A method and system for calculating the stability of a planar concave heterogeneous slope

Abstract

The present application relates to the technical field of slope stability analysis, and discloses a kind of plane recessed heterogeneous slope stability calculation method and system, the method is based on the morphological parameters of plane recessed heterogeneous slope and coal rock mass in research area and three-dimensional numerical simulation technology, the spatial form equation of potential sliding surface of plane recessed heterogeneous slope is established, potential sliding surface is divided into i row, j column micro column, the total anti-sliding force and total sliding force of each row micro column in potential sliding surface are solved, the two-dimensional equivalent mechanical parameters of three-dimensional effect are determined;Two-dimensional equivalent mechanical parameters are introduced into rigid body limit equilibrium method, three-dimensional slope stability problem is converted into equivalent two-dimensional rigid body limit equilibrium problem, and the stability coefficient of plane recessed heterogeneous slope is solved.The present application combines the complex terrain of plane recessed heterogeneous slope, determines the stability coefficient, is simple and efficient, fills the blank of plane recessed slope three-dimensional stability problem research.

Description

Technical Field

[0001] This invention relates to the field of slope stability analysis technology, and in particular to a method and system for calculating the stability of a planar concave heterogeneous slope. Background Technology

[0002] As a key structure connecting the working face in open-pit mines, the stability of the end face has always been a focus of open-pit mine engineering design and safety management. The end face not only bears complex loads from the pit bottom but is also affected by various factors such as topography and soil properties, making its stability particularly important in mining engineering. Domestic and international patent scholars have achieved fruitful results in researching three-dimensional stability calculation methods for end face slopes. Patent CN112287578A discloses a slope stability calculation method under end face mining conditions. This method is based on the theory of non-continuous discontinuous structural surfaces, dividing the end face mining area, establishing the shear strength parameters of the evolving weak layers, and quantitatively analyzing the slope stability under end face mining conditions using the rigid body limit equilibrium method. Patents CN109376465A and CN113420457A both disclose methods for calculating the stability of steep end face slopes, based on the static limit equilibrium theory, calculating the slope stability coefficient after steep slope mining. Patent 115081214A discloses a three-dimensional stability calculation method for a planar polygonal convex slope. This method establishes a mathematical model of the three-dimensional mechanical effect of the planar polygonal convex slope based on the mechanical effect of the slip surface at the bottom of the column. Based on the limit equilibrium theory and the equivalence principle, a two-dimensional equivalent mathematical model of the three-dimensional stability of the planar polygonal convex slope is established. Finally, the residual thrust method is used to calculate the three-dimensional stability coefficient of the planar polygonal convex slope. Patent CN105787176A discloses a three-dimensional stability calculation method for an open-pit coal mine slope containing a dip-side weak layer. This method establishes a simplified sliding body spatial morphology model and derives the expression for the slope stability coefficient.

[0003] In actual open-pit mines, end slopes typically exhibit a planar concave shape. However, the three-dimensional stability studies conducted by these patents have failed to fully consider the three-dimensional characteristics of planar concave heterogeneous slopes and the three-dimensional effects of the mine structure, making it difficult to accurately characterize the stress mechanism of the end slope. Furthermore, due to the complexity of the three-dimensional geometric characteristics and stress boundary conditions of planar concave heterogeneous slopes, existing algorithms still suffer from high computational costs, difficulties in parameter determination, and a need for improved computational accuracy, making them unsuitable for stability analysis of planar concave heterogeneous slopes. Therefore, there is an urgent need to develop a stability calculation method specifically for planar concave heterogeneous slopes to address the challenges in three-dimensional stability analysis of these slopes and provide more reliable theoretical techniques for mining engineering. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for calculating the stability of planar concave heterogeneous slopes. By combining the complex terrain of planar concave heterogeneous slopes, the stability coefficient can be determined. This method is simple and efficient, filling the gap in the research on the three-dimensional stability of planar concave slopes.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] A method for calculating the stability of a planar concave heterogeneous slope, comprising the following steps:

[0007] S1. Based on the engineering geological characteristics of the study area, determine the morphological parameters of the planar concave heterogeneous slope and coal and rock mass in the study area, determine the physical and mechanical parameters of the strata and rock mass in each area, and construct a dataset.

[0008] S2. Based on datasets and three-dimensional numerical simulation technology, the spatial morphological equation of the potential sliding surface of a planar concave heterogeneous slope is established.

[0009] S3, based on the spatial morphology equation, divide the potential slip surface into i rows and j columns of micro-strips, solve for the total anti-slip force and total sliding force of each row of micro-strips superimposed on the main slip line, and determine the two-dimensional equivalent mechanical parameters of the three-dimensional effect;

[0010] S4 introduces two-dimensional equivalent mechanical parameters into the rigid body limit equilibrium method, transforming the three-dimensional slope stability problem into an equivalent two-dimensional rigid body limit equilibrium problem, and solving it to obtain the stability coefficient of the planar concave heterogeneous slope.

[0011] Further, in step S1, the morphological parameters of the planar concave heterogeneous slope and coal-rock mass within the study area include:

[0012] The arch height a of the arc between the top and bottom slopes, the length 2b of the concave slope direction; the slope height H, the slope angle δ; and the range of the potential sliding surface in the direction of the planar concave heterogeneous slope.

[0013] Furthermore, in step S2, based on the dataset and three-dimensional numerical simulation technology, the spatial morphological equation of the potential sliding surface of the planar concave heterogeneous slope is established, specifically including:

[0014] S201. A three-dimensional coordinate system is established with the origin 0 at the toe of the main sliding line of the potential sliding surface of the planar concave heterogeneous slope. The planar concave heterogeneous slope is determined by three parameters: the arch height *a* of the circular arcs between the slope crest and slope base, half the length of the concave slope direction *b*, and the plane radius of curvature *R*. The planar concave heterogeneous slope consists of a series of coaxial circular arcs from the slope crest to the slope base, with the plane radius of curvature of the slope crest being *R*. s The radius of curvature of the lower slope baseline plane is R. x The slope angle of the main sliding profile is δ; the relationship between the plane curvature radius R and the slope angle is:

[0015]

[0016] The tangent of the slope angle is expressed as tanδ=H / (Rs-Rx), which, after conversion, gives the ratio of Rs to the slope height H as:

[0017] R s / H=R x / H+cotδ (2)

[0018] S202, treating the potential sliding surface as an ellipsoid, with a landslide mode of circular arc sliding, the spatial morphology equations of the potential sliding surface include the sliding surface equation and the slope equation; the sliding surface equation uses the ellipsoidal equation z. h This is represented as:

[0019]

[0020] Where A, B, and C are the coefficients of the ellipsoid equation, representing the radii of curvature of the ellipsoid in the x, y, and z directions; x0, y0, and z0 are the spatial coordinates of the center of the ellipsoid.

[0021] Slope equation z p The regions are represented as follows:

[0022]

[0023] Further, in step S3, based on the spatial morphology equation, the potential slip surface is divided into i rows and j columns of micro-strips. The total anti-slip force and total sliding force of each row of micro-strips superimposed on the main slip line are solved to determine the two-dimensional equivalent mechanical parameters of the three-dimensional effect, specifically including:

[0024] S301, divide the ellipsoid into i rows and j columns of micro-strips, solve the force state of the micro-strips through constitutive relations and static equilibrium conditions, and obtain the volume force on the bottom surface of the micro-strips;

[0025] S302, the area between the ellipsoid and the top of the slope is divided into region I, and the area from the top of the slope to the bottom of the slope is divided into region II. The sliding force and anti-sliding force of each row of micro-strip columns are solved in each region.

[0026] S303, the sliding force and anti-slip force of each row of micro-strips are superimposed on the main sliding line to obtain the total anti-slip force and total sliding force of each row of micro-strips;

[0027] S304, determine the two-dimensional equivalent mechanical parameters of the three-dimensional effect, including equivalent bulk density γ, equivalent cohesion c, and internal friction angle.

[0028] Further, in step S301, solving for the force state of the micro-strip column to obtain the volume force on the bottom surface of the micro-strip column specifically includes:

[0029] Define the length and width of the microbar in the i-th row and j-th column as dx and dy, and its height as z. p -z ij The horizontal distance from the main slide line is s, and the coordinates of the center point of the micro-strip column are (x, y, s). ij ,y ij ,z ij The angle between the bottom interface of the micro-strip column and the x-axis in the global coordinate system is α. x The angle between the y-axis and the y-axis is α. y ;

[0030] The volume force on the base of the micro-strip column is:

[0031] dW=γ ij (z p -z ij )sinθdA (5)

[0032] Among them, z ij γ is the height of the base of the micro-strip column; ij Let be the soil unit weight of the micro-strip column in the i-th row and j-th column;

[0033] The angle between the base of the micro-strip column and the x0y plane is θ, and the parameters of θ are:

[0034]

[0035]

[0036] The area dA of the base of the micro-strip column is:

[0037]

[0038] Where dx and dy are the differential lengths of the base of the micro-strip column along the x and y axes, respectively.

[0039] Further, in S302, the area between the ellipsoid and the slope crest line is designated as Region I, and the area from the slope crest line to the slope bottom line is designated as Region II. The sliding force and anti-slip force of each row of micro-strips are solved for each region, specifically including:

[0040] Let α be the angle between the horizontal projection of the base of the non-principal slide bar and the micro-strip bar on the i-th row of the principal slide bar. i Let P0 be the center point of the main slide bar on the i-th row, with coordinates (x0, y0, z0). Let P be the center point of the non-main slide bar micro-strip column. n Coordinates are (x ij ,y ij ,z ij );

[0041]

[0042] Anti-slip force T of micro-strip column in region I x1 and downward force F x1 They are respectively:

[0043]

[0044]

[0045] Where N1 is the normal pressure of the micro-strip column on the ellipsoidal region I, and N;c ij Let be the cohesion of the microstrip column in the i-th row and j-th column; It is the internal friction angle; Let z be the internal friction angle of the micro-strip column in the i-th row and j-th column; ij-I Let z be the center point z of the bottom surface of the micro-strip column in the i-th row and j-th column of region I; θ1 is the angle between the normal of the bottom interface of the micro-strip column and the normal of the ellipsoid, in °;

[0046] Anti-slip force T of micro-strip columns in region II x2 and downward force F x2 They are respectively:

[0047]

[0048]

[0049] Among them, z ij-II Let z be the coordinate of the center point of the bottom surface of the microbar column in the i-th row and j-th column of region II.

[0050] Further, in step S303, the sliding force and anti-slip force of each row of micro-strips are superimposed onto the main sliding line to obtain the total anti-slip force and total sliding force of each row of micro-strips, specifically including:

[0051] The total anti-slip force of the micro-strip in row k is T. k The total downward force is F k for:

[0052]

[0053]

[0054] In the formula, Σ l This indicates summing all columns in the k-th row; l represents the column number; c kl The meaning of , soil cohesion in row k and column l; The meaning of the internal friction angle of the soil in row k and column l;

[0055] Let T be the total anti-slip force of the microbar in the k-th row. k Total downward force F k These are respectively equal to the anti-slip force T of the micro-strip column in the k-th row of the main slip line.xk , downward force F xk ,Right now:

[0056] T k =T xk (16)

[0057] F k =F xk (17)

[0058] Where x represents the main slide line.

[0059] Further, in S304, the two-dimensional equivalent mechanical parameters of the three-dimensional effect are determined, including equivalent bulk density, equivalent cohesion, and internal friction angle, specifically including:

[0060] α xij α yij Let sinθ1 and cosθ1 be the angles between the bottom surface of the i-th row of microstrip columns and the x-axis and y-axis, respectively. Substituting sinθ1 and cosθ1 into equations (14) and (15) above, we obtain the equivalent shear strength parameters of the bottom interface of the k-th row of main sliding line microstrip columns, including the equivalent unit weight γ. k Equivalent cohesion c k and internal friction angle

[0061] In region I, the equivalent bulk density γ at the bottom interface of the micro-strip column of the k-th row of the main sliding line k Equivalent cohesion c k and internal friction angle They are represented as follows:

[0062]

[0063]

[0064]

[0065] In region II, the equivalent unit weight γ of the interface at the bottom of the micro-strip column of the k-th row main slide line. k Equivalent cohesion c k and internal friction angle They are represented as follows:

[0066]

[0067]

[0068]

[0069] This invention also provides a planar concave heterogeneous slope stability calculation system, applied to the above-mentioned planar concave heterogeneous slope stability calculation method, comprising:

[0070] The dataset construction module is used to determine the morphological parameters of the planar concave heterogeneous slope and coal and rock mass in the study area based on the engineering geological characteristics of the study area, determine the physical and mechanical parameters of the strata and rock masses in each area, and construct the dataset.

[0071] The spatial morphology equation establishment module is used to establish the spatial morphology equation of the potential sliding surface of a planar concave heterogeneous slope based on datasets and three-dimensional numerical simulation technology.

[0072] The two-dimensional equivalent mechanical parameter determination module is used to divide the potential slip surface into i rows and j columns of micro-strips based on the spatial morphology equation, solve for the total anti-slip force and total sliding force of each row of micro-strips superimposed on the main slip line, and determine the two-dimensional equivalent mechanical parameters of the three-dimensional effect.

[0073] The stability coefficient solution module is used to introduce two-dimensional equivalent mechanical parameters into the rigid body limit equilibrium method, transforming the three-dimensional slope stability problem into an equivalent two-dimensional rigid body limit equilibrium problem, and solving for the stability coefficient of the planar concave heterogeneous slope.

[0074] According to specific embodiments provided by the present invention, the following technical effects are disclosed: The method and system for calculating the stability of planar concave heterogeneous slopes provided by the present invention, considering the three-dimensional characteristics of the planar concave heterogeneous slope body and the three-dimensional effect of the mining structure, characterizes the force mechanism of the end face, and based on the limit equilibrium theory and the equivalent concept, performs two-dimensional equivalent representation of the three-dimensional mechanical effect of the slope, realizing the two-dimensional equivalent characterization of the three-dimensional stability of planar concave heterogeneous slopes. This avoids the problems of high calculation cost, difficulty in parameter determination, and complex calculation process in traditional slope three-dimensional stability calculation methods, and effectively solves the three-dimensional stability problem of planar concave slopes. It provides more reliable theoretical technology for mining engineering and is of great significance for predicting and preventing slope instability and ensuring safe and efficient mining production. Attached Figure Description

[0075] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0076] Figure 1 This is a flowchart of the method for calculating the stability of a planar concave heterogeneous slope according to the present invention;

[0077] Figure 2 This is a partial diagram illustrating the most dangerous slippery surface of the concave slope at the southwest corner of the southern end of the Nanfen open-pit iron mine, according to an embodiment of the present invention.

[0078] Figure 3 This is a three-dimensional transverse and longitudinal slice cross-sectional view in an embodiment of the present invention;

[0079] Figure 4 This is a force analysis diagram of the micro-strip column in an embodiment of the present invention;

[0080] Figure 5 This is a schematic diagram of potential slip surface partitioning in an embodiment of the present invention;

[0081] Figure 6 This is a diagram illustrating the influence of the radius of curvature on the concave slope in an embodiment of the present invention. Detailed Implementation

[0082] The technical solutions of the embodiments 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, and 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.

[0083] The purpose of this invention is to provide a method and system for calculating the stability of planar concave heterogeneous slopes, solving the problems faced in the three-dimensional stability analysis of planar concave slopes, providing more reliable theoretical technology for mining engineering, and having good engineering application value.

[0084] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0085] like Figure 1 As shown, the method for calculating the stability of a planar concave heterogeneous slope provided by the present invention includes the following steps:

[0086] S1. Based on the engineering geological characteristics of the study area, determine the morphological parameters of the planar concave heterogeneous slope and coal-rock mass within the study area, determine the physical and mechanical parameters of each stratum and rock mass, and construct a dataset. Specifically, the relevant parameters required for the stability calculation method of the planar concave heterogeneous slope can be basically determined from slope deformation and failure mechanism research, engineering geological models, and on-site geological surveys. For example, the morphological parameters of the planar concave heterogeneous slope and coal-rock mass within the study area include: the arch height a of the arc between the slope crest line and the slope bottom line, the length 2b of the concave slope direction; the slope height H, the slope angle δ; and the range of the potential sliding surface in the direction of the planar concave heterogeneous slope, etc.

[0087] S2, based on datasets and 3D numerical simulation techniques, establishes the spatial morphological equations of the potential sliding surface of a planar concave heterogeneous slope, specifically including:

[0088] S201, with the origin 0 at the toe of the main slip line of the potential slip surface, a three-dimensional coordinate system is established. The planar concave slope is determined by three parameters: the arch height *a* of the circular arcs at the top and bottom of the slope, the half-width *b* of the slope direction, and the planar radius of curvature *R*. The slope from the top to the bottom of the slope is a series of coaxial circular arcs. The planar radius of curvature of the top line is *Rs*, and the planar radius of curvature of the bottom line is *Rx*. The slope angle of the main slip line profile of the planar concave slope is *δ*. The relationship of the planar radius of curvature *R* is:

[0089]

[0090] The tangent of the slope angle is expressed as tanδ = H / (R s -R x After conversion, we get R. s The ratio to the slope height H is:

[0091] R s / H=R x / H+cotδ (2)

[0092] S202, treating the potential sliding surface as an ellipsoid, with a landslide mode of circular arc sliding, the spatial morphology equations of the potential sliding surface include the sliding surface equation and the slope equation; the sliding surface equation uses the ellipsoidal equation z. h This is represented as:

[0093]

[0094] Where A, B, and C are the coefficients of the ellipsoid equation, representing the radii of curvature of the ellipsoid in the x, y, and z directions; x0, y0, and z0 are the spatial coordinates of the center of the ellipsoid.

[0095] Slope equation z p The regions are represented as follows:

[0096]

[0097] S3, based on the spatial morphology equation, divides the potential slip surface into i rows and j columns of micro-strips, solves for the total anti-slip force and total sliding force of each row of micro-strips superimposed on the main slip line, and determines the two-dimensional equivalent mechanical parameters of the three-dimensional effect; specifically including:

[0098] S301, the ellipsoid is divided into i rows and j columns of micro-strips. Using constitutive relations and static equilibrium conditions, the force state of the micro-strips is solved, yielding the volume forces acting on the base of the micro-strips. Specifically, the length and width of the micro-strip in the i-th row and j-th column are defined as dx and dy, and its height as z. p -z ij The horizontal distance from the main slide line is s, and the coordinates of the center point of the micro-strip column are (x, y, s). ij ,y ij ,zij The angle between the bottom interface of the micro-strip column and the x-axis in the global coordinate system is α. x The angle between the y-axis and the y-axis is α. y ;

[0099] The volume force on the base of the micro-strip column is:

[0100] dW=γ ij (z p -z ij )sinθdA (5)

[0101] Where γ is the unit weight of the rock and soil mass, z ij γ is the height of the base of the micro-strip column; ij Let be the soil unit weight of the micro-strip column in the i-th row and j-th column.

[0102] The angle between the base of the micro-strip column and the x0y plane is θ, and the parameters of θ are:

[0103]

[0104]

[0105] The area dA of the base of the micro-strip column is:

[0106]

[0107] Where dx and dy are the differential lengths of the base of the micro-strip column along the x and y axes, respectively;

[0108] S302, the area between the ellipsoid and the slope crest line is designated as Region I, and the area from the slope crest line to the slope bottom line is designated as Region II. The sliding force and anti-slip force of each row of micro-strip columns are solved for each region; specifically including:

[0109] Let α be the angle between the horizontal projection of the base of the non-principal slide bar and the micro-strip bar on the i-th row of the principal slide bar. i Let P0 be the center point of the main slide bar on the i-th row, with coordinates (x0, y0, z0). Let P be the center point of the non-main slide bar micro-strip column. n Coordinates are (x ij ,y ij ,z ij );

[0110]

[0111] Anti-slip force T of micro-strip column in region I x1 and downward force F x1 They are respectively:

[0112]

[0113]

[0114] Where N1 is the normal pressure of the micro-strip column on the ellipsoidal region I, and N;c ij Let be the cohesion of the microstrip column in the i-th row and j-th column; It is the internal friction angle; The meaning, Let z be the internal friction angle of the micro-strip column in the i-th row and j-th column; ij-I Let z be the center point z of the bottom surface of the micro-strip column in the i-th row and j-th column of region I; θ1 is the angle between the normal of the bottom interface of the micro-strip column and the normal of the ellipsoid, in °;

[0115] Anti-slip force T of micro-strip columns in region II x2 and downward force F x2 They are respectively:

[0116]

[0117]

[0118] Among them, z ij-II Let z be the coordinate of the center point of the bottom surface of the microbar column in the i-th row and j-th column of region II.

[0119] S303, the sliding force and anti-slip force of each row of micro-strips are superimposed on the main sliding line to obtain the total anti-slip force and total sliding force of each row of micro-strips; specifically including:

[0120] The total anti-slip force of the micro-strip in row k is T. k The total downward force is F k for:

[0121]

[0122]

[0123] In the formula, Σ l This indicates summing all columns in the k-th row; l represents the column number; c kl This represents the soil cohesion in the k-th row and l-th column; This represents the internal friction angle of the soil in the k-th row and l-th column;

[0124] Let T be the total anti-slip force of the microbar in the k-th row. k Total downward force F k These are respectively equal to the anti-slip force T of the micro-strip column in the k-th row of the main slip line. xk , downward force F xk ,Right now:

[0125] T k =T xk (16)

[0126] F k =Fxk (17)

[0127] Where x represents the main slide line.

[0128] S304, wherein S304 determines the two-dimensional equivalent mechanical parameters of the three-dimensional effect, including equivalent bulk density, equivalent cohesion, and internal friction angle, specifically including:

[0129] α xij α yij Let sinθ1 and cosθ1 be the angles between the bottom surface of the i-th row of microstrip columns and the x-axis and y-axis, respectively. Substituting sinθ1 and cosθ1 into equations (14) and (15) above, we obtain the equivalent shear strength parameters of the bottom interface of the k-th row of main sliding line microstrip columns, including the equivalent unit weight γ. k Equivalent cohesion c k and internal friction angle

[0130] In region I, the equivalent bulk density γ at the bottom interface of the micro-strip column of the k-th row of the main sliding line k Equivalent cohesion c k and internal friction angle They are represented as follows:

[0131]

[0132]

[0133]

[0134] In region II, the equivalent unit weight γ of the interface at the bottom of the micro-strip column of the k-th row main slide line. k Equivalent cohesion c k and internal friction angle They are represented as follows:

[0135]

[0136]

[0137]

[0138] The difference between Region I and Region II lies in the different slope range of the micro-strip column in the i-th row and j-th column.

[0139] S4. Two-dimensional equivalent mechanical parameters are introduced into the rigid body limit equilibrium method (e.g., the unbalanced thrust transfer method) to transform the three-dimensional slope stability problem into an equivalent two-dimensional rigid body limit equilibrium problem. The appropriate rigid body limit equilibrium algorithm is selected according to the landslide mode to obtain the stability coefficient of the planar concave heterogeneous slope.

[0140] In this embodiment, taking the Nanfen open-pit iron mine as an example, the slope height H is 216m and the slope angle δ is 32°, as measured by the planar concave slope model at the southwest corner of the southern end of the Nanfen open-pit iron mine. Using the three-dimensional stability determination method for planar concave heterogeneous slopes, the slip surface is divided into two regions: ellipsoidal region I and ellipsoidal region II. Figure 2 This is a typical cross-sectional view of the concave slope at the southwest corner of the southern end of the slope, with the toe of the slope as the origin O and the radius R of the ellipsoid at the rear edge of the landslide body. a =691.95m, major axis R in the y-axis direction b =215.57m.

[0141] This embodiment presents a method for calculating the stability of a planar concave heterogeneous slope, comprising the following steps:

[0142] Step 1: Based on the research on slope deformation and failure mechanism, engineering geological model and on-site geological survey, determine the relevant parameters required for the three-dimensional stability equivalent algorithm of the planar concave slope. In this embodiment, according to the preliminary design, the slope height H is 216m, the slope angle δ is 32°, the slope direction length is about 2b = 702m, and the height of the circular arch at the top of the slope is a = 71.45m.

[0143] Based on previous geological exploration and physical and mechanical tests of soil and rock, the physical and mechanical parameters of the slope rock mass were determined. In this embodiment, based on previous geological exploration and physical and mechanical tests of soil and rock, the physical and mechanical parameters of the soil and rock are shown in Table 1.

[0144] Table 1 Physical and Mechanical Parameters of Slope Soil and Rock Mass

[0145]

[0146]

[0147] Step 2: Establish the spatial slip surface morphology equation. In this embodiment, the slope instability mechanism is studied through three-dimensional numerical simulation to obtain three-dimensional transverse and longitudinal slice profile locations, such as... Figure 3 As shown. The cross-sectional sliding surface morphology is arc-shaped, so the landslide mode of the slope is arc sliding. The results show that for planar concave slopes with different radii of curvature, the spatial morphology equation of the sliding surface can be expressed by the local ellipsoidal surface equation, as shown in formulas (1) and (2).

[0148] Step 3: Superimpose the mechanical effects of the bottom surface of the micro-strip columns, solve for the sliding force and anti-sliding force of each row of micro-strip columns in different slope areas, and determine the equivalent physical and mechanical parameters; In this embodiment, under the condition of fixed boundary of the upper part of the concave slope at the southwest corner of the south end of the Nanfen open-pit iron mine, the arch height a of the circular arc at the top of the concave slope is continuously changed to explore the influence law of the radius of curvature on the stability of the three-dimensional concave slope. According to the slope equation (2), the radius of curvature Ra is constrained by the projected length of the slope surface (i.e. Ra≥360.82m), so the range of the arch height a is determined to be 0~71.45m, and a=15, 30, 45, 60, 65, 71.45m is selected.

[0149] Step 301: Divide the ellipsoid into micro-strips with i rows and j columns. Solve for the force state of the micro-strips using constitutive relations and static equilibrium conditions; for example... Figure 4 .

[0150] Step 302: Divide the area between the ellipsoid and the slope crest line into Region I, and the area from the slope crest line to the slope bottom line into Region II, as follows: Figure 5 The sliding force F and anti-slip force T of each row of micro-strips are solved by dividing the area.

[0151] Step 303: Add the forces of each row of small bars to the main sliding line to obtain the total anti-slip force and total sliding force of each row;

[0152] Step 304: Solve for the two-dimensional equivalent mechanical parameters of the three-dimensional effect; obtain the equivalent shear strength parameters of each block in each stage of the potential sliding surface main sliding line, as shown in Tables 2 to 7.

[0153] Table 2. Equivalent shear strength parameters of the main sliding line block of the potential sliding surface when the arch height a = 15m.

[0154]

[0155] Table 3. Equivalent shear strength parameters of the main sliding line block of the potential sliding surface when the arch height a = 30m.

[0156]

[0157]

[0158] Table 4. Equivalent shear strength parameters of the main sliding line block of the potential sliding surface when the arch height a = 45m.

[0159]

[0160] Table 5. Equivalent shear strength parameters of the main sliding line block of the potential sliding surface when the arch height a = 60m.

[0161]

[0162]

[0163] Table 6. Equivalent shear strength parameters of the main sliding line block of the potential sliding surface when the arch height a = 65m.

[0164]

[0165] Table 7. Equivalent shear strength parameters of the main sliding line block of the potential sliding surface when the arch height a = 71.45m.

[0166]

[0167]

[0168] Step 4: Introduce the equivalent physical and mechanical parameters into the two-dimensional rigid body limit equilibrium method—the unbalanced thrust transfer method—to obtain the stability coefficient F. s ;

[0169] The two-dimensional rigid body limit equilibrium method selects a two-dimensional section of the principal slip line, divides the section into blocks, and uses the anti-slip force and sliding force of each bottom surface to solve for the stability coefficient:

[0170]

[0171] W k =γ k dxk (25)

[0172] Q k =W k sinθ k (26)

[0173]

[0174]

[0175] Where, ψ k W is the thrust transfer coefficient on the side of the k-th block; k Let dx be the weight of the k-th block. k θ is the width of the k-th block; k Let θ be the angle θ between the bottom surface of the micro-strip column in the k-th row of the main slide line and the x0y plane; Q k R is the anti-slip force on the bottom surface of the k-th block; k F is the sliding force on the bottom surface of the k-th block; s The stability coefficient is a three-dimensional coefficient. The two-dimensional rigid body limit equilibrium method selects a two-dimensional section of the main sliding line, divides the section into blocks, and uses the anti-slip force and sliding force on the bottom surface of each block to solve for the stability coefficient.

[0176] The calculated three-dimensional stability coefficients of concave slopes with different radii of curvature are shown in Table 8.

[0177] Table 8. Stability Coefficients of Three-Dimensional Concave Slopes with Different Radius of Curvature

[0178]

[0179] Plot the relationship curve between the radius of curvature and the three-dimensional stability coefficient of the concave slope, as follows: Figure 6 As shown, it can be seen that as the height of the circular arch at the top of the concave slope gradually decreases, the radius of curvature gradually increases, the degree of concavity of the concave slope decreases, and the three-dimensional stability coefficient decreases and then tends to stabilize, exhibiting an exponential function relationship.

[0180] In summary, this invention provides a method for calculating the stability of planar concave heterogeneous slopes. Based on three-dimensional numerical simulation technology, the method first determines the spatial morphology equation of the potential slip surface by identifying its failure mode. Then, the slip surface is divided into micro-strips, and the stress state of the micro-strips is solved through constitutive relations and static equilibrium conditions. The forces of each row of micro-strips are superimposed along the main slip line, and the equivalent shear strength parameters with three-dimensional effects on the micro-strips of each row of main slip lines are obtained using the equivalent concept. Finally, the theoretical formula for the stability coefficient of the three-dimensional planar concave slope is derived using the rigid body limit equilibrium method. The results of this research effectively solve the three-dimensional stability problem of planar concave slopes, providing a more reliable theoretical technology for mining engineering.

[0181] This invention also provides a planar concave heterogeneous slope stability calculation system, applied to the above-mentioned planar concave heterogeneous slope stability calculation method, comprising:

[0182] The dataset construction module is used to determine the morphological parameters of the planar concave heterogeneous slope and coal and rock mass in the study area based on the engineering geological characteristics of the study area, determine the physical and mechanical parameters of the strata and rock masses in each area, and construct the dataset.

[0183] The spatial morphology equation establishment module is used to establish the spatial morphology equation of the potential sliding surface of a planar concave heterogeneous slope based on datasets and three-dimensional numerical simulation technology.

[0184] The two-dimensional equivalent mechanical parameter determination module is used to divide the potential slip surface into i rows and j columns of micro-strips based on the spatial morphology equation, solve for the total anti-slip force and total sliding force of each row of micro-strips superimposed on the main slip line, and determine the two-dimensional equivalent mechanical parameters of the three-dimensional effect.

[0185] The stability coefficient solution module is used to introduce two-dimensional equivalent mechanical parameters into the rigid body limit equilibrium method, transforming the three-dimensional slope stability problem into an equivalent two-dimensional rigid body limit equilibrium problem, and solving for the stability coefficient of the planar concave heterogeneous slope.

[0186] The present invention also provides an electronic device comprising one or more processors; a memory; and one or more application programs, wherein the one or more application programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs being configured to perform the stability calculation method for a planar concave heterogeneous slope as described above.

[0187] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the above-described method for calculating the stability of a planar concave heterogeneous slope.

[0188] Of course, those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware (such as a processor, controller, etc.). The program can be stored in a computer-readable storage medium, and when executed, it can include the processes described in the above method embodiments. The storage medium can be a memory, magnetic disk, optical disk, etc.

[0189] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for calculating the stability of a planar concave heterogeneous slope, characterized in that, Includes the following steps: S1. Based on the engineering geological characteristics of the study area, determine the morphological parameters of the planar concave heterogeneous slope and coal and rock mass in the study area, determine the physical and mechanical parameters of the strata and rock mass in each area, and construct a dataset. S2. Based on datasets and three-dimensional numerical simulation technology, the spatial morphological equation of the potential sliding surface of a planar concave heterogeneous slope is established. S3, based on the spatial morphology equation, divide the potential slip surface into i rows and j columns of micro-strips, solve for the total anti-slip force and total sliding force of each row of micro-strips superimposed on the main slip line, and determine the two-dimensional equivalent mechanical parameters of the three-dimensional effect; S4 introduces two-dimensional equivalent mechanical parameters into the rigid body limit equilibrium method, transforming the three-dimensional slope stability problem into an equivalent two-dimensional rigid body limit equilibrium problem, and solving it to obtain the stability coefficient of the planar concave heterogeneous slope.

2. The method for calculating the stability of a planar concave heterogeneous slope according to claim 1, characterized in that, In step S1, the morphological parameters of the planar concave heterogeneous slope and coal-rock mass within the study area include: The arch height a of the arc between the top and bottom slopes, the length 2b of the concave slope direction; the slope height H, the slope angle δ; and the range of the potential sliding surface in the direction of the planar concave heterogeneous slope.

3. The method for calculating the stability of a planar concave heterogeneous slope according to claim 2, characterized in that, In step S2, based on the dataset and three-dimensional numerical simulation technology, the spatial morphological equation of the potential sliding surface of the planar concave heterogeneous slope is established, specifically including: S201. A three-dimensional coordinate system is established with the origin 0 at the toe of the main sliding line of the potential sliding surface of the planar concave heterogeneous slope. The planar concave heterogeneous slope is determined by three parameters: the arch height *a* of the circular arcs between the slope crest and slope base, half the length of the concave slope direction *b*, and the plane radius of curvature *R*. The planar concave heterogeneous slope consists of a series of coaxial circular arcs from the slope crest to the slope base, with the plane radius of curvature of the slope crest being *R*. s The radius of curvature of the lower slope baseline plane is R. x The slope angle of the main sliding profile is δ; the relationship between the plane curvature radius R and the slope angle is: The tangent of the slope angle is expressed as tanδ = H / (R s -R x After conversion, we get R. s The ratio to the slope height H is: R s / H=R x / H+cotδ (2) S202, treating the potential sliding surface as an ellipsoid, with a landslide mode of circular arc sliding, the spatial morphology equations of the potential sliding surface include the sliding surface equation and the slope equation; the sliding surface equation uses the ellipsoidal equation z. h This is represented as: Where A, B, and C are the coefficients of the ellipsoid equation, representing the radii of curvature of the ellipsoid in the x, y, and z directions; x0, y0, and z0 are the spatial coordinates of the center of the ellipsoid. Slope equation z p The regions are represented as follows:

4. The method for calculating the stability of a planar concave heterogeneous slope according to claim 3, characterized in that, In step S3, based on the spatial morphology equation, the potential slip surface is divided into i rows and j columns of micro-strips. The total anti-slip force and total sliding force of each row of micro-strips superimposed on the main slip line are solved to determine the two-dimensional equivalent mechanical parameters of the three-dimensional effect, specifically including: S301, divide the ellipsoid into i rows and j columns of micro-strips, solve the force state of the micro-strips through constitutive relations and static equilibrium conditions, and obtain the volume force on the bottom surface of the micro-strips; S302, the area between the ellipsoid and the top of the slope is divided into region I, and the area from the top of the slope to the bottom of the slope is divided into region II. The sliding force and anti-sliding force of each row of micro-strip columns are solved in each region. S303, the sliding force and anti-slip force of each row of micro-strips are superimposed on the main sliding line to obtain the total anti-slip force and total sliding force of each row of micro-strips; S304 determines the two-dimensional equivalent mechanical parameters of the three-dimensional effect, including equivalent bulk density, equivalent cohesion, and internal friction angle.

5. The method for calculating the stability of a planar concave heterogeneous slope according to claim 4, characterized in that, In step S301, the force state of the micro-strip column is solved to obtain the volume force on the bottom surface of the micro-strip column, which specifically includes: Define the length and width of the microbar in the i-th row and j-th column as dx and dy, and its height as z. p -z ij The horizontal distance from the main slide line is s, and the coordinates of the center point of the micro-strip column are (x, y, s). ij ,y ij ,z ij The angle between the bottom interface of the micro-strip column and the x-axis in the global coordinate system is α. x The angle between the y-axis and the y-axis is α. y ; The volume force on the base of the micro-strip column is: dW=γ ij (With p -With ij )sinθdA (5) Among them, z ij γ is the height of the base of the micro-strip column; ij Let be the soil unit weight of the micro-strip column in the i-th row and j-th column; The angle between the base of the micro-strip column and the x0y plane is θ, and the parameters of θ are: The area dA of the base of the micro-strip column is: Where dx and dy are the differential lengths of the base of the micro-strip column along the x and y axes, respectively.

6. The method for calculating the stability of a planar concave heterogeneous slope according to claim 5, characterized in that, S302 defines region I as the area between the ellipsoid and the slope crest line, and region II as the area from the slope crest line to the slope bottom line. The sliding force and anti-slip force of each row of micro-strips are then calculated for each region, specifically including: Let α be the angle between the horizontal projection of the base of the non-principal slide bar and the micro-strip bar on the i-th row of the principal slide bar. i Let P0 be the center point of the main slide bar on the i-th row, with coordinates (x0, y0, z0). Let P be the center point of the non-main slide bar micro-strip column. n Coordinates are (x ij ,y ij ,z ij ); Anti-slip force T of micro-strip column in region I x1 and downward force F x1 They are respectively: Where N1 is the normal pressure of the microstrip column on the ellipsoidal region; c ij Let be the cohesion of the microstrip column in the i-th row and j-th column; It is the internal friction angle; Let z be the internal friction angle of the micro-strip column in the i-th row and j-th column; ij-I Let z be the center point z of the bottom surface of the micro-strip column in the i-th row and j-th column of region I; θ1 is the angle between the normal of the bottom interface of the micro-strip column and the normal of the ellipsoid. Anti-slip force T of micro-strip columns in region II x2 and downward force F x2 They are respectively: Among them, z ij-II Let z be the coordinate of the center point of the bottom surface of the microbar column in the i-th row and j-th column of region II.

7. The method for calculating the stability of a planar concave heterogeneous slope according to claim 6, characterized in that, In step S303, the sliding force and anti-slip force of each row of micro-strips are superimposed onto the main sliding line to obtain the total anti-slip force and total sliding force of each row of micro-strips, specifically including: The total anti-slip force of the micro-strip in row k is T. k The total downward force is F k for: In the formula, Σ l This indicates summing all columns in the k-th row; l represents the column number; c kl This represents the soil cohesion in the k-th row and l-th column; This represents the internal friction angle of the soil in the k-th row and l-th column; Let T be the total anti-slip force of the microbar in the k-th row. k Total downward force F k These are respectively equal to the anti-slip force T of the micro-strip column in the k-th row of the main slip line. xk , downward force F xk ,Right now: T k =T xk (16) F k =F xk (17) Where x represents the main slide line.

8. The method for calculating the stability of a planar concave heterogeneous slope according to claim 7, characterized in that, S304 determines the two-dimensional equivalent mechanical parameters of the three-dimensional effect, including equivalent bulk density, equivalent cohesion, and internal friction angle, specifically including: α xij α yij Let sinθ1 and cosθ1 be the angles between the bottom surface of the i-th row of microstrip columns and the x-axis and y-axis, respectively. Substituting sinθ1 and cosθ1 into equations (14) and (15) above, we obtain the equivalent shear strength parameters of the bottom interface of the k-th row of main sliding line microstrip columns, including the equivalent unit weight γ. k Equivalent cohesion c k and internal friction angle In region I, the equivalent bulk density γ at the bottom interface of the micro-strip column of the k-th row of the main sliding line k Equivalent cohesion c k and internal friction angle They are represented as follows: In region II, the equivalent unit weight γ of the interface at the bottom of the micro-strip column of the k-th row main slide line. k Equivalent cohesion c k and internal friction angle They are represented as follows:

9. A planar concave heterogeneous slope stability calculation system, applied to the planar concave heterogeneous slope stability calculation method according to any one of claims 1-8, characterized in that, include: The dataset construction module is used to determine the morphological parameters of the planar concave heterogeneous slope and coal and rock mass in the study area based on the engineering geological characteristics of the study area, determine the physical and mechanical parameters of the strata and rock masses in each area, and construct the dataset. The spatial morphology equation establishment module is used to establish the spatial morphology equation of the potential sliding surface of a planar concave heterogeneous slope based on datasets and three-dimensional numerical simulation technology. The two-dimensional equivalent mechanical parameter determination module is used to divide the potential slip surface into i rows and j columns of micro-strips based on the spatial morphology equation, solve for the total anti-slip force and total sliding force of each row of micro-strips superimposed on the main slip line, and determine the two-dimensional equivalent mechanical parameters of the three-dimensional effect. The stability coefficient solution module is used to introduce two-dimensional equivalent mechanical parameters into the rigid body limit equilibrium method, transforming the three-dimensional slope stability problem into an equivalent two-dimensional rigid body limit equilibrium problem, and solving for the stability coefficient of the planar concave heterogeneous slope.

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