implementation manner

[0050] To solve the above technical method problems, the present invention designs a method for identifying and extracting the potential sliding surface of the slope in two-dimensional numerical simulation calculation. This method conducts numerical simulation calculations to obtain the stress field of the slope. Then, based on the selected shear strength criterion of the rock and soil mass, using the stress information of the numerical units in the numerical model and the Mohr stress circle reflecting the stress state of the numerical units, the local safety factor of each numerical unit is solved, and the most unfavorable shear direction of each numerical unit is obtained. Then, the numerical units on the slope surface layer are extracted from the numerical units, and the numerical unit on the slope surface layer with the minimum local safety factor is used as the boundary position of the potential sliding surface. Further, based on the positional relationship between the numerical units on the slope surface layer with the minimum and the second minimum local safety factors, the identified boundary position of the potential sliding surface is determined as the lower or upper edge boundary position of the potential sliding surface. Subsequently, starting from the center point of the numerical unit on the slope surface layer with the minimum local safety factor, the trend and position of the potential sliding surface are gradually identified in segments, and the corresponding potential sliding points are recorded in sequence. At the same time, it is judged whether the obtained potential sliding points exceed the slope surface, and this is used as the termination basis for identifying the trend and position of the potential sliding surface. Finally, the identified and extracted potential sliding points are connected in sequence to obtain the potential sliding surface of the two-dimensional slope.

[0051] The present invention has the characteristics of wide application range, high precision, good versatility, excellent effect, low cost, etc., and has the characteristics of automation and intelligence, which can provide a strong scientific basis for predicting the potential instability range of slopes and determining the reinforcement area in practical engineering.

[0052] The specific practices and implementation processes of the present invention are as follows:

[0053] (1) As Figure 1 shown, according to the actual slope shape, stratum data, and physical and mechanical parameters of the rock and soil mass, a corresponding two-dimensional slope numerical model is established, and numerical calculations are carried out in combination with numerical simulation software to obtain the slope stress field, and the information of each numerical unit in the two-dimensional slope numerical model is extracted, including number information, coordinate information (such as the center coordinates and vertex coordinates of the unit), and stress information (such as the major principal stress σ1, the minor principal stress σ3, and the normal stress σ z ) in the vertical direction. It should be noted that the two-dimensional slope numerical model is constructed by stretching a unit length in the thickness direction of the two-dimensional section in the three-dimensional slope, and this unit length can be taken as 0.1m to 1.0m.

[0054] (2) As Figure 2 shown, taking any numerical unit as an example, using the major principal stress σ1, the minor principal stress σ3, and the normal stress σ z in the vertical direction obtained from the numerical simulation calculation of this numerical unit, draw the stress analysis diagram of this numerical unit. In the stress analysis diagram of this numerical unit, OA is the plane of action of the minor principal stress, and the acting force on it is the minor principal stress σ3. OB is the plane of action of the major principal stress, and the acting force on it is the major principal stress σ1. Among them, the plane of action OA of the minor principal stress is perpendicular to the plane of action OB of the major principal stress. OD is the horizontal plane, and the acting force on it is the normal stress σ z and the shear stress τ xz , and the angle between OA and OD is α z . OT is the plane of action in different directions in the numerical unit, and the angle between it and the plane of action OA of the minor principal stress is α (0° ≤ α ≤ 90°). The acting forces on OT are the normal stress σ and the shear stress τ.

[0055] (3) As Figure 2 shown, based on the stress analysis of any numerical unit, obtain the Mohr stress circle reflecting the stress state of the numerical unit, and draw the Mohr stress circle in the rectangular coordinate system of the normal stress and the shear stress. Consistent with the actual stress analysis diagram, in the Mohr stress circle, OA represents the plane of action of the minor principal stress, OB represents the plane of action of the major principal stress, OD represents the horizontal plane, and OT represents the plane of action in different directions in the numerical unit. Among them, O is the center point of the Mohr stress circle. The points A and B correspond to the minor principal stress σ3 and the major principal stress σ1 respectively. The stress corresponding to point D is σ z and τ yz, the stresses corresponding to point T are σ and τ. Given that there is a two-fold relationship between the angles in the Mohr stress circle model and the actual stress analysis model, then in the Mohr stress circle, ∠AOD = 2α z and ∠AOT = 2α.

[0056] (4) As Figure 2 shown, based on the Mohr stress circle reflecting the stress state of the numerical element, when α varies in the range of 0° to 90°, it can be known that the value range of the normal stress σ on the working surfaces in different directions in the numerical element is [σ3, σ1]. At the same time, in the Mohr stress circle, according to the spatial geometric relationship of triangle OTE, τ = [(σ1–σ)(σ–σ3)] 1 / 2 , where point E is the intersection of the vertical line passing through point T and the normal stress axis. In addition, the relationship between the normal stress σ and the angle α on the working surfaces in different directions in the numerical element satisfies σ = (σ3 + σ1) / 2 – [(σ1–σ3) / 2]cos2α.

[0057] (5) As Figure 3 shown, based on the selected shear strength criterion of the rock and soil mass, applying the stress information of the numerical element, calculate the local safety factor of each numerical element in the numerical model, and determine the most unfavorable shear direction of each numerical element. The specific implementation steps are as follows: ① Let the general expression of the shear strength criterion of the rock and soil mass be τ f = f(σ), where σ is the normal stress on the working surface and τ f is the shear strength on the working surface; ② Based on the Mohr stress circle reflecting the stress state of the numerical element, determine that the value range of the normal stress σ on the working surfaces in different directions in the numerical element is [σ3, σ1], and obtain the shear stress τ = [(σ1–σ)(σ–σ3)] 1 / 2 on the working surfaces in different directions corresponding to the normal stress in the numerical element; ③ Combine the shear strength criterion of the rock and soil mass to calculate the shear strength τ f = f(σ) on the working surfaces in different directions corresponding to the normal stress; ④ According to the definition of the safety factor, calculate the ratio k f of the shear strength τ s to the shear stress τ, and k s = f(σ) / [(σ1–σ)(σ–σ3)] 1 / 2 ; ⑤ When the normal stress σ is in the interval of [σ3, σ1], use the mathematical method of finding the extreme value to solve the minimum value of k s , and let it be min(k s ), which is the local safety factor F s_Local of the numerical element, that is, F s_Local = min(k s ); ⑥ Based on the most unfavorable shear direction of the numerical element is k sWhen taking the minimum value, the corresponding direction of the acting surface. Using the relationship formula between the normal stress σ and the angle α on the acting surfaces in different directions in the numerical unit, σ = (σ3 + σ1) / 2 – [(σ1 – σ3) / 2]cos2α, solve for the angle α between the most unfavorable shear direction of the numerical unit and the direction of the minor principal stress acting surface k = (1 / 2)×arcos{[(σ3 + σ1) – 2σ k / (σ1 – σ3)}, where σ k is the normal stress corresponding to when k s takes the minimum value; ⑦ Further, using the relationship formula σ = (σ3 + σ1) / 2 – [(σ1 – σ3) / 2]cos2α, solve for the angle α between the horizontal plane and the minor principal stress acting surface z = (1 / 2)×arcos{[(σ3 + σ1) – 2σ z / (σ1 – σ3)}; ⑧ According to the angle between the most unfavorable shear direction of the numerical unit and the direction of the minor principal stress acting surface and the angle between the horizontal plane and the minor principal stress acting surface, it is deduced that the angle between the most unfavorable shear direction and the horizontal plane direction is α critical = α z – α k , where when α critical is greater than 0, the angle direction is counterclockwise, otherwise it is clockwise

[0058] (6) As Figure 4 shown, in the numerical unit, there is a side surface belonging to the unique numerical unit, and this side surface is on 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 which comes 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 numerical units on the slope surface layer are defined as the numerical units including the slope surface. Furthermore, by obtaining the surface layer in the numerical model and excluding the boundary surface to extract the slope surface, and then, according to the matching between the slope surface and the numerical unit, determine the numerical units on the slope surface layer. The specific implementation steps are as follows: ① Obtain the surface layer numbers and the corresponding surface groups in the numerical model. For example, the numerical model divides the surface layer into 6 surface groups such as the upper side, the lower side, the east side, the west side, the south side, and the north side according to the orientation of the outer normal of the surface layer. Among them, the boundary surface is divided into 5 surface groups including 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 4 the lower side of the numerical model, the east side in the surface group corresponds to Figure 4 the rear side of the numerical model, the west side in the surface group corresponds to Figure 4 the front side of the numerical model, the south side in the surface group corresponds to Figure 4 the right side of the numerical model, the north side in the surface group corresponds to Figure 4The left side of the numerical model; ② Extract the nodes included in the surface layer, as well as the node numbers and node coordinates; ③ Exclude the boundary surfaces according to the artificially set boundary conditions. For example, when establishing the xyz-axis coordinate system with the horizontal direction in the two-dimensional slope plane as the x-axis direction, the two-dimensional slope thickness direction as the y-axis direction, and the vertical direction as the z-axis direction, for the boundary surfaces of the lower side surface group, the node coordinates on the surface are all equal to the z-axis lower boundary coordinate z in the numerical model below , based on this, when considering the calculation accuracy of the model, the boundary surfaces with the z-axis coordinates of the nodes on the surface located in the interval [z below –0.001, z below +0.001] can be excluded from the surface layer. The boundary surfaces of the surface groups such as the east side, west side, south side, and north side can all be excluded from the surface layer in this way. Among them, the front and rear boundary coordinates in the x-axis direction of the numerical model are x front and x back , the left and right boundary coordinates in the y-axis direction of the numerical model are y left and y right , and the upper boundary coordinate in the z-axis direction of the numerical model is z above ; ④ Based on the numbers of the surfaces formed by the numerical elements, adopt the method of traversing the numerical elements to determine whether the surfaces formed by the numerical elements belong to the slope surface in the surface layer, and then find the numerical elements that match the slope surface in the surface layer, and further determine the surface layer numerical elements.

[0059] (7) As Figure 5 shown, in the surface layer numerical elements of the slope, sort the surface layer numerical elements of the slope from small to large according to the magnitude relationship of the local safety factors of the numerical elements, and use the surface layer numerical element with the smallest local safety factor as the potential slip surface boundary position. At the same time, compare the position relationship between the surface layer numerical element with the smallest local safety factor and the surface layer numerical element with the second smallest local safety factor in the sorting. If the surface layer numerical element with the smallest local safety factor is closer to the lower part of the slope than the surface layer numerical element with the second smallest local safety factor, the determined surface layer numerical element is the potential slip surface lower edge boundary position; otherwise, if the surface layer numerical element with the smallest local safety factor is closer to the upper part of the slope than the surface layer numerical element with the second smallest local safety factor, the determined surface layer numerical element is the potential slip surface upper edge boundary position.

[0060] (8) As Figure 6As shown in the figure, the center point of the numerical unit on the surface layer of the slope with the minimum local safety factor is taken as the starting point of the potential slip surface. The trend and position of the potential slip surface are gradually identified in segments, and the corresponding potential slip points are recorded in sequence. Among them, the method of gradually identifying in segments is to discretize the potential slip surface into multiple segments, and the length of each segment of the slip surface is Δd. Here, Δd should not be too large nor too small. If it is too large, the recognition accuracy of the potential slip surface is not high; if it is too small, the calculation efficiency is low. Generally, Δd can be taken as 0.1m - 0.5m, with a lower value for small slopes and a higher value for large slopes. Furthermore, using the previous known potential slip point, on the basis of determining the trend of this segment of the slip surface, the length of the slip surface is extended by Δd along the trend of this segment of the slip surface to solve the position of the next unknown potential slip point, and so on until the solved potential slip points exceed the slope surface.

[0061] (9) As Figure 6 shown in the figure, for the trend of each segment of the potential slip surface, the determination principle is that the most unfavorable shear direction of the numerical unit where the previous known potential slip point in this segment of the slip surface is located is taken as the trend of this segment of the slip surface. At the same time, considering the concave shape characteristics of the potential slip surface, the dip angle of the potential slip surface trend should satisfy the constraint condition of increasing successively from bottom to top. If it does not meet the requirement, the trend of this segment of the slip surface will follow the trend of the previous segment of the slip surface. Taking the determined numerical unit on the surface layer of the slope as the lower edge boundary position of the potential slip surface as an example, the previous known potential slip point of the unknown potential slip point i is i - 1, and the previous known potential slip point of point i - 1 is i - 2, then it should satisfy α i–1 ≥α i–2 , otherwise, if α i–1 <α i–2 , then let α i–1 =α i–2 , where α i–1 is the angle between the most unfavorable shear direction of the numerical unit where point i - 1 is located and the horizontal plane direction, and α i–2 is the angle between the most unfavorable shear direction of the numerical unit where point i - 2 is located and the horizontal plane direction.

[0062] (10) As Figure 7As shown in the figure, in each sliding surface segment, for the next unknown potential sliding point solved based on the previous known potential sliding point, the principle for determining the numerical unit where it is located is as follows: Connect the potential sliding point to be determined with the vertices on the side of a certain numerical unit to form a spatial geometric body. At the same time, when connecting to the vertices on each side, multiple spatial geometric bodies will be obtained. If the sum of the volumes of these spatial geometric bodies is equal to the volume of this numerical unit, then this potential sliding point is located within this numerical unit. The specific implementation steps are as follows: ① Obtain the volume of the numerical unit, the sides of the numerical unit, and the numbers and coordinates of their vertices, and extract the area of the sides 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 of the numerical unit, use the coordinates of these 4 points to determine the functional formula of this spatial side, and then, apply the distance formula from a point to a spatial plane to solve the perpendicular distance from the potential sliding point to be determined to the side of the numerical unit; ③ Based on the obtained perpendicular distance from the potential sliding point to be determined to the side of the numerical unit and the area of the side of the numerical unit, calculate the volume and its sum of the spatial geometric bodies formed by connecting the potential sliding point to be determined with the vertices on each side of the selected numerical unit; ④ Traverse all numerical units, and determine whether the sum of the volumes of the spatial geometric bodies formed by connecting the potential sliding point to be determined with the vertices on each side of the selected numerical unit is equal to the volume of this numerical unit. If the two are equal, the numerical unit where the potential sliding point to be determined is located can be obtained.

[0063] (11) As Figure 8 shown, when using the method of segmentally and gradually identifying the trend and position of the potential sliding surface, it is necessary to determine whether the next unknown potential sliding point solved exceeds the slope surface. The identification principle is that if the potential sliding point is a sliding point that exceeds the slope surface, then this potential sliding point will not be on any numerical unit. Therefore, the specific method of determining the numerical unit where the potential sliding point to be determined is located is used to identify whether this potential sliding point exceeds the slope surface, that is, after traversing all numerical units, if the numerical unit where this potential sliding point is located cannot be determined, it can be considered that this potential sliding point exceeds the slope surface, and the identification of the trend and position of the potential sliding surface is stopped. Further, the obtained potential sliding points are connected in sequence to obtain the two-dimensional potential sliding surface of the slope.

[0064] (12) As Figure 9As shown in the figure, the implementation process for identifying and extracting the potential sliding surface of a slope in two-dimensional numerical simulation is as follows: ① Establish a two-dimensional slope numerical calculation model, conduct numerical calculations, 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, and obtain the angle between the most unfavorable shear direction of each numerical unit and the horizontal plane direction; ③ Determine the surface numerical unit of the slope with the minimum local safety factor, and based on the positional relationship between the surface numerical units of the slope with the minimum and the second minimum local safety factors, determine whether the determined surface numerical unit of the slope is the lower edge boundary position or the upper edge boundary position of the potential sliding surface; ④ Take the center point of the determined surface numerical unit of the slope as the starting point for identifying and extracting the potential sliding surface, and let the coordinates of this center point be (x0, z0); ⑤ Apply the segmented step-by-step identification method. Based on the previous known potential sliding point i–1, solve for the position of the next unknown potential sliding point i. The specific calculation formula is x i = x i–1 + Δd × cosα i–1 and z i = z i–1 + Δd × sinα i–1 , where (x i–1 , z i–1 ) are the coordinates of the previous known potential sliding point i–1, (x i , z i ) are the coordinates of the next unknown potential sliding point, Δd is the length of the segmented sliding surface, and α i–1 is the angle between the most unfavorable shear direction of the numerical unit where point i–1 is located and the horizontal plane direction. It should be noted that if the determined surface numerical unit of the slope is the lower edge boundary position of the potential sliding surface, then Δd can be taken as a positive value; otherwise, Δd can be taken as a negative value; ⑥ Calculate the sum of the volumes of the spatial geometric bodies formed by connecting the potential sliding point i to the vertices on each side of each numerical unit, and determine the numerical unit where the potential sliding point i is located based on the equality of this sum of volumes and the volume of a certain numerical unit; ⑦ According to whether the potential sliding point is located on a certain numerical unit, determine whether the potential sliding point i exceeds the slope surface. If the potential sliding point i exceeds the slope surface, stop the identification and extraction of the potential sliding surface; otherwise, repeat steps ⑤ to ⑥; ⑧ Connect the identified and extracted potential sliding points in sequence to obtain the potential sliding surface of the two-dimensional slope.

[0065] The characteristics of the local safety factor solution in the present invention are as follows: By applying numerical simulation calculation technology to obtain the slope stress field, and on the basis of selecting the shear strength criterion of rock and soil masses, combined with the stress information of numerical units in the numerical model and the Mohr stress circle reflecting the stress state of numerical units, the local safety factor of numerical units is solved. This method can utilize the powerful calculation function of existing numerical simulation software and its favorable condition of restoring the actual stress field of the slope in the real scene. At the same time, compared with the solution of the slope safety factor introduced by the strength reduction technology, the solution of the local safety factor does not change the real stress state of the slope. Moreover, when solving the local safety factor of numerical units, the most unfavorable shear direction of numerical units is also obtained. In addition, the solution of the local safety factor does not depend on a specific shear strength criterion of rock and soil masses, making it have strong versatility.

[0066] The characteristics of the identification and extraction of potential slip surfaces in the present invention are as follows: Starting from the center point of the surface numerical unit of the slope with the minimum local safety factor, the trend and position of the potential slip surface are gradually identified in segments, and whether the obtained potential slip surface points exceed the slope surface is used as the termination basis for the identification of the trend and position of the potential slip surface. This method is conducive to the automation and intelligence of the identification and extraction of the slip surface. When gradually identifying the potential slip surface in segments, the length of each segment of the slip surface is controlled, which is easy to realize the refinement of the identification and extraction of the potential slip surface. The identified potential slip surface points are completely matched with the numerical units in the numerical model, and the trend of the slip surface is controlled by the most unfavorable shear direction of the numerical unit where the corresponding potential slip surface point is located, which conforms to the shear failure mechanism of the slope. At the same time, the trend of the slip surface is also controlled by the concave feature of the potential slip surface, thereby ensuring the rationality of the identified and extracted potential slip surface.

[0067] Embodiment

[0068] A method for identifying and extracting potential slip surfaces of slopes in two-dimensional numerical simulation calculations as Figures 1 to 9 shown. For a slope along a certain highway, due to complex geological conditions and low rock and soil strength, there is a large 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 slip surfaces of slopes in two-dimensional numerical simulation calculations invented in this paper is introduced and applied. It has successfully defined the potential range of slope landslide and effectively supported the implementation of reinforcement measures. The specific operations are as follows:

[0069] (1) According to the requirements of the "Code for Geotechnical Investigation" (GB50021-2001), conduct on-site exploration tests on the highway slope to obtain the two-dimensional slope surface shape (slope height H = 10m and slope angle β = 45°), stratum data, and corresponding rock and soil strength parameters in the analysis area. In this embodiment, the rock and soil masses of the slope are severely weathered and fractured and obey the generalized non-linear H-B strength criterion. The specific strength parameters are GSI = 5, σ c = 30MPa, m i= 2 and D = 0; 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;

[0070] (2) According to the actual slope surface shape of the two-dimensional slope, establish the corresponding two-dimensional slope numerical model in the numerical simulation software. Among them, the tensile unit length in the thickness direction is set to 0.1 m. At the same time, assign the corresponding rock and soil layer parameters and their strength parameters, and set the corresponding model boundary constraint conditions;

[0071] (3) Carry out numerical calculations and extract the information of each numerical unit in the numerical model, including the number information, coordinate information (such as the unit center coordinate and the unit vertex coordinate), and stress information (such as the major principal stress σ1, the minor principal stress σ3, and the normal stress σ z ) in the vertical direction;

[0072] (4) Calculate the local safety factor F s_Local of each numerical unit in the numerical model. Among them, the shear strength calculation formula of the rock and soil mass under the generalized nonlinear H-B strength criterion is The calculation formulas for the parameters m b , s, α, and are respectively α = 0.5 + (1 / 6) × [exp(–GSI / 15) – exp(–20 / 3)] and where m b is the material constant, s is the parameter reflecting the degree of rock mass fragmentation, α is the constant related to the rock mass structure form and the surface condition of the structural plane, is the instantaneous internal friction angle of the rock mass;

[0073] (5) Solve the most unfavorable shear direction of each numerical unit and the included angle α critical between the most unfavorable shear direction and the horizontal plane direction;

[0074] (6) Obtain the surface layer of the slope numerical model. The commands "gp.isgroup()" and "gp.pos()" in the software FLAC 3D can be used to extract the nodes, node numbers, and node coordinates included in each surface layer. Then, based on the coordinate characteristics of the nodes in the non-surface layer, exclude all non-surface layers to obtain the surface layer of the actual slope.

[0075] (7) Identify and extract the slope surface numerical units belonging to the surface layer. By traversing the units and using the command "zone.face.isgroup()" in the software FLAC 3D , identify and extract all the slope surface numerical units corresponding to the surface layer.

[0076] (8) Determine the position of the potential slip surface boundary. In the numerical elements on the surface layer of the slope, according to the magnitude relationship of the local safety factors of the numerical elements, sort the numerical elements on the surface layer of the slope from small to large, and take the numerical element on the surface layer of the slope with the smallest local safety factor as the potential slip surface boundary position. For this slope numerical model, the numerical element on the surface layer of the slope with the smallest local safety factor is closer to the lower part of the slope than the numerical element on the surface layer of the slope with the second smallest local safety factor. Thus, the determined numerical element on the surface layer of the slope with the smallest local safety factor is the lower edge boundary position of the potential slip surface.

[0077] (9) Calculate the discrete points of the potential slip surface. Take the center point of the numerical element on the surface layer of the slope with the smallest local safety factor as the starting point of the potential slip surface, and extract its coordinates (x0, z0). Then, extend upward along its sliding trend, with the extension length of each time being Δd, where Δd is taken as 0.3 m. Furthermore, apply the segmented step-by-step identification method to solve the position of the next unknown potential slip point i based on the previous known potential slip point i–1. The specific calculation formula is x i = x i–1 + Δd × cosα i–1 and z i = z i–1 + Δd × sinα i–1 , where α i–1 is the angle between the most unfavorable shear direction of the numerical element where point i–1 is located and the horizontal plane direction; at the same time, in order to satisfy the concave characteristic of the slip surface, α i–1 should satisfy α i–1 ≥ α i–2 , otherwise, if α i–1 < α i–2 , then let α i–1 = α i–2 ;

[0078] (10) Judge the numerical element where the potential slip point i is located and whether it exceeds the slope surface. For each obtained potential slip point i, it is necessary to calculate the sum of the volumes of the spatial geometric bodies formed by connecting the potential slip point i to the vertices on each side surface in each numerical element. Determine the numerical element where the potential slip point i is located based on the equality of this sum of volumes and the volume of a certain numerical element. When the potential slip point is not located in any numerical element, it means that this point has exceeded the slope surface, and stop the identification and extraction of the potential slip points. Then, connect the identified and extracted potential slip points in sequence, and further obtain the two-dimensional slope potential slip surface. In this embodiment, the characteristics of the obtained two-dimensional slope potential slip surface are that the sliding range extends from 0.5 m away from the slope toe to 13.5 m, the maximum sliding depth is 3.4 m, and the sliding range area is 36.9 m 2 .

[0079] Generally speaking, the present invention relates to a method for identifying and extracting potential sliding surfaces of slopes in two-dimensional numerical simulation calculations, belonging to the field of traffic slope engineering. Based on the positional relationship of the numerical units on the surface layer of the slope with the smallest and the second smallest local safety factors, the boundary position of the identified potential sliding surface is defined as the lower or upper edge boundary position of the potential sliding surface; finally, the potential sliding points identified and extracted are connected in sequence to obtain the potential sliding surface of the two-dimensional slope. The present invention does not need to introduce the strength reduction technology and does not limit the shear strength criterion of rock and soil masses, can automatically and intelligently identify and extract the potential sliding surface of the two-dimensional slope, the obtained potential sliding surface conforms to the shear failure mechanism of the slope, and can effectively show the actual failure form of the two-dimensional slope in the real scene; it has the characteristics of wide application range, high precision, good generality, good effect, low cost, etc., and is used to solve the problem of accurately determining the potential sliding surface in actual slope engineering, and can provide a strong scientific basis for predicting the potential instability range of slopes and determining the reinforcement area in actual engineering.

[0080] It is easy for those skilled in the art to understand that the above is only a preferred embodiment of the present invention and is not used to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for identifying and extracting potential sliding surfaces of slopes in two-dimensional numerical simulation calculations, characterized in that: The method comprises the following steps: Step S1: Establish a two-dimensional slope numerical calculation model, carry out numerical calculation, and extract information of each numerical unit in the numerical model; Step S2: Calculate the local safety factor of each numerical unit in the numerical model and obtain the angle between the most unfavorable shear direction of each numerical unit and the horizontal plane direction α critical ; Step S3: determining the slope surface numerical unit with the smallest local safety factor, and judging whether the determined slope surface numerical unit is the lower edge boundary position of the potential sliding surface or the upper edge boundary position of the potential sliding surface based on the positional relationship between the slope surface numerical unit with the smallest local safety factor and the slope surface numerical unit with the second smallest local safety factor; Step S4: The center point of the determined slope surface numerical unit is used as the starting point for potential sliding surface identification and extraction, and the coordinates of the center point are ( x 0, z 0); Step S5: Apply the segmented step-by-step identification method based on the last known potential sliding surface point i – 1. Solve for the next unknown potential sliding point i The specific calculation formula is x i = x i–1 + Δ d × cos α i–1 and z i = z i–1 + Δ d × sin α i–1 ; in, α i–1 For point i – 1 is the angle between the most unfavorable shear direction of the numerical unit and the horizontal plane direction; and if the determined numerical unit of the slope surface is the lower edge boundary position of the potential sliding surface, then take Δ d is a positive value; otherwise, take Δ d is a negative value; in,( x i–1 , z i–1 ) is the last known potential sliding surface point i – 1’s coordinates, ( x i , z i ) is the coordinate of the next unknown potential sliding surface point, Δ d is the length of the segmented sliding surface, α i–1 For point i – 1 is the angle between the most unfavorable shear direction of the numerical unit and the horizontal plane direction; Step S6: Calculate potential sliding points i The sum of the volumes of the spatial geometric bodies connected to the vertices on each side of each numerical unit, and the potential sliding point is determined based on the sum of this volume being equal to the volume of a certain numerical unit. i The numerical unit where it is located; Step S7: Determine whether the potential sliding surface point is located on a certain numerical unit. i Whether it exceeds the slope; if there is a potential sliding point i If it exceeds the slope, the identification and extraction of the potential sliding surface is stopped; otherwise, steps S5 to S6 are repeated; Step S8: sequentially connect the identified and extracted potential sliding surface points to obtain a two-dimensional potential sliding surface of the slope.

2. The method for identifying and extracting potential sliding surfaces of slopes in two-dimensional numerical simulation calculations according to claim 1 is characterized in that: Step S2 specifically includes the following steps: Step S2-1: Let the general expression of the shear strength criterion of rock and soil be τ f = f ( σ ),in, σ is the normal stress on the action surface, τ f is the shear strength on the action surface; Step S2-2: Based on the Mohr stress circle reflecting the stress state of the numerical unit, determine the normal stress on the surface in different directions in the numerical unit σ The value range is [ σ 3. σ 1], and obtain the shear stress on the surface in different directions under the corresponding normal stress in the numerical unit: τ = [( σ 1 – σ )( σ – σ 3)] 1 / 2 ;in, σ 3 is the minor principal stress of the numerical unit, σ 1 is the major principal stress of the numerical unit; Step 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 ); Step S2-4: Calculate the shear strength on the action surface according to the safety factor definition τ f and shear stress τ Ratio k s ,and k s = f ( σ ) / [( σ 1 – σ )( σ – σ 3)] 1 / 2 ; Step S2-5: When the normal stress σ lie in[ σ 3. σ 1] When it is within the interval, use the mathematical method of finding the extreme value to solve k s The minimum value of , and let it be min( k s ), which is the local safety factor of the numerical unit F s_Local ,Right now F s_Local = min( k s ); Step S2-6: The most unfavorable shear direction based on the numerical unit is k s The direction of the action surface corresponding to the minimum value is obtained by using the normal stress on the action surface in different directions in the numerical unit. σ With Angle α The relationship between σ = ( σ 3 + σ 1) / 2 – [( σ 1 – σ 3) / 2]cos2 α , the angle between the most unfavorable shear direction of the numerical unit and the direction of the small principal stress action surface is solved as α k =(1 / 2) × arcos{[( σ 3 + σ 1) – 2 σ k ] / ( σ 1 – σ 3)}, where σ k for k s The normal stress on the corresponding action surface when the minimum value is taken; Step S2-7: Using the relation σ = ( σ 3 + σ 1) / 2 – [( σ 1 – σ 3) / 2]cos2 α , the angle between the horizontal plane and the surface of the minor principal stress is α z = (1 / 2) × arcos{[( σ 3 + σ 1) – 2 σ z ] / ( σ 1 – σ 3)}; σ z is the normal stress of the numerical unit along the vertical direction; Step S2-8: Based on the angle between the most unfavorable shear direction of the numerical unit and the direction of the minor principal stress action surface and the angle between the horizontal plane and the minor principal stress action surface, the angle between the most unfavorable shear direction and the horizontal plane direction is derived as α critical = α z – α k ,in, α critical When it is greater than 0, the angle direction is counterclockwise, otherwise it is clockwise.

3. The method for identifying and extracting potential sliding surfaces of slopes in two-dimensional numerical simulation calculations 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: in, σ c is the uniaxial compressive strength of intact rock, m b is the material constant, s As a parameter reflecting the degree of rock mass fragmentation, α is a constant related to the rock mass structure and surface conditions. φ i is the instantaneous internal friction angle of the rock mass.

4. The method for identifying and extracting potential sliding surfaces of slopes in two-dimensional numerical simulation calculations according to claim 3 is characterized in that: In step S2, the parameters m b , s , α and φ i The calculation formulas are: Among them, GSI is the geological strength index, m i is the material constant of intact rock, D is the disturbance factor of the rock mass.

5. The method for identifying and extracting potential sliding surfaces of slopes in two-dimensional numerical simulation calculations according to claim 4 is characterized in that: In step S5, the coordinates of the center point are extracted ( x 0, z 0), and then extend upward along its sliding trend, with each extension length being Δ d， Among them, Δ d Take it as 0.1~0.5 m, and then apply the segmented step-by-step identification method, based on the last known potential sliding surface point i – 1. Solve for the next unknown potential sliding point i position; and in order to satisfy the concave characteristics of the sliding surface, α i–1 Should meet α i–1 ≥ α i–2 Otherwise, if α i–1 < α i–2 , then let α i–1 = α i–2 .

6. The method for identifying and extracting potential sliding surfaces of slopes in two-dimensional numerical simulation calculations according to any one of claims 1 to 5, characterized in that: Using FLAC software 3D Conduct numerical simulation analysis.

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