A three-dimensional stability calculation method and system for a double inner dump compound type slope

Abstract

The application discloses a kind of double inner dump compound type slope three-dimensional stability calculation method and system, it is related to slope stability analysis technical field, wherein method includes: obtaining the morphological parameters of compound type slope in target area, and the physical and mechanical parameters of each stratum rock-soil body;According to morphological parameters and physical and mechanical parameters, construct numerical simulation model;Determine potential sliding body in numerical simulation model;Potential sliding body is divided into multiple vertical strips;According to the mechanical effect of the bottom surface of each vertical strip, the equivalent physical and mechanical parameters of potential sliding body are calculated;Based on equivalent physical and mechanical parameters, construct function expression f (x) about three-dimensional stability coefficient Fs;Adjust the value of λ and Fs, until the boundary equilibrium equation meets boundary condition, and the current value of Fs is used as the final three-dimensional stability coefficient of compound type slope;The calculation method provided by the application can be applied to the stability solution of irregular, heterogeneous high compound type slope.

Description

Technical Field

[0001] This invention relates to the field of slope stability analysis technology, and in particular to a three-dimensional stability calculation method and system for a composite slope with dual internal spoil disposal sites. Background Technology

[0002] Uneven development of spoil heaps in adjacent open-pit mines within the same coalfield can lead to excessively long exposed weak layers in the mining area. Furthermore, the composite slopes formed by the overlap of spoil heaps and adjacent mine mining areas can reach heights of hundreds of meters and strike lengths of hundreds of meters, making them highly susceptible to large-scale landslides. This poses a significant hazard to the safe and efficient operation of open-pit mines. Therefore, research on the stability of composite slopes is crucial to ensure the safety of workers and prevent substantial economic losses.

[0003] The two-dimensional limit equilibrium method is a relatively effective and commonly used method for slope stability calculation. However, it treats the slope as an approximate plane strain problem, neglecting the anti-slip force on the side of the slip surface. In reality, the slope itself is a three-dimensional problem, so using a two-dimensional method for analysis will inevitably have limitations.

[0004] Existing three-dimensional stability analysis methods are limited to solving the stability of homogeneous slopes with regular shapes. They are not applicable to solving the stability of irregular, heterogeneous, tall, and complex slopes composed of adjacent mines and internal spoil heaps, and cannot meet the design requirements for the coordinated development of internal spoil heaps in adjacent open-pit mines. Summary of the Invention

[0005] To address the problems existing in related technologies, this invention provides a three-dimensional stability calculation method and system for composite slopes with dual internal spoil heaps. This method can reveal the influence of composite slope morphology parameters on slope stability and helps to scientifically guide the collaborative development design of spoil heaps in adjacent mining areas.

[0006] To achieve the above objectives, this invention provides a method for calculating the three-dimensional stability of a composite slope with dual internal spoil heaps, comprising:

[0007] S1: Obtain the morphological parameters of the composite slope in the target area, as well as the physical and mechanical parameters of the soil and rock masses in each stratum;

[0008] S2: Construct a numerical simulation model based on the morphological and physical parameters;

[0009] S3: Identify potential sliding bodies in the numerical simulation model;

[0010] S4: Divide the potential sliding body into multiple vertical strips;

[0011] S5: Calculate the equivalent physical and mechanical parameters of the potential sliding body based on the bottom mechanical effects of each of the vertical blocks;

[0012] S6: Introduce the equivalent physical and mechanical parameters into the Morgenstern-Price method, setting the bulk density λ and the three-dimensional stability coefficient F. s The initial value is set according to the elasticity theory, and the function expression f(x) is set; the function expression f(x) satisfies the boundary equilibrium equation: X i =λf(x)E' i ;

[0013] Among them, E' i X represents the normal force of the block. i Indicates the tangential force of the strip;

[0014] S7: Adjust λ and F s The value of F is taken until the boundary equilibrium equation satisfies the boundary conditions, and the current value of F is then set. s The final three-dimensional stability coefficient of the composite slope is defined as follows: the boundary condition is that the external force acting on the potential sliding body is zero.

[0015] Optionally, S3: determining the potential sliding body in the numerical simulation model specifically includes:

[0016] S31: Draw the three-dimensional perspective displacement cloud map and principal sliding surface contour lines of the numerical simulation model;

[0017] S32: Based on the three-dimensional perspective displacement cloud map and the contour lines of the main slip surface, determine the potential slip surface in the numerical simulation model;

[0018] S33: The sliding body corresponding to the potential sliding surface is taken as the potential sliding body;

[0019] The spatial state equation of the potential slip surface z h The expression is:

[0020]

[0021] Among them, R a R b These represent the radii of the major and minor axes of the ellipsoid, respectively; z0 represents the z-axis coordinate at the center of the circular arc segment on the principal sliding surface; x is the spatial state equation of the potential sliding surface. h x is the x-axis coordinate; x0 is the x-axis coordinate of the center of the arc segment on the main sliding surface; y is the spatial state equation of the potential sliding surface. h The y-axis coordinate.

[0022] Optionally, step S4: dividing the potential sliding body into multiple vertical strips specifically includes:

[0023] S41: Based on the preset height standard, the potential sliding body is divided into one or more sliding body stability calculation models with different rejection and abandonment elevations;

[0024] S42: Divide the stability calculation model of each of the aforementioned discharge elevation sliding bodies into multiple vertical blocks. Optionally, the expression for the normal force dN on the bottom sliding surface of the vertical block is:

[0025] dN=dW cosα x ;

[0026] Where dW is the volume force; α x The angle between the line of intersection of the bottom sliding surface and the plane xoz and the horizontal plane;

[0027] The expression for the sliding force dX on the bottom surface of the vertical strip is:

[0028] dX=dW sinα x ;

[0029] The anti-slip force dT of the bottom sliding surface of the vertical strip x The expression is:

[0030]

[0031] in, denoted as , where is the internal friction angle of the vertical strip; and c is the cohesive force of the vertical strip.

[0032]

[0033] dA is the area of ​​the bottom surface of the vertical strip; α y The angle between the line of intersection of the bottom sliding surface and the plane yoz and the horizontal plane;

[0034] The expression for the volume force dW of the vertical strip is:

[0035] dW=γ(z p -z h )dxdy;

[0036] Where γ is the specific weight of the vertical strip; dx is the length in the x-direction, dy is the length in the y-direction; z h The equation for the smooth surface is z. p Here is the equation for the slope.

[0037] Optionally, step S5: calculating the equivalent physical and mechanical parameters of the potential sliding body based on the bottom surface mechanical effects of each of the vertical blocks, specifically including:

[0038] S51: Superimpose the bottom mechanical effects of each vertical block, and calculate the superimposed sliding force and superimposed anti-slip force of each vertical block under multiple stages;

[0039] S52: Calculate the equivalent physical and mechanical parameters of the potential sliding body at each stage based on the superimposed sliding force and superimposed anti-slip force; the equivalent physical and mechanical parameters include equivalent unit weight, equivalent cohesion and equivalent friction coefficient.

[0040] Optionally, the plurality of stages are specifically three stages, namely stage I, stage II, and stage III;

[0041] The equivalent bulk density includes: the equivalent bulk density γ of stage I. Ⅰdr Phase II equivalent bulk density γ Ⅱdu and the equivalent bulk density γ of stage III Ⅲds ;

[0042] The equivalent cohesive force includes: the equivalent cohesive force c in the first stage. Ⅰdr Stage II equivalent cohesion c Ⅱdu and the equivalent cohesion of stage III c Ⅲds ;

[0043] The equivalent friction coefficient includes: the equivalent friction coefficient for stage I. Stage II equivalent friction factor and the equivalent friction factor of stage III

[0044] This invention also provides a three-dimensional stability calculation system for a composite slope with dual internal spoil heaps, applied to the above method. The system includes:

[0045] The parameter acquisition module is used to acquire the morphological parameters of the composite slope in the target area, as well as the physical and mechanical parameters of the soil and rock masses in each stratum.

[0046] The model building module is used to construct a numerical simulation model based on the morphological parameters and physical and mechanical parameters.

[0047] A sliding body search module is used to identify potential sliding bodies in the numerical simulation model;

[0048] The sliding body division module is used to divide the potential sliding body into multiple vertical strips;

[0049] The calculation and processing module is used for:

[0050] Based on the bottom surface mechanical effects of each of the vertical blocks, calculate the equivalent physical and mechanical parameters of the potential sliding body;

[0051] The equivalent physical and mechanical parameters are introduced into the Morgenstern-Price method, and the bulk density λ and the three-dimensional stability coefficient F are set. s The initial value is set according to the elasticity theory, and the function expression f(x) is set; the function expression f(x) satisfies the boundary equilibrium equation: X i =λf(x)E'i ;

[0052] Among them, E' i X represents the normal force of the block. i Indicates the tangential force of the strip;

[0053] The values ​​of λ and Fs are adjusted until the boundary equilibrium equation satisfies the boundary conditions, and the current value of Fs is taken as the final three-dimensional stability coefficient of the composite slope; the boundary condition is that the external force on the potential sliding body is zero.

[0054] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0055] The three-dimensional stability calculation method for composite slopes provided by this invention constructs a numerical simulation model of the composite slope based on the obtained morphological parameters of the composite slope and the physical and mechanical parameters of the soil and rock masses in each stratum. In this numerical simulation model, potential sliding bodies are identified, and then the potential sliding bodies are divided into multiple vertical blocks. The equivalent physical and mechanical parameters of the potential sliding bodies are calculated based on the bottom mechanical effects of each vertical block. Furthermore, a functional expression f(x) for the three-dimensional stability coefficient Fs can be constructed. Finally, the value of the three-dimensional stability coefficient Fs that satisfies the boundary conditions is determined.

[0056] The method provided by this invention can be applied to solving the three-dimensional stability coefficient of irregular, heterogeneous, tall, and complex slopes; at the same time, the process is simple and easy to operate, and it can provide a theoretical basis for the stability analysis and morphological optimization of irregular, heterogeneous, tall, and complex slopes. Attached Figure Description

[0057] The above and other objects, features and advantages of the present invention will become more apparent from the more detailed description of exemplary embodiments of the invention in conjunction with the accompanying drawings, wherein the same reference numerals generally represent the same parts.

[0058] Figure 1 This is a flowchart illustrating the three-dimensional stability calculation method for a composite slope with dual internal spoil heaps, as shown in an embodiment of the present invention.

[0059] Figure 2 The above is a plan view of the mining and stripping engineering design before and after an embodiment of the present invention;

[0060] Figure 3 This is a geological profile of a composite slope shown in an embodiment of the present invention;

[0061] Figure 4 This is a schematic diagram of a numerical simulation calculation model shown in an embodiment of the present invention;

[0062] Figure 5This is a perspective view of the displacement field shown in an embodiment of the present invention;

[0063] Figure 6 This is a schematic diagram of the geometric elements of a composite slope with a double internal spoil heap, as shown in an embodiment of the present invention.

[0064] Figure 7 This is a schematic diagram of the geometric elements of the major axis of the ellipsoid and the co-development step distance, as shown in an embodiment of the present invention.

[0065] Figure 8 This is a schematic diagram illustrating the stability calculation model of the abandoned elevation sliding body according to an embodiment of the present invention;

[0066] Figure 9 This is a schematic diagram illustrating the micro-strip column division method and stress analysis in an embodiment of the present invention;

[0067] Figure 10 This is a schematic diagram of the stress analysis model and elements of the micro-strip column bottom interface shown in an embodiment of the present invention;

[0068] Figure 11 This is a schematic diagram (top view) illustrating the division of the computational region according to an embodiment of the present invention;

[0069] Figure 12 This is a schematic diagram illustrating the number of blocks and the conversion of superimposed angles in the division of the region according to an embodiment of the present invention;

[0070] Figure 13 This is a schematic diagram of the force analysis of the strip on the main sliding surface in stage III, as shown in an embodiment of the present invention;

[0071] Figure 14 This is a flowchart illustrating the stability calculation of a composite slope with two internal spoil heaps, as shown in an embodiment of the present invention.

[0072] Figure 15 This is a schematic diagram of the module structure of the three-dimensional stability calculation system for a composite slope with dual internal spoil disposal sites, as shown in an embodiment of the present invention.

[0073] Figure 16 This is a schematic diagram of the structure of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0074] 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.

[0075] The purpose of this invention is to provide a method for calculating the three-dimensional stability of a composite slope with two internal spoil heaps, in order to solve for the three-dimensional stability coefficient of irregular, heterogeneous, tall composite slopes. Here, "two internal spoil heaps" refers to the internal spoil heaps of two adjacent mining areas.

[0076] Please see Figure 1 The above-mentioned three-dimensional stability calculation method may include the following steps:

[0077] S1: Obtain the morphological parameters of the composite slope in the target area, as well as the physical and mechanical parameters of the soil and rock masses in each stratum.

[0078] In this application, by analyzing the engineering geological characteristics of the study area, the morphological parameters of the composite slope in the calculation area (target area) are determined, as well as the physical and mechanical parameters of the soil and rock masses in each stratum required for calculation. These physical and mechanical parameters include cohesion, internal friction angle, and natural unit weight. Morphological parameters include the slope height and angle of the internal spoil heap, as well as the slope height and angle of the mining area; in practice, these morphological parameters can be determined based on the parameters of the internal spoil heap and the mining benches (slope angle, height, and bench width).

[0079] The method provided by this invention will be introduced below with a specific calculation example. In this example, the main rock mass engineering properties are soft rock with low strength and extremely developed weak layers. It is a typical soft rock slope with weak interlayers. The physical and mechanical properties of the rock and soil in each layer are shown in Table 1.

[0080] Table 1 Physical and mechanical parameters of soil and rock mass

[0081]

[0082] Select a typical geological profile E1 from the eastern side, such as Figure 2 The composite slope of section E1 was designed according to the spoil disposal parameters of Mine No. 2 (spoil disposal platform width of 60m, step slope angle of 33°, step height of 30m). Based on the final spoil disposal elevation (+1140m), the spoil disposal area within Mine No. 2 was divided into 4 spoil disposal levels. The geological profile of the resulting composite slope is as follows. Figure 3 As shown.

[0083] S2: Construct a numerical simulation model based on morphological and physical mechanical parameters.

[0084] In applications, modeling software (such as CAD or 3Dmine) can be used to create numerical simulation models. Numerical simulation techniques are then employed to analyze the instability mechanism of the slope and determine its landslide mode. The numerical simulation model of the aforementioned composite slope on the eastern side can be found in [reference needed]. Figure 4 .

[0085] S3: Identify potential sliding bodies in the numerical simulation model.

[0086] In one embodiment, identifying potential sliding bodies in a numerical simulation model includes:

[0087] Draw a three-dimensional perspective displacement contour map and principal sliding surface contour lines of the numerical simulation model;

[0088] Based on the three-dimensional perspective displacement cloud map and the contour lines of the main slip surface, the potential slip surface in the numerical simulation model is determined;

[0089] The sliding body corresponding to the potential sliding surface is taken as the potential sliding body.

[0090] In applications, a potential sliding surface can be approximated as an ellipsoid; the sliding body corresponding to the ellipsoid is identified as the potential sliding body.

[0091] like Figure 3 The numerical simulation model shown uses Tecplot360 software to post-process the results of the composite slope numerical simulation, thereby plotting the corresponding 3D perspective displacement contour map and main slip surface contour lines. The processed 3D perspective displacement contour map can be found in [reference needed]. Figure 5 .

[0092] The potential sliding surface of the double-internal spoil heap composite slope is approximated as an ellipsoid. The three-dimensional model of the adjacent double-internal spoil heap composite slope is as follows: Figure 6 As shown. A three-dimensional coordinate system (x, y, z) is established with the center of the ellipsoid as the origin; the equation of the sliding surface is z... h It can be represented as follows:

[0093]

[0094] In the formula, R a R b , respectively, are the radii of the major and minor axes of the ellipsoid, in meters; z0 represents the z-axis coordinate of the center of the circular arc segment on the principal sliding surface; x is the spatial state equation of the potential sliding surface. h x is the x-axis coordinate; x0 is the x-axis coordinate of the center of the arc segment on the main sliding surface; y is the spatial state equation of the potential sliding surface. h The y-axis coordinate.

[0095] Based on the surface morphology of the sliding body, the slope equation z p These can be represented as follows:

[0096]

[0097] In the formula, H is z p1 The distance from the slope to the x-axis; α is the distance from the slope to the x-axis. p2 Angle between the slope and the x-axis; z p1 The equation for the first slope segment; z p2 This is the equation for the second slope segment;

[0098] The slip surface is a combination of an ellipsoid and a weak layer. Let the dip angle of the weak layer be θ. In this case, the equation of the slip surface is as follows:

[0099]

[0100] In the formula, z h1 The equation for the first segment of the slip surface; z h2 This is the equation for the second slip surface; θ is the dip angle of the weak layer.

[0101] For a schematic diagram of the geometric elements of the ellipsoid's major axis and the co-development step size, please refer to [link / reference]. Figure 7 In the figure, δ represents the slope angle when the spoil heap in the open-pit mine reaches the surface of the east side, in degrees; h1, b, and L represent the slope height, the width of the spoil heap platform, and the coordinated development step distance, respectively, in meters.

[0102] See Figure 7 The distance d between the major axis of the sphere and the step size L of coordinated development can be expressed as follows:

[0103]

[0104] Major axis R of ellipsoid b The relationship between the coordinated development step size L and the step size L can be approximated as follows:

[0105]

[0106] Among them, the collaborative development step distance L, as an important parameter in actual engineering, can be used to guide the relative positional development of two internal spoil heaps in two adjacent mining areas.

[0107] Furthermore, stability calculation models for the sliding bodies at elevations of +1050m, +1080m, +1110m, and +1140m were established. Figure 8 The sliding bodies at each abandoned elevation will be named sliding body 1, sliding body 2, sliding body 3 and sliding body 4 respectively. The corresponding key calculation parameters can be found in Table 2.

[0108] Table 2 Key Calculation Parameters of the Sliding Body Corresponding to Different Drainage Elevations

[0109]

[0110] S4: Divide the potential sliding body into multiple vertical strips.

[0111] In one embodiment, the potential sliding body is divided into multiple vertical strips, including:

[0112] Based on the preset height standard, potential sliding bodies are divided into one or more sliding body stability calculation models with different rejection and abandonment elevations;

[0113] The stability calculation model for each row of abandoned high sliding bodies is divided into multiple vertical blocks.

[0114] In applications, the sliding body can be vertically segmented based on slope morphology, subsurface dip distribution, and base morphology. The sliding body is divided into numerous upright columns with rectangular cross-sections, thus transforming this three-dimensional mechanical problem into a plane strain problem. When segmenting the columns, the base of each column is set to a unit length in the y-direction. To ensure calculation accuracy, columns can be segmented separately at slope step inflection points and where the sliding surface intersects with the rock strata. Constrained by the column segmentation method and the boundaries of the sliding surface and slope, any micro-column (vertical block) can be considered as a hexahedron with mutually perpendicular sides.

[0115] Based on the three-dimensional limit equilibrium slice method, mechanical analysis of any micro-slab reveals that each surface of the micro-slab, except the top surface, is subjected to three forces. The lateral surfaces are subjected to a normal force E and a tangential force T. The normal force E is indicated by a subscript representing the surface on which it acts, such as E... y This represents the normal force on a surface with the y-axis as the normal. For a tangential force T, the first subscript indicates the normal to the surface, and the second subscript indicates the direction of the force, such as T0. yx The force acting along the x-direction on the surface with the y-axis as the normal is represented by tangential force dN; the bottom surface is subjected to normal force dN, anti-slip force dT, and volume force dW. α x α y These represent the angles between the intersection lines of the bottom sliding surface with planes xoz and yoz, and the horizontal plane, respectively. Let the length in the x-direction be dx, and the length in the y-direction be dy. The strip-column partitioning model is illustrated below. Figure 9 As shown.

[0116] S5: Calculate the equivalent physical and mechanical parameters of the potential sliding body based on the bottom mechanical effects of each vertical block.

[0117] In applications, the following assumptions can be made regarding the mechanical conditions of vertical strips:

[0118] ① Ignore all tangential and normal forces between the vertical strips, and ensure that the tangential force on the bottom sliding surface is parallel to the main sliding direction. The anti-slip force in the main sliding direction is represented by dT. x It indicates that the point of application of the normal force at the bottom of the vertical strip is located at the midpoint of the bottom of the vertical strip.

[0119] The force analysis model and element diagram of the vertical strip can be found in [reference needed]. Figure 10 .

[0120] Furthermore, based on the force equilibrium condition, the normal force dN and the sliding force dX on the bottom sliding surface of the vertical strip can be obtained as follows:

[0121] dN=dWcosα x

[0122] dX=dWsinα x

[0123] Based on the Mohr-Coulomb strength criterion, the anti-slip force dT of the vertical strip can be obtained.x as follows:

[0124]

[0125] In the formula, denoted as φ, where φ is the internal friction angle of the vertical strip, in degrees; c is the cohesion of the vertical strip, in kPa; and dA is the area of ​​the bottom surface of the vertical strip.

[0126] Using trigonometric relationships and the definition of partial derivatives, we can obtain:

[0127]

[0128] Based on the geometric relationships of the parameters of the sliding surface, we can obtain:

[0129]

[0130]

[0131]

[0132] By analyzing the slope and slip surface morphology, the volume force dW of the vertical strip block can be obtained as follows:

[0133] dW=γ(z p -z h )dxdy;

[0134] In the formula, γ is the unit weight of the microstrip column, in kN / m. 3 .

[0135] In applications, to facilitate the calculation of the volume of vertical blocks, the irregularly shaped spatial volume formed by the slope and slip surface can be divided into three regions for calculation, named Zone A, Zone B, and Zone C respectively. The division of the calculation regions is illustrated below. Figure 11 As shown.

[0136] For the volume force dW of the i-th row and j-th column micro-strip under circular arc sliding, ij It is expressed as follows:

[0137]

[0138] In one embodiment, calculating the equivalent physical and mechanical parameters of the potential sliding body based on the bottom surface mechanical effects of each vertical strip may include the following steps:

[0139] The bottom mechanical effects of each vertical block are superimposed, and the superimposed sliding force and superimposed anti-slip force of each vertical block are calculated under multiple stages.

[0140] Based on the superimposed sliding force and superimposed anti-slip force, the equivalent physical and mechanical parameters of the potential sliding body at each stage are calculated.

[0141] In application, the mechanical effects of the bottom surface of the divided micro-strips (vertical blocks) can be superimposed, and the sliding force X and anti-slip force T of each row of micro-strips can be solved in stages. Then, similar terms can be combined to solve the equivalent physical and mechanical parameters of each stage of the blocks on the main sliding surface.

[0142] When analyzing the anti-slip force and sliding force of each row, it is necessary to clarify the volume of each vertical strip. The volume of each vertical strip can be solved by subtracting the slope equation and the slip surface equation in the x-direction (dip). Since neither the slope equation nor the slip surface equation is composed of a single equation, it needs to be solved in multiple stages. Specifically, the superposition of mechanical effects can be divided into three stages: Stage I, Stage II, and Stage III. Let n be the number of rows of vertical strips in Stage I, and r1 be the number of Zone A strips in the r-th row. The diagram of the number of strips in each zone and the conversion of superposition angle is shown below. Figure 12 As shown.

[0143] The superimposed sliding force X of the r-th row of blocks in stage I r With anti-slip force T r It is expressed as follows:

[0144]

[0145]

[0146]

[0147] Where, γ rj The weight of the vertical strip in row r and column j; z p1 The equation for the first slope segment; z h1 The equation for the first segment of the slip surface; α xrj Let dx be the angle between the intersection of the bottom sliding surface of the vertical strip in row r and column j with plane xoz and the horizontal plane; r ω is the length of the vertical strip in the r-th row in the x-direction; rj The angle (ω) between the bottom sliding surface of the main sliding block in the direction of the vertical block at row r, column j and the plane xoz containing the bottom sliding surface of the vertical block at row r, column j. rj =α xrj -θ); c is the internal friction angle of the vertical strip in the r-th row and j-th column; rj α is the cohesive force of the vertical strip in the r-th row and j-th column; yrj α is the angle between the intersection of the bottom sliding surface of the vertical strip in row r and column j with the plane yoz and the horizontal plane; r The angle between the bottom surface of the r-th row of vertical strips on the main sliding surface and the horizontal line; z' hx (r,j) and z' hx (r,0) represents the partial derivative.

[0148] Let k be the number of zones along the x-direction in stage II, and u1 be the number of Zone B zones in the u-th row. Then the superimposed sliding force X of the zones in the u-th row is... u With anti-slip force T u They are represented as follows:

[0149]

[0150]

[0151] In the formula, cosω uj =cos(α) xuj -θ).

[0152] Where, γ uj The weight of the vertical strip in row u and column j; z p1 The equation for the first slope segment; z h1 The equation for the first segment of the slip surface; α xuj Let dx be the angle between the intersection of the bottom sliding surface of the vertical strip in row u and column j with plane xoz and the horizontal plane; u ω is the length of the vertical strip in the u-th row in the x-direction; uj The angle (ω) between the bottom sliding surface of the main sliding block in the direction of the block at row u, column j and the plane xoz containing the bottom sliding surface of the perpendicular block at row r, column j. uj =α xuj -θ); Let c be the internal friction angle of the vertical strip in row u and column j; uj α is the cohesive force of the vertical strip in row u and column j; yuj θ is the angle between the intersection of the bottom sliding surface of the vertical strip in row u and column j with the plane yoz and the horizontal plane; θ is the dip angle of the weak layer.

[0153] Let p be the number of blocks divided along the x-direction in stage III, and let s1 and s2 be the number of blocks in regions B and C of row s, respectively. According to the analysis of the sliding surface spatial morphology, the change in the size of s2 is negligible as the major axis of the sliding ellipsoid changes.

[0154] The superimposed sliding force X of the s-th row of blocks in stage III s With anti-slip force T s :

[0155]

[0156]

[0157] In the formula, cosω sj =cos(α) xsj -θ).

[0158] in, z represents the weight of the vertical strip in the s-th row and j-th column of region B; p2 The equation for the second slope segment; z h2 This is the equation for the second segment of the slip surface; Let be the length of the vertical strip in the s-th row of region B in the x-direction; Let S be the weight of the vertical strip in the s-th row and j-th column of region C; Let be the angle between the intersection of the bottom sliding surface of the vertical strip in the s-th row and j-th column of region C and the plane xoz, and the horizontal plane; ω is the length of the vertical strip in the s-th row of region C in the x-direction; sj Let xoz be the angle between the bottom surface of the main sliding block in the direction of the vertical block at row s and column j and the plane xoz containing the bottom surface of the vertical block at row s and column j.

[0159] Let be the internal friction angle of the vertical strip in the s-th row and j-th column of region B; Let be the cohesion of the vertical strip in the s-th row and j-th column of region B; Let be the internal friction angle of the vertical strip in the s-th row and j-th column of region C; Let be the cohesion of the vertical strip in the s-th row and j-th column of region C; Let be the angle between the intersection of the bottom sliding surface of the vertical strip in the s-th row and j-th column of region C and the plane yoz, and the horizontal plane.

[0160] By combining the mechanical effects corresponding to the main sliding surface with the superimposed mechanical effects of each row of micro-strips, the equivalent unit weight γ of the strips at each stage of the sliding body can be calculated. d Equivalent cohesion c d and equivalent friction coefficient Force analysis of the blocks on the main sliding surface in stage III is as follows: Figure 13 As shown.

[0161] Let the sliding force and anti-slip force of the bottom interface after the two-dimensional equivalent of the three-dimensional mechanical effect in stage I be X, respectively. Ⅰd T Ⅰd Then, for the r-th vertical block on the main sliding surface, the sliding force X Ⅰdr With anti-slip force T Ⅰdr The following are included:

[0162]

[0163]

[0164] In the formula,

[0165] Where, γ Ⅰdr This represents the equivalent bulk density for Stage I; zp1 The equation for the first slope segment; α r The angle between the bottom surface of the r-th row of vertical strips on the main sliding surface and the horizontal line; dx r Let be the length of the vertical strip in the r-th row in the x-direction; c is the equivalent friction factor for stage I; Ⅰdr The equivalent cohesion for stage I; dy r Let be the length of the sliding boundary corresponding to the vertical strip in the r-th row in the y-direction.

[0166] According to X Ⅰdr =X r T Ⅰdr =T r We can obtain:

[0167]

[0168]

[0169]

[0170] Where r1 is the number of ZoneA blocks in the r-th row, j is the number of columns of ZoneA blocks, and γ rj Let z be the weight of the strip at row r, column j. p1 It is part of the slope equation Zp, and its value is equal to H (H represents z). p1 (distance from the plane to the x-axis), α xrj Let dx be the angle between the intersection of the bottom sliding surface of the strip at row r, column j and plane xoz and the horizontal plane. r ω is the length of the sliding body boundary corresponding to the strip in row r. rj Let ω be the angle (ω) between the bottom sliding surface of the main sliding surface of the strip at row r, column j and the bottom sliding surface of the strip at row r, column j in the plane xoz. rj =α xrj -θ), α r Let dy be the angle between the line of intersection of the r-th strip bottom sliding surface of the main sliding surface and the plane xoz and the horizontal plane. r y is the width of the sliding body boundary corresponding to the vertical strip in the r-th row in the y direction.

[0171] Let the sliding force and anti-slip force of the bottom interface after the two-dimensional equivalent of the three-dimensional mechanical effect in stage II be X, respectively. Ⅱd T Ⅱd Then, for the u-th vertical block on the main sliding surface, the sliding force X at the bottom interface is... Ⅱdu With anti-slip force T Ⅱdu The following are included:

[0172]

[0173]

[0174] In the formula, dy u Let be the length of the vertical strip in the u-th row in the y-direction.

[0175] Where, γ Ⅱdu The equivalent unit weight of the u-th vertical strip on the main sliding surface in stage II; z p22 For z p2 The equations on the principal sliding surface, with respect to the xoz plane; α u dx is the angle between the intersection of the bottom sliding surface of the u-th vertical strip and the plane xoz and the horizontal plane; u dy is the length of the vertical strip in the u-th row in the x-direction. u Let be the width of the sliding body boundary corresponding to the vertical strip in the u-th row in the y-direction; The equivalent friction coefficient of the u-th vertical strip on the main sliding surface in stage II; c Ⅱdu It represents the equivalent cohesion of the u-th vertical strip on the main sliding surface in stage II.

[0176] According to X Ⅱdu =X u T Ⅱdu =T u We can obtain:

[0177]

[0178]

[0179]

[0180] u1 represents the number of vertical stripes in ZoneB of the u-th row, γ uj Let α be the unit weight of the vertical strip at row u, column j. xuj Let dx be the angle between the intersection of the vertical strip bottom surface at row u, column j and plane xoz and the horizontal plane. u ω is the length of the sliding body boundary corresponding to the vertical strip in the u-th row. uj Let ω be the angle (ω) between the bottom sliding surface of the main sliding surface perpendicular to the vertical strip at row u, column j and the bottom sliding surface of the vertical strip at row r, column j in the plane xoz. uj =α xuj -θ), α u The angle between the line of intersection of the u-th vertical strip bottom sliding surface of the main sliding surface and the plane xoz and the horizontal plane; dy u The width of the sliding body boundary corresponding to the vertical block in row u.

[0181] Let the sliding force and anti-slip force of the bottom interface after the three-dimensional mechanical effect of stage III be X and X, respectively. Ⅲd T ⅢdThen, for the bottom interface of the vertical strip in the s-th row on the main sliding surface, the sliding force X Ⅲds With anti-slip force T Ⅲds It should include the following:

[0182] X Ⅲds =γ Ⅲds (z p22 -z h2 )sinθdx s dy s ;

[0183]

[0184] In the formula, z h2 = -xtanθ, dy s is the length of the sliding boundary corresponding to the vertical block in row s.

[0185] Where, γ Ⅲds The equivalent unit weight of the s-th vertical strip on the main sliding surface in stage III; z p22 For z p2 The equations on the principal sliding surface, with respect to the xoz plane; z h2 The equation for the second slip surface; dx s Let be the length of the vertical strip in the s-th row in the x-direction; c is the equivalent friction coefficient of the r-th vertical strip on the main sliding surface in stage III; Ⅲdr This represents the equivalent cohesion of the r-th vertical strip on the main sliding surface in stage III.

[0186] According to X Ⅲds =X s T Ⅰds =T s We can obtain:

[0187]

[0188]

[0189]

[0190] In the formula, dx s dy represents the width of the sliding body boundary corresponding to the vertical strip in the s-th row in the x-direction. s y is the width of the sliding body boundary corresponding to the vertical strip in the s-th row in the y-direction.

[0191] S6: Introduce the equivalent physical and mechanical parameters into the Morgenstern-Price method, setting the bulk density λ and the three-dimensional stability coefficient F. s The initial value is set according to the elasticity theory, and the expression of the function f(x) is set.

[0192] The function expression f(x) satisfies the boundary equilibrium equation: X i =λf(x)E' i ;

[0193] In the formula, E' i X represents the normal force of the block. i This represents the tangential force of the block; λ is a constant between 0 and 1.

[0194] In applications, based on the equivalent physical and mechanical parameters at each stage, the Morgenstern-Price method can be used to construct a functional expression f(x) for the three-dimensional stability coefficient Fs.

[0195] The equivalent physical and mechanical parameters of each stage are introduced into the Morgenstern-Price method. Initial values ​​for λ and Fs are assumed, and the expression for the function f(x) is defined. The normal force E' of the strip is assumed to be... i With tangential force X i The relationship between them is as follows:

[0196] X i =λf(x)E' i .

[0197] The boundary conditions are expressed as follows:

[0198]

[0199] S7: Adjust the values ​​of λ and Fs until the boundary equilibrium equation satisfies the boundary conditions, and use the current value of Fs as the final three-dimensional stability coefficient of the composite slope.

[0200] The boundary condition is that the external force acting on the potential sliding body is zero.

[0201] In the application, the absence of external forces acting on the slope sliding body (boundary condition) is taken as the condition for the calculation process to terminate. Based on the theory of elasticity, the functional expression of the half-sine function f(x) is assumed, and the values ​​of λ and Fs are continuously adjusted and substituted into the boundary condition calculation. Further judgment is made on whether the boundary condition is satisfied. If it is not satisfied, the values ​​are adjusted again; if it is satisfied, the corresponding Fs is output, which is the three-dimensional stability coefficient of the composite slope under the load of the double internal soil dump.

[0202] The calculation process of the above method can be exemplified by [reference needed]. Figure 14 Calculate the major axis R of the sliding body corresponding to different discharge elevations. b The three-dimensional stability coefficient Fs for composite slopes ranging from 200 to 1200m can be found in Table 3.

[0203] Table 3. Calculation results of composite slope stability

[0204]

[0205]

[0206]

[0207] Corresponding to the aforementioned application function implementation method embodiments, the present invention also provides a three-dimensional stability calculation system, equipment, medium, and corresponding embodiments for a composite slope with dual internal spoil disposal sites.

[0208] Please see Figure 15 , Figure 15 This is a schematic diagram of the module structure of a composite slope three-dimensional stability calculation system according to an embodiment of the present invention; the system includes:

[0209] The parameter acquisition module 151 is used to acquire the morphological parameters of the composite slope in the target area, as well as the physical and mechanical parameters of the soil and rock masses in each stratum.

[0210] Model building module 152 is used to build a numerical simulation model based on morphological parameters and physical and mechanical parameters;

[0211] Sliding body search module 153 is used to identify potential sliding bodies in the numerical simulation model;

[0212] Sliding body division module 154 is used to divide a potential sliding body into multiple vertical strips;

[0213] The calculation and processing module 155 is used for:

[0214] Based on the bottom mechanical effects of each vertical block, calculate the equivalent physical and mechanical parameters of the potential sliding body;

[0215] The equivalent physical and mechanical parameters are introduced into the Morgenstern-Price method, and the bulk density λ and the three-dimensional stability coefficient F are set. s The initial values ​​are set according to elasticity theory, and the function expression f(x) is set; the function expression f(x) satisfies the boundary equilibrium equation: X i =λf(x)E' i ; where E' i X represents the normal force of the block. i This represents the tangential force of the strip; λ is a constant between 0 and 1.

[0216] Adjust the values ​​of λ and Fs until the boundary equilibrium equation satisfies the boundary conditions, and take the current value of Fs as the final three-dimensional stability coefficient of the composite slope; the boundary condition is that the external force on the potential sliding body is zero.

[0217] Regarding the system in the above embodiments, the specific ways in which each module performs operations have been described in detail in the embodiments related to the method, and will not be elaborated further here.

[0218] This invention also provides an electronic device, please refer to [link to relevant documentation]. Figure 16 The electronic device 1600 includes a memory 1610 and a processor 1620.

[0219] The processor 1620 can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor.

[0220] Memory 1610 may include various types of storage units, such as system memory, read-only memory (ROM), and permanent storage devices. ROM may store static data or instructions required by processor 1620 or other modules of the computer. Permanent storage devices may be read-write storage devices. Permanent storage devices may be non-volatile storage devices that retain stored instructions and data even when the computer is powered off. In some embodiments, permanent storage devices use mass storage devices (e.g., magnetic or optical disks, flash memory) as permanent storage devices. In other embodiments, permanent storage devices may be removable storage devices (e.g., floppy disks, optical drives). System memory may be a read-write storage device or a volatile read-write storage device, such as dynamic random access memory. System memory may store some or all of the instructions and data required by the processor during operation. Furthermore, memory 1610 may include any combination of computer-readable storage media, including various types of semiconductor memory chips (e.g., DRAM, SRAM, SDRAM, flash memory, programmable read-only memory), and disks and / or optical disks may also be used. In some embodiments, the memory 1610 may include a removable storage device that is readable and / or writable, such as a laser disc (CD), a read-only digital multifunction optical disc (e.g., DVD-ROM, dual-layer DVD-ROM), a read-only Blu-ray disc, an ultra-high-density optical disc, a flash memory card (e.g., SD card, mini SD card, Micro-SD card, etc.), a magnetic floppy disk, etc. Computer-readable storage media do not contain carrier waves or transient electronic signals transmitted wirelessly or via wired connections.

[0221] The memory 1610 stores executable code, which, when processed by the processor 1020, can cause the processor 1620 to execute part or all of the methods described above.

[0222] Furthermore, the method according to the present invention can also be implemented as a computer program or computer program product, which includes computer program code instructions for performing some or all of the steps in the above-described method of the present invention.

[0223] Alternatively, the present invention may also be implemented as a computer-readable storage medium (or a non-transitory machine-readable storage medium or a machine-readable storage medium) storing executable code (or computer program or computer instruction code) thereon, which, when executed by a processor of an electronic device (or server, etc.), causes the processor to perform part or all of the steps of the method described above according to the present invention.

[0224] The various embodiments of the present invention have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical application, or improvement of the technology in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A method for calculating the three-dimensional stability of a composite slope with two internal spoil heaps, characterized in that, include: S1: Obtain the morphological parameters of the composite slope in the target area, as well as the physical and mechanical parameters of the soil and rock masses in each stratum; S2: Construct a numerical simulation model based on the morphological and physical parameters; S3: Identify potential sliding bodies in the numerical simulation model; S4: Divide the potential sliding body into multiple vertical strips; S5: Calculate the equivalent physical and mechanical parameters of the potential sliding body based on the bottom mechanical effects of each of the vertical blocks; S6: Introduce the equivalent physical and mechanical parameters into the Morgenstern-Price method, setting the bulk density λ and the three-dimensional stability coefficient F. s The initial value is set according to the elasticity theory, and the function expression f(x) is set; the function expression f(x) satisfies the boundary equilibrium equation: X i =λf(x)E' i ; Among them, E' i X represents the normal force of the block. i Indicates the tangential force of the strip; S7: Adjust λ and F s The value of F is taken until the boundary equilibrium equation satisfies the boundary conditions, and the current value of F is then set. s The final three-dimensional stability coefficient of the composite slope is defined as follows: the boundary condition is that the external force acting on the potential sliding body is zero.

2. The method for calculating the three-dimensional stability of a composite slope with dual internal spoil heaps according to claim 1, characterized in that, S3: Determining the potential sliding bodies in the numerical simulation model specifically includes: S31: Draw the three-dimensional perspective displacement cloud map and principal sliding surface contour lines of the numerical simulation model; S32: Based on the three-dimensional perspective displacement cloud map and the contour lines of the main slip surface, determine the potential slip surface in the numerical simulation model; S33: The sliding body corresponding to the potential sliding surface is taken as the potential sliding body; The spatial state equation of the potential slip surface z h The expression is: Among them, R a R b These represent the radii of the major and minor axes of the ellipsoid, respectively; z0 represents the z-axis coordinate at the center of the circular arc segment on the principal sliding surface; x is the spatial state equation of the potential sliding surface. h x is the x-axis coordinate; x0 is the x-axis coordinate of the center of the arc segment on the main sliding surface; y is the spatial state equation of the potential sliding surface. h The y-axis coordinate.

3. The method for calculating the three-dimensional stability of a composite slope with dual internal spoil heaps according to claim 1, characterized in that, S4: Dividing the potential sliding body into multiple vertical strips specifically includes: S41: Based on the preset height standard, the potential sliding body is divided into one or more sliding body stability calculation models with different rejection and abandonment elevations; S42: Divide each of the aforementioned displacement elevation sliding body stability calculation models into multiple vertical blocks.

4. The method for calculating the three-dimensional stability of a composite slope with dual internal spoil heaps according to claim 3, characterized in that, The expression for the normal force dN on the bottom sliding surface of the vertical strip is: dN=dWcosα x ; Where dW is the volume force; α x The angle between the line of intersection of the bottom sliding surface and the plane xoz and the horizontal plane; The expression for the sliding force dX on the bottom surface of the vertical strip is: dX=dWsinα x ; The anti-slip force dT of the bottom sliding surface of the vertical strip x The expression is: in, denoted as , where is the internal friction angle of the vertical strip; and c is the cohesive force of the vertical strip. dA is the area of ​​the bottom surface of the vertical strip; α y The angle between the line of intersection of the bottom sliding surface and the plane yoz and the horizontal plane; The expression for the volume force dW of the vertical strip is: dW=γ(z p -With h )dxdy; Where γ is the specific weight of the vertical strip; dx is the length in the x-direction, dy is the length in the y-direction; z h The equation for the smooth surface is z. p Here is the equation for the slope.

5. The method for calculating the three-dimensional stability of a composite slope with dual internal spoil heaps according to claim 1, characterized in that, S5: Based on the bottom surface mechanical effects of each of the vertical blocks, calculate the equivalent physical and mechanical parameters of the potential sliding body, specifically including: S51: Superimpose the bottom mechanical effects of each vertical block, and calculate the superimposed sliding force and superimposed anti-slip force of each vertical block under multiple stages; S52: Calculate the equivalent physical and mechanical parameters of the potential sliding body at each stage based on the superimposed sliding force and superimposed anti-slip force; the equivalent physical and mechanical parameters include equivalent unit weight, equivalent cohesion and equivalent friction coefficient.

6. The method for calculating the three-dimensional stability of a composite slope with dual internal spoil heaps according to claim 5, characterized in that, The multiple stages are specifically divided into three stages: Stage I, Stage II, and Stage III. The equivalent bulk density includes: the equivalent bulk density γ of stage I. Ⅰdr Phase II equivalent bulk density γ Ⅱdu and the equivalent bulk density γ of stage III Ⅲds ; The equivalent cohesive force includes: the equivalent cohesive force c in the first stage. Ⅰdr Stage II equivalent cohesion c Ⅱdu and the equivalent cohesion of stage III c Ⅲds ; The equivalent friction coefficient includes: the equivalent friction coefficient for stage I. Stage II equivalent friction factor and the equivalent friction factor of stage III 7. A three-dimensional stability calculation system for a composite slope with dual internal spoil heaps, characterized in that, The system, applicable to the method of any one of claims 1-6, comprises: The parameter acquisition module is used to acquire the morphological parameters of the composite slope in the target area, as well as the physical and mechanical parameters of the soil and rock masses in each stratum. The model building module is used to construct a numerical simulation model based on the morphological parameters and physical and mechanical parameters. A sliding body search module is used to identify potential sliding bodies in the numerical simulation model; The sliding body division module is used to divide the potential sliding body into multiple vertical strips; The calculation and processing module is used for: Based on the bottom surface mechanical effects of each of the vertical blocks, calculate the equivalent physical and mechanical parameters of the potential sliding body; The equivalent physical and mechanical parameters are introduced into the Morgenstern-Price method, and the bulk density λ and the three-dimensional stability coefficient F are set. s The initial value is set according to the elasticity theory, and the function expression f(x) is set; the function expression f(x) satisfies the boundary equilibrium equation: X i =λf(x)E' i ; Among them, E' i X represents the normal force of the block. i Indicates the tangential force of the strip; The values ​​of λ and Fs are adjusted until the boundary equilibrium equation satisfies the boundary conditions, and the current value of Fs is taken as the final three-dimensional stability coefficient of the composite slope; the boundary condition is that the external force on the potential sliding body is zero.

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