A Dimensionality Reduction Search Method for Three-Dimensional Slope Sliding Surface

Abstract

The invention discloses a dimensionality reduction search method for a three-dimensional slope sliding surface, comprising the following steps: solving a suitable canonical velocity field based on a permeability tensor determined by a maximum stress failure ratio, and generating streamlines by integrating at each node; determining the direction of each sliding surface of a flow channel, and then calculating the safety factor of each flow channel and its intersection line with the slope surface; vectorizing the intersection line between each node flow channel and the slope surface on the potential sliding area of ​​the slope surface, selecting a straight line segment spanning the potential sliding area of ​​the slope surface, and dividing the straight line segment into equal parts; obtaining an intersection line between a three-dimensional sliding surface and the slope surface through each equally divided point according to the above-mentioned vector field integration, and obtaining the safety factor of the three-dimensional sliding surface through a simple interpolation of the intersection line; and making a three-dimensional sliding surface corresponding to the minimum safety factor through the intersection line at this point.

Description

Technical Field

[0001] The invention belongs to the technical field of geotechnical engineering slopes and relates to a dimensionality reduction search method for a three-dimensional slope sliding surface. Background Art

[0002] A core task in slope stability analysis is the search for dangerous sliding surfaces. Regardless of the optimization algorithm, its efficiency is heavily dependent on the dimensionality of the optimization problem. In two-dimensional problems, when the sliding surface is assumed to be a circular arc, the optimization dimension is 3; when the sliding surface is non-circular, the dimension rises to tens or even hundreds. In three-dimensional problems, the increased geometric dimension doubles the number of degrees of freedom, making the limit equilibrium strip method difficult to apply to three-dimensional problems. This dramatic increase in optimization dimension places a significant burden on the optimization algorithm. Effectively reducing the optimization dimension in slope analysis is a key issue in improving optimization efficiency.

[0003] Method for constructing three-dimensional arbitrary-shaped slip surface of slope and method for searching critical slip surface (CN109308396A) Constructing slip surface requires preset entry and exit points and the maximum width of the landslide range, while the method described in the present invention does not require any requirements for the entry and exit points of the slip surface and the landslide range, making the search process simpler. A method for searching three-dimensional critical slip surface of slope (CN105787277 A) requires assuming the shape of the slip surface as an ellipsoid based on the slope size; while the method described in the present invention does not require any assumptions about the shape of the slip surface, thus expanding the search range and making the shape of the dangerous slip surface obtained by the search more accurate. A method for determining instability criterion of homogeneous slope stability using strength reduction method (CN106874649A) determines the critical slip surface by calculating the maximum plastic strain through-band as the critical slip surface and uses the plastic stress field for judgment, resulting in low computational efficiency. The method described in the present invention is based on the finite element elastic stress field, which greatly improves computational efficiency.

[0004] Quasi-strict and non-strict three-dimensional limit equilibrium methods for slopes of general shapes. This method (Quasi-strict and non-strict three-dimensional limit equilibrium methods for slopes of general shapes, Deng Dongping, Li Liang, School of Civil Engineering, Central South University, Changsha, Hunan 410075) requires assumptions about the inter-strip forces between soil columns, while the method described in the present invention does not require any assumptions about the inter-strip forces between soil columns, and the calculation results are more accurate.

[0005] A three-dimensional sliding surface search method for slopes based on finite element calculation (Three-dimensional sliding surface search for slopes based on finite element calculationLin Yongsheng, Chen Shenghong, State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072) requires a direct search for the most dangerous three-dimensional sliding surface. The method described in the present invention greatly reduces the workload of searching for the most dangerous sliding surface by converting the three-dimensional sliding surface search problem into a one-dimensional problem. Summary of the Invention

[0006] A core task of slope stability analysis is the search for dangerous sliding surfaces. Regardless of the optimization algorithm, its efficiency is heavily dependent on the dimension of the optimization problem. In two-dimensional problems, when the sliding surface is assumed to be a circular arc, the optimization dimension is 3; and when the sliding surface is non-circular arc, the dimension rises to dozens or hundreds; in three-dimensional problems, due to the improvement of the geometric dimension, the degree of freedom is doubled, making it difficult to apply the limit equilibrium strip method to three-dimensional problems. The sharp increase in optimization dimension brings a huge burden to the optimization algorithm. How to effectively reduce the optimization dimension of slope analysis is a key issue to improve optimization efficiency. The purpose of this invention is to provide a method to reduce the three-dimensional slope sliding surface search problem to a one-dimensional boundary value problem.

[0007] The present invention is achieved through at least one of the following technical solutions.

[0008] A dimensionality reduction search method for a three-dimensional slope sliding surface comprises the following steps:

[0009] The first step is to solve the velocity field based on the permeability tensor determined by the maximum stress-failure ratio, and generate streamlines based on the velocity field by integrating each node on the slope surface (potential sliding area);

[0010] The second step is to determine the direction of each sliding surface of the flow channel based on the direction of the streamline tangent and the second principal stress, and then calculate the safety factor of each flow channel and its intersection with the slope surface, thereby reducing the three-dimensional slope problem to a two-dimensional slope sliding surface search problem;

[0011] Step 3: Vectorize the intersection lines between the flow channel and the slope surface at each node on the potential sliding area of ​​the slope surface, select a straight line segment across the potential sliding area of ​​the slope surface, and divide the straight line segment into equal parts;

[0012] Step 4: Integrate the vector field at each equally divided point to obtain the intersection line between the three-dimensional sliding surface and the slope surface. Based on this intersection line, a simple interpolation is performed to obtain the safety factor of the three-dimensional sliding surface. The minimum value of the safety factors at each equally divided point is the minimum safety factor of the three-dimensional slope.

[0013] Step 5: The intersection line of the equal-division point corresponding to the minimum safety factor is the intersection line of the potential failure surface and the slope surface. Draw a streamline on the intersection line to obtain the three-dimensional sliding surface corresponding to the minimum safety factor.

[0014] Furthermore, the method for determining the direction of the permeability tensor is:

[0015] Let the permeability tensor be K1 is parallel to the direction of the failure line AD in the plane formed by the axis σ1 and the axis σ3, K2 is along the direction of the σ2 axis, and K3 is along the orthogonal direction of K1K2, that is, the direction cosine of K1 is: [R 11 R 12 R 13 ]T =AN T ·[cosβ0sinβ] T ; K2 direction cosine is [R 21 R 22 R 23 ]=[l2 m2 n2]; K3 direction cosine is [R 31 R 32 R 33 ]=K2×K3, where K1, K2, K3 are the permeability tensors, R 11 、R 12 、R 13 They are K1 direction tensor, AN is the principal stress direction tensor, β is the angle between K1 and the horizontal axis, l2, m2, n2 are the cosines of the angles between K2 and the three coordinate axes, R 31 、R 32 、R 33 are the K3 direction tensors respectively.

[0016] Furthermore, the direction of the failure line AD in the σ1σ3 plane is determined as follows: first, the elastic displacement field of the slope is calculated using a finite element program, and the failure direction needs to be consistent with the direction of the elastic displacement field. From a planar perspective, each point in the displacement field has two failure surfaces and one displacement direction. The failure surface with the smallest angle with the displacement direction is selected as the failure direction.

[0017] Furthermore, the method of constructing the flow channel is to construct the sliding surface using the tangent of the streamline and the intermediate principal stress σ2, and point P is an arbitrary point on the streamline. By using the vector along the tangent direction of the streamline at point P, Construct the sliding surface with the σ2 axis direction vector; determine n points P1~P on the streamline n After the unit sliding surface is located, the sliding surfaces on the entire streamline are connected. The sliding surface formed by each unit segment is drawn on a streamline S in the three-dimensional slope and connected to form a long strip flow channel representing the streamline S.

[0018] Furthermore, the method for calculating the safety factor of the flow channel is: the stress state at point P and the vector along the tangent direction of the streamline are known. The shear stress along the tangent direction is τ n , the total stress is T, through Get the sliding surface direction vector Where: is the direction vector of the intermediate principal stress, α, η, and γ are the angles between the sliding surface direction vector and the three coordinate axes respectively;

[0019] First, use formula (1) to calculate the normal stress at point P:

[0020]

[0021] Where:

[0022]

[0023] where σ n is the normal stress at point P, σ x , σ y , σ z is the normal stress component acting on point P along the x, y, and z directions, τ xy , τ yz , τ xz is the shear stress component acting on point P along the x, y, and z directions. T(1), T(2), and T(3) are all intermediate variables. n is the shear stress value along the streamline tangent direction at point P;

[0024] The safety factor of each flow channel can be calculated by further using the safety factor calculation formula.

[0025] Furthermore, the sliding surface with the smallest safety factor is obtained through preliminary calculation. A straight line segment across two streamlines is selected near the sliding surface for further equal division and encryption, and the fourth step is repeated to find a streamline with a smaller safety factor.

[0026] Furthermore, the starting points and end points of the streamlines are all connected to obtain a closed surface representing the most dangerous sliding surface.

[0027] Furthermore, K1 and K2 take K max In order to achieve the maximum permeability coefficient on the failure surface, K3 takes the minimum value, achieving the goal of allowing the water inside the slope to flow along the direction that is most susceptible to failure.

[0028] Furthermore, when constructing the permeability tensor, in order to avoid the singularity when the maximum stress failure ratio is 0 and to reduce the degree of inhomogeneity and anisotropy caused by the maximum stress failure ratio, a background flow factor needs to be added for adjustment.

[0029] Furthermore, in order to suppress the sensitivity of the boundary, a directional highly permeable pipe network is embedded in the isotropic homogeneous material, so that the final potential field depends largely on the pipe network, thereby effectively suppressing the sensitivity of the boundary.

[0030] Compared with the existing technology, the beneficial effects of the present invention are:

[0031] 1. Dimensionality reduction optimization: by converting the three-dimensional sliding surface search problem into a one-dimensional problem, the workload of searching for the most dangerous sliding surface is greatly reduced;

[0032] 2. The method provided by the present invention does not require any assumptions about the shape of the sliding surface, thus expanding the search range and making the shape of the dangerous sliding surface obtained more accurate;

[0033] 3. The method provided by the present invention is based on the finite element elastic stress field, which greatly improves the calculation efficiency. At the same time, there is no need to assume the inter-strip force of the soil, and the calculation results are more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 A flowchart of a method for dimensionality reduction search of a three-dimensional slope sliding surface is provided in an embodiment of the present invention;

[0035] Figure 2 Schematic diagram of the main directions of the permeability tensor provided in an embodiment of the present invention;

[0036] Figure 3 This is a schematic diagram of determining the destruction direction based on the displacement field provided in an embodiment of the present invention;

[0037] Figure 4 3D Slope Slip Surface Structure Schematic Diagram provided in an embodiment of the present invention;

[0038] Figure 5 is a schematic diagram of a flow channel generated based on streamlines provided in an embodiment of the present invention;

[0039] Figure 6 It is an encrypted graph near the minimum safety factor streamline provided in an embodiment of the present invention;

[0040] Figure 7 This is a dimension diagram of the calculation model provided in Example 2 of the present invention;

[0041] Figure 8 is a calculation result diagram provided in Example 2 of the present invention;

[0042] Figure 9 This is a dimension diagram of the calculation model provided in Example 3 of the present invention;

[0043] Figure 10 is a calculation result diagram provided in Example 3 of the present invention;

[0044] Figure 11 This is a dimension diagram of the calculation model provided in Example 4 of the present invention;

[0045] Figure 12 This is a calculation result diagram provided in Example 4 of the present invention. DETAILED DESCRIPTION

[0046] The specific implementation method of the present invention is described in detail below with reference to the accompanying drawings. It should be understood that the specific implementation method described herein is only used to illustrate and explain the present invention and is not used to limit the present invention.

[0047] Example 1

[0048] A dimensionality reduction search method for a three-dimensional slope sliding surface in this embodiment includes the following steps:

[0049] (1) Based on the permeability tensor determined by the maximum stress-failure ratio, Darcy's law is used to solve a suitable canonical velocity field, and based on this velocity field, streamlines are generated by integrating each node on the slope surface (potential sliding area).

[0050] like Figure 2 As shown in the figure, the method to determine the direction of the permeability tensor is to make the main direction of the permeability tensor K1 is parallel to the direction of the failure line AD in the plane formed by σ1 and σ3, K2 is along the σ2 axis, and K3 is along the orthogonal direction of K1K2. That is, the K1 direction cosine is: [R 11 R 12 R 13 ] T =AN T ·[cosβ0sinβ] T ; K2 direction cosine is: [R 21 R 22 R 23 ]=[l2 m2 n2]; K3 direction cosine is: [R 31 R 32 R 33 ]=K2×K3. Where: K1, K2, K3 are the permeability tensors, R 11 、R 12 、R 13 They are K1 direction tensor, AN is the principal stress direction tensor, β is the angle between K1 and the horizontal axis, l2, m2, n2 are the cosines of the angles between K2 and the three coordinate axes, R 31 、R 32 、R 33 are the K3 direction tensors respectively.

[0051] (2) The direction of each sliding surface of the “flow channel” is determined according to the direction of the streamline tangent and the second principal stress, and then the safety factor of each flow channel and its intersection with the slope surface are calculated, thereby reducing the three-dimensional slope problem to a two-dimensional slope sliding surface search problem.

[0052] The method for determining the direction of the failure line AD in the σ1σ3 plane is as follows: first, the elastic displacement field of the slope is calculated using a finite element program, and the failure direction needs to be basically consistent with the direction of the elastic displacement field. From a plane perspective, if Figure 3 As shown in the figure, PM and PM′ are the two failure directions calculated from point P, PN is the displacement direction of point P in the elastic displacement field, and the failure direction is determined according to the angles φ1 and φ2 between PN, PM and PM′, that is, the failure surface direction closer to PN is selected as the failure direction.

[0053] Furthermore, the method of constructing the flow channel is to construct the sliding surface using the tangent of the streamline and the intermediate principal stress σ2, as shown in Figure 4 As shown, point P is any point on the streamline, and the vector along the tangent direction of the streamline at point P is used. Construct the sliding surface with the σ2-axis direction vector.

[0054] Furthermore, n points P1~P on the streamline are determined. n After the unit sliding surface is located, the sliding surfaces on the entire streamline are connected. Figure 5 , S is a streamline in the three-dimensional slope. The sliding surface formed by each unit segment on the streamline S is drawn and connected to form a long strip flow channel representing the streamline S.

[0055] (3) Vectorize the intersection lines between the flow channel and the slope surface at each node on the potential sliding area of ​​the slope. Select a straight line segment across the potential sliding area of ​​the slope and divide the straight line segment into equal parts.

[0056] (4) Through each equally divided point, the vector field integral is used to obtain the intersection line between the three-dimensional sliding surface and the slope surface. Based on this intersection line, the safety factor of the three-dimensional sliding surface can be obtained by simple interpolation. The minimum value of the safety factors at each equally divided point is the minimum safety factor of the three-dimensional slope.

[0057] The method for calculating the safety factor of the flow channel is: the stress state at point P and the vector along the tangent direction of the streamline are known. The shear stress along the tangent direction is τ n , the total stress is T, through Get the sliding surface direction vector Where: is the direction vector of the intermediate principal stress, and α, η, and γ are the angles between the sliding surface direction vector and the three coordinate axes.

[0058] First, use formula (1) to calculate the normal stress at point P:

[0059]

[0060] Where:

[0061]

[0062] where σ n is the normal stress at point P, σ x , σ y , σ z is the normal stress component acting on point P along the x, y, and z directions, τ xy , τ yz , τ xz is the shear stress component acting on point P along the x, y, and z directions. T(1), T(2), and T(3) are all intermediate variables. nis the shear stress value along the streamline tangent direction at point P;

[0063] Note that formula (3) cannot be used to calculate τ here. n , because the calculated result is τ n Not necessarily along direction.

[0064]

[0065] The safety factor of each flow channel can be calculated by further using the safety factor calculation formula.

[0066] (5) The intersection line passing through this point is the intersection line of the potential failure surface and the slope surface. By drawing a streamline on this intersection line, we can obtain the three-dimensional sliding surface corresponding to the minimum safety factor.

[0067] In step 4, the sliding surface with the smallest safety factor is obtained by preliminary calculation. It is necessary to select a straight line segment across two streamlines in the vicinity of the sliding surface for further equal division and encryption, and repeat step 4 to find a streamline with a smaller safety factor. Figure 6 .

[0068] In step 5, the starting points and end points of all streamlines must be connected to obtain a closed surface representing the most dangerous slip surface.

[0069] Example 2

[0070] This embodiment is a slope with a top that is loaded. Figure 7 Soil density γ=18.8kN / m 3 , cohesion c=30kPa, internal friction angle The elastic modulus E = 100 MPa, Poisson's ratio μ = 0.3, and the top surface of the slope is subjected to a uniformly distributed load p = 100 kPa. When using this method to calculate slope stability, it is also necessary to add a head boundary condition to generate a virtual seepage field, where the top head is 23.2 m, applied within the range of 44.4 to 64.4 m in the x-axis direction; the bottom head is 22.2 m, applied within the range of 0 to 32 m in the x-axis direction. Using the above method, the safety factor is 1.762, and the critical sliding surface is as follows: Figure 8 .

[0071] Example 3

[0072] This example is a double-layered non-homogeneous slope. The model size is as follows: Figure 9 Soil layer 1 soil density γ1=16kN / m 3 , cohesion c1=15kPa, internal friction angle Elastic modulus E1 = 100 MPa, Poisson's ratio μ1 = 0.35; soil density γ2 = 20 kN / m 3, cohesion c2=12.38kPa, internal friction angle Elastic modulus E2 = 120 MPa, Poisson's ratio μ2 = 0.3. When using this method to calculate slope stability, it is also necessary to add a hydraulic head boundary condition to generate a virtual seepage field, where the hydraulic head at the top of the slope is 21 m, applied over a range of 20 to 35 m in the x-axis direction; and the hydraulic head at the bottom of the slope is 20 m, applied over a range of 0 to 13.5 m in the x-axis direction. Using the above method, the safety factor is 1.287, and the critical sliding surface is as follows: Figure 10 .

[0073] Example 4

[0074] This example is a non-homogeneous slope composed of three different soil layers. The model size is as follows: Figure 11 Soil layer 1 soil density γ=19.5kN / m 3 , cohesion c=0, internal friction angle Elastic modulus E = 10 MPa, Poisson's ratio μ = 0.25; soil density γ = 19.5 kN / m 3 , cohesion c=5.3kPa, internal friction angle Elastic modulus E = 10 MPa, Poisson's ratio μ = 0.25; soil density γ = 19.5 kN / m 3 , cohesion c=7.2kPa, internal friction angle Elastic modulus E = 10 MPa, Poisson's ratio μ = 0.25. When using this method to calculate slope stability, it is also necessary to add head boundary conditions to generate a virtual seepage field, where the head at the top of the slope is 36 m, applied over a range of 50 to 70 m in the x-axis direction; the head at the bottom of the slope is 35 m, applied over a range of 20 to 40 m in the x-axis direction. Using the above method, the safety factor is 1.517, and the critical sliding surface is as follows: Figure 12 .

[0075] The preferred embodiments of the present invention disclosed above are intended only to help illustrate the present invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the present invention to the specific embodiments described. Obviously, many modifications and variations are possible based on the content of this specification. These embodiments are selected and described in detail in this specification to better explain the principles and practical applications of the present invention, thereby enabling those skilled in the art to better understand and utilize the present invention. The present invention is limited only by the claims and their full scope and equivalents.

Claims

1. A dimensionality reduction search method for a three-dimensional slope sliding surface, characterized by: The following steps are involved: The first step is to solve the velocity field based on the permeability tensor determined by the maximum stress-failure ratio, and generate streamlines based on the velocity field by integrating each node of the potential sliding area on the slope surface; The second step is to determine the direction of each sliding surface of the flow channel based on the direction of the streamline tangent and the second principal stress, and then calculate the safety factor of each flow channel and its intersection with the slope surface, thereby reducing the three-dimensional slope problem to a two-dimensional slope sliding surface search problem; Step 3: Vectorize the intersection lines of the flow channels at each node on the potential sliding area of ​​the slope and the slope to form a vector field, select a straight line segment across the potential sliding area of ​​the slope, and divide the straight line segment into equal parts; Step 4: Integrate the vector field at each equally divided point to obtain the intersection line between the three-dimensional sliding surface and the slope surface. Interpolate the intersection line to obtain the safety factor of the three-dimensional sliding surface. The minimum value of the safety factors at each equally divided point is the minimum safety factor of the three-dimensional slope. Step 5: The intersection line of the equal-division point corresponding to the minimum safety factor is the intersection line of the potential failure surface and the slope surface. Draw a streamline on the intersection line to obtain the three-dimensional sliding surface corresponding to the minimum safety factor.

2. A dimensionality reduction search method for a three-dimensional slope sliding surface according to claim 1, characterized in that: The method to determine the direction of the permeability tensor is: Let the permeability tensor be K1 is parallel to the direction of the failure line AD in the plane formed by the axis σ1 and the axis σ3, K2 is along the direction of the σ2 axis, and K3 is along the orthogonal direction of K1K2, that is, the direction cosine of K1 is: [R 11 R 12 R 13 ] T =AN T ·[cosβ 0sinβ] T ; K2 direction cosine is [R 21 R 22 R 23 ]=[l2 m2 n2]; K3 direction cosine is [R 31 R 32 R 33 ]=K2×K3, where K1, K2, K3 are the permeability tensors, R 11 、R 12 、R 13 They are the K1 direction tensor, AN is the principal stress direction tensor, β is the angle between K1 and the horizontal axis, l2, m2, and n2 are the cosines of the angles between K2 and the three coordinate axes, and R 31 、R 32 、R 33 are the K3 direction tensors respectively.

3. The dimensionality reduction search method for a three-dimensional slope sliding surface according to claim 2, characterized in that: The method for determining the direction of the failure line AD in the σ1σ3 plane is as follows: first, the elastic displacement field of the slope is calculated using a finite element program, and the failure direction needs to be consistent with the direction of the elastic displacement field. From a planar perspective, each point in the displacement field has two failure surfaces and one displacement direction. The failure surface with the smallest angle with the displacement direction is selected as the failure direction.

4. The method for dimensionality reduction search of a three-dimensional slope sliding surface according to claim 1, characterized in that: The method of constructing the flow channel is to construct the sliding surface by using the tangent of the streamline and the intermediate principal stress σ2. Point P is any point on the streamline. By using the vector along the tangent direction of the streamline at point P, the sliding surface is constructed. Construct the sliding surface with the σ2 axis direction vector; determine n points P1~P on the streamline n After the unit sliding surface is located, the sliding surfaces on the entire streamline are connected. The sliding surface formed by each unit segment is drawn on a streamline S in the three-dimensional slope and connected to form a long strip flow channel representing the streamline S.

5. The method for dimensionality reduction search of a three-dimensional slope sliding surface according to claim 1, characterized in that: The method for calculating the safety factor of the flow channel is: the stress state at point P and the vector along the tangent direction of the streamline are known. The shear stress along the tangent direction is τ n , the total stress is T, through Get the sliding surface direction vector Where: is the direction vector of the intermediate principal stress, α, η, and γ are the angles between the sliding surface direction vector and the three coordinate axes respectively; First, use formula (1) to calculate the normal stress at point P: Where: T(1)=σ x ·cosα+τ xy ·cosβ+τ xz ·cosγ T(2)=τ xy ·cosα+σ y ·cosβ+τ yz ·cosγ (2) T(3)=τ xz ·cosα+τ yz ·cosβ+σ z ·cosγ where σ n is the normal stress at point P, σ x , σ y , σ z is the normal stress component acting on point P along the x, y, and z directions, τ xy , τ yz , τ xz is the shear stress component acting on point P along the x, y, and z directions. T(1), T(2), and T(3) are all intermediate variables. n is the shear stress value along the streamline tangent direction at point P; The safety factor of each flow channel can be calculated by further using the safety factor calculation formula.

6. The method for dimensionality reduction search of a three-dimensional slope sliding surface according to claim 1, characterized in that: The sliding surface with the smallest safety factor is obtained through preliminary calculation. It is necessary to select a straight line segment across two streamlines near it for further equal division and encryption processing, and repeat the fourth step to find a streamline with a smaller safety factor.

7. The method for searching a three-dimensional slope sliding surface by dimensionality reduction according to claim 1, wherein: Connect the starting point and end point of the streamlines in sequence to obtain a closed surface representing the most dangerous sliding surface.

8. The method for searching a three-dimensional slope sliding surface by dimensionality reduction according to claim 2, wherein: K1 and K2 take K max In order to achieve the maximum permeability coefficient on the failure surface, K3 takes the minimum value, achieving the goal of allowing the water inside the slope to flow along the direction that is most susceptible to failure.

9. The method for searching a three-dimensional slope sliding surface by dimensionality reduction according to claim 2, wherein: When constructing the permeability tensor, in order to avoid the singularity when the maximum stress failure ratio is 0 and to reduce the degree of inhomogeneity and anisotropy caused by the maximum stress failure ratio, a background flow factor needs to be added for adjustment.

10. The method for searching a three-dimensional slope sliding surface by dimensionality reduction according to claim 1, characterized in that: In order to suppress the sensitivity of the boundary, a directional highly permeable pipe network is embedded in the isotropic homogeneous material, so that the resulting potential field depends on the pipe network, thereby suppressing the sensitivity of the boundary.

Images