A method and system for calculating the stability of a v-like shaped slope

Abstract

The application discloses a kind of V-shaped slope stability calculation method and system, it is related to strip mining technical field.Based on three-dimensional numerical simulation technology, determine its failure mode first determine the spatial form equation of potential sliding body, then the sliding body is divided into regional division micro column, through constitutive relation and static equilibrium condition, the stress state of micro column is solved, the force of each row micro column is superposed along the direction of main sliding surface, and the two-dimensional equivalent shear strength parameters with three-dimensional effect on each row of main sliding surface micro column are obtained using equivalent idea, then the three-dimensional V-shaped slope stability coefficient is derived using rigid body limit equilibrium method.The application avoids the problems of high calculation cost, difficult parameter determination and complex calculation process in the traditional three-dimensional slope stability calculation method, solves the three-dimensional stability problem of this special form slope, provides more reliable theory and technology for the design, mining, prevention and management of slope, and has important practical significance for ensuring mining safety and efficient production.

Description

Technical Field

[0001] This invention belongs to the field of open-pit mining technology, specifically relating to a method and system for calculating the stability of a V-shaped slope. Background Technology

[0002] Due to limitations imposed by factors such as ore body occurrence conditions, mining rights boundaries, and important surface facilities, most open-pit mine slopes exhibit irregular shapes or structures in plan view. However, existing calculation methods cannot account for the quantitative impact of irregular shapes on slope stability. Numerous experts and scholars have achieved fruitful results in researching calculation methods for the stability of irregular slopes.

[0003] Patent CN 115081214 A discloses a method for calculating the three-dimensional stability of a planar polygonal convex slope. It establishes a mathematical model of the three-dimensional mechanical effects of the planar polygonal convex slope and obtains the three-dimensional stability coefficient of the slope based on the residual thrust method. Patent CN115391897A discloses a method for calculating the three-dimensional stability of a slope under the action of internal drainage and sloping action in open-pit mining. Based on the morphology of the mining slope, the weak layer of the sliding body, and the morphology of the potential sliding surface within the study area, it establishes a spatial morphology equation for the potential sliding surface, transforming the three-dimensional slope stability problem into a two-dimensional problem for calculation of the stability coefficient. Patent CN118886194A discloses a method for assessing the stability of a slope containing a reverse-dip fault. It first obtains the name of the reverse-dip fault. Information such as location, length, dip, dip angle, strike, and fault properties is used to establish a slope model containing reverse-dip faults for stability analysis and numerical simulation calculations. Patent CN115081214B discloses a three-dimensional stability calculation method for a planar polygonal convex slope. This method treats the slip surface of the planar polygonal convex slope as an ellipsoid or a combination of an ellipsoid and a weak surface, establishes the slip surface equation and a two-dimensional equivalent mathematical model of the three-dimensional stability of the planar polygonal convex slope, and finally uses the residual thrust method to calculate the three-dimensional stability coefficient of the planar polygonal convex slope. This method avoids the problems of poor numerical convergence and complex calculation process in traditional slope three-dimensional stability calculation methods, and effectively solves the problem of slope stability analysis and design under this condition. These patents have studied three-dimensional stability calculation methods for slopes with several special shapes or structures. Some have also studied slope stability calculation methods under fault conditions and the effects of internal drainage and slope support during transverse mining. However, they have not considered special slope shapes such as the V-shaped slopes found in open-pit coal mines like the Hesigewula South and Jilangde, and there are currently no reports on such slopes. Therefore, there is an urgent need to find a method and system for calculating the stability of V-shaped slopes, to improve the three-dimensional stability calculation method system for special slope shapes in open-pit mines, and to provide technical support for the engineering design, mining, and treatment of open-pit coal mine slopes. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for calculating the stability of V-shaped slopes. Combining the special topography of V-shaped slopes in open-pit mines, this method calculates the stability coefficient based on limit equilibrium theory and slope spatial mechanics effects. It is simple and efficient, filling the gap in the research on the three-dimensional stability of V-shaped slopes.

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

[0006] S1: Determine the morphological parameters of V-shaped slopes and the physical and mechanical parameters of rock masses in each stratum within the study area;

[0007] Specifically, based on the V-shaped slope characteristics within the study area, an origin is selected, with the direction perpendicular to the slope's strike as the positive X-axis, the direction parallel to the strike as the positive Y-axis, and the direction perpendicular to the ground upwards as the positive Z-axis, establishing a three-dimensional coordinate system. The morphological parameters of the V-shaped slope within the study area include: slope height H, slope angle δ, the angle β between the inclined weak surface and the direction parallel to the slope's strike, the angle ψ between the inclined weak surface and the direction perpendicular to the ground, and the angle v between the projection of the intersection of the inclined weak surface and the slope surface onto the horizontal plane and the slope's strike direction. The physical and mechanical parameters of the rock mass in each stratum include soil unit weight γ, cohesion c, and internal friction angle. The inclined weak layer is symmetrically inclined;

[0008] S2: Based on the morphological parameters of V-shaped slopes in the study area and the physical and mechanical parameters of rock masses in various strata, establish the spatial morphological equation of potential landslide bodies of V-shaped slopes; the spatial morphological equation of potential landslide bodies includes the slope equation, the ellipsoid equation, and the equation of inclined weak bedding planes.

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

[0010]

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

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

[0013]

[0014] Among them, R a and R b, , and , respectively, are the coefficients of the ellipsoid equation, representing the radii of curvature of the ellipsoid in the X and Y directions; (x0, y0, z0) are the spatial coordinates of the center of the ellipsoid, where x0 is the X-axis component of the spatial coordinates of the center of the ellipsoid, y0 is the Y-axis component of the spatial coordinates of the center of the ellipsoid, and z0 is the Z-axis component of the spatial coordinates of the center of the ellipsoid.

[0015] Based on the three-dimensional coordinate system established in S1, the equation of the inclined weak layer of the V-shaped slope is determined.

[0016] The tilted weak layers are symmetrically distributed about the XOZ plane. Let the equation for the tilted weak layer to the left of the XOZ plane be g1, and the equation for the tilted weak layer to the right of the XOZ plane be g2. Based on the angles between the tilted weak layers and the X and Y axes, the equations for the tilted weak layers are obtained as follows:

[0017]

[0018] S3: Divide the potential sliding body of the V-shaped slope into m rows and n columns of micro-strips. Based on the spatial morphology equation of the potential sliding body of the V-shaped slope, solve for the total anti-sliding force and total sliding force of each row of micro-strips in the potential sliding body.

[0019] S301: Divide the potential sliding body into m rows and n columns of micro-strips. Solve the force state of each micro-strip through constitutive relations and static equilibrium conditions to obtain the volume force on the bottom surface of the micro-strip.

[0020] The volume force acting on the bottom surface of the micro-strip column is:

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

[0022] Where dW is the volume force on the bottom surface of the micro-strip column; z p -z ij Let z be the height of the microbar in the i-th row and j-th column. pij Let z be the height of the top surface of the microbar column in the i-th row and j-th column. ij γ is the height of the bottom surface of the micro-strip column in the i-th row and j-th column; ij Let be the unit weight of the soil in the i-th row and j-th column of the micro-strip column, dA be the area of ​​the base of the micro-strip column, and θ be the angle between the base of the micro-strip column and the XOY plane. Then:

[0023]

[0024]

[0025] Where, α xij Let α be the angle between the bottom interface of the microbar in the i-th row and j-th column and the X-axis in the three-dimensional coordinate system. yijLet be the angle between the bottom interface of the microbar column in the i-th row and j-th column and the Y-axis in the three-dimensional coordinate system;

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

[0027]

[0028] Where dx is the differential length of the microstrip column along the X-axis, and dy is the differential length of the microstrip column along the Y-axis;

[0029] S302: Based on the volume force on the bottom surface of the micro-strip column, solve for the sliding force and anti-slip force of each micro-strip column;

[0030] The potential sliding body's bottom interface is an ellipsoid. The angle between the horizontal projection of the bottom surface of the micro-strips on the non-principal sliding surface and the i-th row of micro-strips on the principal sliding surface is α. i The main sliding surface is the center surface of the potential sliding body;

[0031]

[0032] Among them, the coordinates of the center point P0 of the i-th row of micro-stripes on the main sliding surface are (x1, 0, z1), and the coordinates of the center point P of the i-th row and j-th column of micro-stripes on the non-main sliding surface are... n Coordinates are (x pij ,y pij ,z pij );

[0033] Therefore, the anti-slip force T of the micro-strip column in the i-th row and j-th column of the potential sliding body bottom interface is an ellipsoid. ij-d1 and downward force F ij-d1 They are respectively:

[0034] Where N1 is the normal pressure of the micro-strip cylinder on the ellipsoidal surface, N; c ij θ1 is the cohesion of the microstrip column in the i-th row and j-th column; θ1 is the angle between the normal of the bottom interface of the microstrip column and the normal of the ellipsoid. Let be the internal friction angle of the micro-strip column in the i-th row and j-th column;

[0035] The anti-slip force T of the i-th row and j-th column micro-strip column at the bottom interface of the potential sliding body is an inclined surface. ij-d2 and downward force F ij-d2 They are respectively:

[0036]

[0037] S303: Calculate the total anti-slip force and total sliding force of the i-th row of micro-strips based on the sliding force and anti-slip force of each micro-strip;

[0038] When the bottom interface of the potential sliding body is an ellipsoid, the total anti-slip force and total sliding force of the i-th row of micro-strips are:

[0039]

[0040] F i1 =∑ i F(i,j)=2∑ i [dWsin(θ1+α i )],y>0 (16)

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

[0042] When the bottom interface of the potential sliding body is an inclined surface, the total anti-slip force and total sliding force of the i-th row of micro-strips are:

[0043]

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

[0045] Among them, T i2 F represents the total anti-slip force of all columns of micro-stripes with an inclined bottom interface of the potential sliding body. i2 The total sliding force of all columns of micro-stripes with the bottom interface of the potential sliding body being an inclined surface;

[0046] S4: The total anti-slip force and total sliding force of each row of micro-strips are superimposed on the micro-strips on the main sliding surface of that row, and the two-dimensional equivalent shear strength parameters with three-dimensional effect are calculated; the two-dimensional equivalent shear strength parameters with three-dimensional effect include the equivalent unit weight, equivalent cohesion and internal friction angle of the bottom interface of the micro-strips on the main sliding surface;

[0047] S401: Let T be the total anti-slip force of the microbar in the i-th row. i Total downward force F i The anti-slip force T of the i-th row of micro-stripes on the main sliding surface is respectively equal to the anti-slip force T. i0 and downward force F i0 ,Right now:

[0048] T i =T i0 (19)

[0049] F i =F i0 (20)

[0050] S402: Substituting sinθ1 and cosθ1 into equations (19) and (20) yields the equivalent bulk density, equivalent cohesion, and internal friction angle of the micro-strip column bottom interface on the i-th row of main sliding surface;

[0051] For a potential sliding body with an ellipsoidal base interface, the equivalent unit weight γ of the micro-strip column base interface on the i-th row of principal sliding surfaces is... i-1 Equivalent cohesion c i-1 and internal friction angle They are represented as follows:

[0052]

[0053] For a potential sliding body with an inclined bottom interface, the equivalent unit weight γ of the bottom interface of the micro-strip column on the i-th row of the main sliding surface is... i-2 Equivalent cohesion c i-2 and internal friction angle They are represented as follows:

[0054]

[0055] S5: The two-dimensional equivalent shear strength parameter with three-dimensional effect is introduced into the rigid body limit equilibrium method, and the three-dimensional slope stability problem is transformed into an equivalent two-dimensional rigid body limit equilibrium problem. The rigid body limit equilibrium algorithm is selected according to the landslide mode, and the stability coefficient of the V-shaped slope is obtained by solving it.

[0056] A second aspect of the present invention provides a V-shaped slope stability calculation system for implementing the aforementioned V-shaped slope stability calculation method, comprising:

[0057] The parameter acquisition module is used to determine the morphological parameters of V-shaped slopes and the physical and mechanical parameters of rock masses in each stratum within the study area based on the engineering geological characteristics of the study area.

[0058] The spatial morphology equation establishment module is used to establish the spatial morphology equation 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 strata, and three-dimensional numerical simulation technology.

[0059] The two-dimensional equivalent mechanical parameter determination module is used to divide the potential sliding body into m rows and n columns of micro-strips according to the spatial morphology 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-strips superimposed on the main sliding surface, and determine the two-dimensional equivalent mechanical parameters with three-dimensional effect.

[0060] The stability coefficient solution module is used to introduce two-dimensional equivalent mechanical parameters with three-dimensional effects 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 V-shaped slope.

[0061] A third aspect of the present invention provides an electronic device, comprising: 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 communicates with the memory via the bus, and when the machine-readable instructions are executed by the processor, the steps of the aforementioned method for calculating the stability of a V-shaped slope are performed.

[0062] A fourth aspect of the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, performs the steps of a method for calculating the stability of a V-shaped slope as described above.

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

[0064] The stability calculation method for V-shaped slopes provided by this invention takes into account the three-dimensional effects of the special strata and characteristic structures of V-shaped slopes. Based on the limit equilibrium theory and the concept of equivalence, it performs two-dimensional equivalent representation of the three-dimensional mechanical effects of the slope, realizing a two-dimensional equivalent characterization of the three-dimensional stability of V-shaped 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. It effectively solves the three-dimensional stability problem of this special slope shape, providing a more reliable theoretical technology for slope design, mining, prevention, and treatment, and has important practical significance for ensuring safe and efficient mining production. Attached Figure Description

[0065] 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.

[0066] Figure 1 This is a flowchart of the method for calculating the stability of a V-shaped slope according to the present invention;

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

[0068] Figure 3 This is a three-dimensional slice cross-sectional view of a V-shaped slope in an embodiment of the present invention;

[0069] Figure 4This is a force analysis diagram of the micro-strip column in an embodiment of the present invention. Detailed Implementation

[0070] 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.

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

[0072] 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.

[0073] This invention provides a method for calculating the stability of a V-shaped slope, such as... Figure 1 As shown, it includes the following steps:

[0074] S1: Based on the engineering geological characteristics of the study area, 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;

[0075] Specifically, the approach can be approached from aspects such as slope deformation and failure mechanism research, engineering geological models, and on-site geological surveys. Based on the characteristics of V-shaped slopes within the study area, an origin point is selected, with the direction perpendicular to the slope's strike as the positive X-axis, the direction parallel to the strike as the positive Y-axis, and the direction perpendicular to the ground as the positive Z-axis, establishing a three-dimensional coordinate system. Then, based on this established three-dimensional coordinate system, the relevant parameters required for calculating the stability of V-shaped slopes are determined. For example, the morphological parameters of the V-shaped slopes within the study area include: slope height H, slope angle δ, the angle β between the inclined weak surface and the direction parallel to the slope's strike, the angle ψ between the inclined weak surface and the direction perpendicular to the ground, and the angle v between the projection of the intersection of the inclined weak surface and the slope surface onto the horizontal plane and the slope's strike direction. The physical and mechanical parameters of the rock mass in each stratum include soil unit weight γ, cohesion c, and internal friction angle. The inclined weak layer is symmetrically inclined;

[0076] In this embodiment, a homogeneous slope with a downward gradient is taken as an example. Figure 2The origin O is located at the point where the symmetrical, gently dipping weak slope intersects the slope surface. The direction perpendicular to the slope strike is the positive X-axis, the direction parallel to the strike is the positive Y-axis, and the direction perpendicular to the ground and upwards is the positive Z-axis. The slope height is 117m, the slope angle is 20°, and the angles between the gently dipping weak slope and the X-axis and Y-axis are 9°.

[0077] Based on previous geological exploration and physical and mechanical tests of soil and rock masses, the physical and mechanical parameters of the rock mass in each stratum of the slope were determined. In this embodiment, based on previous geological exploration and physical and mechanical tests of soil and rock masses, Figure 3 The numerical simulation results for the V-shaped slope are shown in Table 1, with the physical and mechanical parameters of the rock mass in each stratum as shown.

[0078] Table 1 Physical and mechanical parameters of the rock mass in different strata of the slope

[0079]

[0080] S2: Based on the morphological parameters of V-shaped slopes within the study area and the physical and mechanical parameters of the rock masses in various strata, the spatial morphological equations of potential sliding bodies of V-shaped slopes are established, specifically including:

[0081] 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 in the figure, the three-dimensional numerical simulation results show that the potential landslide mode of the V-shaped slope is a combination of ellipsoidal and inclined surface sliding, and the potential sliding surface is regarded as a combination of ellipsoidal and inclined surface sliding surface. Therefore, the spatial morphological equations of the potential landslide body include the slope equation, the ellipsoidal equation, and the inclined weak surface equation;

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

[0083]

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

[0085] Based on the three-dimensional coordinate system established in S1, the ellipsoid equation of the V-shaped slope is determined;

[0086] The general form of the equation of an ellipsoid is expressed as:

[0087] R a (x-x0) 2 +R b (y-y0) 2 +R c(z-z0) 2 =1 (2)

[0088] Among them, R a R b and R c , , respectively, are the coefficients of the ellipsoid equation, representing the radii of curvature of the ellipsoid in the X, Y, and Z directions; (x0, y0, z0) are the spatial coordinates of the center of the ellipsoid, where x0 is the X-axis component of the spatial coordinates of the center of the ellipsoid, y0 is the Y-axis component of the spatial coordinates of the center of the ellipsoid, and z0 is the Z-axis component of the spatial coordinates of the center of the ellipsoid.

[0089] Since the ellipsoid is symmetrical about the XOZ plane, and the slip surface is a circular arc on the XOZ section, the equation of the ellipsoid is z. h It can also be expressed as:

[0090]

[0091] Based on the three-dimensional coordinate system established in S1, the equation of the inclined weak layer of the V-shaped slope is determined.

[0092] The tilted weak layers are symmetrically distributed about the XOZ plane. Let the equation for the tilted weak layers to the left of the XOZ plane be g1, and the equation for the tilted weak layers to the right of the XOZ plane be g2. The general form of the tilted weak layer equation can be expressed as:

[0093]

[0094] Where: A1, B1, C1, D1, A2, B2, C2 and D2 are all coefficients of the tilted weak layer;

[0095] Based on the angles between the inclined weak plane and the X-axis and Y-axis, the equation of the inclined weak plane can be obtained as follows:

[0096]

[0097] S3: Divide the potential sliding body of the V-shaped slope into m rows and n columns of micro-strips. Based on the spatial morphology equation of the potential sliding body of the V-shaped slope, solve for the total anti-sliding force and total sliding force of each row of micro-strips in the potential sliding body.

[0098] S301: Divide the potential sliding body into m rows and n columns of micro-strips. Solve the force state of each micro-strip using constitutive relations and static equilibrium conditions, such as... Figure 4 The volume force on the bottom surface of the micro-strip column is obtained;

[0099] The volume 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 volume force on the bottom surface of the micro-strip column; z p -z ij Let z be the height of the microbar in the i-th row and j-th column. pij Let z be the height of the top surface of the microbar column in the i-th row and j-th column. ij γ is the height of the bottom surface of the micro-strip column in the i-th row and j-th column; ij Let be the unit weight of the soil in the i-th row and j-th column of the micro-strip column, dA be the area of ​​the base of the micro-strip column, and θ be the angle between the base of the micro-strip column and the XOY plane. Then:

[0102]

[0103]

[0104] Where, α xij Let α be the angle between the bottom interface of the microbar in the i-th row and j-th column and the X-axis in the three-dimensional coordinate system. yij Let be the angle between the bottom interface of the microbar column in the i-th row and j-th column and the Y-axis in the three-dimensional coordinate system;

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

[0106]

[0107] Where dx is the differential length of the microstrip column along the X-axis, and dy is the differential length of the microstrip column along the Y-axis;

[0108] S302: Based on the volume force on the bottom surface of the micro-strip column, solve for the sliding force and anti-slip force of each micro-strip column;

[0109] The potential sliding body's bottom interface is an ellipsoid. The angle between the horizontal projection of the bottom surface of the micro-strips on the non-principal sliding surface and the i-th row of micro-strips on the principal sliding surface is α. i The main sliding surface is the center surface of the potential sliding body;

[0110]

[0111] Among them, the coordinates of the center point P0 of the i-th row of micro-stripes on the main sliding surface are (x1, 0, z1), and the coordinates of the center point P of the i-th row and j-th column of micro-stripes on the non-main sliding surface are... n Coordinates are (x pij ,y pij ,z pij );

[0112] Therefore, the anti-slip force T of the micro-strip column in the i-th row and j-th column of the potential sliding body bottom interface is an ellipsoid. ij-d1 and downward force F ij-d1 They are respectively:

[0113] Where N1 is the normal pressure of the micro-strip cylinder on the ellipsoidal surface, N; c ij Let θ be the cohesion of the microstrip column in the i-th row and j-th column; θ1 is the angle between the normal of the bottom interface of the microstrip column and the normal of the ellipsoid, in °; Let be the internal friction angle of the micro-strip column in the i-th row and j-th column;

[0114] The anti-slip force T of the i-th row and j-th column micro-strip column at the bottom interface of the potential sliding body is an inclined surface. ij-d2 and downward force F ij-d2 They are respectively:

[0115]

[0116]

[0117] S303: Calculate the total anti-slip force and total sliding force of the i-th row of micro-strips based on the sliding force and anti-slip force of each micro-strip;

[0118] When the bottom interface of the potential sliding body is an ellipsoid, the total anti-slip force and total sliding force of the i-th row of micro-strips are:

[0119]

[0120] F i1 =∑ i F(i,j)=2∑ i [dWsin(θ1+α i )],y>0 (16)

[0121] In the formula, T i1 F represents the total antislip force of all columns of microstripes in the i-th row of the potential sliding body with an ellipsoidal bottom interface. i1 Σ represents the total sliding force of all micro-stripes in the i-th row of the potential sliding body with an ellipsoidal bottom interface. i This represents the summation of all columns in the i-th row where y>0; T(i,j) is the anti-slip force of the microbar in the i-th row and j-th column, and F(i,j) is the sliding force of the microbar in the i-th row and j-th column.

[0122] When the bottom interface of the potential sliding body is an inclined surface, the total anti-slip force and total sliding force of the i-th row of micro-strips are:

[0123]

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

[0125] Among them, T i2 F represents the total anti-slip force of all columns of micro-stripes with an inclined bottom interface of the potential sliding body.i2 The total sliding force of all columns of micro-stripes with the bottom interface of the potential sliding body being an inclined surface;

[0126] S4: Superimpose the total anti-slip force and total sliding force of each row of micro-strips onto the micro-strips 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 at the bottom interface of the micro-strips on the main sliding surface; specifically including:

[0127] S401: Let T be the total anti-slip force of the microbar in the i-th row. i Total downward force F i The anti-slip force T of the i-th row of micro-stripes on the main sliding surface is respectively equal to the anti-slip force T. i0 and downward force F i0 ,Right now:

[0128] T i =T i0 (19)

[0129] F i =F i0 (20)

[0130] S402: Substituting sinθ1 and cosθ1 into equations (19) and (20) yields the equivalent bulk density, equivalent cohesion, and internal friction angle of the micro-strip column bottom interface on the i-th row of main sliding surface;

[0131] For a potential sliding body with an ellipsoidal base interface, the equivalent unit weight γ of the micro-strip column base interface on the i-th row of principal sliding surfaces is... i-1 Equivalent cohesion c i-1 and internal friction angle They are represented as follows:

[0132]

[0133] For a potential sliding body with an inclined bottom interface, the equivalent unit weight γ of the bottom interface of the micro-strip column on the i-th row of the main sliding surface is... i-2 Equivalent cohesion c i-2 and internal friction angle They are represented as follows:

[0134]

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

[0136] Table 2. Equivalent shear strength parameters of micro-strips on the main sliding surface of the potential sliding body.

[0137]

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

[0139] S5: Introduce the two-dimensional equivalent shear strength parameter with three-dimensional effect into the rigid body limit equilibrium method (e.g., 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 to implement the aforementioned V-shaped slope stability calculation method, including:

[0142] The parameter acquisition module is used to determine the morphological parameters of V-shaped slopes and the physical and mechanical parameters of rock masses in each stratum within the study area based on the engineering geological characteristics of the study area.

[0143] The spatial morphology equation establishment module is used to establish the spatial morphology equation 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 strata, and three-dimensional numerical simulation technology.

[0144] The two-dimensional equivalent mechanical parameter determination module is used to divide the potential sliding body into m rows and n columns of micro-strips according to the spatial morphology 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-strips superimposed on the main sliding surface, and determine the two-dimensional equivalent mechanical parameters with three-dimensional effect.

[0145] The stability coefficient solution module is used to introduce two-dimensional equivalent mechanical parameters with three-dimensional effects 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 V-shaped slope.

[0146] In summary, this invention provides a method and system for calculating the stability of V-shaped slopes. Based on three-dimensional numerical simulation technology, the spatial morphology equation of the potential sliding body is determined first to identify the failure mode. Then, the sliding surface is divided into micro-strips. Through constitutive relations and static equilibrium conditions, the stress state of the micro-strips is solved. The forces of each row of micro-strips are superimposed along the main sliding surface direction, and the equivalent shear strength parameters with three-dimensional effects on the micro-strips of each row of the main sliding surface are obtained using the equivalent concept. Finally, the theoretical formula for the stability coefficient of the three-dimensional V-shaped slope is derived using the rigid body limit equilibrium method. The results of this research effectively solve the three-dimensional stability problem of V-shaped slopes, providing a more reliable theoretical technology 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 that can be executed by the processor. When the electronic device is running, the processor communicates with the memory through the bus. When the machine-readable instructions are executed by the processor, the steps of the aforementioned method for calculating the stability of a V-shaped slope are performed.

[0148] In this embodiment, a computer-readable storage medium is also provided, which stores a computer program that, when executed by a processor, performs the steps of the method for calculating the stability of a V-shaped slope as described above. The storage medium may be a memory, magnetic disk, optical disk, etc.

[0149] 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 V-shaped slope, characterized in that, Includes the following steps: S1: Determine the morphological parameters of V-shaped slopes and the physical and mechanical parameters of rock masses in each stratum within the study area; Based on the V-shaped slope characteristics within the study area, an origin point was selected, with the direction perpendicular to the slope strike as the positive X-axis, the direction parallel to the strike as the positive Y-axis, and the direction perpendicular to the ground upwards as the positive Z-axis, establishing a three-dimensional coordinate system. The morphological parameters of the V-shaped slope within the study area include: slope height H, slope angle δ, angle β between the inclined weak layer and the direction parallel to the slope strike, 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 slope strike direction. The physical and mechanical parameters of the rock mass in each stratum include soil unit weight γ, cohesion c, and internal friction angle φ. The inclined weak layer exhibits a symmetrical dip-sloping characteristic. S2: Based on the morphological parameters of V-shaped slopes in the study area and the physical and mechanical parameters of rock masses in various strata, establish the spatial morphological equation of potential landslide bodies of V-shaped slopes; the spatial morphological equation of potential landslide bodies includes the slope equation, the ellipsoid equation, and the equation of inclined weak bedding planes. Based on the three-dimensional coordinate system established in S1, the slope equation z of the V-shaped slope is determined. p ; （1） Where tanδ represents the tangent of the slope angle, (x,y,z) are the spatial coordinates in the three-dimensional coordinate system, x is the component of the X-axis in the spatial coordinate system, y is the component of the Y-axis in the spatial coordinate system, and z is the component of the Z-axis in the spatial coordinate system. Based on the three-dimensional coordinate system established in S1, the ellipsoid equation of the V-shaped slope is determined. （3） Among them, R a and R b , , and , respectively, are the coefficients of the ellipsoid equation, representing the radii of curvature of the ellipsoid in the X and Y directions; (x0, y0, z0) are the spatial coordinates of the center of the ellipsoid, where x0 is the X-axis component of the spatial coordinates of the center of the ellipsoid, y0 is the Y-axis component of the spatial coordinates of the center of the ellipsoid, and z0 is the Z-axis component of the spatial coordinates of the center of the ellipsoid. Based on the three-dimensional coordinate system established in S1, the equation of the inclined weak layer of the V-shaped slope is determined. The tilted weak layers are symmetrically distributed about the XOZ plane. Let the equation for the tilted weak layer to the left of the XOZ plane be g1, and the equation for the tilted weak layer to the right of the XOZ plane be g2. Based on the angles between the tilted weak layers and the X and Y axes, the equations for the tilted weak layers are obtained as follows: （5）； S3: Divide the potential sliding body of the V-shaped slope into m rows and n columns of micro-strips. Based on the spatial morphology equation of the potential sliding body of the V-shaped slope, solve for the total anti-sliding force and total sliding force of each row of micro-strips in the potential sliding body. S4: The total anti-slip force and total sliding force of each row of micro-strips are superimposed on the micro-strips on the main sliding surface of that row, and the two-dimensional equivalent shear strength parameters with three-dimensional effect are calculated; the two-dimensional equivalent shear strength parameters with three-dimensional effect include the equivalent unit weight, equivalent cohesion and internal friction angle of the bottom interface of the micro-strips on the main sliding surface; S5: The two-dimensional equivalent shear strength parameter with three-dimensional effect is introduced into the rigid body limit equilibrium method, and the three-dimensional slope stability problem is transformed into an equivalent two-dimensional rigid body limit equilibrium problem. The rigid body limit equilibrium algorithm is selected according to the landslide mode, and the stability coefficient of the V-shaped slope is obtained by solving it.

2. The method for calculating the stability of a V-shaped slope according to claim 1, characterized in that, Step 3 specifically includes: S301: Divide the potential sliding body into m rows and n columns of micro-strips. Solve the force state of each micro-strip through constitutive relations and static equilibrium conditions to obtain the volume force on the bottom surface of the micro-strip. The volume force acting on the bottom surface of the micro-strip column is: （6） Where dW is the volume force on the bottom surface of the micro-strip column; Let z be the height of the microbar in the i-th row and j-th column. pij Let z be the height of the top surface of the microbar column in the i-th row and j-th column. ij γ is the height of the bottom surface of the micro-strip column in the i-th row and j-th column; ij Let be the unit weight of the soil in the i-th row and j-th column of the micro-strip column, dA be the area of ​​the base of the micro-strip column, and θ be the angle between the base of the micro-strip column and the XOY plane. Then: （7） （8） Where, α xij Let α be the angle between the bottom interface of the microbar in the i-th row and j-th column and the X-axis in the three-dimensional coordinate system. yij Let be the angle between the bottom interface of the microbar column in the i-th row and j-th column and the Y-axis in the three-dimensional coordinate system; The area dA of the bottom surface of the micro-strip column is: （9） Where dx is the differential length of the microstrip column along the X-axis, and dy is the differential length of the microstrip column along the Y-axis; S302: Based on the volume force on the bottom surface of the micro-strip column, solve for the sliding force and anti-slip force of each micro-strip column; The potential sliding body's bottom interface is an ellipsoid. The angle between the horizontal projection of the bottom surface of the micro-strips on the non-principal sliding surface and the i-th row of micro-strips on the principal sliding surface is . The main sliding surface is the center surface of the potential sliding body; （10） Among them, the coordinates of the center point P0 of the i-th row of micro-stripes on the main sliding surface are (x1, 0, z1), and the coordinates of the center point P of the i-th row and j-th column of micro-stripes on the non-main sliding surface are... n Coordinates are (x pij , y pij , z pij ); Therefore, the anti-slip force T of the micro-strip column in the i-th row and j-th column of the potential sliding body bottom interface is an ellipsoid. ij-d1 and downward force F ij-d1 They are respectively: （11） （12） Where N1 is the normal pressure of the microstrip column on the ellipsoid; c ij φ is the cohesion of the microstrip column in the i-th row and j-th column; θ1 is the angle between the normal of the bottom interface of the microstrip column and the normal of the ellipsoid; φ ij Let be the internal friction angle of the micro-strip column in the i-th row and j-th column; The anti-slip force T of the i-th row and j-th column micro-strip column at the bottom interface of the potential sliding body is an inclined surface. ij-d2 and downward force F ij-d2 They are respectively: （13） （14） S303: Calculate the total anti-slip force and total sliding force of the i-th row of micro-strips based on the sliding force and anti-slip force of each micro-strip; When the bottom interface of the potential sliding body is an ellipsoid, the total anti-slip force and total sliding force of the i-th row of micro-strips are: ，y>0 （15） ，y>0 （16） In the formula, T i1 F represents the total antislip force of all columns of microstripes in the i-th row of the potential sliding body with an ellipsoidal bottom interface. i1 Σ represents the total sliding force of all micro-stripes in the i-th row of the potential sliding body with an ellipsoidal bottom interface. i This represents the summation of all columns in the i-th row where y>0; T(i,j) is the anti-slip force of the microbar in the i-th row and j-th column, and F(i,j) is the sliding force of the microbar in the i-th row and j-th column. When the bottom interface of the potential sliding body is an inclined surface, the total anti-slip force and total sliding force of the i-th row of micro-strips are: ， y>0 （17） ，y>0 （18） Among them, T i2 F represents the total anti-slip force of all columns of micro-stripes with an inclined bottom interface of the potential sliding body. i2 The total sliding force is the total sliding force of all columns of micro-strips with the bottom interface of the potential sliding body being an inclined surface.

3. The method for calculating the stability of a V-shaped slope according to claim 2, characterized in that, Step 4 specifically includes: S401: Let T be the total anti-slip force of the microbar in the i-th row. i Total downward force F i The anti-slip force T of the i-th row of micro-stripes on the main sliding surface is respectively equal to the anti-slip force T. i0 and downward force F i0 ,Right now: （19） （20） S402: Substituting sinθ1 and cosθ1 into equations (19) and (20) yields the equivalent bulk density, equivalent cohesion, and internal friction angle of the micro-strip column bottom interface on the i-th row of main sliding surface; For a potential sliding body with an ellipsoidal base interface, the equivalent unit weight γ of the micro-strip column base interface on the i-th row of principal sliding surfaces is... i-1 Equivalent cohesion c i-1 and internal friction angle φ i-1 They are represented as follows: （21） For a potential sliding body with an inclined bottom interface, the equivalent unit weight γ of the bottom interface of the micro-strip column on the i-th row of the main sliding surface is... i-2 Equivalent cohesion c i-2 and internal friction angle φ i-2 They are represented as follows: （22）。 4. A V-shaped slope stability calculation system, used to implement the V-shaped slope stability calculation method according to any one of claims 1-3, characterized in that, include: The parameter acquisition module is used to determine the morphological parameters of V-shaped slopes and the physical and mechanical parameters of rock masses in each stratum within the study area based on the engineering geological characteristics of the study area. The spatial morphology equation establishment module is used to establish the spatial morphology equation 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 strata, 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-strips according to the spatial morphology 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-strips superimposed on the main sliding surface, and determine the two-dimensional equivalent mechanical parameters with three-dimensional effect. The stability coefficient solution module is used to introduce two-dimensional equivalent mechanical parameters with three-dimensional effects 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 V-shaped slope.

5. An electronic device, characterized in that, include: The device includes a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the electronic device is running, the processor communicates with the memory via the bus. When the machine-readable instructions are executed by the processor, they perform the steps of the method for calculating the stability of a V-shaped slope as described in any one of claims 1-3.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps of the method for calculating the stability of a V-shaped slope as described in any one of claims 1-3.

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