V-shaped slope stability calculation method and system

Abstract

The invention discloses a V-shaped slope stability calculation method and system, and relates to the technical field of open-pit mining. On the basis of a three-dimensional numerical simulation technology, the damage mode of the sliding body is judged, a spatial form equation of a potential sliding body is determined firstly, then the sliding body is divided into micro-strip columns in a regional mode, the stress state of the micro-strip columns is solved through a constitutive relation and a static balance condition, and the force of each row of micro-strip columns is superposed in the direction of a main sliding surface; and obtaining two-dimensional equivalent shear strength parameters with a three-dimensional effect on each row of main sliding surface micro-strip columns by using an equivalent thought, and then deducing a three-dimensional V-shaped slope stability coefficient by using a rigid body limit equilibrium method. According to the method, the problems of high calculation cost, difficulty in parameter determination and complex calculation process in a traditional slope three-dimensional stability calculation method are avoided, the problem of three-dimensional stability of the slope in the special form is solved, a more reliable theoretical technology is provided for design, mining, prevention and treatment of the slope, and the method is worthy of popularization and application. The method has important practical significance for guaranteeing safe and efficient production of mining.

Description

Technical Field

[0001] The present invention belongs to the technical field of open-pit mining, and specifically relates to a calculation method and system for the stability of a V-shaped slope. Background Art

[0002] Restricted by factors such as orebody occurrence conditions, mining rights boundaries, and important surface facilities, the plane shapes of slopes in most open-pit mines are irregular or have complex structures. However, existing calculation methods cannot consider the quantitative impact of irregular shapes on slope stability. Many experts and scholars have achieved fruitful results in the research on the calculation methods for the stability of irregular-shaped slopes.

[0003] Patent CN 115081214 A discloses a three-dimensional stability calculation method for a plane polyline convex slope, establishes a mathematical model of the three-dimensional mechanical effect of the plane polyline convex slope, and obtains the three-dimensional stability coefficient of the plane polyline convex slope based on the residual thrust method; Patent CN115391897A discloses a three-dimensional stability calculation method for a slope under the action of transverse mining and internal dumping pressure in an open-pit mine. According to the shape of the slope in the mining area, the weak plane of the sliding body, and the shape of the potential sliding surface, a spatial shape equation of the potential sliding surface is established, and the three-dimensional slope stability problem is transformed into a two-dimensional problem for solution to calculate the stability coefficient; Patent CN118886194A discloses a method for evaluating the stability of a slope containing an inverse-dipping fault. First, obtain information such as the name, location, length, dip direction, dip angle, strike, and fault property of the inverse-dipping fault, establish a slope model containing the inverse-dipping fault, and perform stability analysis and numerical simulation calculations; Patent CN115081214B discloses a three-dimensional stability calculation method for a plane polyline convex slope. The sliding surface of the plane polyline convex slope is regarded as an ellipsoid or a combination of an ellipsoid and a weak plane, a sliding surface equation and a two-dimensional equivalent mathematical model of the three-dimensional stability of the plane polyline convex slope are established, and finally the three-dimensional stability coefficient of the plane polyline convex slope is calculated using the residual thrust method, avoiding the problems of poor numerical convergence and complex calculation process in the traditional three-dimensional slope stability calculation method, and effectively solving the problems of slope stability analysis and design under such conditions. These patents have studied the three-dimensional stability calculation methods for slopes with several special shapes or structures, and some have separately studied the stability calculation methods for slopes containing faults and under the action of transverse mining and internal dumping pressure, but have not considered slopes with special shapes such as V-shaped slopes existing in open-pit coal mines such as Hesig Ulan South Open-pit Coal Mine and Girande Open-pit Coal Mine, and there have been no relevant reports yet. Therefore, there is an urgent need to seek a calculation method and system for the stability of V-shaped slopes to improve the three-dimensional stability calculation method system for special-shaped slopes in open-pit mines and provide technical support for the slope engineering design, mining, and treatment of open-pit coal mines. Summary of the Invention

[0004] Aiming at the deficiencies of the prior art, the purpose of the present invention is to provide a method and system for calculating the stability of a V-shaped slope, which combines the special terrain of the open-pit mine V-shaped slope and calculates its stability coefficient based on the limit equilibrium theory and the spatial mechanical effect of the slope, which is simple and efficient, filling the gap in the research on the three-dimensional stability problem of the V-shaped slope.

[0005] The first aspect of the present invention provides a method for calculating the stability of a V-shaped slope, including the following steps:

[0006] S1: Determine the morphological parameters of the V-shaped slope and the physical and mechanical parameters of each stratum rock mass within the research area;

[0007] Specifically, select the origin according to the characteristics of the V-shaped slope within the research area, take the direction perpendicular to the slope strike as the positive direction of the X-axis, the direction parallel to the strike as the positive direction of the Y-axis, and the direction perpendicular to the ground upward as the positive direction of the Z-axis to establish a three-dimensional coordinate system. The morphological parameters of the V-shaped slope within the research area include: slope height H, slope angle δ, the angle β between the inclined weak plane and the direction parallel to the slope strike, the angle ψ between the inclined weak plane and the direction perpendicular to the ground, and the angle v between the projection of the intersection line of the inclined weak plane and the slope surface on the horizontal plane and the slope strike direction; the physical and mechanical parameters of each stratum rock mass include soil unit weight γ, cohesion c, and internal friction angle The inclined weak plane is symmetrically dipping downstream;

[0008] S2: Based on the morphological parameters of the V-shaped slope and the physical and mechanical parameters of each stratum rock mass within the research area, establish the spatial morphological equation of the potential sliding mass of the V-shaped slope; the spatial morphological equation of the potential sliding mass includes the slope surface equation, the ellipsoid surface equation, and the inclined weak plane equation;

[0009] Based on the three-dimensional coordinate system established in S1, determine the slope surface equation z of the V-shaped slope p ;

[0010]

[0011] Among them, tanδ represents the tangent value of the slope angle, (x, y, z) are the spatial coordinates in the three-dimensional coordinate system, x is the component in the X-axis direction of the spatial coordinates, y is the component in the Y-axis direction of the spatial coordinates, and z is the component in the Z-axis direction of the spatial coordinates;

[0012] Based on the three-dimensional coordinate system established in S1, determine the ellipsoid surface equation of the V-shaped slope;

[0013]

[0014] Among them, R a and R b are the coefficients of the ellipsoid surface equation respectively, representing the radii of curvature of the ellipsoid surface in the X and Y directions; (x0 , y 0 , z 0 ) are the spatial coordinates of the center of the ellipsoid surface, x 0 is the component in the X-axis direction of the spatial coordinates of the center of the ellipsoid surface, y 0 is the component in the Y-axis direction of the spatial coordinates of the center of the ellipsoid surface, z 0 is the component in the Z-axis direction of the spatial coordinates of the center of the ellipsoid surface;

[0015] Based on the three-dimensional coordinate system established in S1, determine the inclined weak plane equation of the V-shaped slope;

[0016] The inclined weak layer is symmetrically distributed with respect to the XOZ plane. Set the inclined weak plane equation on the left side of the XOZ plane as g 1 , and the inclined weak plane equation on the right side of the XOZ plane as g 2 . According to the angles between the inclined weak plane and the X-axis and Y-axis, the inclined weak plane equation is obtained as:

[0017]

[0018] S3: Divide the potential sliding mass of the V-shaped slope into micro-strip columns with m rows and n columns. Based on the spatial shape equation of the potential sliding mass of the V-shaped slope, solve the total anti-sliding force and total sliding-down force of each row of micro-strip columns in the potential sliding mass;

[0019] S301: Divide the potential sliding mass into micro-strip columns with m rows and n columns. Through the constitutive relationship and static equilibrium conditions, solve the stress state of each micro-strip column to obtain the body force received by the bottom surface of the micro-strip column;

[0020] The body force received by the bottom surface of the micro-strip column is:

[0021] dW = γ ij (z pij - z ij )sinθdA (6)

[0022] Among them, dW is the body force received by the bottom surface of the micro-strip column; z p - z ij is the height of the micro-strip column in the i-th row and j-th column, z pij is the height of the top surface of the micro-strip column in the i-th row and j-th column, z ij is the height of the bottom surface of the micro-strip column in the i-th row and j-th column; γ ij is the soil unit weight of the micro-strip column in the i-th row and j-th column, dA is the bottom surface area of the micro-strip column, and θ is the angle between the bottom surface of the micro-strip column and the XOY plane. There is:

[0023]

[0024]

[0025] Among them, αxij is the angle between the bottom interface of the micro-strip column in the i-th row and j-th column and the X-axis in the three-dimensional coordinate system, α yij is the angle between the bottom interface of the micro-strip column in the i-th row and j-th column and the Y-axis in the three-dimensional coordinate system;

[0026] The bottom surface area dA of the micro-strip column is:

[0027]

[0028] where dx is the differential length of the micro-strip column along the X-axis, and dy is the differential length of the micro-strip column along the Y-axis;

[0029] S302: Solve the sliding force and anti-sliding force of each micro-strip column according to the volume force on the bottom surface of the micro-strip column;

[0030] The angle between the projection of the bottom surface of the micro-strip column on the non-main sliding surface with an ellipsoidal bottom interface of the potential sliding mass and the micro-strip column in the i-th row on the main sliding surface is α i , and the main sliding surface is the central plane of the potential sliding mass;

[0031]

[0032] where the center point P of the micro-strip column in the i-th row on the main sliding surface 0 has coordinates (x 1 , 0, z 1 ), and the center point P of the micro-strip column in the i-th row and j-th column on the non-main sliding surface n has coordinates (x pij , y pij , z pij );

[0033] Therefore, the anti-sliding force T ij-d1 and the sliding force F ij-d1 of the micro-strip column in the i-th row and j-th column with an ellipsoidal bottom interface of the potential sliding mass are respectively:

[0034] where N 1 is the normal pressure of the micro-strip column on the ellipsoid surface, N; c ij is the cohesion of the micro-strip column in the i-th row and j-th column; θ 1 is the angle between the normal of the bottom interface of the micro-strip column and the normal of the ellipsoid surface; is the internal friction angle of the micro-strip column in the i-th row and j-th column;

[0035] The anti-sliding force T ij-d2 and the sliding force F ij-d2 of the micro-strip column in the i-th row and j-th column with an inclined bottom interface of the potential sliding mass are respectively:

[0036]

[0037] S303: Calculate the total anti-sliding force and total sliding force of the micro-strip columns in the i-th row according to the sliding force and anti-sliding force of each micro-strip column.

[0038] When the bottom interface of the potential sliding mass is an ellipsoidal surface, the total anti-sliding force and total sliding force of the micro-strip columns in the i-th row are:

[0039]

[0040] F i1 = ∑ i F(i,j) = 2∑ i [dWsin(θ 1 + α i )], y > 0 (16)

[0041] In the formula, T i1 is the total anti-sliding force of all column micro-strip columns in the i-th row where the bottom interface of the potential sliding mass is an ellipsoidal surface, F i1 is the total sliding force of all column micro-strip columns in the i-th row where the bottom interface of the potential sliding mass is an ellipsoidal surface, Σ i represents the summation of all columns with y > 0 in the i-th row; T(i,j) is the anti-sliding force of the micro-strip column in the i-th row and j-th column, and F(i,j) is the sliding force of the micro-strip column in the i-th row and j-th column.

[0042] When the bottom interface of the potential sliding mass is an inclined plane, the total anti-sliding force and total sliding force of the micro-strip columns in the i-th row are:

[0043]

[0044] F i2 = ∑ i F(i,j) = 2∑ i [dWcosψ], y > 0 (18)

[0045] Among them, T i2 is the total anti-sliding force of all column micro-strip columns where the bottom interface of the potential sliding mass is an inclined plane, F i2 is the total sliding force of all column micro-strip columns where the bottom interface of the potential sliding mass is an inclined plane;

[0046] S4: Superimpose the total anti-sliding force and total sliding force of each row of micro-strip columns on the micro-strip columns on the main sliding surface of that row, and calculate the two-dimensional equivalent shear strength parameters with three-dimensional effects; the two-dimensional equivalent shear strength parameters with three-dimensional effects include the equivalent unit weight, equivalent cohesion and internal friction angle of the bottom interface of the micro-strip columns on the main sliding surface.

[0047] S401: Let the total anti-sliding force T i and total sliding force F i of the upper micro-strip columns in the i-th row be respectively equal to the anti-sliding force T i0 and sliding force F i0, namely:

[0048] T i = T i0 (19)

[0049] F i = F i0 (20)

[0050] S402: Substitute sinθ 1 and cosθ 1 into equations (19) and (20) to obtain the equivalent unit weight, equivalent cohesion and internal friction angle of the bottom interface of the micro-strip column on the i-th row of the main sliding surface;

[0051] For the potential sliding mass with an ellipsoidal bottom interface, the equivalent unit weight γ i-1 equivalent cohesion c i-1 and internal friction angle of the bottom interface of the micro-strip column on the i-th row of the main sliding surface are respectively expressed as:

[0052]

[0053] For the potential sliding mass with an inclined bottom interface, the equivalent unit weight γ i-2 equivalent cohesion c i-2 and internal friction angle of the bottom interface of the micro-strip column on the i-th row of the main sliding surface are respectively expressed as:

[0054]

[0055] S5: Introduce the two-dimensional equivalent shear strength parameters with three-dimensional effects into the rigid limit equilibrium method, transform the three-dimensional slope stability problem into an equivalent two-dimensional rigid limit equilibrium problem, select the rigid limit equilibrium algorithm according to the landslide mode, and solve to obtain the stability coefficient of the V-shaped slope.

[0056] The second aspect of the present invention provides a V-shaped slope stability calculation system for implementing the V-shaped slope stability calculation method described above, including:

[0057] A parameter acquisition module for determining the morphological parameters of the V-shaped slope and the physical and mechanical parameters of each stratum rock mass in the research area based on the engineering geological characteristics of the research area;

[0058] A spatial morphological equation establishment module for establishing the spatial morphological equation of the potential sliding mass of the V-shaped slope based on the morphological parameters of the V-shaped slope and the physical and mechanical parameters of each stratum rock mass in the research area and three-dimensional numerical simulation technology;

[0059] The two-dimensional equivalent mechanical parameter determination module is used to divide the potential sliding mass of the V-shaped slope into micro-strip columns with m rows and n columns according to the spatial form equation of the potential sliding mass of the V-shaped slope, solve the total anti-sliding force and the total sliding-down force superimposed on the main sliding surface of each row of micro-strip columns in the potential sliding mass, and determine the two-dimensional equivalent mechanical parameters with three-dimensional effects;

[0060] The stability coefficient solving module is used to introduce the two-dimensional equivalent mechanical parameters with three-dimensional effects into the rigid body limit equilibrium method, transform the three-dimensional slope stability problem into an equivalent two-dimensional rigid body limit equilibrium problem, and solve the stability coefficient of the V-shaped slope.

[0061] A third aspect of the present invention provides an electronic device, including: a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the electronic device runs, the processor communicates with the memory through the bus. When the machine-readable instructions are executed by the processor, the steps of the V-shaped slope stability calculation method are executed.

[0062] A fourth aspect of the present invention provides a computer-readable storage medium. A computer program is stored in the computer-readable storage medium. When the computer program is run by a processor, the steps of the V-shaped slope stability calculation method are executed.

[0063] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0064] The V-shaped slope stability calculation method provided by the present invention takes into account the three-dimensional effects of the special strata and characteristic structures of the V-shaped slope. Based on the limit equilibrium theory and the equivalent idea, the three-dimensional mechanical effects of the slope are two-dimensionally equivalent, realizing the two-dimensional equivalent characterization of the three-dimensional stability of the V-shaped slope, avoiding the problems of high calculation cost, difficult parameter determination, and complex calculation process in the traditional three-dimensional slope stability calculation method, and well solving the three-dimensional stability problem of this special-shaped slope, providing more reliable theoretical technologies for the design, mining, prevention, and treatment of slopes, and having important practical significance for ensuring the safe and efficient production of mining. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0066] Figure 1 It is a flowchart of the V-shaped slope stability calculation method of the present invention;

[0067] Figure 2 Schematic diagram of a V-shaped slope in an embodiment of the present invention;

[0068] Figure 3 Position map of the three-dimensional slice profile of the V-shaped slope in an embodiment of the present invention;

[0069] Figure 4 Force analysis diagram of micro-strip columns in an embodiment of the present invention. Specific embodiments

[0070] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0071] The purpose of the present invention is to provide a method and system for calculating the stability of a V-shaped slope, solve the problems faced by the three-dimensional stability analysis of the V-shaped slope, provide more reliable theoretical technologies for mining engineering, and have good engineering application value.

[0072] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0073] On the one hand, the present invention provides a method for calculating the stability of a V-shaped slope, as Figure 1 shown, including the following steps:

[0074] S1: Based on the engineering geological characteristics of the research area, determine the morphological parameters of the V-shaped slope in the research area and the physical and mechanical parameters of each stratum rock mass;

[0075] Specifically, it can start from aspects such as the research on the slope deformation and failure mechanism, the engineering geological model, and the on-site geological measurement and inspection. Select the origin according to the characteristics of the V-shaped slope in the research area, take the direction perpendicular to the slope strike as the positive direction of the X-axis, the direction parallel to the strike as the positive direction of the Y-axis, and the direction perpendicular to the ground upward as the positive direction of the Z-axis to establish a three-dimensional coordinate system. Then, based on the established three-dimensional coordinate system, determine the relevant parameters required for the method for calculating the stability of the V-shaped slope. For example, the morphological parameters of the V-shaped slope in the research area include: slope height H, slope angle δ, the angle β between the inclined weak plane and the direction parallel to the slope strike, the angle ψ between the inclined weak plane and the direction perpendicular to the ground, and the angle v between the projection of the intersection line of the inclined weak plane and the slope surface on the horizontal plane and the slope strike direction; the physical and mechanical parameters of each stratum rock mass include soil unit weight γ, cohesion c, and internal friction angle The inclined weak plane is symmetrically inclined downstream;

[0076] In this embodiment, taking a homogeneous slope with gentle dip as an example, see Figure 2 , find the point where the symmetrically gently dipping weak plane intersects the slope surface as the origin O, the positive direction of the X-axis is perpendicular to the slope strike direction, the positive direction of the Y-axis is parallel to the strike direction, and the positive direction of the Z-axis is perpendicular to the ground upwards. The slope height is 117m, the slope angle is 20°, and the angles between the gently dipping weak plane and the X-axis and Y-axis are 9°.

[0077] Based on the previous geological exploration and geotechnical physical and mechanical test results, determine the physical and mechanical parameters of the rock masses in each stratum of the slope: In this embodiment, based on the previous geological exploration and geotechnical physical and mechanical test results, Figure 3 For the numerical simulation results of the V-shaped slope, the physical and mechanical parameters of the rock masses in each stratum are shown in Table 1.

[0078] Table 1 Physical and mechanical parameter table of the rock masses in each stratum of the slope

[0079]

[0080] S2: Based on the morphological parameters of the V-shaped slope and the physical and mechanical parameters of the rock masses in each stratum within the research area, establish the spatial morphological equation of the potential sliding mass of the V-shaped slope, specifically including:

[0081] In the embodiment, through three-dimensional numerical simulation to study the slope instability mechanism, obtain the three-dimensional transverse and longitudinal section position diagrams, as Figure 3 shown. It can be seen from the three-dimensional numerical simulation results that the potential landslide mode of the V-shaped slope is the combined sliding of an ellipsoidal surface and an inclined surface, and the potential sliding surface is regarded as the combined sliding surface of the ellipsoidal surface and the inclined surface. Therefore, the spatial morphological equation of the potential sliding mass includes the slope surface equation, the ellipsoidal surface equation, and the gently dipping weak plane equation;

[0082] Based on the three-dimensional coordinate system established in S1, determine the slope surface equation z of the V-shaped slope p ;

[0083]

[0084] Among them, tanδ represents the tangent value of the slope angle, (x, y, z) are the spatial coordinates in the three-dimensional coordinate system, x is the component in the X-axis direction of the spatial coordinates, y is the component in the Y-axis direction of the spatial coordinates, and z is the component in the Z-axis direction of the spatial coordinates;

[0085] Based on the three-dimensional coordinate system established in S1, determine the ellipsoidal surface equation of the V-shaped slope;

[0086] The general form of the ellipsoidal surface equation is expressed as:

[0087] R a (x - x 0 )2 +R b (y - y 0 ) 2 +R c (z - z 0 ) 2 =1 (2)

[0088] Among them, R a , R b and R c are the coefficients of the ellipsoid equation, representing the radii of curvature of the ellipsoid in the X, Y, and Z directions; (x 0 , y 0 , z 0 ) are the spatial coordinates of the center of the ellipsoid, x 0 is the component of the spatial coordinates of the center of the ellipsoid in the X-axis direction, y 0 is the component of the spatial coordinates of the center of the ellipsoid in the Y-axis direction, z 0 is the component of the spatial coordinates of the center of the ellipsoid in the Z-axis direction;

[0089] Since the ellipsoid is symmetric about the XOZ plane and the sliding surface is an arc in the XOZ section, the ellipsoid equation z h can also be expressed as:

[0090]

[0091] Based on the three-dimensional coordinate system established in S1, determine the inclined weak bedding plane equation of the V-shaped slope;

[0092] The inclined weak layer is symmetrically distributed about the XOZ plane. Set the inclined weak bedding plane equation on the left side of the XOZ plane as g 1 , and the inclined weak bedding plane equation on the right side of the XOZ plane as g 2 . The general form of the inclined weak bedding plane equation can be expressed as:

[0093]

[0094] Among them: A 1 , B 1 , C 1 , D 1 , A 2 , B 2 , C 2 and D 2 are all the coefficients of the inclined weak bedding plane;

[0095] According to the angles between the inclined weak bedding plane and the X-axis and Y-axis, the inclined weak bedding plane equation can be obtained as:

[0096]

[0097] S3: Divide the potential sliding mass of the V-shaped slope into micro-strip columns arranged in m rows and n columns. Based on the spatial shape equation of the potential sliding mass of the V-shaped slope, solve the total anti-sliding force and total sliding-down force of each row of micro-strip columns in the potential sliding mass.

[0098] S301: Divide the potential sliding mass into micro-strip columns arranged in m rows and n columns. Solve the stress state of each micro-strip column through the constitutive relationship and static equilibrium conditions, such as Figure 4 , and obtain the body force acting on the bottom surface of the micro-strip column.

[0099] The body force acting on the bottom surface of the micro-strip column is:

[0100] dW = γ ij (z pij -z ij )sinθdA (6)

[0101] where dW is the body force acting on the bottom surface of the micro-strip column; z p -z ij is the height of the micro-strip column in the i-th row and j-th column, z pij is the height of the top surface of the micro-strip column in the i-th row and j-th column, z ij is the height of the bottom surface of the micro-strip column in the i-th row and j-th column; γ ij is the unit weight of the soil mass of the micro-strip column in the i-th row and j-th column, dA is the bottom surface area of the micro-strip column, and θ is the angle between the bottom surface of the micro-strip column and the XOY plane. There is:

[0102]

[0103]

[0104] where α xij is the angle between the bottom interface of the micro-strip column in the i-th row and j-th column and the X-axis in the three-dimensional coordinate system, and α yij is the angle between the bottom interface of the micro-strip column in the i-th row and j-th column and the Y-axis in the three-dimensional coordinate system;

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

[0106]

[0107] where dx is the differential length of the micro-strip column along the X-axis, and dy is the differential length of the micro-strip column along the Y-axis;

[0108] S302: Solve the sliding-down force and anti-sliding force of each micro-strip column based on the body force acting on the bottom surface of the micro-strip column.

[0109] The angle between the projection of the bottom surface of the micro-strip column on the non-main sliding surface with an ellipsoidal bottom interface of the potential sliding mass in the horizontal direction and the micro-strip column in the i-th row on the main sliding surface is α i , and the main sliding surface is the central plane of the potential sliding mass;

[0110]

[0111] Among them, the center point P of the i-th row of micro-strip columns on the main slip surface 0 has coordinates (x 1 , 0, z 1 ), and the center point P of the i-th row and j-th column of micro-strip columns on the non-main slip surface n has coordinates (x pij , y pij , z pij );

[0112] Therefore, the anti-sliding force T ij-d1 and the sliding-down force F ij-d1 of the i-th row and j-th column of micro-strip columns with the bottom interface of the potential sliding mass being an ellipsoid surface are respectively:

[0113] Among them, N 1 is the normal pressure of the micro-strip column on the ellipsoid surface, N; c ij is the cohesion of the i-th row and j-th column of micro-strip columns; θ 1 is the angle between the normal of the bottom interface of the micro-strip column and the normal of the ellipsoid surface, °; is the internal friction angle of the i-th row and j-th column of micro-strip columns;

[0114] The anti-sliding force T ij-d2 and the sliding-down force F ij-d2 of the i-th row and j-th column of micro-strip columns with the bottom interface of the potential sliding mass being an inclined surface are respectively:

[0115]

[0116]

[0117] S303: Calculate the total anti-sliding force and total sliding-down force of the i-th row of micro-strip columns according to the sliding-down force and anti-sliding force of each micro-strip column;

[0118] When the bottom interface of the potential sliding mass is an ellipsoid surface, the total anti-sliding force and total sliding-down force of the i-th row of micro-strip columns are:

[0119]

[0120] F i1 = ∑ i F(i, j) = 2∑ i [dWsin(θ 1 +α i )], y > 0 (16)

[0121] In the formula, T i1 is the total anti-sliding force of all column micro-strip columns in the i-th row with the bottom interface of the potential sliding mass being an ellipsoid surface, F i1The total sliding force of all column micro - strip columns in the i - th row where the bottom interface of the potential sliding mass is an ellipsoidal surface, Σ i denotes the summation over all columns with y > 0 in the i - th row; T(i,j) is the anti - sliding force of the micro - strip column in the i - th row and j - th column, and F(i,j) is the sliding force of the micro - strip column in the i - th row and j - th column;

[0122] When the bottom interface of the potential sliding mass is an inclined plane, the total anti - sliding force and total sliding force of the micro - strip columns in the i - th row are:

[0123]

[0124] F i2 = ∑ i F(i,j)=2∑ i [dWcosψ], y > 0 (18)

[0125] where, T i2 is the total anti - sliding force of all column micro - strip columns where the bottom interface of the potential sliding mass is an inclined plane, and F i2 is the total sliding force of all column micro - strip columns where the bottom interface of the potential sliding mass is an inclined plane;

[0126] S4: Superimpose the total anti - sliding force and total sliding force of each row of micro - strip columns on the micro - strip columns on the main sliding surface of that row, and calculate the two - dimensional equivalent shear strength parameters with three - dimensional effects, including the equivalent unit weight, equivalent cohesion, and internal friction angle of the bottom interface of the micro - strip columns on the main sliding surface; specifically including:

[0127] S401: Let the total anti - sliding force T i and total sliding force F i of the micro - strip columns in the i - th row be equal to the anti - sliding force T i0 and sliding force F i0 of the micro - strip columns in the i - th row on the main sliding surface, respectively, that is:

[0128] T i = T i0 (19)

[0129] F i = F i0 (20)

[0130] S402: Substitute sinθ 1 and cosθ 1 into equations (19) and (20) to obtain the equivalent unit weight, equivalent cohesion, and internal friction angle of the bottom interface of the micro - strip columns on the i - th row of the main sliding surface;

[0131] For the potential sliding mass with the bottom interface being an ellipsoidal surface, the equivalent unit weight γ i-1 , equivalent cohesion c i-1 and internal friction angle of the bottom interface of the micro - strip columns on the i - th row of the main sliding surface are respectively expressed as:

[0132]

[0133] For a potential sliding mass with an inclined bottom surface, the equivalent unit weight γ i-2 of the bottom surface of the micro-strip column on the i-th main sliding surface, the equivalent cohesion c i-2 and the internal friction angle are respectively expressed as:

[0134]

[0135] In this embodiment, the equivalent shear strength parameters of the bottom surface of the micro-strip column on the main sliding surface are shown in Table 2.

[0136] Table 2 Equivalent Shear Strength Parameter Table of Micro-Strip Column on Main Sliding Surface of Potential Sliding Mass

[0137]

[0138] Note: x' is the length from the center point of the micro-strip column to the center of the circle.

[0139] S5: Introduce the two-dimensional equivalent shear strength parameters with three-dimensional effects into the rigid body limit equilibrium method (such as the unbalanced thrust transfer method), transform the three-dimensional slope stability problem into an equivalent two-dimensional rigid body limit equilibrium problem, select an appropriate rigid body limit equilibrium algorithm according to the landslide mode, and solve to obtain the stability coefficient of the V-shaped slope.

[0140] The three-dimensional stability coefficient of the V-shaped slope in this embodiment is calculated to be 1.231.

[0141] In this embodiment, a V-shaped slope stability calculation system is also provided for implementing the described V-shaped slope stability calculation method, including:

[0142] A parameter acquisition module for determining the morphological parameters of the V-shaped slope and the physical and mechanical parameters of each stratum rock mass in the research area based on the engineering geological characteristics of the research area;

[0143] A spatial morphological equation establishment module for establishing the spatial morphological equation of the potential sliding mass of the V-shaped slope based on the morphological parameters of the V-shaped slope in the research area, the physical and mechanical parameters of each stratum rock mass, and the three-dimensional numerical simulation technology;

[0144] A two-dimensional equivalent mechanical parameter determination module for dividing the potential sliding mass into micro-strip columns with m rows and n columns according to the spatial morphological equation of the potential sliding mass of the V-shaped slope, solving the total anti-sliding force and total sliding force superimposed on the main sliding surface of each row of micro-strip columns in the potential sliding mass, and determining the two-dimensional equivalent mechanical parameters with three-dimensional effects;

[0145] A stability coefficient solving module, which is used to introduce two-dimensional equivalent mechanical parameters with three-dimensional effects into the rigid body limit equilibrium method, transform the three-dimensional slope stability problem into an equivalent two-dimensional rigid body limit equilibrium problem, and solve to obtain the stability coefficient of the V-shaped slope-like;

[0146] In summary, the present invention provides a method and system for calculating the stability of a V-shaped slope-like. Based on three-dimensional numerical simulation technology, the failure mode is determined first to determine the spatial shape equation of the potential sliding mass, and then the sliding surface is divided into micro-strip columns in regions. Through the constitutive relationship and static equilibrium conditions, the stress state of the micro-strip columns is solved. The forces of each row of micro-strip columns are superimposed along the main sliding surface direction, and the two-dimensional equivalent shear strength parameters with three-dimensional effects on the main sliding surface micro-strip columns of each row are obtained using the equivalent idea. Then, the theoretical formula for the stability coefficient of the three-dimensional V-shaped slope-like is derived using the rigid body limit equilibrium method. The research results of this study have well solved the three-dimensional stability problem of the V-shaped slope-like and provided more reliable theoretical technologies for mining engineering.

[0147] In this embodiment, an electronic device is also provided, including: a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the electronic device runs, the processor communicates with the memory through the bus. When the machine-readable instructions are executed by the processor, the steps of the method for calculating the stability of a V-shaped slope-like are executed;

[0148] In this embodiment, a computer-readable storage medium is also provided. A computer program is stored in the computer-readable storage medium. When the computer program is run by a processor, the steps of the method for calculating the stability of a V-shaped slope-like are executed. The storage medium can be a memory, a magnetic disk, an optical disc, etc.

[0149] In this article, specific examples are used to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manner and application scope. In summary, 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 V-shaped slope, characterized in that: The following steps are involved: S1: Determine the morphological parameters of the V-shaped slope and the physical and mechanical parameters of the rock mass in each stratum within the study area; S2: Based on the morphological parameters of the V-shaped slopes and the physical and mechanical parameters of the rock masses in each stratum in the study area, the spatial morphological equation of the potential sliding body of the V-shaped slope is established; the spatial morphological equation of the potential sliding body includes the slope surface equation, the ellipsoid surface equation and the inclined weak surface equation; S3: Divide the potential sliding body of the V-shaped slope into m rows and n columns of micro-columns. Based on the spatial morphological equation of the potential sliding body of the V-shaped slope, solve the total anti-sliding force and total sliding force of each row of micro-columns in the potential sliding body. S4: superimposing the total anti-sliding force and the total sliding force of each row of micro-columns on the main sliding surface of the row of micro-columns, and calculating the two-dimensional equivalent shear strength parameters with three-dimensional effect; the two-dimensional equivalent shear strength parameters with three-dimensional effect include the equivalent bulk density, equivalent cohesion and internal friction angle of the bottom interface of the micro-columns on the main sliding surface; S5: The two-dimensional equivalent shear strength parameters with three-dimensional effect are introduced into the rigid limit equilibrium method, and the three-dimensional slope stability problem is transformed into an equivalent two-dimensional rigid limit equilibrium problem. The rigid limit equilibrium algorithm is selected according to the landslide mode, and the stability coefficient of the V-shaped slope is solved.

2. A method for calculating the stability of a V-shaped slope according to claim 1, characterized in that: Step 1 is specifically as follows: according to the characteristics of the V-shaped slope in the study area, the origin is selected, and a three-dimensional coordinate system is established with the direction perpendicular to the slope as the positive direction of the X axis, the direction parallel to the direction as the positive direction of the Y axis, and the direction perpendicular to the ground upward as the positive direction of the Z axis. The morphological parameters of the V-shaped slope in the study area include: slope height H, slope angle δ, angle β between the inclined weak layer and the direction parallel to the slope direction, angle ψ between the inclined weak layer and the direction perpendicular to the ground, and angle v between the projection of the intersection line of the inclined weak layer and the slope surface on the horizontal plane and the direction of the slope direction; the physical and mechanical parameters of the rock mass in each stratum include soil bulk density γ, cohesion c and internal friction angle The inclined weak layer surface is symmetrically inclined.

3. A method for calculating the stability of a V-shaped slope according to claim 2, characterized in that: Step 2 specifically includes: Based on the three-dimensional coordinate system established in S1, determine the slope equation z of the V-shaped slope p ; Wherein, tanδ represents the tangent value of the slope angle, (x, y, z) represents the spatial coordinates in the three-dimensional coordinate system, x represents the component in the X-axis direction of the spatial coordinates, y represents the component in the Y-axis direction of the spatial coordinates, and z represents the component in the Z-axis direction of the spatial coordinates; Based on the three-dimensional coordinate system established in S1, determine the ellipsoidal surface equation of the V-shaped slope; Among them, R a and R b are the coefficients of the ellipsoid equation, representing the radius of curvature of the ellipsoid in the X and Y directions; (x0, y0, z0) are the spatial coordinates of the center of the ellipsoid, x0 is the component of the spatial coordinates of the center of the ellipsoid in the X-axis direction, y0 is the component of the spatial coordinates of the center of the ellipsoid in the Y-axis direction, and z0 is the component of the spatial coordinates of the center of the ellipsoid in the Z-axis direction; Based on the three-dimensional coordinate system established in S1, determine the inclined weak layer equation of the V-shaped slope; The inclined weak layer is symmetrically distributed about the XOZ plane. The equation of the inclined weak layer on the left side of the XOZ plane is set to g1, and the equation of the inclined weak layer on the right side of the XOZ plane is set to g2. According to the angles between the inclined weak layer and the X-axis and the Y-axis, the equation of the inclined weak layer is obtained as follows:

4. A method for calculating the stability of a V-shaped slope according to claim 3, characterized in that: Step 3 specifically includes: S301: Divide the potential sliding body into m rows and n columns of micro-columns, solve the stress state of each micro-column through the constitutive relationship and static equilibrium condition, and obtain the volume force on the bottom surface of the micro-column; The volume force on the bottom surface of the micro-column is: dW=γ ij (With pij -With ij )sinθdA (6) Where dW is the volume force on the bottom of the micro-column; z p -z ij is the height of the micro-bar in the i-th row and j-th column, z pij is the height of the top surface of the micro-column in the i-th row and j-th column, z ij is the height of the bottom surface of the micro-column in the i-th row and j-th column; γ ij is the soil bulk density of the i-th row and j-th column micro-column, dA is the bottom area of ​​the micro-column, θ is the angle between the bottom of the micro-column and the XOY plane, and we have: Among them, α xij is the angle between the bottom interface of the micro-column in the i-th row and j-th column and the X-axis in the three-dimensional coordinate system, α yij is the angle between the bottom interface of the micro-column in the i-th row and j-th column and the Y-axis in the three-dimensional coordinate system; The bottom surface area dA of the micro-column is: Wherein, dx is the differential length of the micro-column along the X-axis, and dy is the differential length of the micro-column along the Y-axis; S302: according to the volume force on the bottom surface of the micro-column, solve the sliding force and anti-sliding force of each micro-column; The bottom interface of the potential sliding body is an ellipsoid. The angle between the horizontal projection of the bottom surface of the micro-column on the non-main sliding surface and the i-th row of micro-columns on the main sliding surface is α. i , the main sliding surface is the center surface of the potential sliding body; The coordinates of the center point P0 of the i-th row of micro-columns on the main sliding surface are (x1,0,z1), and the coordinates of the center point P0 of the i-th row and j-th column of micro-columns on the non-main sliding surface are (x1,0,z1). n The coordinates are (x pij ,y pij ,z pij ); Therefore, the anti-sliding force T of the i-th row and j-th column of the potential sliding body bottom interface is the ellipsoid surface. ij-d1 and the sliding force F ij-d1 They are: Where N1 is the normal pressure of the microcolumn on the ellipsoidal surface, N; c ij is the cohesion of the micro-column in the i-th row and j-th column; θ1 is the angle between the normal direction of the bottom interface of the micro-column and the normal direction of the ellipsoid surface; is the internal friction angle of the micro-column in the i-th row and j-th column; The anti-sliding force T of the i-th row and j-th column of the potential sliding body with an inclined surface at the bottom interface ij-d2 and the sliding force F ij-d2 They are: S303: Calculate the total anti-sliding force and total sliding force of the i-th row of micro-columns according to the sliding force and anti-sliding force of each micro-column; When the bottom interface of the potential sliding body is an ellipsoidal surface, the total anti-sliding force and total sliding force of the i-th row of micro-columns are: F i1 ∑ i F(i,j)=2∑ i [dWsin(θ1+α i )],y>0 (16) Where, T i1 is the total anti-sliding force of all micro-columns in the ith row whose bottom interface of the potential sliding body is an ellipsoid, F i1 is the total sliding force of all micro-columns in the ith row whose bottom interface of the potential sliding body is an ellipsoid, Σ i It means summing all the columns of the i-th row with y>0; T(i,j) is the anti-sliding force of the i-th row and j-th column micro-column, and F(i,j) is the sliding force of the i-th row and j-th column micro-column; When the bottom interface of the potential sliding body is an inclined surface, the total anti-sliding force and total sliding force of the i-th row of micro-columns are: F i2 =∑ i F(i,j)=2∑ i [dWcosψ],y>0 (18) Among them, T i2 is the total anti-sliding force of all micro-columns whose bottom interface of the potential sliding body is an inclined surface, F i2 It is the total sliding force of all micro-columns whose bottom interface of potential sliding body is an inclined surface.

5. A method for calculating the stability of a V-shaped slope according to claim 4, characterized in that: Step 4 specifically includes: S401: Let the total anti-slip force of the micro-columns on the i-th row be T i and the total sliding force F i are equal to the anti-sliding force T of the i-th row of micro-columns on the main sliding surface i0 and the sliding force F i0 ,Right now: T i =T i0 (19) F i =F i0 (20) S402: Substitute sinθ1 and cosθ1 into equations (19) and (20) to obtain the equivalent bulk density, equivalent cohesion and internal friction angle of the interface at the bottom of the micro-column on the i-th row of main sliding surface; For a potential sliding body with a bottom interface on an ellipsoidal surface, the equivalent bulk density γ of the bottom interface of the micro-column on the i-th row of main sliding surfaces is i-1 , equivalent cohesion c i-1 and internal friction angle Respectively expressed as: For a potential sliding body with an inclined bottom interface, the equivalent bulk density γ i-2 , equivalent cohesion c i-2 and internal friction angle Respectively expressed as:

6. A V-shaped slope stability calculation system, used to implement a V-shaped slope stability calculation method according to any one of claims 1 to 5, characterized in that: include: The parameter acquisition module is used to determine the morphological parameters of the V-shaped slope and the physical and mechanical parameters of the rock mass in each stratum in the study area based on the engineering geological characteristics of the study area; The module for establishing spatial morphological equations is used to establish the spatial morphological equations of potential sliding bodies of V-shaped slopes based on the morphological parameters of V-shaped slopes in the study area, the physical and mechanical parameters of rock masses in various formations, and three-dimensional numerical simulation technology; The two-dimensional equivalent mechanical parameter determination module is used to divide the potential sliding body into m rows and n columns of micro-columns according to the spatial morphological equation of the potential sliding body of the V-shaped slope, solve the total anti-sliding force and total sliding force of each row of micro-columns in the potential sliding body superimposed on the main sliding surface, and determine the two-dimensional equivalent mechanical parameters with three-dimensional effect; The stability coefficient solving module is used to introduce two-dimensional equivalent mechanical parameters with three-dimensional effects into the rigid body limit equilibrium method, transform the three-dimensional slope stability problem into an equivalent two-dimensional rigid body limit equilibrium problem, and solve the V-shaped slope stability coefficient.

7. An electronic device, characterized in that: include: A processor, a memory and a bus, wherein the memory stores machine-readable instructions executable by the processor, and when the electronic device is running, the processor and the memory communicate via the bus, and when the machine-readable instructions are executed by the processor, the steps of a method for calculating the stability of a V-shaped slope as described in any one of claims 1 to 5 are performed.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, which, when executed by a processor, executes the steps of a method for calculating the stability of a V-shaped slope as described in any one of claims 1 to 5.

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