Three-dimensional slope sliding surface intelligent searching method

Abstract

The invention discloses a three-dimensional side slope sliding surface intelligent searching method. The method comprises the steps that a three-dimensional side slope geometric model of an area needing to be analyzed is constructed; performing physical grid division on the three-dimensional slope analysis area to generate a discrete model of the three-dimensional slope; performing primary elastic or elastic-plastic analysis on the slope model by using a numerical manifold method; setting a three-dimensional sliding surface background grid of any side slope and setting an initial background grid; the slope sliding surface control parameter is used as an independent variable, and the calculated tentative safety coefficient is used as a dependent variable; the local part of the sliding surface is limited to protrude towards the slope body, and a constraint equation is constructed; and in combination with constraint equation specificity, a mode search algorithm is improved, intelligent optimization is carried out based on the improved mode search algorithm to search the most unfavorable sliding surface, slope sliding surface control parameters are updated, a tentative safety coefficient is calculated, and a final key sliding surface and a corresponding safety coefficient are obtained. The method can provide theoretical and technical support for reducing geological disasters related to slope damage.

Description

Technical Field

[0001] The invention relates to the field of slope numerical calculation, and in particular to a three-dimensional slope sliding surface intelligent search method. Background Art

[0002] The failure of rock / soil slopes usually leads to serious consequences, such as casualties and economic losses. Therefore, it is necessary to perform stability analysis on slopes to predict the critical failure surface and safety factor of the slope, two of the most important indicators in slope stability evaluation and design. In the past few decades, with the needs 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 the existing technology, the experimental method for evaluating slope stability is limited in effect. Numerical methods and limit equilibrium methods are mainly concentrated in two-dimensional slope analysis. Three-dimensional analysis methods have many restrictions. For example, the three-dimensional limit equilibrium method limits the sliding surface to an ellipsoid, such as the paper: Zhang Kun et al. 2017. Application of adaptive differential evolution algorithm in slope sliding surface search. Rock and Soil Mechanics 38, 1503–1509. The strength reduction method requires a large number of iterative elastic-plastic calculations, which is time-consuming, such as the thesis: Zhang Yajun, 2024. Slope stability analysis based on three-dimensional numerical manifold method (Master). Hainan University), the labor and time costs are high, and it is difficult to apply on a large scale. Summary of the invention

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

[0005] Specifically, it is achieved through the following scheme:

[0006] The three-dimensional slope sliding surface intelligent search method includes the following steps:

[0007] Step S1: construct a three-dimensional slope geometric model of the area to be analyzed;

[0008] Step S2: Physically meshing the three-dimensional slope analysis area to generate a discrete model of the three-dimensional slope, and grouping the slope materials and boundary surfaces to prepare for numerical analysis;

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

[0010] Step S4: constructing a background control grid of the slope sliding surface, performing Boolean operations on the background control grid and the slope, cutting off redundant parts, and generating an initial trial sliding surface;

[0011] Step S5: Calculate the trial safety factor using the control parameters of the background control grid as independent variables and the trial safety factor of the trial sliding surface as the objective function. In order to ensure the rationality of the shape of the background grid and avoid obvious local convexity or concavity of the generated trial sliding surface, a constraint condition is added to the objective function;

[0012] Step S6: Perform intelligent optimization based on the pattern search algorithm, update the slope sliding 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 obtains the key sliding surface and the corresponding safety factor.

[0013] Further optimization, in step S3, the numerical manifold method is used to calculate the elastic-plastic stress field of the slope model, which specifically includes the following steps:

[0014] Step S3.1: Define the basic control equations and boundary conditions of the static elastoplastic problem of the three-dimensional slope analysis area Ω; the basic control equation is:

[0015] σ ij,j +b i =0,inΩ;

[0016] In the above formula, σ ij represents the Cauchy stress tensor, σ ij,j Represents the ij Find the spatial partial derivative, b i represents the body load vector, i represents the direction of the stress, j represents the external normal direction of the surface where the stress is located, and Ω represents the analysis area of ​​the three-dimensional slope.

[0017] The boundary conditions are:

[0018]

[0019] In the above formula, represents the displacement boundary action area, represents the stress boundary action area, u i represents the displacement vector, Represents displacement boundary A given displacement vector on σ ij represents the Cauchy stress tensor, n j Represents stress boundary The direction of the external normal, Represents stress boundary The specified traction force on the surface, i represents the direction of the stress, and j represents the direction of the external normal line of the surface where the stress is located;

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

[0021]

[0022] Numerical Manifold Method Physics PPT k The weight function w kγ (x) Generally, the following three conditions are met:

[0023]

[0024] 0≤w kγ (x)≤1,if x∈PP k ,

[0025]

[0026] Among them, when the manifold unit ME γ Physical film PP k When covered, the weight function w kγ The range of (x) is 0-1. Otherwise, when it is not covered, the weight function is 0. Define the manifold unit ME γ The eight physical slices of the manifold are covered by the manifold unit, and their weight functions all satisfy 0≤w kγ (x)≤1, and the sum is 1.

[0027] Override function u kγ (x) can be constructed using a polynomial function of any order. The present invention uses a 0-order polynomial function as the weight function to avoid linear correlation problems. The structured hexahedral grid is used to construct the mathematical covering system, so the shape function of the eight-node hexahedral unit is used to construct the weight function w kγ (x).

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

[0029]

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

[0031] Step S3.2: According to the control equation and the corresponding boundary conditions, the following function I(u) of the elastic-plastic problem is obtained:

[0032]

[0033] Step S3.3: Since the mathematical covering system in numerical manifold methods usually does not match the physical grid, The displacement boundary conditions on are usually not directly satisfied; the displacement boundary conditions are imposed by the penalty function method, and the corresponding above function is modified to:

[0034]

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

[0036] Let δI * (u) = 0, then the system equilibrium equation of the elastic-plastic problem can be written in the following matrix form:

[0037] Kd = f;

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

[0039]

[0040] In the above formula, N and B represent the shape function matrix and strain matrix respectively, D ep represents the elastic-plastic matrix; B = L d N; operator L d for:

[0041]

[0042] Unlike the strength reduction method in the prior art, which requires a large number of repeated elastic-plastic analysis calculations, the present invention only needs to perform an elastic-plastic calculation on the slope under the action of gravity. At this time, the slope strength parameters are not reduced, the slope is often not in a critical state, the number of iterations of the elastic-plastic analysis is generally not large, and the calculation consumption is small. After performing an elastic-plastic calculation on the slope, the slope stress field is derived. In the subsequent steps, based on the slope stress field, interpolation can obtain the stress state of any point inside the slope body.

[0043] Further optimization is performed to construct a three-dimensional slope sliding surface based on the three-dimensional slope geometric information. There are many possibilities for the position and shape of the three-dimensional slope sliding surface. The most common way to construct a three-dimensional sliding surface is an ellipsoid, but this sliding surface is too ideal and cannot describe a complex sliding surface. Therefore, in order to simulate any three-dimensional sliding surface, a series of control points can be used to obtain it through spline surface fitting or interpolation.

[0044] Step S4 of the present invention utilizes the background grid to simulate a three-dimensional slope sliding surface of any shape, which specifically includes the following steps:

[0045] Step S4.1: define the background grid of the slope sliding surface, fix the coordinates of all nodes on the background grid in the X and Y coordinate axes, take the coordinates in the Z coordinate axis as variables, and obtain the column vector H composed of the control parameters of the three-dimensional slope sliding surface background grid, which is:

[0046]

[0047] In the above formula, Θ represents the number of control points, h β Indicates the height of the βth control point, that is, the value of the βth control point on the Z coordinate axis;

[0048] Step S4.2: Perform Boolean operations on the background control grid and the slope, cut off the redundant parts, and generate the trial sliding surface required for calculating the safety factor.

[0049] The three-dimensional slope sliding surface determined by H is not necessarily reasonable. For example, the sliding surface cannot have local mutations, obvious convexity or concavity. Such unreasonable sliding surfaces can be deleted by manual elimination, but this method is obviously inefficient. For example, the paper: Lin Yongsheng et al., 2013. Search for three-dimensional sliding surface of slope based on finite element calculation. Rock and Soil Mechanics 34, 1191–1196, records that the sliding surface generated by control points can simulate the actual sliding surface more realistically, and can also simulate sliding surfaces of arbitrary shapes. However, the sliding surface generated by the control points has obvious local convexity and concavity, and the safety factor calculated based on this simulated sliding surface may be too large.

[0050] In order to realize the automatic search of the sliding surface of a three-dimensional slope, it is necessary to give appropriate constraints to avoid obvious local convexity or concavity of the sliding surface. The most common approach is to assume in advance that the shape of the three-dimensional sliding surface is a convex geometric shape. For example, Chinese patent CN201610116074.0, a method for searching the three-dimensional critical sliding surface of a slope, directly uses the ellipsoid equation as the assumed shape of the critical sliding surface; the paper Zhang Kun et al., 2017. Application of adaptive differential evolution algorithm in slope sliding surface search. Rock and Soil Mechanics 38, 1503–1509. to modify the ellipsoid equation to describe the three-dimensional sliding surface. The above method assumes the shape of the sliding surface, loses the arbitrariness of the sliding surface shape, and is not very consistent with the actual situation.

[0051] In order to define the shape constraints of the slope sliding surface, for the two-dimensional sliding 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, but this method cannot be applied to the shape constraints of the three-dimensional sliding surface.

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

[0053] Step S5.1: The sliding surface is limited to be partially convex toward the slope, that is, for any plane where a triangular unit on the sliding surface is located, its normal direction points to the slope, and other points on the sliding surface are located in the positive half plane of the plane.

[0054] Set The three vertices of the triangle unit corresponding to the local constraint are and Constraint Points The triangle normal direction is calculated as:

[0055]

[0056] in for:

[0057]

[0058] The distance from other points on the sliding surface to the plane where the triangular element is located must be greater than or equal to 0, so the following local constraint equation exists:

[0059]

[0060] Drop the denominator and we get:

[0061]

[0062] Bring in point and Coordinate values, write the local constraint equation in matrix form:

[0063]

[0064] Among them, there are:

[0065]

[0066]

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

[0068] AH≤0

[0069] Where A is the inequality constraint matrix, which is obtained by The matrix is ​​assembled; H is the vector composed of the heights of each control point, and the The matrix is ​​assembled.

[0070] Further optimization, the safety factor is calculated by the following steps:

[0071] Based on the three-dimensional slope stress field obtained by the elastic-plastic analysis of the numerical manifold method, the stress state of any point G on the test sliding surface S is obtained; the stress tensor at the point G is set to σ G , To test the unit normal direction of the tangent plane at point G on the sliding surface, the direction pointing to the sliding body is positive, then the force acting on the slope body by point G on the sliding body is obtained: Test the normal and tangential forces of the sliding body on the slope at point G on the sliding surface and And the normal stress of the slope on the sliding body at the 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 at any point on the sliding surface is:

[0074]

[0075] Among them, c is the cohesion parameter of the slope rock and soil, φ is the internal friction angle parameter of the slope rock and soil, To test the potential sliding direction of the slope at point c on the sliding surface,

[0076] Based on the anti-sliding shear stress vector of each point on the sliding surface, the ultimate anti-sliding shear stress resultant of the slope on the sliding body is obtained by integrating on the sliding surface:

[0077]

[0078] Determine the global main potential sliding direction based on the ultimate anti-sliding shear stress resultant

[0079]

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

[0081]

[0082] The force exerted by the sliding body on the slope at any point G on the sliding surface is: That is, the sliding force of the sliding body at any point G on the sliding surface is Direct the anti-slip force and the sliding force toward the main potential sliding direction of the whole Project and integrate over the entire sliding surface to obtain the tentative safety factor of the slope:

[0083]

[0084] In the above formula, It represents the projection of the resultant anti-sliding force of the slope on the sliding body in the main potential sliding direction. It represents the projection of the resultant force of the sliding body on the main potential sliding direction, represents the main potential sliding direction of the sliding body, It represents the sliding force at any point on the sliding body. It represents the anti-sliding force of the slope at any point on the sliding surface.

[0085] Further optimization, the matrix in each local constraint equation Assemble A as follows:

[0086] For constraint equations involving points and Number The corresponding control point height is

[0087] set up,

[0088]

[0089] Then, the column vector All elements of are taken as the inequality constraint matrix A. Row, No. The elements of the column, that is In addition, the inequality constraint matrix A The values ​​of the other columns of the row are 0. All elements of the matrix H are Elements of a row;

[0090] Similarly, other constraint equation matrices Substitute the elements in according to the above formula to obtain the final inequality constraint matrix A.

[0091] Further optimization, the sliding surface search based on the pattern search intelligent algorithm is actually an optimization problem. In order to consider the inequality constraints, one approach is to use the penalty function method to add the inequality constraints to the objective function. However, since the penalty parameter value does not have physical meaning, this method needs to be manually adjusted, and the actual effect is not good. To this end, step S6 of the present invention improves the process of the pattern search intelligent algorithm, adds the satisfaction of the inequality constraints to the optimization process, to increase the robustness and efficiency of the algorithm, and specifically includes the following steps:

[0092] Step S6.1: From the given initial sliding surface control parameter H 0 First, according to the Z coordinates of all Θ control points e1, e2, ..., e β ,…,e Θ direction, with a specified step size δ k Perform trial moves; each time select an independent variable h β , only move it, then e β =[0,0,…,1,…,0], only the βth term is 1, and the rest are 0, that is, one background grid control point is moved each time;

[0093] Step S6.2: For the βth control point, perform the following movement detection along the Z coordinate axis, removing h β The other independent variables will not move and therefore have known values, so we have:

[0094]

[0095] That is, the column vector All elements of are taken as the inequality constraint matrix A. Row, No. The elements of the column, that is In addition, the inequality constraint matrix A The values ​​of other columns of the row are 0; Indicates The row number corresponding to each constraint.

[0096] Step S6.2.1: Divide h β Move the other variables to the right side of the inequality, and get only one variable h β The inequality equations are as follows:

[0097]

[0098] Thus, h is calculated β The value range of A feasible detection area was determined for subsequent detection.

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

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

[0101] If not, perform the following motion detection: first perform positive direction detection, β The value range of Inside, move H to H+e β δ k , calculate (H+e β δ k ) Corresponding tentative safety factor if This indicates that the detection is successful, and H = H + e β δ k ; Otherwise, if the detection fails, try again in the opposite direction, specifically: β The value range of Inside, move H to He β δ k , calculate (He β δ k ) Corresponding tentative safety factor if This indicates that the detection is successful, and H = He β δ k , otherwise the detection fails and H remains unchanged;

[0102] Step S6.3: According to the detection method in the β-th axis direction, traverse the heights of all background grid control points and repeatedly try to optimize;

[0103] Step S6.4: When a round of trials is completed, reduce the step size δ k Repeat steps S6.2 and S6.3 to continue iterative optimization until the change in the safety factor is less than the set first threshold, or the step length δ k When the value is less than the set second threshold, the algorithm converges and the safety factor and critical sliding surface are obtained; if the maximum number of iterations is reached and the algorithm still fails to converge, the parameter δ is adjusted. k Or rearrange the background grid for further calculations.

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

[0105] Taking a three-dimensional slope as an example, the present invention not only considers the real stress field distribution inside the natural slope, but also only needs to perform an elastic-plastic analysis once. At the same time, it also has a more universal failure surface shape, can more flexibly search for the safety factor and key sliding surface of the three-dimensional slope, and automatically search for the key sliding surface of the three-dimensional slope based on the existing intelligent optimization algorithm, providing a reference for stability evaluation and design, and can provide theoretical support for reducing geological disasters related to slope failure. BRIEF DESCRIPTION OF THE DRAWINGS

[0106] Figure 1 is a flow chart of the three-dimensional slope sliding surface intelligent search method of the present invention;

[0107] Figure 2 It is the three-dimensional slope geometric model diagram of the present invention;

[0108] Figure 3 It is a schematic diagram of the discrete model of the numerical manifold method of the three-dimensional slope of the present invention;

[0109] Figure 4 It is a stress field cloud diagram obtained by the elastic-plastic analysis of the three-dimensional slope numerical manifold method described in the present invention;

[0110] Figure 5 It is a schematic diagram of the three-dimensional slope background grid and control points of the present invention;

[0111] Figure 6 is a schematic diagram of the initial sliding surface of the three-dimensional slope of the present invention;

[0112] Figure 7 It is a schematic diagram of constructing the convexity constraint condition of the three-dimensional slope sliding surface according to the present invention;

[0113] Figure 8 It is a schematic diagram of assembling the three-dimensional sliding surface shape constraint inequality of the present invention;

[0114] Fig. 9 is the stress state at a point on the three-dimensional slope test sliding surface of the present invention;

[0115] Fig.10 The unreasonable sliding surface is caused by not constraining the shape of the three-dimensional slope sliding surface of the present invention;

[0116] Fig.11 is the key sliding surface background grid obtained by intelligent optimization according to the present invention;

[0117] Fig.12 It is the key sliding surface obtained by cutting the key sliding surface background grid and the slope body of the present invention;

[0118] Fig.13 It is a curve showing the variation of the tentative safety factor during the iterative process of the sliding surface search of the present invention. DETAILED DESCRIPTION

[0119] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0120] like Figure 1 The three-dimensional slope sliding surface intelligent search method comprises the following steps:

[0121] Step S1: Construct a three-dimensional slope geometry 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 three-dimensional slope analysis area to generate a discrete model of the three-dimensional slope, such as Figure 3 As shown, materials and boundary surfaces are grouped to prepare for numerical analysis.

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

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

[0125] Step S5: Construct a regular background grid, which consists of some control points and triangular unit faces, such as Figure 5 As shown. Among them, the horizontal coordinates of the control points are fixed, and the background grid control points can move up and down in the vertical direction. The height of the background grid is used as the independent variable of the optimization problem in the present invention, and the column vector H composed of the control parameters of the three-dimensional slope sliding surface background grid is obtained, which is:

[0126] When the independent variable vector H in the optimization problem is h β When different values ​​are taken, the corresponding background grid control points move up and down to form different background grids. Then the background grid and the slope are Boolean operated to cut off the redundant parts and leave the part inside the slope to obtain the trial sliding surface required for calculating the trial safety factor.

[0127] Step S5: Set an initial background grid, which cuts the slope geometry model into slope and sliding body parts, such as Figure 6 shown.

[0128] Step S6: the background grid control parameters are used as independent variables, and the tentative safety factor calculated by the trial sliding surface is used as the objective function;

[0129] Step S7: See attached Figure 7 To ensure the rationality of the shape of the background grid and avoid obvious local convexity or concavity of the generated trial sliding surface, the sliding surface is limited to be convex towards the slope, that is, for any plane where a triangular unit on the sliding surface is located, its normal direction points to the slope, and other points on the sliding surface are located in the positive half plane of the plane. The corresponding constraint equation is given. And follow Figure 8 The assembly method shown assembles each local constraint to form an overall constraint equation;

[0130] AH≤0

[0131] Where A is the inequality constraint matrix, which is obtained by The matrix is ​​assembled; H is the vector composed of the heights of each control point, and the The matrix is ​​assembled.

[0132] Specifically, Figure 8 Lieutenant General In the constraint equations, the column vector All elements of are taken as the inequality constraint matrix A. Row, No. The elements of the column, that is In addition, the inequality constraint matrix A The values ​​of the other columns of the row are 0. All elements of the matrix H are Similarly, the elements of the other constraint equation matrices Substitute the elements in according to the above formula to obtain the final inequality constraint matrix A.

[0133] Step S8: wherein, refer to the attached Fig. 9 , the stress tensor at point G is σ G , To test the unit normal direction of the tangent plane at point G on the sliding surface (the direction pointing to the sliding body is positive), the force acting on the slope body by point G on the sliding body can be obtained: for:

[0134]

[0135] Further, the normal and tangential forces acting on the slope at point A on the test sliding surface can be obtained: and

[0136]

[0137] Direct the anti-slip force and the sliding force toward the main potential sliding direction of the whole Project and integrate over the entire sliding surface to obtain the tentative safety factor of the slope:

[0138]

[0139] In the above formula, represents the main potential sliding direction of the sliding body, represents the force exerted by any point on the sliding body on the slope body, It represents the anti-sliding force of the slope at any point on the sliding surface.

[0140] Step S9: Based on the improved pattern search algorithm, intelligent optimization is performed to update the slope sliding surface control parameters and calculate the trial safety factor, and check whether the change in the trial safety factor is less than the set threshold value, and finally obtain the key sliding 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 appears partially convex or concave, which is obviously not in line with reality. This shows that it is necessary to add shape constraints in the three-dimensional sliding surface search of the present invention.

[0142] Step S11: When the three-dimensional sliding surface shape constraint is added in the present invention, the calculated key sliding surface background grid shape is reasonable, such as Fig.11 The background mesh of the key sliding surface is Boolean operated with the slope, and the redundant parts are cut off to obtain the final key sliding surface and the corresponding safety factor, as shown in Fig.12 shown.

[0143] Step S12: In this embodiment, the threshold is set to 0.01, and the change data of the tentative safety factor during the sliding surface search iteration is shown in Table 1, and the change curve is as follows: Fig.13 As shown in the figure, the final safety factor converges to 2.70. This is close to the safety factor of 2.619 calculated by 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 sliding surface search method for slopes of the present invention is feasible.

[0144] Table 1 Changes in safety factor during iteration

[0145] 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 searched key sliding surface and the corresponding safety factor, stability analysis and protection plan formulation are performed.

[0147] The above descriptions are merely embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A three-dimensional slope sliding surface intelligent search method, characterized in that: The following steps are involved: Step S1: construct a three-dimensional slope geometric model of the area to be analyzed; Step S2: Physically meshing the three-dimensional slope analysis area to generate a discrete model of the three-dimensional slope, and grouping the slope materials and boundary surfaces to prepare for numerical analysis; Step S3: setting boundary conditions according to slope material parameters, using numerical manifold method to perform elastic or elastoplastic analysis on the slope model, and deriving stress field data and material field data; Step S4: constructing a background control grid of the slope sliding surface, performing Boolean operations on the background control grid and the slope, cutting off redundant parts, and generating an initial trial sliding surface; Step S5: taking the control parameters of the background control grid as independent variables and the tentative safety factor of the trial sliding surface as the objective function, calculating the tentative safety factor, and adding constraints to the objective function; Step S6: Perform intelligent optimization based on the pattern search algorithm, update the slope sliding 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 obtains the key sliding surface and the corresponding safety factor.

2. The three-dimensional slope sliding surface intelligent search method according to claim 1 is characterized in that: In step S3, the numerical manifold method is used to calculate the elastic-plastic stress field of the slope model, which specifically includes the following steps: Step S3.1: Define the basic control equations and boundary conditions of the static elastoplastic problem of the three-dimensional slope analysis area Ω; the basic control equation is: s ij,j +b i =0.inΩ; In the above formula, σ ij represents the Cauchy stress tensor, σ ij,j Represents the ij Find the spatial partial derivative, b i represents the body load vector, i represents the direction of the stress, j represents the external normal direction of the surface where the stress is located, and Ω represents the analysis area of ​​the three-dimensional slope; The boundary conditions are: In the above formula, represents the displacement boundary action area, represents the stress boundary action area, u i represents the displacement vector, Represents displacement boundary A given displacement vector on n j Represents stress boundary The direction of the external normal, Represents stress boundary Specified traction on Step S3.2: According to the control equation and the corresponding boundary conditions, the following function I(u) of the elastic-plastic problem is obtained: Step S3.3: Apply the displacement boundary condition by penalty function method, and the corresponding function is modified to: In the above formula, α1 is the penalty parameter corresponding to the displacement boundary condition; Let δI * (u) = 0, then the system equilibrium equation of the elastic-plastic problem can be written in the following matrix form: Kd = f; Where d is the global displacement vector, K and f are the generalized global stiffness matrix and force vector; In the above formula, N and B represent the shape function matrix and strain matrix respectively, D ep represents the elastic-plastic matrix; B = L d N; operator L d for:

3. The three-dimensional slope sliding surface intelligent search method according to claim 2 is characterized in that: The step S4 specifically comprises the following steps: Step S4.1: define the background grid of the slope sliding surface, fix the coordinates of all nodes on the background grid in the X and Y coordinate axes, use the coordinates in the Z coordinate axis as variables, and obtain the column vector H composed of the control parameters of the three-dimensional slope sliding surface background grid, which is: In the formula, Θ represents the number of control points, h β Indicates the height of the βth control point, that is, the value of the βth control point on the Z coordinate axis; Step S4.2: Perform Boolean operations on the background control grid and the slope, cut off the redundant parts, and generate the trial sliding surface required for calculating the safety factor.

4. The three-dimensional slope sliding surface intelligent search method according to claim 3 is characterized in that: In step S5, the shape constraint conditions of the three-dimensional slope sliding surface are set according to the following steps: Step S5.1: The local sliding surface is limited to be convex toward the slope, that is, for any plane where a triangular unit on the sliding surface is located, its normal direction points to the slope, and other points on the sliding surface are located in the positive half plane of the plane; then the local constraint equation is: Among them, setting The three vertices of the triangle unit corresponding to the local constraint are and Constraint Points Then we have: Step S5.2: Construct the global constraint equation based on the local constraint equation in step S5.1: AH≤0 Where A is the inequality constraint matrix, which is obtained by The matrix is ​​assembled; H is the vector composed of the heights of each control point, and the The matrix is ​​assembled.

5. The three-dimensional slope sliding surface intelligent search method according to claim 4 is characterized in that: The safety factor is calculated by the following steps: based on the three-dimensional slope stress field obtained by the numerical manifold method elastoplastic analysis, the stress state of any point G on the test sliding surface S is obtained; the stress tensor at the point G is set to σ G , To test the unit normal direction of the tangent plane at point G on the sliding surface, the direction pointing to the sliding body is positive, then the force acting on the slope body by point G on the sliding body is obtained: Test the normal and tangential forces of the sliding body on the slope at point G on the sliding surface and And the normal stress of the slope on the sliding body at the point G on the sliding surface for: According to the Mohr-Coulomb strength criterion, the ultimate anti-sliding shear stress of the slope at any point on the sliding surface is: Among them, c is the cohesion parameter of the slope rock and soil, φ is the internal friction angle parameter of the slope rock and soil, To test the potential sliding direction of the slope at point G on the sliding surface, Based on the anti-sliding shear stress vector of each point on the sliding surface, the ultimate anti-sliding shear stress resultant of the slope on the sliding body is obtained by integrating on the sliding surface: Determine the global main potential sliding direction based on the ultimate anti-sliding shear stress resultant In addition to the shear stress, the anti-sliding force vector of the slope on the sliding body also includes the normal stress part. The anti-sliding force vector of the slope on the sliding body at any point G on the sliding surface is: The force exerted by the sliding body on the slope at any point G on the sliding surface is: That is, the sliding force of the sliding body at any point G on the sliding surface is Direct the anti-slip force and the sliding force toward the main potential sliding direction of the whole Project and integrate over the entire sliding surface to obtain the tentative safety factor of the slope: In the above formula, It represents the projection of the resultant anti-sliding force of the slope on the sliding body in the main potential sliding direction. It represents the projection of the resultant force of the sliding body on the main potential sliding direction, represents the main potential sliding direction of the sliding body, It represents the sliding force at any point on the sliding body. It represents the anti-sliding force of the slope at any point on the sliding surface.

6. The three-dimensional slope sliding surface intelligent search method according to claim 4 is characterized in that: The matrices in each local constraint equation Assemble A as follows: For constraint equations involving points and Number The corresponding control point height is set up, Then, the column vector All elements of are taken as the inequality constraint matrix A. Row, No. The elements of the column, the column vector All elements of the matrix H are Elements of a row; Similarly, substitute the elements in other constraint equation matrices according to the above formula to obtain the final inequality constraint matrix A.

7. The three-dimensional slope sliding surface intelligent search method according to claim 4 is characterized in that: The step S6 specifically includes the following steps: Step S6.1: From the given initial sliding surface control parameter H 0 First, according to the Z coordinates of all control points e1, e2, ..., e β ,…,e Θ direction, with a specified step size δ k Perform trial moves; each time select an independent variable h β , only move it, then e β =[0,0,…,1,…,0], only the βth term is 1, and the rest are 0, that is, one background grid control point is moved each time; Step S6.2: For the βth control point, the following movement detection is performed along the Z coordinate axis direction, then: In the above formula, Indicates The row number corresponding to each constraint; Step S6.2.1: Divide h β Move the other variables to the right side of the inequality, and get only one variable h β The inequality equations are as follows: Thus, h is calculated β The value range of Step S6.2.2: Determination Is it greater than or equal to If so, the βth control point cannot be moved at this time; If not, perform the following motion detection: first perform positive direction detection, β The value range of Inside, move H to H+e β δ k , calculate (H+e β δ k ) Corresponding tentative safety factor if This indicates that the detection is successful, and H = H + e β δ k ; Otherwise, if the detection fails, try again in the opposite direction, specifically: β The value range of Inside, move H to He β δ k , calculate (He β δ k ) Corresponding tentative safety factor if This indicates that the detection is successful, and H = He β δ k , otherwise the detection fails and H remains unchanged; Step S6.3: According to the detection method in the β-th axis direction, traverse the heights of all background grid control points and repeatedly try to optimize; Step S6.4: When a round of trials is completed, reduce the step size δ k Repeat steps S6.2 and S6.3 to continue iterative optimization until the change in the safety factor is less than the set first threshold, or the step length δ k When the value is less than the set second threshold, the algorithm converges and the safety factor and critical sliding surface are obtained; if the maximum number of iterations is reached and the algorithm still fails to converge, the parameter δ is adjusted. k Or rearrange the background grid for further calculations.

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