Method and device for determining stability of rock slope wedge failure

Abstract

The present application relates to the technical field of rock slope engineering stability analysis, and discloses a method and device for determining the stability of wedge-shaped body failure of rock slope, which comprises the following steps: establishing a three-dimensional Cartesian coordinate system according to the determined parameters of two spatial structural planes and the shape of the wedge-shaped body in the rock slope, determining the structural plane equation and the wedge-shaped body slope surface equation; dividing the potential sliding body of the wedge-shaped body into a plurality of vertical micro-strip columns with rectangular cross sections; the cross section lengths of the plurality of vertical micro-strip columns are different at different positions; performing mechanical analysis on each vertical micro-strip column according to the two spatial structural plane parameters, the structural plane equation and the wedge-shaped body slope surface equation, and determining the mechanical parameters of each vertical micro-strip column; dividing the wedge-shaped body into a plurality of regions according to the intersection characteristics of the sliding surface and the slope surface, and performing regional force superposition in combination with the two spatial structural plane parameters, the structural plane equation and the wedge-shaped body slope surface equation to determine the stability coefficient of the wedge-shaped body failure.

Description

Technical Field

[0001] This invention relates to the field of stability analysis technology for rock slope engineering, and in particular to a method and apparatus for determining the stability of wedge-shaped rock slope failure. Background Technology

[0002] Faults, joints and other structural planes are commonly found in rock slopes. When two spatial structural planes intersect, they can easily form a wedge-shaped potential landslide. Shear failure of such landslides along the double structural planes is one of the main modes of instability of rock slopes.

[0003] Current methods for analyzing the stability of wedge-shaped bodies suffer from three major technical challenges: First, traditional two-dimensional limit equilibrium methods ignore the spatial geometric features of the structural surfaces, making it difficult to accurately construct the sliding surface equations and leading to deviations in the identification of potential sliding body boundaries. Second, the sliding body division often uses uniform blocks without optimization for key locations, resulting in large errors in the assignment of mechanical parameters. Third, the lack of regional force superposition calculation logic makes it impossible to accurately reflect the synergistic influence of the two structural surfaces on the stability of the sliding body, and it is easy to misjudge the failure mode and stability coefficient.

[0004] Therefore, there is an urgent need in this field for a solution that can accurately calculate the stability of wedge failure in rock slopes. Summary of the Invention

[0005] The purpose of this invention is to provide at least one method and apparatus for determining the stability of wedge-shaped rock slope failure, which can at least solve the problem of inaccurate stability calculation of wedge-shaped rock slope failure, and can at least achieve accurate identification of potential landslides and sliding surfaces, clarify the slope failure mode, and realize the scientific assessment of landslide disaster risk.

[0006] To address the aforementioned technical problems, at least one embodiment of this application provides a method for determining the stability of wedge-shaped rock slope failure, comprising: establishing a three-dimensional Cartesian coordinate system based on the determined parameters of two spatial structural surfaces constituting the wedge and the wedge's morphology, and determining the structural surface equation and the wedge slope equation; dividing the potential sliding body of the wedge into multiple upright micro-strips with rectangular cross-sections; wherein the cross-sectional lengths of the multiple upright micro-strips are different at different locations; performing mechanical analysis on each upright micro-strip based on the two spatial structural surface parameters, the structural surface equation, and the wedge slope equation to determine the mechanical parameters of each upright micro-strip; dividing the wedge into multiple regions according to the intersection characteristics of the sliding surface and the slope surface, and performing regional force superposition by combining the two spatial structural surface parameters, the structural surface equation, and the wedge slope equation to determine the stability coefficient of the wedge failure.

[0007] The stability determination method for wedge-shaped rock slope failure provided in this application takes a wedge-shaped rock composed of two structural planes as the research object. Based on a constructed three-dimensional Cartesian coordinate system, it accurately locks the potential sliding surface boundary through structural plane equations, solving the slip surface identification error problem of traditional methods. By differentiating the length of the blocks at different key locations, it reduces the error in assigning mechanical parameters. Through regional force superposition logic, it fully reflects the synergistic constraint effect of the two structural planes on the stability of the sliding body, avoiding the stability coefficient deviation caused by single-region calculation. It can accurately identify the potential sliding body boundary and sliding surface morphology of the slope under the influence of structural planes, clarify the "wedge shear along the two structural planes" failure mode, and provide a scientific basis for stability analysis and disaster risk assessment of rock slopes with complex structural planes. It is applicable to rock slope engineering design in fields such as water conservancy, mining, and transportation. Verified through engineering examples, the stability coefficient calculation results of this method are in high agreement with the field monitoring data. It can effectively identify the "dual-structure shear type" failure mode. For rock slopes with multiple complex structural surfaces, such as open-pit mine slopes, water conservancy slopes, and road cut slopes, it can provide full-process technical support from landslide identification and failure mode determination to risk classification, significantly improving the scientificity and reliability of slope landslide disaster risk assessment and filling the technical gap in three-dimensional limit equilibrium analysis of rock slopes with complex structural surfaces.

[0008] In some optional embodiments, a three-dimensional Cartesian coordinate system is established based on the determined parameters of the two spatial structural surfaces constituting the wedge in the rock slope and the wedge shape, and the equations of the structural surfaces and the wedge slope are determined. This includes: determining the parameters of the two spatial structural surfaces constituting the wedge in the rock slope and the wedge shape based on field geological logging, semantic segmentation of UAV aerial images, and drilling data; establishing a three-dimensional Cartesian coordinate system based on the wedge shape, with the intersection of the wedge and the slope toe as the origin, the x-axis pointing outward along the main sliding direction, the y-axis perpendicular to the x-axis in the horizontal direction, and the z-axis pointing vertically upward; and determining the equations of the structural surfaces and the wedge slope based on the three-dimensional Cartesian coordinate system and the determined equations of the two spatial structural surfaces and the wedge shape.

[0009] Through the methods described above, the on-site geological logging, UAV aerial image semantic segmentation, and drilling data contain a large amount of spatial structural and geological data. From these, the parameters of the two spatial structural planes constituting the wedge in the rock slope and the morphology of the wedge can be obtained. This effectively overcomes the limitations of identifying the spatial distribution of structural planes from a single data source, significantly improving the completeness and reliability of the structural plane parameter acquisition, and laying a solid data foundation for subsequent stability analysis.

[0010] In some optional embodiments, the different positions include: a first position and a second position; the first position includes: the inflection point of the slope step in the main sliding direction of the slope, and the intersection of the sliding surface and the rock layer in the main sliding direction of the slope; the second position is the remaining position in the main sliding direction of the slope excluding the first position; any of the upright micro-strips is a hexahedron with mutually perpendicular sides; the cross-sectional length of the plurality of upright micro-strips in the first position is a first unit length; the cross-sectional length of the plurality of upright micro-strips in the second position is a second unit length; the first unit length is less than the second unit length.

[0011] By setting different segmentation lengths—a smaller first unit length at the first location and a larger second unit length at the second location—a non-uniform, focused segmentation mechanism is achieved. This ensures higher spatial resolution in key control areas, thereby more accurately capturing local slip surface dip angle changes, abrupt changes in contact area, and discontinuities in rock mass mechanical parameters. In non-critical areas, the segmentation granularity is appropriately relaxed to balance computational efficiency. This strategy effectively balances the contradiction between computational accuracy and resource consumption, avoids redundant calculations caused by global fine segmentation, and overcomes the problem of uniform coarse segmentation masking the instability characteristics of key areas.

[0012] In some optional embodiments, based on the two spatial structural surface parameters, the structural surface equation, and the wedge-shaped slope equation, a mechanical analysis is performed on each of the vertical micro-strip columns to determine the mechanical parameters of each vertical micro-strip column. This includes: based on the two spatial structural surface parameters, the structural surface equation, and the wedge-shaped slope equation, and using the three-dimensional limit equilibrium slice method, force assumptions and force balance derivations are made for each vertical micro-strip column to determine the normal force, anti-slip force, and volume force of each vertical micro-strip column as mechanical parameters; wherein, the point of application of the normal force is located at the centroid of the bottom surface of each micro-strip column, the anti-slip force is parallel to the main sliding direction, and the volume force is obtained by analyzing the slope and sliding surface morphology.

[0013] Using the above method, within the framework of three-dimensional limit equilibrium theory, and combining the parameters of two spatial structural surfaces, structural surface equations, and wedge-shaped slope equations, a systematic force assumption and force balance derivation are performed for each upright micro-strip column. This process not only strictly follows the basic principles of statics but also fully considers the three-dimensional sliding constraint mechanism formed by the intersection of the two structural surfaces, giving each micro-strip column's mechanical model a clear physical basis and engineering interpretability, significantly superior to the simplified treatment of the sliding force system in traditional two-dimensional or pseudo-three-dimensional methods. The determination process of the above mechanical parameters deeply couples the geometric boundaries described by the structural surface equations with the strength characteristics defined by the rock mass mechanical parameters. Since all micro-strip columns share a unified three-dimensional Cartesian coordinate system and equation system, and the derivation logic of the mechanical parameters is consistent, the mechanical analysis of the entire sliding body possesses the dual advantages of good overall coordination and local refinement.

[0014] In some optional embodiments, the wedge is divided into multiple regions based on the intersection characteristics of the sliding surface and the slope surface. The forces in each region are superimposed using the two spatial structural surface parameters, the structural surface equation, and the wedge slope equation to determine the stability coefficient of the wedge failure. This includes: dividing the wedge into multiple regions based on the intersection characteristics of the sliding surface and the slope surface; each region includes multiple upright micro-strips; superimposing the mechanical effects of the bottom surfaces of the multiple upright micro-strips in each region according to the two spatial structural surface parameters, the structural surface equation, and the wedge slope equation; solving in stages the superimposed sliding force and superimposed anti-slip force of the multiple upright micro-strips in each region; combining similar terms of the superimposed sliding force and superimposed anti-slip force of the multiple upright micro-strips in each region to solve for the equivalent physical and mechanical parameters of the upright micro-strips at each stage on the main sliding surface, and determining the stability coefficient of the wedge failure.

[0015] Using the above method, this study focuses on a wedge-shaped body composed of two structural planes. Based on a constructed three-dimensional Cartesian coordinate system, it accurately identifies the potential sliding surface boundary through structural plane equations, solving the slip surface identification bias problem of traditional methods. By differentiating the length of the blocks at different key locations, it reduces the error in assigning mechanical parameters. Through regional force superposition logic, it fully reflects the synergistic constraint effect of the two structural planes on the stability of the sliding body, avoiding the stability coefficient deviation caused by single-region calculations. It can accurately identify the potential sliding body boundary and sliding surface morphology of slopes under the influence of structural planes, clarify the "wedge-shaped body shearing along the two structural planes" failure mode, and provide a scientific basis for the stability analysis and disaster risk assessment of rock slopes with complex structural planes. It is applicable to the engineering design of rock slopes in fields such as water conservancy, mining, and transportation.

[0016] In some optional embodiments, the wedge-shaped slope equation includes: a first slope elevation equation and a second slope elevation equation; the plurality of regions include: a first wedge region, a second wedge region, and a third wedge region; the top surface of the upright micro-strip column in the first wedge region is linearly constrained by the first slope elevation equation; the top surface of the upright micro-strip column in the second wedge region is nonlinearly constrained by both the first and second slope elevation equations; the top surface of the upright micro-strip column in the third wedge region is linearly constrained by the second slope elevation equation.

[0017] Using the above method, the wedge-shaped body is divided into three regions with clear geometric and mechanical significance based on the segmented slope morphology of the actual engineering slope, and each region is assigned a constraint relationship with the corresponding slope elevation equation. This division method closely matches the engineering characteristics of real rock slopes, which often have multiple steps, multiple slope segments, and discontinuous slopes. This allows stability analysis to move beyond the idealized assumption of a single slope and realistically reflect the spatial coupling relationship between the sliding body and the slope under complex terrain conditions. In some optional embodiments, the two spatial structural surfaces include: a first spatial structural surface and a second spatial structural surface; the parameters of the two spatial structural surfaces include: the dip direction, dip angle, internal friction angle, cohesion, bottom slip surface area, and rock mass unit weight of the first spatial structural surface, and the dip direction, dip angle, internal friction angle, cohesion, bottom slip surface area, and rock mass unit weight of the second spatial structural surface; the wedge shape includes: slope height and slope angle.

[0018] By employing the aforementioned methods, the geometric and mechanical parameters of the first and second spatial structural surfaces are obtained and accurately characterized. Combined with their corresponding engineering properties such as bottom sliding surface area and rock mass unit weight, as well as the slope surface morphology characterized by slope height and slope angle, a complete three-dimensional wedge-shaped sliding body geometry and force boundary conditions under the control of the dual structural surfaces can be constructed. This spatial structural surface parameter system provides the necessary input foundation for subsequently establishing a three-dimensional Cartesian coordinate system and deriving the structural surface equations and slope equations, thereby achieving accurate identification of potential sliding body boundaries and effectively overcoming the ambiguity and subjectivity of traditional two-dimensional or simplified three-dimensional methods in sliding surface positioning.

[0019] At least one embodiment of this application also provides a stability determination device for the failure of a wedge-shaped rock slope, comprising: The module for determining the structural plane and wedge slope equations is used to establish a three-dimensional Cartesian coordinate system and determine the structural plane equations and wedge slope equations based on the parameters of the two spatial structural planes constituting the wedge and the shape of the wedge in the determined rock slope. The module for dividing the wedge into vertical micro-strips is used to divide the potential sliding body of the wedge into multiple vertical micro-strips with rectangular cross-sections; the cross-sectional lengths of the multiple vertical micro-strips are different at different locations. The mechanical analysis module is used to perform mechanical analysis on each vertical micro-strip based on the two spatial structural plane parameters, the structural plane equations, and the wedge slope equations to determine the mechanical parameters of each vertical micro-strip. The stability coefficient determination module is used to divide the wedge into multiple regions according to the intersection characteristics of the sliding surface and the slope surface, and perform regional force superposition by combining the two spatial structural plane parameters, the structural plane equations, and the wedge slope equations to determine the stability coefficient for wedge failure.

[0020] At least one embodiment of this application also provides an electronic device, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the above-described method for determining the stability of rock slope wedge failure.

[0021] At least one embodiment of this application also provides a computer-readable storage medium storing a computer program, characterized in that, when the computer program is executed by a processor, it implements the above-described method for determining the stability of a rock slope wedge failure. Attached Figure Description

[0022] One or more embodiments are illustrated by way of example with reference to the accompanying drawings, and these illustrative descriptions do not constitute a limitation on the embodiments.

[0023] Figure 1 This is a flowchart of a method for determining the stability of a rock slope wedge failure according to an embodiment of this application.

[0024] Figure 2 This is a schematic diagram of the geometric analysis model of slope wedge failure provided in the embodiments of this application.

[0025] Figure 3 This is a schematic diagram of the mechanical analysis of the wedge-shaped microstrip column unit provided in the embodiments of this application.

[0026] Figure 4 This is a schematic diagram of the wedge-shaped sliding body partition provided in the embodiments of this application.

[0027] Figure 5 This is a schematic diagram of the stability determination device for the failure of a wedge-shaped rock slope provided in an embodiment of this application. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the various embodiments of this application will be described in detail below with reference to the accompanying drawings. However, those skilled in the art will understand that many technical details have been provided in the various embodiments of this application to help readers better understand this application. However, the technical solutions claimed in this application can be implemented even without these technical details and various changes and modifications based on the following embodiments. The division of the various embodiments below is for the convenience of description and should not constitute any limitation on the specific implementation of this application. The various embodiments can be combined with and referenced by each other without contradiction.

[0029] To facilitate understanding of the embodiments of this application, relevant content regarding rock slopes will be introduced first.

[0030] Faults, joints, and other structural planes are commonly found in rock slopes. When two spatial structural planes intersect, they easily form wedge-shaped potential landslides. Shear failure of such landslides along the dual structural planes is one of the main modes of instability in rock slopes. Current methods for analyzing the stability of wedge-shaped landslides suffer from three major technical challenges: First, traditional two-dimensional limit equilibrium methods ignore the spatial geometric characteristics of structural planes, making it difficult to accurately construct the slip surface equations and leading to biases in the identification of potential landslide boundaries. Second, landslide division often uses uniform blocks without optimization for key locations such as slope step inflection points and structural plane intersections, resulting in large errors in the assignment of mechanical parameters. Third, the lack of regional force superposition calculation logic fails to accurately reflect the synergistic influence of the dual structural planes on landslide stability, easily leading to misjudgments of failure modes and stability coefficients.

[0031] For example, existing stability calculation methods based on single structural planes (such as the Bishop method) cannot be adapted to wedge-shaped bodies with two structural planes; some three-dimensional analysis methods, although considering spatial effects, do not clearly define the criteria for regional division, and the force superposition process is oversimplified, resulting in large errors in the calculation of the stability coefficient. Therefore, there is an urgent need to construct a stability calculation method that integrates geometric modeling of structural planes, refined segment division, and regional mechanical analysis to solve the problem of stability assessment of rock slopes with complex structural planes.

[0032] To address the above issues, this embodiment proposes a method for determining the stability of wedge-shaped rock slope failure. The implementation details of this method are described below. The following details are provided for ease of understanding and are not essential for implementing this solution.

[0033] Example 1: The stability determination method for wedge-shaped rock slope failure in this embodiment can be applied to electronic devices with communication, computing, and data storage capabilities. It can accurately identify potential landslides and sliding surfaces, clarify slope failure modes, and achieve a scientific assessment of landslide risk. This embodiment focuses on geometric modeling, segmentation, mechanical analysis, regional overlay, and stability calculation. For wedge-shaped rocks formed by two structural surfaces, it achieves accurate stability calculations by constructing spatial geometric equations and performing three-dimensional stability analysis. The specific process is as follows: Figure 1 As shown, it includes: Step 101: Based on the determined parameters of the two spatial structural surfaces that constitute the wedge in the rock slope and the shape of the wedge, establish a three-dimensional Cartesian coordinate system and determine the equations of the structural surfaces and the slope surface of the wedge.

[0034] Specifically, a rock slope wedge is composed of two intersecting spatial structural surfaces. Based on these two surfaces, the corresponding spatial structural surface parameters can be determined. Furthermore, the wedge formed by the two intersecting spatial structural surfaces has morphological characteristics, namely the wedge shape. By combining the parameters of the two spatial structural surfaces, a three-dimensional Cartesian coordinate system is established, and the structural surface equations and the wedge slope equations are determined.

[0035] Based on a three-dimensional Cartesian coordinate system, the potential sliding surface boundary is accurately located through the structural surface equation, which solves the problem of sliding surface identification deviation caused by neglecting the spatial geometric features of the structural surface in the two-dimensional planar system in traditional methods, thus enabling the accurate construction of the sliding surface equation.

[0036] In some embodiments, based on the parameters of the two spatial structural surfaces constituting the wedge in the determined rock slope and the shape of the wedge, a three-dimensional Cartesian coordinate system is established to determine the structural surface equations and the wedge slope equations, including: Based on on-site geological logging, semantic segmentation of UAV aerial images, and drilling data, the parameters of the two spatial structural surfaces that constitute the wedge in the rock slope and the morphology of the wedge were determined. Based on the wedge shape, a three-dimensional Cartesian coordinate system is established with the intersection of the wedge and the slope toe as the origin, the x-axis pointing outward along the main sliding direction, the y-axis perpendicular to the x-axis in the horizontal direction, and the z-axis pointing vertically upward. Based on the three-dimensional Cartesian coordinate system, the equations of the structural surfaces and the slope of the wedge are determined according to the parameters of the two spatial structural surfaces and the shape of the wedge.

[0037] Specifically, the field geological logging, UAV aerial image semantic segmentation, and drilling data contain a large amount of spatial structural and geological data, from which the parameters of the two spatial structural planes constituting the wedge in the rock slope and the morphology of the wedge can be obtained. This effectively overcomes the limitations of a single data source in identifying the spatial distribution of structural planes, significantly improves the completeness and reliability of structural plane parameter acquisition, and lays a solid data foundation for subsequent stability analysis.

[0038] In some embodiments, the two spatial structural surfaces mentioned above include: a first spatial structural surface and a second spatial structural surface; Two spatial structure parameters, including: the dip direction of the first spatial structure plane. D 1. Inclination angle I 1. Angle of internal friction φ 1. Cohesion c1, Area of ​​bottom sliding surface d A 1. The unit weight γ1 of the rock mass and the dip direction of the second spatial structural plane. D 2. Inclination angle I 2. Angle of internal friction φ 2. Cohesion c2, bottom sliding surface area d A 2. Rock mass unit weight γ2.

[0039] Wedge-shaped morphology, including: slope height H , slope angle α.

[0040] Specifically, in the tendency to obtain the first spatial structure plane D 1. Tension of the second spatial structure plane D At time 2, the measurement accuracy was controlled within ±1°; the tilt angle of the first spatial structure surface was obtained. I 1. Inclination angle of the second spatial structural plane I At 2 o'clock, the measurement accuracy was controlled within ±0.5°. By acquiring and accurately characterizing the geometric parameters (dip and dip angle) and mechanical parameters (internal friction angle and cohesion) of the first and second spatial structural surfaces, and combining them with their corresponding engineering properties such as bottom sliding surface area and rock mass unit weight, as well as the slope surface morphology characterized by slope height and slope angle, a complete three-dimensional wedge-shaped sliding body geometry and force boundary conditions under the control of dual structural surfaces can be constructed. This spatial structural surface parameter system provides the necessary input foundation for subsequent establishment of a three-dimensional Cartesian coordinate system and derivation of structural surface equations and slope equations, thereby achieving accurate identification of potential sliding body boundaries and effectively overcoming the ambiguity and subjectivity of traditional two-dimensional or simplified three-dimensional methods in sliding surface positioning.

[0041] In the embodiments, Figure 2 A schematic diagram of the geometric analysis model for slope wedge failure is shown below. Figure 2 As shown, based on the wedge shape, a three-dimensional Cartesian coordinate system is established with the intersection of the wedge and the slope toe as the origin. The x-axis points outward along the main sliding direction, the y-axis is perpendicular to the x-axis in the horizontal direction, and the z-axis points vertically upward. This system closely reflects the actual sliding mechanism of the engineering project. The geometric relationship between structural plane A and structural plane B can be clearly represented using this three-dimensional Cartesian coordinate system. This system not only has clear physical meaning but also closely matches the actual failure direction of the wedge, avoiding mechanical projection distortion or computational redundancy caused by the arbitrary selection of traditional coordinate systems. This greatly enhances the intuitiveness and accuracy of subsequent mechanical modeling.

[0042] Based on the established three-dimensional Cartesian coordinate system, and combined with the precisely obtained parameters of the two spatial structural surfaces and the wedge shape, the spatial plane equations of the two structural surfaces and the slope equation of the wedge can be analytically derived. These equations not only rigorously characterize the spatial geometric relationships of the potential sliding surface, but also provide a mathematical foundation for subsequent key mechanical steps such as micro-strip column division, contact area calculation, and decomposition of normal and tangential forces. Most importantly, the explicit expression of the structural surface equations allows for the precise integration of key geometric quantities such as the sliding surface intersection line, sliding body volume, and sliding surface area, thus fundamentally solving the boundary error problem caused by the simplification or approximation of the sliding surface in traditional methods.

[0043] In this embodiment, the structural surface equations are determined as follows:

[0044] in, z h1 The structural surface equation is for the first spatial structural surface; z h2 The structural surface equation for the second spatial structural surface; D 1 represents the inclination of the first spatial structure plane; I 1 represents the inclination angle of the first spatial structural plane; D 2 represents the inclination of the two-dimensional structural plane; I 2 represents the inclination angle of the second spatial structure surface.

[0045] In this embodiment, a wedge-shaped slope equation is constructed based on the actual surface morphology of the slope and the characteristics of slope elevation variation. The characteristics of slope elevation variation can be derived from the slope height... H Characterization. The actual surface morphology of a slope can be characterized by the slope angle α.

[0046] The equation of a wedge-shaped slope reflects the spatial distribution of the slope in a coordinate system. The equation of a single-step wedge-shaped slope is determined as follows:

[0047] in, z p1 The equation for the elevation of the first slope segment; z p2 The equation for the elevation of the second slope segment; H α is the slope height; α is the slope angle.

[0048] This embodiment accurately obtains structural surface parameters through multi-source data fusion, constructs a three-dimensional Cartesian coordinate system consistent with the failure mechanism, and generates structural surface and slope equations accordingly, achieving high-fidelity modeling of the wedge geometry and sliding boundary. This significantly improves the geometric realism and mechanical rigor of the stability analysis of rock slope wedges, providing reliable prerequisites for subsequent regional micro-strip column mechanical analysis and stability coefficient calculation, thereby supporting the scientific identification and accurate risk assessment of rock slope wedge failure modes.

[0049] Step 102: Divide the wedge-shaped potential sliding body into multiple upright micro-strips with rectangular cross-sections; the cross-sectional lengths of the multiple upright micro-strips are different at different locations.

[0050] Specifically, in order to transform the three-dimensional mechanics problem into a calculable plane strain problem, the potential sliding body of the wedge is divided into multiple upright micro-strips with rectangular cross-sections. By dividing the multiple upright micro-strips into different cross-sectional lengths at different locations, the strips are finely divided at key locations. This can effectively solve the problem of large mechanical parameter assignment errors caused by the uniform strip division method in the existing technology, and can effectively reduce the mechanical parameter assignment errors.

[0051] In some embodiments, the above-mentioned different positions include: a first position and a second position; the first position includes: the inflection point of the slope step in the main sliding direction of the slope, and the intersection of the sliding surface and the rock layer in the main sliding direction of the slope; the second position is the remaining position in the main sliding direction of the slope excluding the first position; any vertical micro-strip column is a hexahedron with mutually perpendicular sides; The cross-sectional length of the multiple upright micro-strips at the first position is the first unit length; The cross-sectional length of the multiple upright micro-strips at the second position is the second unit length; The first unit length is less than the second unit length.

[0052] By dividing the main sliding direction of the slope into a first location and a second location, a more refined classification of the main sliding direction is achieved. Specifically, the slope step inflection points and the intersection lines between the sliding surface and rock strata within the main sliding direction typically correspond to high-risk areas of stress concentration, abrupt changes in sliding surface morphology, or discontinuities in shear strength. Therefore, a more precise classification is required, and a shorter first unit length is used to limit the cross-sectional length of multiple upright micro-strips at the first location. For the remaining locations, which are areas with relatively gentle geometry and mechanics, a longer second unit length can be used to limit the cross-sectional length of multiple upright micro-strips at the second location.

[0053] Specifically, the cross-sectional length of all micro-strips along the y-direction (perpendicular to the main sliding direction of the slope) is controlled to be the first unit length and the second unit length. At the first critical locations, such as the slope step inflection point and the intersection of the sliding surface and the rock strata, the first unit length is used to finely divide the micro-strips, ensuring that each micro-strip is a hexahedron with mutually perpendicular sides. At the second critical locations, the second unit length is used to divide the upright micro-strips. For the divided upright micro-strips, the length in the x-direction is d. x , y The directional length is dy; α x α y The bottom sliding surface and the flat surface are respectively. xoz ,flat yoz The angle between the line of intersection and the horizontal plane.

[0054] By setting different segmentation lengths, using a smaller first unit length at the first location and a larger second unit length at the second location (where the first unit length is smaller than the second unit length), a non-uniform, focused segmentation mechanism is achieved. This ensures higher spatial resolution in key control areas, thereby more accurately capturing local slip surface dip angle changes, abrupt changes in contact area, and discontinuities in rock mass mechanical parameters. In non-critical areas, the segmentation granularity is appropriately relaxed to balance computational efficiency. This strategy effectively balances the contradiction between computational accuracy and resource consumption, avoids redundant calculations caused by global fine segmentation, and overcomes the problem of uniform coarse segmentation masking the instability characteristics of key areas.

[0055] Step 103: Based on the two spatial structural surface parameters, structural surface equations, and wedge-shaped slope equations, perform mechanical analysis on each upright micro-strip column to determine the mechanical parameters of each upright micro-strip column.

[0056] Specifically, based on the spatial structural surface parameters of the first and second spatial structural surfaces obtained above, and the structural surface equations and wedge-shaped slope equations obtained analytically through a three-dimensional Cartesian coordinate system, Complete boundary conditions and material property inputs are provided for each upright microstrip. Based on this, the actual contact area between each upright microstrip and the two structural surfaces can be accurately calculated, and mechanical analysis can be performed accordingly to determine the mechanical parameters of each upright microstrip. This mechanical modeling method based on real geometric and physical parameters is significantly superior to the simplified superposition of uniform equivalent sliding surface or average strength parameters for the entire sliding body in traditional methods.

[0057] In some embodiments, a mechanical analysis is performed on each upright micro-slab column based on two spatial structural surface parameters, the structural surface equation, and the wedge-shaped slope equation to determine the mechanical parameters of each upright micro-slab column, including: Based on the two spatial structural surface parameters, the structural surface equation, and the wedge-shaped slope equation, and using the three-dimensional limit equilibrium slice method, force assumptions and force balance derivations are made for each upright micro-strip column, and the normal force, anti-slip force, and volume force of each upright micro-strip column are determined as mechanical parameters. Among them, the point of application of the normal force is located at the centroid of the bottom surface of each micro-strip column, the anti-slip force is parallel to the main sliding direction, and the volume force is obtained by analyzing the slope and sliding surface morphology.

[0058] Figure 3 This is a schematic diagram of the mechanical analysis of a wedge-shaped micro-strip column element, as shown below. Figure 3 Specifically, based on the three-dimensional limit equilibrium slice method, the force assumptions and force equilibrium derivation of the micro-strip column are performed: neglecting the tangential and normal forces between the strips, the normal force d on the bottom sliding surface of the micro-strip column is... N Anti-slip force d T and volume force d WThere are a total of 3 forces acting, including the anti-slip force d. T Parallel to the main sliding direction, use d T x It indicates that the normal force d N The point of application is located at the center of the base surface.

[0059] Based on the force equilibrium condition, the normal force d on the sliding surface at the bottom of the micro-strip column can be obtained. N and the downward force d X as follows:

[0060]

[0061] Where, α x α y The bottom sliding surface and the flat surface are respectively. xoz ,flat yoz The angle between the line of intersection and the horizontal plane.

[0062] Based on the Mohr-Coulomb strength criterion, the anti-slip force d of the micro-strip column can be obtained. T x as follows:

[0063] in, φ Let be the internal friction angle of the microstrip column, (°); c The cohesive force of the microstrip column is kPa; d A Let m be the area of ​​the base of the micro-strip column. 2 .

[0064] Based on the geometric relationships of the parameters of the sliding surface, we obtain:

[0065] The volumetric force d of the micro-strip column can be obtained by analyzing the slope and slip surface morphology. W as follows:

[0066] in, γ The unit weight of the micro-strip column is kN / m³. 3 , z h The equation is for the structural surface. z p The equation for the slope of a wedge-shaped body is given.

[0067] The above α x α y Derivation using partial derivatives of the structural surface equation and trigonometric functions:

[0068]

[0069]

[0070] in, R a Let be the characteristic radius of the sliding surface in the x-direction; R b Let be the characteristic radius of the sliding surface in the y-direction.

[0071] This embodiment, within the framework of three-dimensional limit equilibrium theory, combines two spatial structural surface parameters, structural surface equations, and wedge-shaped slope equations to implement systematic force assumptions and force balance derivations for each upright micro-strip column. This process not only strictly adheres to the fundamental principles of statics but also fully considers the three-dimensional sliding constraint mechanism formed by the intersection of the two structural surfaces. This ensures that the mechanical model of each micro-strip column has a clear physical basis and engineering interpretability, significantly outperforming the simplified treatment of the sliding force system in traditional two-dimensional or pseudo-three-dimensional methods. The determination process of the aforementioned mechanical parameters deeply couples the geometric boundaries described by the structural surface equations with the strength characteristics defined by the rock mass mechanical parameters. Because all micro-strip columns share a unified three-dimensional Cartesian coordinate system and equation system, and the derivation logic of the mechanical parameters is consistent, the mechanical analysis of the entire sliding body possesses the dual advantages of good overall coordination and local refinement.

[0072] Step 104: Divide the wedge into multiple regions according to the intersection characteristics of the sliding surface and the slope surface. Combine the parameters of the two spatial structural surfaces, the structural surface equation and the wedge slope equation to perform regional force superposition and determine the stability coefficient of the wedge failure.

[0073] Specifically, by introducing a regional division strategy based on the intersection characteristics of the slip surface and the slope surface, and combining the parameters of the two spatial structural surfaces with the equation system to implement regional force superposition, not only is the non-uniformity of the mechanical response under the synergistic effect of the two structural surfaces accurately characterized, but the scientific nature and engineering guidance value of the stability coefficient calculation are also fundamentally improved. This provides reliable technical support for risk warning, support design and disaster prevention of complex rock slopes in water conservancy, mining, transportation and other fields.

[0074] In some embodiments, the wedge is divided into multiple regions based on the intersection characteristics of the sliding surface and the slope surface. By combining the parameters of the two spatial structural surfaces, the structural surface equation, and the wedge slope equation, regional force superposition is performed to determine the stability coefficient for wedge failure, including: The wedge is divided into multiple regions based on the intersection characteristics of the sliding surface and the slope surface; each region includes multiple upright micro-strip columns; Based on the two spatial structural surface parameters, structural surface equations and wedge slope equations, the mechanical effects of the bottom surfaces of multiple upright micro-strip columns in each region are superimposed, and the superimposed sliding force and superimposed anti-slip force of the multiple upright micro-strip columns in each region are solved in stages. By combining the superimposed sliding force and superimposed anti-slip force of multiple upright micro-strips contained in each region, the equivalent physical and mechanical parameters of the upright micro-strips at each stage on the main sliding surface are solved, and the stability coefficient of the wedge failure is determined.

[0075] Specifically, since different regions of the wedge are constrained by different structural surfaces, the wedge is divided into multiple regions based on the spatial intersection characteristics of the sliding surface and the slope surface. Each region includes multiple upright micro-strip columns.

[0076] In some embodiments, the plurality of regions include: a first wedge region, a second wedge region, and a third wedge region; The top surface of the upright micro-strip column in the first wedge region is linearly constrained by the first slope elevation equation. The top surface of the upright micro-strip column in the second wedge region is subject to the joint nonlinear constraint of the first and second slope elevation equations. The top surface of the upright micro-strip column in the third wedge region is linearly constrained by the second slope elevation equation.

[0077] Figure 4 A schematic diagram of the wedge-shaped sliding body partitioning, as shown below. Figure 4 As shown, specifically, the wedge is divided into three regions based on the intersection characteristics of the sliding surface and the slope surface: the first wedge region I, the second wedge region II, and the third wedge region III. Among them, the top surface of the upright micro-strip column in the first wedge region I is subject to the elevation equation of the first segment of the slope. z p1 Linear constraints, the top surface of the upright micro-strip column in the second wedge region II is subject to the elevation equation of the first slope segment. z p1 Second Slope Elevation Equation z p2 Under common nonlinear constraints, the top surface of the upright micro-strip column in the third wedge region III is subject to the second slope elevation equation. z p2 Linear constraints.

[0078] If there are more than three regions, potential wedges are screened by combining them in pairs to obtain three regions. The stability coefficient of each wedge is calculated, and finally the wedge with the smallest stability coefficient is selected as the focus of risk management, which further improves the accuracy of risk assessment for complex slopes.

[0079] This embodiment divides the wedge into three regions with clear geometric and mechanical significance based on the segmented slope morphology of the actual engineering slope, and assigns each region a constraint relationship with the corresponding slope elevation equation. This division method closely matches the engineering characteristics of real rock slopes, which often have multiple steps, multiple slope segments, and discontinuous slopes. This allows stability analysis to move beyond the idealized assumption of a single slope and instead realistically reflect the spatial coupling relationship between the sliding body and the slope under complex terrain conditions.

[0080] Based on the first wedge-shaped region I, the second wedge-shaped region II, and the third wedge-shaped region III, the mechanical effects on the bottom surface of the divided micro-strips are superimposed, and the sliding force of the micro-strips in each region is solved in stages. X ( X r , X u , X s ), anti-slip force T ( T r , T u , T s By combining like terms, the equivalent physical and mechanical parameters of the bars at each stage on the main sliding surface are solved; Region I, 1 r Structural surfaces corresponding to row columns z h1 With slope, two structural surfaces and structural surfaces z h2 The points of intersection with the slope are respectively denoted as a r1 , a r2 , a r3 Region II u Line, Region III s The row representation method is similar.

[0081] For the first wedge-shaped region I, the top surface of the micro-strip column is affected by the slope. z p1 Linear constraints, sliding body boundary is z h1 , z h2 and z p1 , No. r Superimposed downward force of strips X r With superimposed anti-slip force T r It is expressed as follows:

[0082]

[0083] in, X r For the first r The superimposed downward force of the strip blocks; T r For the first r The superimposed anti-slip force of strip blocks; z h1 The structural surface equation is for the first spatial structural surface; z h2 The structural surface equation for the second spatial structural surface; z p1 The equation for the elevation of the first slope segment; z p2 The second slope elevation equation; γ is the unit weight of the rock mass; φ ω is the internal friction angle; c is the cohesive force.

[0084] For the second wedge-shaped region II, the top surface of the micro-strip column is affected by the slope. z p1 and z p2 Common nonlinear constraints, the first u Superimposed downward force of strips X u With superimposed anti-slip force T u They are represented as follows:

[0085]

[0086] in, X u For the first u The superimposed downward force of the strip blocks; T u For the first u The superimposed anti-slip force of strip blocks; z h1 The structural surface equation is for the first spatial structural surface; z h2 The structural surface equation for the second spatial structural surface; z p1 The equation for the elevation of the first slope segment; z p2 The second slope elevation equation; γ is the unit weight of the rock mass; φ ω is the internal friction angle; c is the cohesive force.

[0087] For the third wedge-shaped region III, the top surface of the micro-strip column is affected by the slope. z p2 Linear constraints, sliding body boundary isz h1 , z h2 and z p2 , No. s Superimposed downward force of strips X s With superimposed anti-slip force T s :

[0088]

[0089] in, X s For the first s The superimposed downward force of the strip blocks; T s For the first s The superimposed anti-slip force of strip blocks; z h1 The structural surface equation is for the first spatial structural surface; z h2 The structural surface equation for the second spatial structural surface; z p1 The equation for the elevation of the first slope segment; z p2 The second slope elevation equation; γ is the unit weight of the rock mass; φ ω is the internal friction angle; c is the cohesive force.

[0090] In the embodiment, the stability coefficient of the wedge failure can be solved according to the definition of the stability coefficient. F s for:

[0091] in, F s To determine the stability coefficient of the wedge-shaped body in case of failure; X r For the first r The superimposed downward force of the strip blocks; T r For the first r The superimposed anti-slip force of strip blocks; X u For the first u The superimposed downward force of the strip blocks; T u For the first u The superimposed anti-slip force of strip blocks; X s For the first s The superimposed downward force of the strip blocks; T sFor the first s The anti-slip force of the superimposed strips.

[0092] The stability determination method for wedge-shaped rock slope failure provided in this application takes a wedge-shaped rock composed of two structural planes as the research object. Based on a constructed three-dimensional Cartesian coordinate system, it accurately locks the potential sliding surface boundary through structural plane equations, solving the slip surface identification error problem of traditional methods. By differentiating the length of the blocks at different key locations, it reduces the error in assigning mechanical parameters. Through regional force superposition logic, it fully reflects the synergistic constraint effect of the two structural planes on the stability of the sliding body, avoiding the stability coefficient deviation caused by single-region calculation. It can accurately identify the potential sliding body boundary and sliding surface morphology of the slope under the influence of structural planes, clarify the "wedge shear along the two structural planes" failure mode, and provide a scientific basis for stability analysis and disaster risk assessment of rock slopes with complex structural planes. It is applicable to rock slope engineering design in fields such as water conservancy, mining, and transportation. Verified through engineering examples, the stability coefficient calculation results of this method are in high agreement with the field monitoring data. It can effectively identify the "dual-structure shear type" failure mode. For rock slopes with multiple complex structural surfaces, such as open-pit mine slopes, water conservancy slopes, and road cut slopes, it can provide full-process technical support from landslide identification and failure mode determination to risk classification, significantly improving the scientificity and reliability of slope landslide disaster risk assessment and filling the technical gap in three-dimensional limit equilibrium analysis of rock slopes with complex structural surfaces.

[0093] This application also provides a specific example of a method for determining the stability of a wedge-shaped rock slope failure. Taking a rock slope on the north side of an open-pit mine as an engineering example, the technical solution in this application embodiment is clearly and completely described, and the specific implementation process is as follows: The slope contains two main structural planes: structural plane 1 (D1=128°, I1=74°, structural plane 2 (D2=205°, I2=37°), rock mass unit weight γ=26kN / m³, and internal friction angle. φ =37.8°, cohesion c=4230kPa; slope height 10m, slope angle 40°, specific parameters of the slope model are shown in Table 1 for slope surface and structural surface attitude, and Table 2 for rock mass physical and mechanical parameters.

[0094] Table 1

[0095] Table 2

[0096] The constructed slope equation is as follows:

[0097] Establish a Cartesian coordinate system and divide the sliding body into 20 micro-bars, with the bar at the step inflection point... xThe length of the column in the x-direction is 1.5m, and the length of the column in the x-direction at the intersection of the structural surfaces is 0.8m. The length of the column in the remaining areas is 1.5m. x The directional length is 3m. The equation of the structural surface is derived as follows:

[0098] Region I (x=0~50m, y=-8~8m): Superposition yields X r=1200kN, T r=1560kN; Region II (x=50~58m, y=-9~9m): Superposition yields X u =1800kN, T u =2340kN; Region III (x=58~72m, y=-9~-9m): Superposition yields X u =900kN, T u =1170kN.

[0099] The slope stability coefficient is calculated as follows:

[0100] In this example, the number of areas can be adjusted according to the actual number and shape of the slope's structural surfaces. If there are three or more structural surfaces, potential wedges can be screened by combining them in pairs. Then, the stability coefficient of each wedge is calculated using this method. Finally, the wedge with the smallest stability coefficient is selected as the focus of risk control, further improving the accuracy of risk assessment for complex slopes.

[0101] This application provides a stability calculation method for the failure of wedge-shaped rock slopes, solving the problems of difficulty in identifying potential sliding bodies and sliding surfaces and inaccurate determination of failure modes in rock slopes with multiple complex structural planes, thus achieving accurate assessment of slope landslide disaster risks. This method takes a wedge-shaped rock slope composed of two structural planes as the research object. First, a three-dimensional Cartesian coordinate system and structural plane equations and slope equations are established based on the geometric parameters (dip and dip angle) of the structural planes. Then, the sliding body is divided into vertical micro-strips (unit length along the y-direction, separately divided at key locations). Mechanical analysis of the micro-strips is performed using the three-dimensional limit equilibrium slice method, deriving the calculation formulas for the normal force, sliding force, and anti-sliding force of the strips. Subsequently, the wedge-shaped rock slope is divided into three regions: I, II, and III. The sliding force and anti-sliding force of each strip are superimposed on each region. Finally, the stability coefficient of the wedge-shaped rock slope failure is solved based on the definition of the stability coefficient. This method can accurately identify the potential landslide boundary and sliding surface morphology of slopes under the influence of structural planes, and clarify the "wedge-shaped body shearing along double structural planes" failure mode. It provides a scientific basis for the stability analysis and disaster risk assessment of rock slopes with complex structural planes, and is applicable to the engineering design of rock slopes in fields such as water conservancy, mining, and transportation.

[0102] Example 2: Another embodiment of this application relates to a stability determination device for wedge-shaped rock slope failure. The implementation details of this embodiment's stability determination device are described below. The following details are provided for ease of understanding and are not essential for implementing this solution. A schematic diagram of the stability determination device for wedge-shaped rock slope failure in this embodiment can be seen as follows: Figure 5 As shown, it includes a module 501 for determining the equations of structural surfaces and wedge-shaped slopes, a module 502 for dividing vertical micro-strip columns, a mechanical analysis module 503, and a stability coefficient determination module 504.

[0103] This embodiment provides a stability determination device for the failure of a wedge-shaped rock slope, comprising: The module 501 for determining the equations of structural surfaces and wedge slopes is used to establish a three-dimensional Cartesian coordinate system and determine the equations of structural surfaces and wedge slopes based on the parameters of the two spatial structural surfaces that constitute the wedge in the determined rock slope and the shape of the wedge. The upright micro-strip column division module 502 is used to divide the wedge-shaped potential sliding body into multiple upright micro-strip columns with rectangular cross sections; the cross sections of the multiple upright micro-strip columns are divided at different positions with different lengths; The mechanical analysis module 503 is used to perform mechanical analysis on each vertical micro-strip column based on two spatial structural surface parameters, structural surface equations and wedge slope equations, and to determine the mechanical parameters of each vertical micro-strip column. The stability coefficient determination module 504 is used to divide the wedge into multiple regions according to the intersection characteristics of the sliding surface and the slope surface, and combine the two spatial structural surface parameters, structural surface equations and wedge slope equations to perform regional force superposition to determine the stability coefficient of wedge failure.

[0104] It is worth mentioning that all modules involved in this embodiment are logical modules. In practical applications, a logical unit can be a physical unit, a part of a physical unit, or a combination of multiple physical units. Furthermore, to highlight the innovative aspects of this application, this embodiment does not introduce units that are not closely related to solving the technical problems proposed in this application; however, this does not mean that other units are absent in this embodiment.

[0105] Example 3: Another embodiment of this application relates to an electronic device, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the stability determination method for rock slope wedge failure in the above embodiments.

[0106] The memory and processor are connected via a bus, which can include any number of interconnecting buses and bridges, connecting various circuits of one or more processors and memories. The bus can also connect various other circuits, such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and will not be described further herein. The bus interface provides an interface between the bus and the transceiver. The transceiver can be a single element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by the processor is transmitted over the wireless medium via an antenna, which further receives data and transmits it to the processor.

[0107] The processor manages the bus and general processing, and also provides various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory is used to store data used by the processor during operation.

[0108] Example 4: Another embodiment of this application relates to a computer-readable storage medium storing a computer program. When executed by a processor, the computer program implements the above-described method for determining the stability of a wedge-shaped rock slope in the event of failure.

[0109] That is, those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. This program is stored in a storage medium and includes several instructions to cause a device (which may be a microcontroller, chip, etc.) or processor to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as a USB flash drive, a portable hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0110] Those skilled in the art will understand that the above embodiments are specific embodiments for implementing this application, and in practical applications, various changes can be made to them in form and detail without departing from the spirit and scope of this application.

Claims

1. A method for determining the stability of a wedge-shaped rock slope in case of failure, characterized in that, include: Based on the determined parameters of the two spatial structural surfaces that constitute the wedge in the rock slope and the shape of the wedge, a three-dimensional Cartesian coordinate system is established to determine the equations of the structural surfaces and the wedge slope surface. The wedge-shaped potential sliding body is divided into multiple upright micro-strips with rectangular cross-sections; the cross-sectional lengths of the multiple upright micro-strips are different at different positions; Based on the two spatial structural surface parameters, structural surface equations, and wedge-shaped slope equations, a mechanical analysis is performed on each of the vertical micro-strip columns to determine the mechanical parameters of each vertical micro-strip column. The wedge is divided into multiple regions based on the intersection characteristics of the sliding surface and the slope surface. By combining the parameters of the two spatial structural surfaces, the structural surface equation, and the wedge slope equation, the regional forces are superimposed to determine the stability coefficient of the wedge failure.

2. A method for determining the stability of a rock slope wedge failure as described in claim 1, characterized in that, Based on the determined parameters of the two spatial structural surfaces constituting the wedge in the rock slope and the shape of the wedge, a three-dimensional Cartesian coordinate system is established to determine the equations of the structural surfaces and the wedge slope surface, including: Based on on-site geological logging, semantic segmentation of UAV aerial images, and drilling data, the parameters of the two spatial structural surfaces that constitute the wedge in the rock slope and the morphology of the wedge were determined. Based on the wedge shape, a three-dimensional Cartesian coordinate system is established with the intersection of the wedge and the slope toe as the origin, the x-axis pointing outward along the main sliding direction, the y-axis perpendicular to the x-axis in the horizontal direction, and the z-axis pointing vertically upward. Based on the three-dimensional Cartesian coordinate system, the structural surface equation and the wedge slope equation are determined according to the two spatial structural surface parameters and the wedge shape.

3. A method for determining the stability of a rock slope wedge failure as described in claim 1, characterized in that, The different positions include: a first position and a second position; the first position includes: the inflection point of the slope step in the main sliding direction of the slope, and the intersection of the sliding surface and the rock layer in the main sliding direction of the slope; the second position is the remaining position in the main sliding direction of the slope excluding the first position; any of the upright micro-strip columns is a hexahedron with mutually perpendicular sides; The cross-sectional length of the plurality of upright micro-strips at the first position is the first unit length; The cross-sectional length of the multiple upright micro-strips at the second position is the second unit length; The first unit length is less than the second unit length.

4. A method for determining the stability of a rock slope wedge failure as described in claim 1, characterized in that, Based on the two spatial structural surface parameters, the structural surface equation, and the wedge-shaped slope equation, a mechanical analysis is performed on each of the vertical micro-strip columns to determine the mechanical parameters of each vertical micro-strip column, including: Based on the two spatial structural surface parameters, structural surface equations, and wedge-shaped slope equations, and using the three-dimensional limit equilibrium slice method, force assumptions and force balance derivations are made for each of the vertical micro-strip columns to determine the normal force, anti-slip force, and volume force of each vertical micro-strip column as mechanical parameters; wherein, the point of application of the normal force is located at the centroid of the bottom surface of each micro-strip column, the anti-slip force is parallel to the main sliding direction, and the volume force is obtained by analyzing the slope and sliding surface morphology.

5. A method for determining the stability of a rock slope wedge failure as described in claim 1, characterized in that, The wedge is divided into multiple regions based on the intersection characteristics of the sliding surface and the slope surface. By combining the parameters of the two spatial structural surfaces, the structural surface equation, and the wedge slope equation, regional force superposition is performed to determine the stability coefficient for wedge failure, including: The wedge is divided into multiple regions based on the intersection characteristics of the sliding surface and the slope surface; each region includes multiple upright micro-strip columns; Based on the two spatial structural surface parameters, structural surface equations and wedge slope equations, the mechanical effects of the bottom surfaces of multiple upright micro-strip columns contained in each region are superimposed, and the superimposed sliding force and superimposed anti-slip force of multiple upright micro-strip columns contained in each region are solved in stages. By combining the superimposed sliding force and superimposed anti-slip force of the multiple upright micro-strips contained in each region, the equivalent physical and mechanical parameters of the upright micro-strips at each stage on the main sliding surface are solved, and the stability coefficient of the wedge failure is determined.

6. A method for determining the stability of a rock slope wedge failure as described in claim 1 or 5, characterized in that, The equations for the wedge-shaped slope include: the first slope elevation equation and the second slope elevation equation. The plurality of regions include: a first wedge region, a second wedge region, and a third wedge region; The top surface of the upright micro-strip column in the first wedge-shaped region is linearly constrained by the first slope elevation equation. The top surface of the upright micro-strip column in the second wedge region is subject to the joint nonlinear constraint of the first and second slope elevation equations; The top surface of the upright micro-strip column in the third wedge region is linearly constrained by the second slope elevation equation.

7. A method for determining the stability of a rock slope wedge failure as described in claim 1, characterized in that, The two spatial structural surfaces include: a first spatial structural surface and a second spatial structural surface; The parameters of the two spatial structural surfaces include: the dip direction, dip angle, internal friction angle, cohesion, bottom slip surface area and rock mass unit weight of the first spatial structural surface, and the dip direction, dip angle, internal friction angle, cohesion, bottom slip surface area and rock mass unit weight of the second spatial structural surface. The wedge shape includes: slope height and slope angle.

8. A device for determining the stability of wedge-shaped failure in rock slopes, characterized in that, include: The module for determining the equations of structural surfaces and wedge slopes is used to establish a three-dimensional Cartesian coordinate system and determine the equations of structural surfaces and wedge slopes based on the parameters of the two spatial structural surfaces that constitute the wedge in the determined rock slope and the shape of the wedge. The upright micro-strip column division module is used to divide the wedge-shaped potential sliding body into multiple upright micro-strip columns with rectangular cross-sections; the multiple upright micro-strip columns are divided into cross-sectional lengths at different positions; The mechanical analysis module is used to perform mechanical analysis on each of the two spatial structural surface parameters, structural surface equations and wedge slope equations, and to determine the mechanical parameters of each of the vertical micro-strip columns. The stability coefficient determination module is used to divide the wedge into multiple regions according to the intersection characteristics of the sliding surface and the slope surface, and combine the two spatial structural surface parameters, structural surface equations and wedge slope equations to perform regional force superposition to determine the stability coefficient of wedge failure.

9. An electronic device, characterized in that, include: At least one processor; as well as, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the stability determination method for rock slope wedge failure as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the stability determination method for the failure of a wedge-shaped rock slope as described in any one of claims 1 to 7.

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