Three-dimensional slope slip surface intelligent search method

Abstract

This invention discloses a three-dimensional slope slip surface intelligent search method, including constructing a three-dimensional slope geometric model of the area to be analyzed; physically meshing the three-dimensional slope analysis area to generate a discrete model of the three-dimensional slope; performing an elastic or elastoplastic analysis on the slope model using the numerical manifold method; setting an arbitrary three-dimensional slip surface background mesh and an initial background mesh; using slope slip surface control parameters as independent variables and the calculated trial safety factor as the dependent variable; constraining that the slip surface locally bulges towards the slope body to construct constraint equations; improving the pattern search algorithm based on the specific constraint equations; intelligently optimizing and searching for the most unfavorable slip surface based on the improved pattern search algorithm; updating the slope slip surface control parameters and calculating the trial safety factor to obtain the final critical slip surface and its corresponding safety factor. This method can provide theoretical and technical support for reducing geological hazards related to slope failure.

Description

Technical Field

[0001] This invention relates to the field of slope numerical calculation, specifically to a three-dimensional slope slip surface intelligent search method. Background Technology

[0002] Failure of rock / soil slopes often leads to severe consequences, such as casualties and economic losses. Therefore, it is necessary to conduct slope stability analysis to predict the critical failure surface and safety factor, two of the most important indicators in slope stability evaluation and design. Over the past few decades, with the increasing demands of engineering construction and disaster prevention and mitigation, many methods for slope stability analysis have been developed, including experimental methods, numerical methods, and limit equilibrium methods.

[0003] However, in existing technologies, experimental methods have limited effectiveness in evaluating slope stability. Numerical methods and limit equilibrium methods mainly focus on two-dimensional slope analysis, while three-dimensional analysis methods have many limitations. For example, the three-dimensional limit equilibrium method restricts the slip surface to an ellipsoid, as shown in the paper: Zhang Kun et al. 2017. Application of Adaptive Differential Evolution Algorithm in Slope Slip Surface Search. Rock and Soil Mechanics 38, 1503–1509. The strength reduction method requires a large number of iterative elastoplastic calculations, which consumes a lot of time, as shown in the dissertation: Zhang Yajun, 2024. Slope Stability Analysis Based on Three-Dimensional Numerical Manifold Method (Master's Thesis). Hainan University. Both labor and time costs are high, making it difficult to apply on a large scale. Summary of the Invention

[0004] In view of this, the present invention provides a three-dimensional slope slip surface intelligent search method, which can be used for three-dimensional slope slip surface intelligent search and stability evaluation.

[0005] Specifically, this can be achieved through the following approach:

[0006] The intelligent search method for three-dimensional slope slip surfaces includes the following steps:

[0007] Step S1: Construct a three-dimensional slope geometry model for the area to be analyzed;

[0008] Step S2: Physically mesh the three-dimensional slope analysis area to generate a discrete model of the three-dimensional slope, and group the slope by material and boundary surface to prepare for numerical analysis.

[0009] Step S3: Set boundary conditions according to the slope material parameters, perform an elastic or elastoplastic analysis on the slope model using the numerical manifold method, and export stress field data and material field data to prepare for subsequent calculation of the safety factor;

[0010] Step S4: Construct the background control grid of the slope slip surface, perform Boolean operations on the background control grid and the slope body, trim off the excess parts, and generate the initial test slip surface;

[0011] Step S5: Using the control parameters of the background control mesh as independent variables and the test safety factor of the test surface as the objective function, calculate the test safety factor. To ensure the reasonable shape of the background mesh and avoid obvious local convexity or concavity of the generated test surface, constraints are added to the objective function;

[0012] Step S6: Perform intelligent optimization based on the pattern search algorithm, update the slope slip surface control parameters and calculate the trial safety factor. When the change in the trial safety factor is less than the set threshold, the pattern search algorithm converges, and finally the key slip surface and the corresponding safety factor are obtained.

[0013] Further optimization involves using the numerical manifold method to calculate the elastoplastic stress field of the slope model in step S3, specifically including the following steps:

[0014] Step S3.1: Define the basic governing equations and boundary conditions for the static elastoplastic problem of the three-dimensional slope analysis domain Ω; whereby the basic governing equations are:

[0015] σ ij,j +b i =0,inΩ;

[0016] In the above formula, σ ij Let σ represent the Cauchy stress tensor. ij,j Indicates σ ij Find the spatial partial derivative, b i Let Ω represent the volume load vector, i represent the direction of the stress, j represent the direction of the outward normal of the surface where the stress is located, and Ω represent the analysis region of the three-dimensional slope.

[0017] The boundary conditions are:

[0018]

[0019] In the above formula, Represents the region of action of the displacement boundary. Represents the region of stress boundary action, u i Represents the displacement vector. Displacement boundary Given a displacement vector on σ. ij Let n represent the Cauchy stress tensor. j Represents stress boundary outward normal direction, Indicates stress boundary The specified traction force, where i represents the direction of the stress and j represents the outward normal direction of the surface where the stress is located;

[0020] Numerical manifold method in the γth manifold unit ME γ Global displacement approximation function on It is the weight function wkγ (x) and covering function u kγ The inner product of (x) is expressed as:

[0021]

[0022] Numerical manifold method physics sheet PP k weight function w kγ (x) generally satisfies the following three conditions:

[0023]

[0024] 0≤w kγ (x)≤1, if x∈PP k ,

[0025]

[0026] Where, when the manifold unit ME γ Physical film PP k During coverage, the weight function w kγ The range of (x) is 0-1; conversely, when it is not covered, the weight function is 0. Define the manifold unit ME. γ The manifold is covered on all eight physical slices, and their weight functions all satisfy 0 ≤ w kγ (x)≤1, and the sum is 1.

[0027] Covering function u kγ (x) can be constructed using polynomial functions of any order. This invention uses a 0th-order polynomial function as the weight function to avoid linear dependence problems. A structured hexahedral mesh is used to construct the mathematical covering system; therefore, the shape function of an eight-node hexahedral element is used to construct the weight function w. kγ (x).

[0028] Global displacement approximation function of numerical manifold method It can be represented in a compact form as follows:

[0029]

[0030] Where N γ This is called the shape function matrix, d k It is a column vector containing all the degrees of freedom associated with the eight physical pieces mentioned above, which are used to form this manifold unit ME. γ .

[0031] Step S3.2: Based on the governing equations and the corresponding boundary conditions, the following function I(u) for the elastoplastic problem is obtained:

[0032]

[0033] Step S3.3: Since the mathematical covering system in the numerical manifold method usually does not match the physical mesh, The displacement boundary conditions on the surface are usually not directly satisfyable; by applying the displacement boundary conditions using the penalty function method, the corresponding function above is modified as follows:

[0034]

[0035] In the above formula, α1 is the penalty parameter corresponding to the displacement boundary condition;

[0036] Let δI * If (u) = 0, then the system equilibrium equation for the elastoplastic problem can be written in matrix form as follows:

[0037] Kd = f;

[0038] Where d is the global displacement vector, and K and f are the generalized global stiffness matrix and force vector, respectively;

[0039]

[0040] In the above formula, N and B represent the shape function matrix and strain matrix, respectively, and D ep Denotes the elastoplastic matrix; B = L d N; Operator L d for:

[0041]

[0042] Unlike existing methods that require numerous repetitive elastoplastic analysis calculations, this invention only requires a single elastoplastic calculation of the slope under gravity. In this case, the slope strength parameters are not reduced, the slope is often not in a critical state, and the number of iterations in the elastoplastic analysis is generally not large, resulting in lower computational costs. After performing the elastoplastic calculation on the slope, the slope stress field is derived. Subsequent steps, based on this stress field, can interpolate to obtain the stress state at any point within the slope.

[0043] Further optimization involves constructing a three-dimensional slope slip surface based on the three-dimensional slope geometry. The location and shape of the three-dimensional slope slip surface have many possibilities; the most common construction method is an ellipsoid, but this slip surface is too idealistic to describe complex slip surfaces. Therefore, to simulate arbitrary three-dimensional slip surfaces, a series of control points can be obtained through spline surface fitting or interpolation.

[0044] Step S4 of this invention uses a background mesh to simulate a three-dimensional slope slip surface of arbitrary shape, specifically including the following steps:

[0045] Step S4.1: Define the background mesh of the slope slip surface. Fix the X and Y coordinates of all nodes on the background mesh, and use the Z coordinate as a variable to obtain the column vector H composed of the control parameters of the three-dimensional slope slip surface background mesh, which is:

[0046]

[0047] In the above formula, Θ represents the number of control points, and h β This represents the height of the β-th control point, i.e., the value of the β-th control point on the Z-axis.

[0048] Step S4.2: Perform Boolean operations on the background control mesh and the slope to trim away the excess parts and generate the test slip surface required for calculating the safety factor.

[0049] The three-dimensional slip surface determined by H is not necessarily reasonable. For example, the slip surface should not exhibit local abrupt changes, obvious upward convexity, or downward concavity. Such unreasonable slip surfaces can be deleted manually, but this method is significantly less efficient. For example, the paper "Lin Yongsheng et al., 2013. Search for three-dimensional slip surfaces of slopes based on finite element calculation. Rock and Soil Mechanics 34, 1191–1196" records that although the slip surface generated by control points can realistically simulate the actual slip surface and can simulate slip surfaces of arbitrary shapes, the slip surface generated by control points has obvious local upward convexity and downward concavity phenomena. The safety factor calculated based on this simulated slip surface may be too large.

[0050] To achieve automatic search of three-dimensional slope slip surfaces, appropriate constraints need to be given to avoid obvious local convexity or concavity of the slip surface. The most common approach is to pre-assume that the three-dimensional slip surface has an outwardly convex geometry. For example, Chinese patent CN201610116074.0, "A Method for Searching Three-Dimensional Critical Slip Surfaces of Slopes," directly uses the ellipsoid equation as the assumed shape of the critical slip surface; and the paper Zhang Kun et al., 2017, "Application of Adaptive Differential Evolution Algorithm in Slope Slip Surface Search," Rock and Soil Mechanics, 38, 1503–1509, modifies the ellipsoid equation to describe the three-dimensional slip surface. The above methods assume the shape of the slip surface, lose the arbitrariness of the slip surface shape, and do not quite conform to the real situation.

[0051] To define the shape constraints of a slope slip surface, for a two-dimensional slip surface, the paper Liu Gaoyang et al., 2017. Slope stability analysis based on independent covering manifold method and vector sum method. Chinese Journal of Rock Mechanics and Engineering 36, 1434–1442, records that this can be achieved by controlling the coordinates of each control point and the slope of each straight line segment. However, this method cannot be applied to three-dimensional slip surface shape constraints.

[0052] Therefore, in step S5 of this invention, a shape constraint condition for the three-dimensional slope slip surface is added, which is specifically set according to the following steps:

[0053] Step S5.1: Define that the local sliding surface protrudes towards the slope, that is, for any triangular unit on the sliding surface, its normal direction points towards the slope, and other points on the sliding surface are located in the positive half-plane of this plane.

[0054] Setting the first The three vertices of the triangular element corresponding to each local constraint are respectively and constraint points The normal direction of the triangle is calculated as follows:

[0055]

[0056] in for:

[0057]

[0058] The distance from other points on the sliding surface to the plane containing this triangular element must be greater than or equal to 0. Therefore, the following local constraint equations exist:

[0059]

[0060] Removing the denominator, we get:

[0061]

[0062] Point of entry and Coordinate values, write the local constraint equations in matrix form:

[0063]

[0064] Among them are:

[0065]

[0066]

[0067] Step S5.2: Construct the global constraint equations based on the local constraint equations in step S5.1:

[0068] AH≤0

[0069] Where A is the inequality constraint matrix, which is obtained by applying the inequality constraints in each local constraint equation. The matrix is ​​assembled; H is a vector composed of the heights of each control point, obtained by combining the local constraint equations. Obtained by matrix assembly.

[0070] To further optimize, the safety factor is calculated through the following steps:

[0071] Based on the three-dimensional slope stress field obtained from the elastoplastic analysis using the numerical manifold method, the stress state at any point G on the test slip surface S is obtained; the stress tensor at point G is set to σ. G , To determine the direction of the unit normal to the tangent plane at point G on the sliding surface, with the direction pointing towards the sliding body as positive, the force exerted by point G on the slope body can be calculated. Investigate the normal and tangential forces exerted by the sliding body on the slope at point G on the sliding surface. and And to test the anti-skid normal stress of the slope at point G on the sliding surface. for:

[0072]

[0073] According to the Mohr-Coulomb strength criterion, the ultimate anti-sliding shear stress of the slope body at any point on the sliding surface is:

[0074]

[0075] Where c is the cohesion parameter of the slope soil and rock mass, and φ is the internal friction angle parameter of the slope soil and rock mass. To investigate the potential sliding direction of the slope at point c on the sliding surface,

[0076] Based on the anti-slip shear stress vector at each point on the sliding surface, integration on the sliding surface yields the resultant ultimate anti-slip shear stress of the slope on the sliding body:

[0077]

[0078] The global principal potential sliding direction is determined based on the resultant force of the ultimate anti-slip shear stress.

[0079]

[0080] In addition to shear stress, the anti-sliding force vector of the slope body on the sliding body also includes the normal stress component. The anti-sliding force vector of the slope body on the sliding body at any point G on the sliding surface is:

[0081]

[0082] The force exerted by the sliding body at any point G on the sliding surface on the slope is That is, the sliding force of the sliding body at any point G on the sliding surface is Directing the anti-slip force and sliding force towards the overall potential sliding direction. Project the slope and integrate over the entire slip surface to obtain the trial safety factor.

[0083]

[0084] In the above formula, This represents the projection of the resultant force of the slope's resistance to the sliding mass onto the main potential sliding direction. This represents the projection of the resultant force of the sliding body's downward sliding force onto the main potential sliding direction. Indicates the main potential sliding direction of the sliding body. This represents the downward force at any point on the sliding body. It represents the anti-slip force of the slope body on the sliding body at any point on the sliding surface.

[0085] Further optimization involves the matrices in each local constraint equation. A is obtained by assembling as follows:

[0086] For the There are several constraint equations, involving the point... and Number The corresponding control point height is

[0087] set up,

[0088]

[0089] Then, the column vector All elements in the inequality constraint matrix A are used as the first element in the inequality constraint matrix A. Okay, number The elements of the column, that is In addition, the inequality constraint matrix A is... The values ​​of all other columns in the row are 0. Convert the column vector... All elements in matrix H are used as the first element of matrix H. Row elements;

[0090] Similarly, the other constraint equation matrices Substituting the elements into the above formula yields the final inequality constraint matrix A.

[0091] Further optimization is needed. Sliding surface search based on the pattern search intelligent algorithm is essentially an optimization problem. To account for inequality constraints, one approach is to add these constraints to the objective function using a penalty function. However, this method is ineffective because the penalty parameter has no physical meaning and requires manual adjustment. Therefore, step S6 of this invention improves the flow of the pattern search intelligent algorithm by adding the satisfaction of inequality constraints to the optimization process, thereby increasing the algorithm's robustness and efficiency. Specifically, the steps include:

[0092] Step S6.1: From the given initial sliding surface control parameters H 0 Starting with the Z-coordinates of all Θ control points, e1, e2, ..., e β ,…,e Θ Direction, using a specified step size δ k Perform trial moves; each time, select an independent variable h. β Only move it, at this time e β = [0,0,…,1,…,0], where only the βth term is 1 and the rest are 0, meaning that each time a background grid control point is moved;

[0093] Step S6.2: For the β-th control point, perform the following movement and detection along the Z-axis direction, excluding h. β Since the other independent variables do not shift and are therefore known values, we have:

[0094]

[0095] That is, the column vector All elements in the inequality constraint matrix A are used as the first element in the inequality constraint matrix A. Okay, number The elements of the column, i.e. In addition, the inequality constraint matrix A is... The value of all other columns in the row is 0; Indicates the first The row number corresponding to each constraint condition.

[0096] Step S6.2.1: Remove h β Moving all other variables to the right side of the inequality, we get only one variable, h. β The system of inequalities is shown below:

[0097]

[0098] Therefore, h is calculated. β The range of values This identified a feasible exploration area for subsequent exploration.

[0099] Step S6.2.2: Determine Is it greater than or equal to?

[0100] If so, then the βth control point cannot be moved at this time;

[0101] If not, then perform the following movement detection: First, perform forward detection, at h β The range of values Inside, move H to H+e β δ k Calculate (H+e) β δ k The corresponding trial safety factor if This indicates the detection was successful; let H = H + e. β δ k Conversely, if the probe fails, a reverse probe is then performed, specifically: at h β The range of values Inside, move H to He β δ k Calculate (He) β δ k The corresponding trial safety factor if This indicates the detection was successful; let H = He. β δ k Conversely, if the detection fails, H remains unchanged;

[0102] Step S6.3: Following the detection method along the β-th axis, traverse the height of all background grid control points and repeatedly try and optimize.

[0103] Step S6.4: When a round of probing ends, decrease the step size δ k Repeat steps S6.2 and S6.3 to continue iterative optimization until the change in the trial safety factor is less than the set first threshold, or the step size δ. k The algorithm converges when the value is less than the set second threshold, yielding the safety factor and the critical smooth surface; if convergence is not achieved after reaching the maximum number of iterations, the parameter δ is adjusted. k Alternatively, the background mesh can be rearranged for further calculations.

[0104] Compared with the prior art, the present invention has the following advantages:

[0105] This invention takes a three-dimensional slope as an example. It not only considers the actual stress field distribution inside the natural slope but also only requires one elastoplastic analysis. Furthermore, it features a more versatile failure surface shape, enabling more flexible searching of the safety factor and critical sliding surface of the three-dimensional slope. Based on existing intelligent optimization algorithms, it automatically searches for the critical sliding surface of the three-dimensional slope, providing a reference for stability evaluation and design, and offering theoretical support for reducing geological hazards related to slope failure. Attached Figure Description

[0106] Figure 1 This is a flowchart of the intelligent search method for three-dimensional slope slip surface described in this invention;

[0107] Figure 2 This is a diagram of the three-dimensional slope geometric model described in this invention;

[0108] Figure 3 This is a schematic diagram of the numerical manifold method discretization model of the three-dimensional slope described in this invention;

[0109] Figure 4 This is a stress field cloud map obtained from the elastoplastic analysis of the three-dimensional slope using the numerical manifold method described in this invention;

[0110] Figure 5 This is a schematic diagram of the three-dimensional slope background grid and control points described in this invention;

[0111] Figure 6 This is a schematic diagram of the initial slip surface of the three-dimensional slope described in this invention;

[0112] Figure 7 This is a schematic diagram illustrating the construction of the convexity constraint condition of the three-dimensional slope sliding surface as described in this invention;

[0113] Figure 8 This is a schematic diagram of the assembly of the three-dimensional sliding surface shape constraint inequality described in this invention;

[0114] Figure 9 This refers to the stress state at a point on the sliding surface of the three-dimensional slope test described in this invention;

[0115] Figure 10 The unreasonable sliding surface is caused by the lack of constraint on the shape of the three-dimensional slope sliding surface described in this invention;

[0116] Figure 11 It is the key smooth surface background mesh obtained by the intelligent optimization described in this invention;

[0117] Figure 12 The key sliding surface is obtained by cutting the background grid and the slope body of the key sliding surface in this invention;

[0118] Figure 13 This is the curve showing the change of the safety factor during the sliding surface search iteration process of this invention. Detailed Implementation

[0119] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0120] like Figure 1 The aforementioned three-dimensional slope slip surface intelligent search method includes the following steps:

[0121] Step S1: Construct a three-dimensional slope geometric model of the area to be analyzed, and prepare boundary conditions and load conditions, such as... Figure 2 As shown;

[0122] Step S2: Physically mesh the 3D slope analysis region to generate a discrete model of the 3D slope, such as... Figure 3 As shown, materials and boundary surfaces are grouped to prepare for numerical analysis.

[0123] Step S3: Based on the slope material parameters set by the indoor test data or the survey report, set appropriate boundary conditions, and, as needed, use the numerical manifold method to perform an elastic or elastoplastic analysis on the slope numerical model.

[0124] Step S4: Export stress field data and material field data, such as Figure 4 As shown, this is in preparation for the subsequent calculation of the safety factor;

[0125] Step S5: Construct a regular background mesh, which consists of control points and triangular unit faces, such as... Figure 5 As shown. The horizontal coordinates of the control points are fixed, while the background grid control points can move vertically up and down. The height of the background grid serves as the independent variable in the optimization problem of this invention. The column vector H, composed of the control parameters of the three-dimensional slope slip surface background grid, is obtained as follows:

[0126] When the independent variable vector H in the optimization problem has each h β When different values ​​are selected, the corresponding background grid control points move up and down to form different background grids. Then, a Boolean operation is performed between the background grid and the slope body to trim off the excess parts, leaving the part located inside the slope body to obtain the test slip surface required for calculating the test safety factor.

[0127] Step S5: Set an initial background mesh that cuts the slope geometry model into slope and landslide portions, such as... Figure 6 As shown.

[0128] Step S6: The background mesh control parameters are used as independent variables, and the trial safety factor calculated from the trial slip surface is used as the objective function;

[0129] Step S7: See Appendix Figure 7 To ensure the reasonable shape of the background mesh and avoid obvious local convexity or concavity of the generated test surface, the surface is constrained to convex towards the slope. That is, for any triangular element on the surface, its normal direction points towards the slope, and other points on the surface are located in the positive half-plane of this plane. The corresponding constraint equations are given. And in accordance with Figure 8 The assembly method shown assembles the various local constraints to form the overall constraint equations;

[0130] AH≤0

[0131] Where A is the inequality constraint matrix, which is obtained by applying the inequality constraints in each local constraint equation. The matrix is ​​assembled; H is a vector composed of the heights of each control point, obtained by combining the local constraint equations. Obtained by matrix assembly.

[0132] Specifically, Figure 8 Lieutenant General In the constraint equations, the column vectors All elements in the inequality constraint matrix A are used as the first element in the inequality constraint matrix A. Okay, number The elements of the column, that is In addition, the inequality constraint matrix A is... The values ​​of all other columns in the row are 0. Convert the column vector... All elements in matrix H are used as the first element of matrix H. The elements of the row; similarly, the other constraint equation matrices Substituting the elements into the above formula yields the final inequality constraint matrix A.

[0133] Step S8: Wherein, refer to Appendix Figure 9 The stress tensor at point G is σ. G , To determine the direction of the unit normal to the tangent plane at point G on the sliding surface (positive for the direction pointing towards the sliding body), the force exerted by point G on the slope body can be calculated. for:

[0134]

[0135] Furthermore, the normal and tangential forces exerted by the sliding body at point A on the test sliding surface on the slope can be determined. and

[0136]

[0137] Directing the anti-slip force and sliding force towards the overall potential sliding direction. Project the slope and integrate over the entire slip surface to obtain the trial safety factor.

[0138]

[0139] In the above formula, Indicates the main potential sliding direction of the sliding body. This represents the force exerted by any point on the sliding body on the slope. This represents the resistance of the slope to the sliding mass at any point on the sliding surface.

[0140] Step S9: Perform intelligent optimization based on the improved pattern search algorithm, update the slope slip surface control parameters and calculate the trial safety factor, check whether the change in the trial safety factor is less than the set threshold, and finally obtain the key slip surface and the corresponding safety factor.

[0141] Step S10: To illustrate the necessity of the three-dimensional sliding surface shape constraint, when the three-dimensional sliding surface shape constraint is not added, the obtained sliding surface shows local convexity or concavity, which is obviously not in line with reality. This shows that it is necessary to add shape constraint in the three-dimensional sliding surface search of the present invention.

[0142] Step S11: When adding a three-dimensional sliding surface shape constraint in this invention, the calculated key sliding surface background mesh shape is reasonable, such as... Figure 11 As shown. A Boolean operation is performed between the obtained background mesh of the critical slip surface and the slope mass to remove excess parts, yielding the final critical slip surface and its corresponding safety factor, as shown. Figure 12 As shown.

[0143] Step S12: In this embodiment, the threshold is set to 0.01. Table 1 shows the change data of the trial safety factor during the sliding surface search iteration process, and the change curve is as follows. Figure 13 As shown, the final safety factor converges to 2.70. This is close to the safety factor of 2.619 calculated using the three-dimensional strength reduction method in the reference: Yang, Y., Liu, F., Wu, W., 2022. Assessing Slope Stability with an Improved 3D Numerical Manifold Method. Rock Mech Rock Eng 55, 6409–6423., indicating that the three-dimensional slip surface search method for slopes in this invention is feasible.

[0144] Table 1. Changes in the safety factor during the iteration process.

[0145] Number of iterations Safety factor 0 3.45 10 2.95 20 2.85 30 2.79 40 2.76 50 2.73 60 2.72 70 2.71 80 2.70 90 2.70 100 2.70

[0146] Step S13: Based on the key slip surfaces obtained from the search and the corresponding safety factors, conduct stability analysis and formulate protection schemes.

[0147] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A three-dimensional intelligent search method for slope slip surface, characterized in that, Includes the following steps: Step S1: Construct a three-dimensional slope geometry model for the area to be analyzed; Step S2: Physically mesh the three-dimensional slope analysis area to generate a discrete model of the three-dimensional slope, and group the slope by material and boundary surface to prepare for numerical analysis. Step S3: Set boundary conditions based on slope material parameters, perform an elastic or elastoplastic analysis on the slope model using the numerical manifold method, and export stress field data and material field data; specifically including the following steps: Step S3.1: Define the basic governing equations and boundary conditions for the static elastoplastic problem of the three-dimensional slope analysis domain Ω; whereby the basic governing equations are: s ij,j +b i =0.inΩ; In the above formula, σ ij Let σ represent the Cauchy stress tensor. ij,j Indicates σ ij Find the spatial partial derivative, b i Ω represents the volume load vector, i represents the direction of the stress, j represents the outward normal direction of the surface where the stress is located, and Ω represents the analysis region of the three-dimensional slope. The boundary conditions are: In the above formula, Represents the region of action of the displacement boundary. Represents the region of stress boundary action, u i Represents the displacement vector. Displacement boundary The given displacement vector on; n j Represents stress boundary outward normal direction, Indicates stress boundary The specified traction force; Step S3.2: Based on the governing equations and the corresponding boundary conditions, the following function I(u) for the elastoplastic problem is obtained: Step S3.3: Apply displacement boundary conditions using the penalty function method; the corresponding modified function is as follows: In the above formula, α1 is the penalty parameter corresponding to the displacement boundary condition; Let δI * If (u) = 0, then the system equilibrium equation for the elastoplastic problem can be written in matrix form as follows: Kd = f; Where d is the global displacement vector, and K and f are the generalized global stiffness matrix and force vector, respectively; In the above formula, N and B represent the shape function matrix and strain matrix, respectively, and D ep Denotes the elastoplastic matrix; B = L d N; Operator L d for: Step S4: Construct the background control grid of the slope slip surface, perform Boolean operations on the background control grid and the slope body, trim off the excess parts, and generate the initial test slip surface; Step S5: Using the control parameters of the background control grid as independent variables and the test safety factor of the test surface as the objective function, calculate the test safety factor and add constraints to the objective function; Step S6: Perform intelligent optimization based on the pattern search algorithm, update the slope slip surface control parameters and calculate the trial safety factor. When the change in the trial safety factor is less than the set threshold, the pattern search algorithm converges, and finally the key slip surface and the corresponding safety factor are obtained.

2. The intelligent search method for three-dimensional slope slip surface according to claim 1, characterized in that, Step S4 specifically includes the following steps: Step S4.1: Define the background mesh of the slope slip surface. Fix the X and Y coordinates of all nodes on the background mesh, and use the Z coordinate as a variable to obtain the column vector H composed of the control parameters of the three-dimensional slope slip surface background mesh, which is: In the formula, Θ represents the number of control points, and h β This represents the height of the β-th control point, i.e., the value of the β-th control point on the Z-axis. Step S4.2: Perform Boolean operations on the background control mesh and the slope to trim away the excess parts and generate the test slip surface required for calculating the safety factor.

3. The intelligent search method for three-dimensional slope slip surface according to claim 2, characterized in that, In step S5, the shape constraint conditions of the three-dimensional slope slip surface are set according to the following steps: Step S5.1: The local constraint equations are defined as follows: for any triangular element on the sliding surface, its normal direction points towards the slope, and all other points on the sliding surface lie in the positive half-plane of this plane. The local constraint equations are then: Among them, the first is set The three vertices of the triangular element corresponding to each local constraint are respectively and constraint points Then we have: Step S5.2: Construct the global constraint equations based on the local constraint equations in step S5.1: AH≤0 Where A is the inequality constraint matrix, which is obtained by applying the inequality constraints in each local constraint equation. The matrix is ​​assembled; H is a vector composed of the heights of each control point, obtained by combining the local constraint equations. Obtained by matrix assembly.

4. The intelligent search method for three-dimensional slope slip surface according to claim 3, characterized in that, The safety factor is calculated through the following steps: Based on the three-dimensional slope stress field obtained by numerical manifold elastoplastic analysis, the stress state at any point G on the test slip surface S is obtained; the stress tensor at point G is set to σ. G , To determine the direction of the unit normal to the tangent plane at point G on the sliding surface, with the direction pointing towards the sliding body as positive, the force exerted by point G on the slope body can be calculated. Investigate the normal and tangential forces exerted by the sliding body on the slope at point G on the sliding surface. and And to test the anti-skid normal stress of the slope at point G on the sliding surface. for: According to the Mohr-Coulomb strength criterion, the ultimate anti-sliding shear stress of the slope body at any point on the sliding surface is: Where c is the cohesion parameter of the slope soil and rock mass, and φ is the internal friction angle parameter of the slope soil and rock mass. To investigate the potential sliding direction of the slope at point G on the slip surface, Based on the anti-slip shear stress vector at each point on the sliding surface, integration on the sliding surface yields the resultant ultimate anti-slip shear stress of the slope on the sliding body: The global principal potential sliding direction is determined based on the resultant force of the ultimate anti-slip shear stress. In addition to shear stress, the anti-sliding force vector of the slope body on the sliding body also includes the normal stress component. The anti-sliding force vector of the slope body on the sliding body at any point G on the sliding surface is: The force exerted by the sliding body at any point G on the sliding surface on the slope is That is, the sliding force of the sliding body at any point G on the sliding surface is Directing the anti-slip force and sliding force towards the overall potential sliding direction. Project the slope and integrate over the entire slip surface to obtain the trial safety factor. In the above formula, This represents the projection of the resultant force of the slope's resistance to the sliding mass onto the main potential sliding direction. This represents the projection of the resultant force of the sliding body's downward sliding force onto the main potential sliding direction. Indicates the main potential sliding direction of the sliding body. This represents the downward force at any point on the sliding body. It represents the anti-slip force of the slope body on the sliding body at any point on the sliding surface.

5. The intelligent search method for three-dimensional slope slip surface according to claim 3, characterized in that, Matrix in each local constraint equation A is obtained by assembling as follows: For the There are several constraint equations, involving the point... and Number The corresponding control point height is set up, Then, the column vector All elements in the inequality constraint matrix A are used as the first element in the inequality constraint matrix A. Okay, number The elements of the column will form a column vector. All elements in matrix H are used as the first element of matrix H. Row elements; Similarly, by substituting the elements of the other constraint equation matrices into the above formula, we obtain the final inequality constraint matrix A.

6. The intelligent search method for three-dimensional slope slip surface according to claim 3, characterized in that, Step S6 specifically includes the following steps: Step S6.1: From the given initial sliding surface control parameters H 0 Begin by using the Z-coordinate axes e1, e2, ..., e of all control points. β ,…,e Θ Direction, using a specified step size δ k Perform trial moves; each time, select an independent variable h. β Only move it, at this time e β = [0,0,…,1,…,0], where only the βth term is 1 and the rest are 0, meaning that each time a background grid control point is moved; Step S6.2: For the β-th control point, perform the following movement and detection along the Z-coordinate axis: In the above formula, Indicates the first The row number corresponding to each constraint condition; Step S6.2.1: Remove h β Moving all other variables to the right side of the inequality, we get only one variable, h. β The system of inequalities is shown below: Therefore, h is calculated. β The range of values Step S6.2.2: Determine Is it greater than or equal to? If so, then the βth control point cannot be moved at this time; If not, then perform the following movement detection: First, perform forward detection, at h β The range of values Inside, move H to H+e β δ k Calculate (H+e) β δ k The corresponding trial safety factor if This indicates the detection was successful; let H = H + e. β δ k Conversely, if the probe fails, a reverse probe is then performed, specifically: at h β The range of values Inside, move H to He β δ k Calculate (He) β δ k The corresponding trial safety factor if This indicates the detection was successful; let H = He. β δ k Conversely, if the detection fails, H remains unchanged; Step S6.3: Following the detection method along the β-th axis, traverse the height of all background grid control points and repeatedly try and optimize. Step S6.4: When a round of probing ends, decrease the step size δ k Repeat steps S6.2 and S6.3 to continue iterative optimization until the change in the trial safety factor is less than the set first threshold, or the step size δ. k The algorithm converges when the value is less than the set second threshold, yielding the safety factor and the critical smooth surface; if convergence is not achieved after reaching the maximum number of iterations, the parameter δ is adjusted. k Alternatively, the background mesh can be rearranged for further calculations.

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