A method for calculating three-dimensional stability of a slope under the action of cross-cut mining, internal discharge and pressure on the slope in an open pit

Abstract

The application discloses a kind of open-pit mine horizontal mining inner discharge pressure slope under the action of three-dimensional stability calculation method of side slope, comprising: S1, according to the form of the side slope of the mining area in the research area, weak layer of sliding body and potential sliding surface form, using three-dimensional numerical simulation technology, potential sliding surface spatial form equation is established;S2, based on spatial form equation, the side slope is divided into several i rows, j column micro column, and the stress analysis is carried out to each micro column, respectively calculate the anti-sliding force and the sliding force of each micro column in each region;S3, the force of each row micro column is superimposed along the main sliding line direction, and the total anti-sliding force and the total sliding force on the main sliding line are obtained;S4, three-dimensional slope stability problem is converted into two-dimensional problem solution, and the stability coefficient is calculated using unbalanced thrust method, and the application can provide important theoretical support and technical guidance for safe and efficient recovery of deep slope coal resources.

Description

Technical Field

[0001] This invention relates to the field of open-pit mining technology, and more specifically to a method for calculating the three-dimensional stability of slopes under the action of internal drainage and sloping in open-pit mining. Background Technology

[0002] With my country's increasing energy demand, the scale and depth of open-pit coal mining are also increasing. Compared with shallow slopes, deep end slopes in open-pit coal mines are affected by various factors such as stratum lithology and occurrence, geological structure, and hydrogeology. Furthermore, they form a complex spatial structure with internal spoil heaps and working slopes, collectively limiting the potential sliding width of deep end slopes. This poses a significant challenge to three-dimensional slope stability analysis and affects the safe and efficient production of open-pit coal mines. Previous studies have typically employed generalized two-dimensional rigid body limit equilibrium methods and numerical simulations to address three-dimensional slope stability issues. However, these methods cannot adequately describe the three-dimensional stability of end slopes under three-dimensional clamping and retaining effects. Therefore, researching methods for analyzing the stability of deep end slopes and calculating their three-dimensional stability is a pressing issue for researchers in the mining engineering field. Summary of the Invention

[0003] In view of this, the purpose of this invention is to provide a method for calculating the three-dimensional stability of slopes under the action of internal drainage and rib pressing in open-pit mines, thereby solving the problem that the existing technology cannot accurately calculate the three-dimensional stability of end slopes under the effect of three-dimensional clamping and retaining.

[0004] To achieve the above objectives, the present invention provides the following technical solution:

[0005] A method for calculating the three-dimensional stability of a slope under the action of internal drainage and rib stabilization in open-pit mines includes the following steps:

[0006] S1. Based on the morphology of the mining slope, the weak layer of the sliding body, and the morphology of the potential sliding surface in the study area, three-dimensional numerical simulation technology is used to establish the spatial morphology equation of the potential sliding surface, including: the potential sliding surface equation, the weak layer equation, and the slope equation.

[0007] S2, based on the spatial morphology equation, divides the slope into several micro-strips of i rows and j columns, and performs stress analysis on each micro-strip. Let the range between the ellipsoid and the top line of the slope be region I, and the range from the top line of the slope to the intersection of the ellipsoid and the inclined surface be region II. The inclined surface is the region Calculate the anti-slip force and sliding force of the micro-strip column in each region;

[0008] S3, superimpose the forces of each row of micro-strips along the main sliding line to obtain the total anti-slip force and total sliding force on the main sliding line, and calculate the forces in region I and region II respectively. and region Equivalent unit weight at the bottom interface of the micro-strip column in the k-th row of the main slide line Equivalent cohesion and internal friction angle And determine the two-dimensional equivalent mechanical parameters of the three-dimensional effect;

[0009] S4. Using two-dimensional equivalent mechanical parameters, the three-dimensional slope stability problem is transformed into a two-dimensional problem for solution, and the stability coefficient is calculated using the unbalanced thrust method.

[0010] Furthermore, in step S1, based on the morphology of the mining slope, the weak layer of the landslide body, and the morphology of the potential sliding surface within the study area, three-dimensional numerical simulation technology is used to establish the spatial morphology equation of the potential sliding surface, including: the potential sliding surface equation, the weak layer equation, and the slope equation; the potential landslide body equation, the weak layer equation, and the slope equation are specifically as follows:

[0011] Let the equation of the ellipsoid be: The equation of the inclined plane is Then the spatial morphological function of the combined slip surface of the slope is: ,in Indicates at point Smooth surface The height of the intersection point of the planes is expressed by the equation of the ellipsoid as:

[0012]

[0013] in: A,B,C These are the coefficients of the equation of the ellipsoid, representing the ellipsoid's surface in... x , y , z The radius of curvature in the direction; , , These are the spatial coordinates of the center of the ellipsoid;

[0014] The equation for the inclined plane is expressed as:

[0015]

[0016] The equation for the smooth surface is then expressed as:

[0017]

[0018] in: Indicates smooth surface and x Angle between axes; Indicates smooth surface and y Angle between axes; θ Let be the angle of inclination of the inclined surface, when any point on the sliding surface... satisfy At that time, the point lies on the ellipsoid, and the value of the slip surface function is determined by the projection of that point onto the ellipsoid. To the origin distance and The product of the two is used to obtain the value of the slip surface function; otherwise, the point lies on a weak plane, and the value of the slip surface function is determined by the height of the point on the weak plane and the origin. The square root of the height difference is used, and the sign is determined by the direction of the sliding surface;

[0019] Slope equation The divisible regions are represented as follows:

[0020]

[0021] in: δ The slope angle; H This represents the slope height.

[0022] Further, in step S2, based on the spatial morphology equation, the slope is divided into several micro-strips in rows i and columns j, and a force analysis is performed on each micro-strip. Let the area between the ellipsoid and the top line of the slope be region I, the area from the top line of the slope to the intersection of the ellipsoid and the inclined surface be region II, and the inclined surface be region III. The anti-sliding force and sliding force of the micro-strips in each region are calculated respectively, specifically as follows:

[0023] Step S2-1: Let the first... i Line number j The length and width of the column of micro bars are , The height is The horizontal distance from the main sliding line is s The coordinates of the center point of the micro-strip column are The bottom interface of the micro-strip column in the global coordinate system and x The included angle of the axis is ,and y The included angle of the axis is ；

[0024] The volume force on the base of the micro-strip column is:

[0025]

[0026] in: The unit weight of the rock and soil mass. The height of the base of the micro-strip column, and the height of the base of the micro-strip column with respect to... The included angle of the face is θ From geometric relations, we get:

[0027]

[0028] micro-strip column base area for:

[0029]

[0030] in: and The bottom edge of the micro-strip column x , y The differential length of the axis;

[0031] Step S2-2: Calculate the projection of the bottom surface of the non-principal sliding line micro-strip column in the horizontal direction and the first projection on the principal sliding line. i The included angle of the micro-bars on the row ;

[0032] Let the main slide be at the th i The points on the row are ,point The tangent vector is By taking the partial derivative of the equation of the ellipsoid, we can obtain the normal vector of the ellipsoid at that point. ; merging the normal vector with the principal slide direction vector Perform the cross product to obtain the tangent vector: ;

[0033] For the center of the micro-strip column on the non-main slide line ,point arrive The vector is V Set up points Coordinates are Non-principal slide line micro-strip column points Coordinates are Then point Time vector V Represented as: ; Calculate vectors V With point tangent vector The included angle β ,Right now From the above, we can conclude that... ,Right now

[0034]

[0035] Steps 2-3: Let the area between the ellipsoid and the slope crest line be region I, the area from the slope crest line to the intersection of the ellipsoid and the inclined surface be region II, and the inclined surface be region III. Calculate the anti-sliding force and sliding force of the micro-strip column in each region.

[0036] Anti-slip force of micro-strip columns in elliptical region I Tx 1 and downward force Fx 1 are respectively:

[0037]

[0038] in: The normal pressure of the micro-strip column on ellipsoidal region I. ; The angle between the normal to the bottom interface of the micro-strip column and the normal to the ellipsoid;

[0039] Anti-slip force of micro-strips in elliptical region II and downward force They are respectively:

[0040]

[0041] For the micro-strip columns within the inclined surface region III, their anti-slip force and downward force They are respectively:

[0042]

[0043] in, The normal pressure of the micro-strip column on inclined surface III is expressed in N. The angle between the micro-strip column in inclined plane III and the horizontal plane.

[0044] Furthermore, in step S3, the forces of each row of micro-strips are superimposed along the main sliding line to obtain the total anti-slip force and total sliding force on the main sliding line, and the equivalent unit weight at the bottom interface of the micro-strips in region I, region II, and region III in the k-th row of the main sliding line is calculated respectively. Equivalent cohesion and internal friction angle And determine the two-dimensional equivalent mechanical parameters of the three-dimensional effect;

[0045] Step 3-1: Let the first... k The total anti-skid force on the track is The total downward force is Then we have:

[0046]

[0047]

[0048] In the formula: Indicates the first k Sum all columns of the row;

[0049] At this time, the k The total anti-skid force on the track is The total downward force is They are respectively equal to the principal slide line number k Anti-slip force of micro-strip columns , downward force ,Right now , ;

[0050] Step 3-2: Calculate the first step for ellipsoidal region I, ellipsoidal region II, and inclined surface region III respectively. k Equivalent bulk density of the interface at the bottom of the main sliding line micro-strip column Equivalent cohesion and internal friction angle ;

[0051] , They are respectively the first slip surface i The bottom surface of the micro-strip column and x axis, y The included angle of the axis; , , , Substituting into the above equation, we can obtain the first... k The equivalent shear strength parameters of the interface at the bottom of the micro-strip column of the main sliding line; therefore, in ellipsoidal region I, the first k Equivalent bulk density of the interface at the bottom of the main sliding line micro-strip column Equivalent cohesion and internal friction angle They are respectively:

[0052]

[0053] In ellipsoidal region II, the first k Equivalent bulk density of the interface at the bottom of the main sliding line micro-strip column Equivalent cohesion and internal friction angle They are respectively:

[0054]

[0055] Inclined surface region Ⅲ-1 intersects with the ellipsoid at the th k The number of strips in regions II and III-1 of row are respectively s 1. s 2. At this point, the equivalent bulk density of the main slide bar column... Equivalent cohesion and internal friction angle They are respectively:

[0056]

[0057]

[0058] In the weak-layered inclined plane region Ⅲ-2, the first k Equivalent bulk density of the interface at the bottom of the main sliding line micro-strip column Equivalent cohesion and internal friction angle They are respectively:

[0059]

[0060]

[0061] Furthermore, in step S4, two-dimensional equivalent mechanical parameters are used to transform the three-dimensional slope stability problem into a two-dimensional problem for solution, and the stability coefficient is calculated using the unbalanced thrust method: specifically:

[0062]

[0063] In the formula, , —The resultant force of the anti-slip forces on the base surfaces of the i-th and n-th columns; , They are respectively the i-th column and the i-th column. n The resultant force of the downward sliding force on the bottom surface of the column.

[0064] According to specific embodiments provided by the present invention, the present invention has the following technical effects:

[0065] This application considers the constraint of the internal spoil heap and the support on both sides of the working slope on the south side of the mining area, which limits the spatial range of the potential landslide, and explores how to calculate the three-dimensional stability of deep slopes. Through numerical simulation, the spatial morphology equations of the slope surface and sliding surface in the potential landslide are fitted. Based on the three-dimensional limit equilibrium strip division method, the bottom surface of the landslide is divided into micro-strips along the horizontal and vertical directions. The stress conditions of the strips in different spatial locations between the landslide and the slope crest line are analyzed, and the expressions for the normal force and shear force at the bottom of the micro-strip are derived. Applying the concept of equivalence, the mechanical effects of each row of micro-strips are superimposed and applied to the micro-strips on the main sliding line of the landslide, thereby obtaining the equivalent shear strength parameters at the interface of the main sliding line column to establish a three-dimensional stability equivalent algorithm. The research results can provide important theoretical support and technical guidance for the safe and efficient recovery of coal resources from deep slopes. Attached Figure Description

[0066] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0067] The following description, in conjunction with the accompanying drawings, further illustrates the method for calculating the three-dimensional stability of slopes under the action of internal drainage and sloping in open-pit mines according to the present invention.

[0068] Figure 1This is the overall flowchart of the method for calculating the three-dimensional stability of slopes under the action of internal drainage and rib pressing in open-pit mines provided by the present invention;

[0069] Figure 2 This is a schematic diagram of the three-dimensional slip surface of the slope in the three-dimensional stability calculation method for the slope under the action of internal drainage and rib pressing in open-pit mining provided by the present invention;

[0070] Figure 3 This is a micro-strip column stress analysis diagram in the three-dimensional stability calculation method for slope under the action of internal drainage and rib pressing in open-pit mines provided by the present invention;

[0071] Figure 4 This is a two-dimensional sliding stability result diagram of the existing slope in the three-dimensional stability calculation method of the slope under the action of internal drainage and sloping in open-pit mining provided by the present invention;

[0072] Figure 5 This is a diagram showing the three-dimensional slippage stability results of the slope in the three-dimensional stability calculation method for the slope under the action of internal drainage and rib pressing in open-pit mining provided by the present invention;

[0073] Figure 6 This is a curve showing the relationship between the slip body dip length and the three-dimensional stability coefficient of the slope in the three-dimensional stability calculation method for the slope under the action of internal drainage and sloping in open-pit mining provided by the present invention. Detailed Implementation

[0074] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0075] To better understand the purpose, structure, and function of this invention, the invention will be described in further detail below with reference to the accompanying drawings.

[0076] This invention provides a method for calculating the three-dimensional stability of a slope under the action of internal drainage and sloping action in open-pit mines, comprising the following steps:

[0077] Numerical simulation methods were used to reveal the deformation and failure mechanism of slopes under the action of internal drainage and sloping in open-pit mines.

[0078] like Figure 1 He Ru Figure 2 As shown, S1, based on the morphology of the mining slope, the weak layer of the sliding body and the morphology of the potential sliding surface in the study area, three-dimensional numerical simulation technology is used to establish the spatial morphology equation of the potential sliding surface, including: the potential sliding surface equation, the weak layer equation and the slope equation.

[0079] S2, based on the spatial morphology equation, divide the slope into several i rows and j columns of micro-strips, and perform force analysis on each micro-strip. Let the range between the ellipsoid and the top line of the slope be region I, the range from the top line of the slope to the intersection of the ellipsoid and the inclined surface be region II, and the inclined surface be region III. Calculate the anti-sliding force and sliding force of the micro-strips in each region respectively.

[0080] S3, superimpose the forces of each row of micro-strips along the main sliding line to obtain the total anti-slip force and total sliding force on the main sliding line, and calculate the equivalent unit weight at the bottom interface of the micro-strips in region I, region II and region III in the k-th row of the main sliding line respectively. Equivalent cohesion and internal friction angle And determine the two-dimensional equivalent mechanical parameters of the three-dimensional effect;

[0081] S4. Using two-dimensional equivalent mechanical parameters, the three-dimensional slope stability problem is transformed into a two-dimensional problem for solution, and the stability coefficient is calculated using the unbalanced thrust method.

[0082] In step S1, based on the morphology of the mining slope, the weak layer of the landslide body, and the morphology of the potential sliding surface within the study area, three-dimensional numerical simulation technology is used to establish the spatial morphology equation of the potential sliding surface, including: the potential sliding surface equation, the weak layer equation, and the slope equation; the potential landslide body equation, the weak layer equation, and the slope equation are specifically as follows:

[0083] Let the equation of the ellipsoid be: The equation of the inclined plane is Then the spatial morphological function of the combined slip surface of the slope is: ,in Indicates at point Smooth surface The height of the intersection point of the planes is expressed by the equation of the ellipsoid as:

[0084]

[0085] in: A,B,C These are the coefficients of the equation of the ellipsoid, representing the ellipsoid's surface in... x , y , z The radius of curvature in the direction; , , These are the spatial coordinates of the center of the ellipsoid;

[0086] The equation for the inclined plane is expressed as:

[0087]

[0088] The equation for the smooth surface is then expressed as:

[0089]

[0090] in: Indicates smooth surface and x Angle between axes; Indicates smooth surface and y Angle between axes; Let be the angle of inclination of the inclined surface, when any point on the sliding surface... satisfy At that time, the point lies on the ellipsoid, and the value of the slip surface function is determined by the projection of that point onto the ellipsoid. To the origin distance and The product of the two is used to obtain the value of the slip surface function; otherwise, the point lies on a weak plane, and the value of the slip surface function is determined by the height of the point on the weak plane and the origin. The square root of the height difference is used, and the sign is determined by the direction of the sliding surface;

[0091] Slope equation The divisible regions are represented as follows:

[0092]

[0093] in: δ The slope angle; H This represents the slope height.

[0094] In step S2, based on the spatial morphology equation, the slope is divided into several micro-strips in rows i and columns j, and a force analysis is performed on each micro-strip. Let the area between the ellipsoid and the top line of the slope be region I, the area from the top line of the slope to the intersection of the ellipsoid and the inclined surface be region II, and the inclined surface be region III. The anti-sliding force and sliding force of the micro-strips in each region are calculated respectively, specifically as follows:

[0095] Step S2-1: Let the first... i Line number j The length and width of the column of micro bars are , The height is The horizontal distance from the main sliding line is s The coordinates of the center point of the micro-strip column are The bottom interface of the micro-strip column in the global coordinate system and x The included angle of the axis is ,and y The included angle of the axis is ；

[0096] The volume force on the base of the micro-strip column is:

[0097]

[0098] in: The unit weight of the rock and soil mass. The height of the base of the micro-strip column, and the height of the base of the micro-strip column with respect to... The included angle of the face is θ From geometric relations, we get:

[0099]

[0100] micro-strip column base area for:

[0101]

[0102] in: and The bottom edge of the micro-strip column x , y The differential length of the axis;

[0103] Step S2-2: Calculate the projection of the bottom surface of the non-principal sliding line micro-strip column in the horizontal direction and the first projection on the principal sliding line. i The included angle of the micro-bars on the row ;

[0104] Let the main slide be at the th i The points on the row are ,point The tangent vector is By taking the partial derivative of the equation of the ellipsoid, we can obtain the normal vector of the ellipsoid at that point. ; merging the normal vector with the principal slide direction vector Perform the cross product to obtain the tangent vector: ;

[0105] For the center of the micro-strip column on the non-main slide line ,point arrive The vector is V Set up points Coordinates are Non-principal slide line micro-strip column points Coordinates are Then point Time vector V Represented as: ; Calculate vectors V With point tangent vector The included angle β ,Right now From the above, we can conclude that... ,Right now

[0106]

[0107] Steps 2-3: Let the area between the ellipsoid and the slope crest line be region I, the area from the slope crest line to the intersection of the ellipsoid and the inclined surface be region II, and the inclined surface be region III. Calculate the anti-sliding force and sliding force of the micro-strip column in each region.

[0108] Anti-slip force of micro-strip columns in elliptical region I and downward force They are respectively:

[0109]

[0110] in: N 1 represents the normal pressure of the micro-strip column on ellipsoidal region I. ; The angle between the normal to the bottom interface of the micro-strip column and the normal to the ellipsoid;

[0111] Anti-slip force of micro-strips in elliptical region II and downward force They are respectively:

[0112]

[0113] For the micro-strip columns within the inclined surface region III, their anti-slip force and downward force They are respectively:

[0114]

[0115] in, The normal pressure of the micro-strip column on inclined surface III is expressed in N. The angle between the micro-strip column in inclined plane III and the horizontal plane.

[0116] In step S3, the forces of each row of micro-strips are superimposed along the main sliding line to obtain the total anti-slip force and total sliding force on the main sliding line. The equivalent unit weight at the bottom interface of the micro-strips in region I, region II, and region III in the k-th row of the main sliding line is then calculated. Equivalent cohesion and internal friction angle And determine the two-dimensional equivalent mechanical parameters of the three-dimensional effect;

[0117] Step 3-1: Let the first... k The total anti-skid force on the track is The total downward force is Then we have:

[0118]

[0119] In the formula: Indicates the first kSum all columns of the row;

[0120] At this time, the k The total anti-skid force on the track is The total downward force is They are respectively equal to the principal slide line number k Anti-slip force of micro-strip columns , downward force ,Right now , ;

[0121] Step 3-2: Calculate the first step for ellipsoidal region I, ellipsoidal region II, and inclined surface region III respectively. k Equivalent bulk density of the interface at the bottom of the main sliding line micro-strip column Equivalent cohesion and internal friction angle ;

[0122] , They are respectively the first slip surface i The bottom surface of the micro-strip column and x axis, y The included angle of the axis; , , , Substituting into the above equation, we can obtain the first... k The equivalent shear strength parameters of the interface at the bottom of the micro-strip column of the main sliding line; therefore, in ellipsoidal region I, the first k Equivalent bulk density of the interface at the bottom of the main sliding line micro-strip column Equivalent cohesion and internal friction angle They are respectively:

[0123]

[0124] In ellipsoidal region II, the first k Equivalent bulk density of the interface at the bottom of the main sliding line micro-strip column γ II. Equivalent cohesion and internal friction angle They are respectively:

[0125]

[0126]

[0127] Inclined surface region Ⅲ-1 intersects with the ellipsoid at the th k The number of strips in regions II and III-1 of row are respectively s 1. s 2. At this point, the equivalent bulk density of the main slide bar column... Equivalent cohesion and internal friction angle They are respectively:

[0128]

[0129]

[0130] In the weak-layered inclined plane region Ⅲ-2, the first k Equivalent bulk density of the interface at the bottom of the main sliding line micro-strip column Equivalent cohesion and internal friction angle They are respectively:

[0131]

[0132]

[0133] In step S4, two-dimensional equivalent mechanical parameters are used to transform the three-dimensional slope stability problem into a two-dimensional problem for solution, and the stability coefficient is calculated using the unbalanced thrust method: specifically:

[0134]

[0135] In the formula, , ——No. i Columns and the first n The resultant force of the anti-slip force on the bottom surface of the column; , The first i Columns and the first n The resultant force of the downward sliding force on the bottom surface of the column.

[0136] The present invention further provides the following embodiments:

[0137] This embodiment takes an open-pit coal mine area as an example. The east-west length of this mine area is 7.51 km to 8.49 km, with an average of 8.00 km; the north-south width is 5.49 km to 6.17 km, with an average of 5.88 km; and the surface area is 47.54 km². 2 The south side of the mining area is adjacent to the west working side and the east inner spoil heap. Its strata, from top to bottom, include Quaternary loose rocks, Tertiary Pliocene and Cretaceous Bayanhua Group Shengli Formation. The main coal seams of the Shengli Formation are coal seams 4, 5 and 6, among which coal seam 6 on the south side is located at +888~+828.

[0138] This embodiment presents a method for calculating the three-dimensional stability of a slope under the action of internal drainage and rib stabilization in open-pit mines, comprising the following steps:

[0139] Step 1: Determine the soil and rock parameters and safety reserve factor;

[0140] The physical and mechanical parameters of each soil and rock layer selected for slope stability analysis are shown in Table 1. Based on the safety reserve factor requirements in the "Code for Design of Open-Pit Coal Mines," the safety reserve factor for the western slope of the "old landslide" on the south side of the mining area was determined to be 1.2.

[0141] Table 1. Physical and mechanical parameters of the rock mass

[0142]

[0143] Step 2: Based on the two-dimensional rigid body limit equilibrium method for stability calculation, a stability analysis is conducted on the existing slope on the west side of the "old landslide body" on the south side of the mining area. According to the slope geological data and on-site reconnaissance, the weak layer of the No. 6 coal seam floor dips from east to west, and the weak layer may be exposed at the toe of the slope in the deep +843 bench area. From the perspective of the difficulty of slope failure, the landslide mode is conservatively considered to be sliding out from the toe of the slope along the weak layer of the No. 6 coal seam floor. The two-dimensional stability calculation results are as follows: Figure 4 As shown, the results are summarized in Table 2.

[0144] Table 2 Summary of Two-Dimensional Sliding Stability Results of Existing Slopes

[0145]

[0146] Step 3: Based on the numerical simulation results, it is determined that the three-dimensional retaining effect must be considered in the study area, and the potential sliding space is constrained. Therefore, the equivalent calculation method of three-dimensional slope stability is applied.

[0147] Step 4: Based on the two-dimensional calculation in Step 2, the east-west width of the three-dimensional potential landslide body is controlled ( Using the three-dimensional stability equivalent calculation method, the three-dimensional stability results corresponding to different landslide areas were calculated as follows: Figure 5 As shown, the results are summarized in Table 3, and the relationship between the potential sliding mass tendency length and the three-dimensional stability coefficient of the slope is plotted (see Table 3). Figure 6 It can be seen that the three-dimensional stability coefficient of the slope under the confined space of the potential landslide gradually decreases with the increase of the dip length of the ellipsoid, showing an approximately quadratic parabolic relationship; the most dangerous potential landslide area on the deep slope on the west side of the "old landslide" on the south side of the mining area is the combined failure along the fault-weak layer, and the three-dimensional stability coefficient of the slope is 1.228, which meets the safety reserve coefficient requirement.

[0148] Table 3 Summary of Three-Dimensional Sliding Stability Results of Existing Slopes

[0149]

[0150] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for calculating the three-dimensional stability of a slope under the action of internal drainage and sloping action in open-pit mines, characterized in that, Includes the following steps: S1. Based on the morphology of the mining slope, the weak layer of the sliding body, and the morphology of the potential sliding surface in the study area, three-dimensional numerical simulation technology is used to establish the spatial morphology equation of the potential sliding surface, including: the potential sliding surface equation, the weak layer equation, and the slope equation. In S1, 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, three-dimensional numerical simulation technology is used to establish the spatial morphology equation of the potential sliding surface, including: the potential sliding surface equation, the weak layer equation, and the slope equation; the potential sliding surface equation, the weak layer equation, and the slope equation are specifically as follows: Let the equation of the ellipsoid be: The equation of the inclined plane is Then the spatial morphological function of the combined slip surface of the slope is: ,in Indicates at point Smooth surface The height of the intersection point of the planes is expressed by the equation of the ellipsoid as: ； in: A,B,C These are the coefficients of the equation of the ellipsoid, representing the ellipsoid's surface in... x , y , z The radius of curvature in the direction; , , These are the spatial coordinates of the center of the ellipsoid; The equation for the inclined plane is expressed as: ； The equation for the smooth surface is then expressed as: ； in: Indicates smooth surface and x Angle between axes; Indicates smooth surface and y Angle between axes; Let be the angle of inclination of the inclined surface, when any point on the sliding surface... satisfy At that time, the point lies on the ellipsoid, and the value of the slip surface function is determined by the projection of that point onto the ellipsoid. To the origin distance and The product of the two is used to obtain the value of the slip surface function; otherwise, the point lies on a weak plane, and the value of the slip surface function is determined by the height of the point on the weak plane and the origin. The square root of the height difference is used, and the sign is determined by the direction of the sliding surface; Slope equation The divisible regions are represented as follows: ； in: δ The slope angle; H This refers to the slope height; S2, based on the spatial morphology equation, divide the slope into several i rows and j columns of micro-strips, and perform force analysis on each micro-strip. Let the range between the ellipsoid and the top line of the slope be region I, the range from the top line of the slope to the intersection of the ellipsoid and the inclined surface be region II, and the inclined surface be region III. Calculate the anti-sliding force and sliding force of the micro-strips in each region respectively. S3, superimpose the forces of each row of micro-strips along the main sliding line to obtain the total anti-slip force and total sliding force on the main sliding line, and calculate the equivalent unit weight at the bottom interface of the micro-strips in region I, region II and region III in the k-th row of the main sliding line respectively. Equivalent cohesion and internal friction angle And determine the two-dimensional equivalent mechanical parameters of the three-dimensional effect; S4. Using two-dimensional equivalent mechanical parameters, the three-dimensional slope stability problem is transformed into a two-dimensional problem for solution, and the stability coefficient is calculated using the unbalanced thrust method.

2. The method for calculating the three-dimensional stability of an open-pit mine slope under the action of internal drainage and sloping action as described in claim 1, is characterized in that, In step S2, based on the spatial morphology equation, the slope is divided into several micro-strips in rows i and columns j, and a force analysis is performed on each micro-strip. Let the area between the ellipsoid and the top line of the slope be region I, the area from the top line of the slope to the intersection of the ellipsoid and the inclined surface be region II, and the inclined surface be region III. The anti-sliding force and sliding force of the micro-strips in each region are calculated respectively, specifically as follows: Step S2-1: Let the first... i Line number j The length and width of the column of micro bars are , The height is The horizontal distance from the main sliding line is s The coordinates of the center point of the micro-strip column are The bottom interface of the micro-strip column in the global coordinate system and x The included angle of the axis is ,and y The included angle of the axis is ； The volume force on the base of the micro-strip column is: ； in: The unit weight of the rock and soil mass. The height of the base of the micro-strip column, and the height of the base of the micro-strip column with respect to... The included angle of the face is θ From geometric relations, we get: ； micro-strip column base area for: ； in: and The bottom edge of the micro-strip column x , y The differential length of the axis; Step S2-2: Calculate the projection of the bottom surface of the non-principal sliding line micro-strip column in the horizontal direction and the first projection on the principal sliding line. i The included angle of the micro-bars on the row ; Let the main slide be at the th i The points on the row are ,point The tangent vector is By taking the partial derivative of the equation of the ellipsoid, we can obtain the normal vector of the ellipsoid at that point. ; merging the normal vector with the principal slide direction vector Perform the cross product to obtain the tangent vector: ; For the center of the micro-strip column on the non-main slide line ,point arrive The vector is V Set up points Coordinates are Non-principal slide line micro-strip column points Coordinates are Then point Time vector V Represented as: ; Calculate vectors V With point tangent vector The included angle β ,Right now From the above, we can conclude that... ,Right now ； Steps 2-3: Let the area between the ellipsoid and the slope crest line be region I, the area from the slope crest line to the intersection of the ellipsoid and the inclined surface be region II, and the inclined surface be region III. Calculate the anti-sliding force and sliding force of the micro-strip column in each region. Anti-slip force of micro-strip columns in elliptical region I and downward force They are respectively: ； in: The normal pressure of the micro-strip column on ellipsoidal region I. ; The angle between the normal to the bottom interface of the micro-strip column and the normal to the ellipsoid; Anti-slip force of micro-strip columns in elliptical region II and downward force They are respectively: ； For the micro-strip columns within the inclined surface region III, their anti-slip force and downward force They are respectively: ； in, The normal pressure of the micro-strip column on inclined surface III is expressed in N. The angle between the micro-strip column in inclined plane III and the horizontal plane.

3. The method for calculating the three-dimensional stability of an open-pit mine slope under the action of internal drainage and sloping action as described in claim 1, is characterized in that... In step S3, the forces of each row of micro-strips are superimposed along the main sliding line to obtain the total anti-slip force and total sliding force on the main sliding line. The equivalent unit weight at the bottom interface of the micro-strips in region I, region II, and region III in the k-th row of the main sliding line is then calculated. Equivalent cohesion and internal friction angle And determine the two-dimensional equivalent mechanical parameters of the three-dimensional effect; Step 3-1: Let the first... k The total anti-skid force on the track is The total downward force is Then we have: ； ； In the formula: Indicates the first k Sum all columns of the row; At this time, the k The total anti-skid force on the track is The total downward force is They are respectively equal to the principal slide line number k Anti-slip force of micro-strip column , downward force ,Right now , ; Step 3-2: Calculate the first step for ellipsoidal region I, ellipsoidal region II, and inclined surface region III respectively. k Equivalent bulk density of the interface at the bottom of the main sliding line micro-strip column Equivalent cohesion and internal friction angle ; , They are respectively the first slip surface i The bottom surface of the micro-strip column and x axis, y The included angle of the axis; , , , Substituting into the above equation, we can obtain the first... k The equivalent shear strength parameters of the interface at the bottom of the micro-strip column of the main sliding line; therefore, in ellipsoidal region I, the first k Equivalent bulk density of the interface at the bottom of the main sliding line micro-strip column Equivalent cohesion and internal friction angle They are respectively: ； In ellipsoidal region II, the first k Equivalent bulk density of the interface at the bottom of the main sliding line micro-strip column Equivalent cohesion and internal friction angle They are respectively: ； Inclined surface region Ⅲ-1 intersects with the ellipsoid at the th k The number of strips in regions II and III-1 of row are respectively s 1. s 2. At this point, the equivalent bulk density of the main slide bar column... Equivalent cohesion and internal friction angle They are respectively: ； ； In the weak-layered inclined surface region Ⅲ-2, the first k Equivalent bulk density of the interface at the bottom of the main sliding line micro-strip column Equivalent cohesion and internal friction angle They are respectively: ； 4. The method for calculating the three-dimensional stability of an open-pit mine slope under the action of internal drainage and sloping action as described in claim 1, characterized in that, In step S4, two-dimensional equivalent mechanical parameters are used to transform the three-dimensional slope stability problem into a two-dimensional problem for solution, and the stability coefficient is calculated using the unbalanced thrust method: specifically: ； In the formula, , ——No. i Columns and the first n The resultant force of the anti-slip force on the bottom surface of the column; , The first i Columns and the first n The resultant force of the downward sliding force on the bottom surface of the column.

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