A system and method for evaluating the stability of a dangerous rock with steeply inclined fissures in the trailing edge

Abstract

The present application relates to the field of engineering geology and geological disaster prevention technology, in particular to a system and method for evaluating the stability of dangerous rock with steeply inclined fissures in the rear edge, comprising: S1, obtaining high-precision point cloud data of the dangerous rock surface by using unmanned aerial vehicle oblique photography, aerial remote sensing or airborne LiDAR, and constructing a triangular mesh model of the dangerous rock surface; S2, constructing a three-dimensional entity model according to the boundary conditions and sliding surface of the dangerous rock; S3, extracting the volume, barycenter position, sliding surface area and spatial occurrence information of the sliding surface from the three-dimensional entity model, and calculating the self-weight of the dangerous rock by combining the rock mass bulk density and the additional weight of the water in the fissure; the present application constructs a fine three-dimensional scene model of the dangerous rock based on unmanned aerial vehicle oblique photography or LiDAR point cloud, which can accurately extract key geometric parameters such as the volume, barycenter, sliding surface area and inclination of the dangerous rock, avoids the morphological distortion problem caused by two-dimensional simplification, and makes the stability analysis more close to the actual engineering scene.

Description

Technical Field

[0001] This invention relates to the field of engineering geology and geological disaster prevention technology, specifically to a system and method for assessing the stability of rockfalls with steeply dipping fractures at the rear edge. Background Technology

[0002] Unstable rock formations refer to rock masses located on steep slopes or cliffs, fractured by fissures and posing a potential risk of instability. They are a typical type of geological hazard widely distributed globally. Rockfalls are characterized by complex formations, sudden occurrence, and difficulty in prediction; once they occur, they can cause severe casualties and property damage. In recent years, rockfalls have frequently occurred in Hokkaido, Japan; the Swiss Alps; Brazil; India; Italy; and southwestern China, causing significant impacts on local socio-economic development. In my country, rockfalls are one of the three major geological hazards in mountainous areas, particularly prevalent in the Three Gorges Reservoir area and western regions. According to data released by the Ministry of Natural Resources of China, 2,176 landslides occurred nationwide in 2023, accounting for 59.3% of all geological hazards, highlighting the urgency of preventing and controlling rockfalls.

[0003] The core of preventing rockfalls lies in the accurate identification and stability analysis of unstable rock masses. Currently, the academic community has developed various methods for evaluating the stability of unstable rock masses, including the limit equilibrium method, fracture propagation theory, energy method, dynamic time history analysis, catastrophe theory, and numerical simulation. Among these, the limit equilibrium method, due to its simple calculations and reliable results, is widely used in engineering practice and is the main evaluation method recommended by Chinese standards.

[0004] Rockfall instability is essentially the process by which a rock mass slides or detaches entirely along a sliding surface under the combined effects of its own weight, fissure water pressure, and seismic forces. Therefore, accurately calculating the geometric parameters, weight, and fissure water pressure of the rock mass is crucial for stability assessment. While the traditional two-dimensional profiling method is widely used, it neglects the true three-dimensional geometry of the rock mass and the spatial distribution of water pressure, making it difficult to reflect the actual stability condition and potentially leading to assessment errors.

[0005] In recent years, the rapid development of 3D detection technologies such as UAV oblique photography, aerial remote sensing, and airborne LiDAR has made it possible to obtain high-precision 3D point clouds of unstable rocks, providing a technical foundation for establishing realistic 3D models and conducting 3D stability analysis. Some researchers have established 3D slip models based on limit equilibrium theory, while others have proposed calculation methods for special structural types (such as intermediate bonding and peripheral penetration). However, existing methods generally assume that the unstable rock has a regular shape or only consider the water-filling effect of a single trailing edge fracture, which cannot meet the analysis needs of complex unstable rock shapes and the combined effects of multiple fractures in actual engineering. Summary of the Invention

[0006] This invention comprehensively utilizes 3D point cloud modeling technology to establish a realistic 3D solid model of the unstable rock mass. Combining limit equilibrium theory, it considers the spatial combination of multiple fractures at the trailing edge and the vector superposition effect of water pressure. By projecting the fracture water pressure onto the local coordinate system of the slip surface, it accurately decomposes the normal force and sliding force of the slip surface, thereby achieving high-precision 3D calculation of the stability of the unstable rock mass. This method has been verified in engineering examples, and sensitivity analysis further illustrates the influence of the rock mass's geometry on its stability.

[0007] To achieve the above objectives, the present invention provides the following technical solution: This invention provides a method for assessing the stability of sliding rockfalls with steeply dipping fractures at the rear edge, comprising the following steps: S1. Use UAV oblique photography, aerial remote sensing or airborne LiDAR to acquire high-precision point cloud data of the dangerous rock surface and construct a triangular network model of the dangerous rock surface. S2. Construct a three-dimensional solid model based on the boundary conditions of the dangerous rock and the slip surface; S3. Extract the volume, center of gravity, slip surface area, and slip surface spatial orientation information of the dangerous rock from the three-dimensional solid model, and calculate the self-weight of the dangerous rock by combining the unit weight of the rock mass and the additional weight of the water in the fissure. S4. Calculate the resultant force of the hydraulic pressure in the trailing edge fracture and project it onto the local coordinate system x', y', z' where the slip surface is located, where x' is the horizontal direction along the dip of the slip surface, y' is the horizontal direction along the strike of the slip surface, and z' is the vertical upward direction; in the local coordinate system, extract the sliding component and the vertical component of the resultant force of the hydraulic pressure along the slip surface direction; S5. Calculate the buoyancy force of the sliding surface by considering the water pressure on the sliding surface in the three-dimensional state as an integral of the water pressure of countless two-dimensional profiles.

[0008] S6. Based on the limit equilibrium theory, calculate the anti-sliding force and sliding force of the unstable rock, and obtain the three-dimensional sliding stability coefficient.

[0009] Furthermore, the three-dimensional solid model is used to directly derive the geometric characteristic parameters of the unstable rock, including volume, center of gravity position, bottom slip surface area and outer surface area; the volume is obtained by accumulating three-dimensional spatial volume elements, the center of gravity position is obtained by calculating the three-dimensional centroid integral, and the area parameters are obtained by summing the areas of triangular mesh patches, so as to provide accurate geometric input for self-weight, fracture water pressure and stability analysis.

[0010] Furthermore, the self-weight of the unstable rock mass It can be calculated using the following formula: In the formula, Due to the weight of the unstable rock mass, The density of the unstable rock mass, This represents the volume of the unstable rock mass.

[0011] Furthermore, the stability coefficient of the unstable rock under the two-dimensional simplified model. The simplified two-dimensional model can be derived from the formula: In the formula: The stability coefficient of the unstable rock; For the weight of the unstable rock mass; The height of water filling the trailing edge fissure (m); For fissure water pressure, This represents the horizontal component of the seismic force. This represents the vertical component of the seismic force. The inclination angle (º) of the contact surface between the unstable rock mass and the base. Slip cohesion; Slippage internal friction angle (º); The slip length is in meters (m). The pressure of the slip surface water.

[0012] Furthermore, the trailing-edge fracture water pressure is calculated in differential form in the global rectangular coordinate system x, y, z: In the formula, The resultant force of the water pressure in the trailing edge fracture, For the first Each differential unit The density of water, Due to water pressure, For the height of the infinitesimal element, For the first The projected width or equivalent width of the fracture surface.

[0013] Furthermore, the resultant force of the water pressure is projected onto the local coordinate system x', y', z' of the sliding surface through a coordinate transformation matrix, and the sliding component V_w along the sliding surface direction and the vertical component N_w are extracted for subsequent calculation of the anti-slip force and sliding force of the sliding surface.

[0014] Furthermore, the buoyancy force U on the sliding surface is calculated using a three-dimensional integral method, treating the water pressure on the sliding surface in the three-dimensional state as the sum of water pressures in countless two-dimensional profiles. The infinitesimal element of the buoyancy force in any profile is: In the formula, For the buoyancy force of a single two-dimensional cross-sectional micro-element, The density of water, For the first The water depth at each cross-section For the first One section width, The water pressure in the three-dimensional state is the sum of the above equations, so we have: In the formula, The total buoyancy force of the sliding surface. For the first The buoyancy force of a differential profile For the first The differential length of a cross section along the sliding surface direction.

[0015] Furthermore, in a three-dimensional state, the anti-sliding force of the unstable rock... and downward force They can be represented as: Anti-skid force calculation: Calculation of glide force: In the formula, For the anti-sliding force of dangerous rocks, To compensate for the weight of the dangerous rock, The seismic force is distributed along the slip surface direction. The angle of inclination of the smooth surface. The component of water pressure perpendicular to the sliding surface. For the buoyancy of the sliding surface, The internal friction angle of the sliding surface. For smooth surface cohesion, The surface area is the area of ​​the smooth surface. For the sliding force of the unstable rock, To compensate for the weight of the dangerous rock, This represents the vertical force component of the earthquake. The angle of inclination of the smooth surface. For the horizontal force components of the earthquake, This is the component of water pressure along the sliding surface.

[0016] Furthermore, the three-dimensional sliding stability coefficient of the unstable rock was calculated. To determine the stability of unstable rock under different working conditions, including unfilled fissures, single fissure filled with water, and combinations of multiple fissures filled with water, the calculation formula is as follows: ,in For the sliding force of the unstable rock, This refers to the anti-sliding force of unstable rocks.

[0017] On the other hand, a stability assessment system for rockfalls with steeply dipping fractures at the rear edge is provided, the system comprising: The dangerous rock surface acquisition module uses UAV oblique photography, aerial remote sensing or LiDAR to acquire point cloud data of the dangerous rock surface, constructs a triangular mesh model and combines it with the boundary structure surface to generate a three-dimensional solid model, and extracts geometric parameters such as volume, center of gravity and slip surface area. The module for calculating the self-weight of unstable rock and the pressure of water in fissures calculates the self-weight based on a three-dimensional solid model and the unit weight of the unstable rock, and also considers the additional weight formed by water in the fissures at the rear edge; it calculates the resultant force of water pressure in multiple fissures by decomposing the coordinate system. The module for extracting the buoyancy force and water pressure component of the sliding surface divides the water pressure of the sliding surface into the buoyancy force by dividing the water pressure of the sliding surface into the differential section area, and projects the water pressure of the fissure onto the local coordinate system of the sliding surface to extract the components along the sliding surface and the vertical components. The three-dimensional stability calculation module calculates the anti-slip force and sliding force of the sliding surface based on the limit equilibrium theory, and obtains the three-dimensional sliding stability coefficient of the dangerous rock to evaluate the stability under different working conditions. The working condition analysis and result output module supports various working condition analyses and exports the stability calculation results and geometric parameters of dangerous rocks, providing a basis for engineering decision-making and risk assessment.

[0018] Beneficial effects Compared with known public technologies, the technical solution provided by this invention has the following beneficial effects: This invention fully integrates the real three-dimensional morphological characteristics of unstable rock formations with the spatial distribution characteristics of multiple sets of fractures at the rear edge, proposing a three-dimensional stability calculation method suitable for sliding unstable rock formations. Compared with traditional two-dimensional profile analysis and three-dimensional methods that only consider the effect of a single fracture, it has significant technical advantages. First, this invention constructs a detailed three-dimensional real-scene model of the unstable rock formation based on UAV oblique photography or LiDAR point clouds, which can accurately extract key geometric parameters such as the rock formation's volume, center of gravity, slip surface area, and dip angle, avoiding the morphological distortion problems caused by two-dimensional simplification, and making the stability analysis closer to the actual engineering scenario. Second, this invention is the first to systematically consider the vector superposition effect of water pressure when multiple sets of steeply dipping fractures at the rear edge are filled with water. Through spatial force vector decomposition and local coordinate system projection, the sliding component and vertical component are extracted respectively, which can accurately characterize the comprehensive influence of fracture water pressure on the sliding force and anti-sliding force of the unstable rock formation. Third, this invention uses a three-dimensional integral method to calculate the slip surface buoyancy force, making the buoyancy force distribution consistent with the real morphology of the slip surface, improving the physical rationality of the calculation results. Ultimately, this invention constructs a three-dimensional slip stability coefficient calculation model based on limit equilibrium theory, which is effectively applicable to irregularly shaped unstable rock formations with complex forms. Through engineering examples and numerical simulations, the stability coefficient calculation results of this invention are found to be more accurate and have stronger applicability, providing reliable technical support for rockfall risk assessment and prevention design. Attached Figure Description

[0019] Figure 1 This is a simplified diagram for calculating the stability of sliding unstable rock formations according to the present invention; Figure 2 This is a diagram of the water pressure in the steeply inclined fracture at the trailing edge of the present invention. Figure 3 This is a simplified diagram for calculating the trailing edge fissure water pressure of the present invention; Figure 4 This is a diagram illustrating the coordinate transformation of the trailing edge fissure water pressure of the present invention. Figure 5 This is a diagram of the dangerous rock formation at the sluice gate, as described in this invention. Figure 5.1 This is a diagram of the dangerous rock formation at the sluice gate, as described in this invention. Figure 6 This invention provides oblique photography point clouds of the dangerous rock surface. Figure 7 Construction of the dangerous rock surface model for this invention; Figure 8 This invention provides a three-dimensional model of the unstable rock mass and related information. Figure 9 This is a diagram of the numerical analysis model for dangerous rocks in this invention; Figure 10 The image shows the displacement of the unstable rock under the strength reduction method of this invention. The images in the image are a, b, and c in sequence. Figure 11 These are diagrams illustrating different forms of unstable rock formations according to the present invention. Figure 12 This is a flowchart of the method of the present invention. Detailed Implementation

[0020] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. 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 should fall within the scope of protection of the present invention.

[0021] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but includes other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0022] The present invention will now be described in further detail with reference to the accompanying drawings: A method for assessing the stability of rockfalls with steeply dipping fractures at the rear edge. Example: When the trailing edge fissure is filled with water, the water pressure is distributed in a triangular pattern; simultaneously, the buoyancy force generated by the water at the slip surface is also distributed in a triangular pattern. like Figure 1 As shown: Simplified diagram for calculating the stability of sliding unstable rock. (1) In the formula: The stability coefficient of the unstable rock; The self-weight of the unstable rock mass (kN / m); The height of water filling the trailing edge fissure (m); The value is the fissure water pressure (kN / m). ; This represents the horizontal component of the seismic force (kN / m). This represents the vertical component of the seismic force (kN / m). The inclination angle (º) of the contact surface between the unstable rock mass and the base. Slip cohesion (kPa); Slip friction angle (º); The slip length is in meters (m). The pressure of the slip surface water is (kN / m). .

[0023] The calculation of the anti-sliding stability coefficient of dangerous rocks based on the rigid body limit equilibrium theory can be summarized as the ratio of anti-sliding force to sliding force, and the specific expression is shown in equation (2).

[0024] (2) Based on the above fundamental principles, this method is extended to three-dimensional space. For sliding unstable rocks with steeply dipping fractures at the rear edge, the anti-sliding force still consists of two parts: one is the force generated by the cohesion of the sliding surface; the other is the frictional force generated by the normal stress of the sliding surface. The sliding force is the sum of the rock's gravity, seismic force, and the downward component of the water pressure along the sliding surface from the steeply dipping fracture surface at the rear edge. In three-dimensional space, there may be multiple steeply dipping fractures at the rear edge. In this case, the water pressure generated by the steeply dipping fractures at the rear edge is the resultant force of the water pressure from multiple fractures. Its component along the sliding surface downwards is expressed as The component perpendicular to the sliding surface is expressed as The buoyancy force generated by the water at the slippery surface is used for This indicates that, in a three-dimensional state, the anti-sliding force of the unstable rock is... and downward force They can be represented as: (3) (4) In the formula: This represents the surface area of ​​the smooth surface.

[0025] In the above solution process, the self-weight of the unstable rock mass needs to be calculated by establishing a three-dimensional model of the unstable rock mass and combining it with its volume and unit weight; the sliding surface area of ​​the unstable rock mass... Precise measurements can also be taken using a three-dimensional model of the unstable rock. The key to solving formulas (3) and (4) lies in determining the component of the resultant force of the water pressure in the multiple steeply dipping fractures at the rear edge along the slip surface. and components perpendicular to the sliding surface And the buoyancy generated by the slippery groundwater Therefore, the three-dimensional calculation of the stability of unstable rockfalls can be achieved through the following steps: (1) Conduct investigations and surveys of dangerous rocks to obtain basic information about them; (2) Construct a three-dimensional geological model of the dangerous rock; (3) Extract relevant information from the three-dimensional model, including the volume of the unstable rock mass. Smooth surface area wait; (4) Calculate the resultant force of the water pressure in the steeply inclined fracture at the trailing edge, and its component along the slip surface. and the component perpendicular to the sliding surface ; (5) Calculate the resultant force of the water pressure on the slip surface. ; (6) Calculate the stability according to formulas (2), (3) and (4).

[0026] 1.2 Water pressure in steeply dipping fractures at the trailing edge In three-dimensional space, there may be multiple trailing-edge fractures. When these fractures are filled with water, the resulting water pressure is the resultant force of these multiple fracture water pressures. Therefore, the calculation of the trailing-edge water pressure requires a resultant force calculation using spatial vector methods. Specifically, the water pressure on each set of steeply dipping trailing-edge fracture surfaces can be decomposed into fixed global coordinates x, y, and z, which can be established using a geodetic coordinate system. Figure 2 The global coordinate system shown has the north as the positive x-axis, the east as the positive y-axis, and the vertical upward as the positive z-axis. Then, the components in each direction are summed to obtain the resultant force of the water pressure. Peng Haiyou et al.

[10] proposed a method for solving the water pressure on the trailing edge fracture surface of arbitrary shape based on the differential principle. Its calculation diagram is shown below. Figure 3 As shown, the specific calculation formula is shown in equation (5).

[0027] (5) For a specific trailing edge crack (preferably...) Inclination angle is Through spatial geometry, it can be determined that the unit normal vector of the crack plane is .

[0028] When there are multiple steeply dipping fractures at the trailing edge, the resultant force of the water pressure is the vector sum of the forces exerted by the fracture water, which can be expressed by the following formulas (6), (7), and (8): (6) (7) (8) In the formula: Let be the water pressure in the i-th steeply inclined trailing edge fracture; , and The components of the resultant water pressure force along the x, y, and z axes in a rectangular coordinate system.

[0029] The resultant force of water pressure in equations (6), (7), and (8) is expressed in terms of three components (x, y, and z) in a rectangular coordinate system. In stability calculations, this resultant force needs to be projected onto the plane containing the slip surface. Let the dip direction of the plane containing the slip surface be... ,inclination Establish an independent coordinate system x', y', z' in the plane containing the sliding surface. Define the horizontal axis along the dip of the sliding surface as x', the horizontal axis along the direction of the sliding surface as y', and the vertically upward axis as z'. , and After transforming the coordinates to an independent coordinate system x', y', z', the water pressure in the three directions x', y', and z' of this coordinate system is: (9) (10) (11) In the formula: , and The components of the resultant water pressure force along the x', y', and z' directions in the rectangular coordinate system are respectively.

[0030] In equations (9), (10), and (11), Perpendicular to the slip surface, therefore no force is generated that causes the water pressure to slide down the slip surface. In this case, the downward component of the resultant water pressure along the slip surface... and components perpendicular to the sliding surface It can be calculated using the following formulas (12) and (13): (12) (13) When the trailing edge fracture surface is perpendicular, that is, when Equations (12) and (13) can be simplified to equations (14) and (15): (14) (15) When there is only one trailing edge fracture and it is perpendicular, and the direction of the trailing edge fracture surface is consistent with the direction of the slip surface, that is... , , Equations (12) and (13) can be simplified to: (16) (17) Equations (16) and (17) are two-dimensional profile analysis formulas, which are consistent with the stability calculation formulas for sliding unstable rocks in the Code for Investigation of Collapse Prevention Engineering (T / CAGHP011-2018).

[0031] 1.3 Integral of buoyancy force on the slip surface The integral of the buoyancy force on the slip surface is calculated using a two-dimensional method. According to the principle of differentiation, water pressure in a three-dimensional state can be understood as the sum of water pressure in countless two-dimensional cross-sections.

[0032] The water pressure at any given cross-section can be expressed as: (18) The water pressure in the three-dimensional state is the sum of the above equations, so we have: (19) For the above formula, to simplify the calculation, we assume the water filling height of the trailing edge fracture. For a constant value And there is The water-filled surface area is represented as Then we have: (20) 2. Engineering Examples 2.1 Project Background The Dazhakou dangerous cliff is located in Lizhi Street, Fuling District, Chongqing. The steep cliff sits on a downward slope in a low mountain and hilly terrain. The lithology is mainly Upper Triassic Jialingjiang Formation limestone, with a dip of 75°∠18°. The dangerous rock mass W1 is located at the front edge of the cliff, with a top elevation of 324.0–326.0 m, a bottom elevation of 281.0–284.5 m, a top width of 16.20 m, a bottom width of 18.30 m, and a thickness of 3–8.5 m. The dangerous rock mass has a quadrangular prism shape, as shown in the image. Figure 5 As shown. The trailing edge of the unstable rock mass exhibits well-developed fractures, with the main trailing fracture approximately 12.7m long, having an opening of 20–200cm and a visible depth of 2–20m. The left-side fracture L1 dips... The crack has a dip angle of approximately 90°, is nearly vertical, and is about 12m long. The crack opening ranges from 12 to 35cm, with a visible depth of 4m. The right-side crack L2 dips... The rock mass has a dip angle of approximately 90° and is nearly vertical, with a length of about 10m, an opening of 12-25cm, and a visible depth of 5m. The failure mode of this unstable rock mass is sliding, with the potential sliding surface at the bottom along the weak surface L3 of the rock strata, and its dip angle being 75°∠18°.

[0033] 2.2 Three-dimensional geological modeling Geometrically, a single unstable rock mass can be considered as a rock block cut by boundaries composed of different structural planes. Therefore, the 3D model of a sliding unstable rock mass can be composed of the outer surface of the unstable rock, the boundary structural planes, and the slip surface. In the 3D modeling process, the boundary conditions of the unstable rock mass, such as fractures, are first obtained through field surveys, including information on the orientation, location, and length of the fractures. Subsequently, images and point cloud data of the rock mass surface are acquired using UAV oblique photography or LiDAR technology, such as... Figure 6 As shown. Next, the discrete point cloud data of the dangerous rock surface is processed to construct a triangular mesh model of the dangerous rock surface [8], as shown. Figure 7 As shown.

[0034] Based on the boundary conditions of the unstable rock mass, planar models of the left boundary surface L1, right boundary surface L2, and bottom sliding surface L3 are established. The surface models of the unstable rock mass are then spatially combined and cut with the boundary planes to ultimately form a solid model of the unstable rock mass, as shown below. Figure 8 As shown in the figure, the model can accurately reproduce the morphological features of the unstable rock surface, such as details like cavities, and also accurately reflect the two side boundaries and the bottom slip surface of the unstable rock mass. Furthermore, the 3D model of the unstable rock mass allows for convenient reading of information such as its volume, center of gravity, and bottom surface area, which will be used for subsequent stability analysis calculations. For example, the volume of unstable rock mass W1 is 1979.43 m³, and the bottom slip surface area is 97.28 m².

[0035] 2.3 Stability Analysis Based on the method for calculating the stability coefficient of unstable rockfalls proposed in this paper, the stability coefficient of the unstable rockfalls at Dazhakou under different working conditions was calculated and analyzed in detail. This calculation covered five working conditions, as follows: The trailing edge fissure was not filled with water; The backwater height of the single fracture L1 at the rear edge is 3.6 m; The backwater height of the single fracture L1 at the rear edge is 5.1 m (heavy rain); The backwater height of the single fracture L2 at the rear edge is 3.6 m; The backwater height of the single fracture L2 at the rear edge is 5.1 m (heavy rain); The water filling height of the trailing double fissures L1 and L2 is 3.6 m; The backwater height of the two fractures L1 and L2 at the rear edge is 5.1 m (heavy rain).

[0036] Geological surveys and tests were conducted on the dangerous rock at Dazhakou to obtain parameters such as its unit weight and sliding surface strength. Considering the influence of the added weight of water within the rock fissures on its unit weight, the unit weights of the dangerous rock were 26.6, 27.0, and 27.8 kN / m³ when the rear fissures were not filled with water, when the water level was 3.6 m, and when the backwater level was 5.1 m (due to heavy rain). Specific parameters are shown in Table 1. The stability coefficient of the dangerous rock at Dazhakou under different working conditions was calculated and analyzed using the method proposed in this paper. The calculation process and results are shown in Table 1. When the rear fissures were not filled with water, the rock slip stability coefficient was 1.454, indicating a stable state. Under heavy rain conditions, when the backwater level of the rear double fissures L1 and L2 reached 5.1 m, the stability coefficient was only 1.093, indicating an unstable state. In contrast, under heavy rain conditions, when a single fracture L1 or a single fracture L2 is filled with water, the stability coefficients are 1.151 and 1.176 respectively, both indicating a basically stable state. This shows a significant difference in the calculated stability coefficients under single-fracture and double-fracture filling conditions. Traditional two-dimensional profile model calculation methods can only consider single fractures at the rear edge and cannot handle cases with double or multiple fracture combinations. Under heavy rain conditions, the stability coefficient for double-fracture filling is 5.5% lower than that of the two-dimensional model. Therefore, under heavy rain conditions, if multiple steeply dipping fractures exist at the rear edge of a dangerous rock mass and are all filled with water, using a simplified two-dimensional profile model to calculate the surrounding rock stability will ignore the combined effect of multiple fractures filling with water, resulting in an overestimation of the calculated stability coefficient and failing to accurately reflect the actual stability status. Figure 6 ).

[0037] Table 1. Calculation Table of Three-Dimensional Stability of Dangerous Rock

[0038] 2.4 Numerical Analysis Comparison This paper uses FLAC3D software to conduct numerical analysis on the stability of a dangerous rock mass. Based on the established three-dimensional model of the dangerous rock mass, a three-dimensional numerical analysis model of the dangerous rock mass was constructed, with dimensions of 36 m high, 21 m wide, and 18 m deep. The rock mass in contact with and behind the dangerous rock mass was only used as a boundary condition and was simplified during the modeling process. Displacement constraint boundary conditions were used at the bottom and around the perimeter of the model, and the free surface of the dangerous rock mass was a free surface, as shown in the figure. Figure 9 As shown in (a), the unstable rock mass is simulated using solid elements, while the fracture surface is simulated using interface elements, as shown in Figure 9(b). The physical and mechanical parameters of the model are shown in Table 2, and the constitutive model adopts the Mohr-Coulomb model.

[0039] Table 2 Calculation Parameters

[0040] like Figure 10 As shown, since Zienkiewicz et al.

[36] first proposed the strength reduction method in 1975, this method has been increasingly widely used in the stability analysis of rock slopes and unstable rocks [37-40]. This paper uses the structural surface strength reduction method to analyze the stability of unstable rocks. The strength of the unstable rock sliding surface is calculated by gradually reducing it in increments of 0.01 from the initial state. When the reduction coefficient increases from 1.0 to 1.45, the model can converge quickly and the overall displacement of the unstable rock is small. When the reduction coefficient reaches 1.46, the unstable rock begins to show obvious displacement, but the displacement is relatively small at this time, with a value of 3.75 mm. The model still converges as a whole, and the unstable rock has not experienced overall instability. However, when the reduction coefficient is further increased to 1.47, the model calculation no longer converges, and the displacement of the unstable rock exceeds 10 cm and continues to increase, indicating that the unstable rock has experienced overall instability. Therefore, the overall stability coefficient of the unstable rock is 1.46. The calculated result is very close to the three-dimensional stability coefficient of 1.454 (without water filling the trailing edge fracture) based on the limit equilibrium theory, with a deviation of only 0.4%, which further verifies the reliability and applicability of the three-dimensional limit equilibrium method for unstable rocks established in this paper.

[0041] 3.1 Morphological Sensitivity Analysis In three dimensions, the morphology of the unstable rock directly affects its gravity and center of gravity, the shape and area of ​​the slip surface, and the water pressure after the rear edge fissure is filled with water, thus significantly affecting its stability. Based on the case in reference

[10] , this paper adjusts the slip surface dip angle to 15° and establishes a system as follows: Figure 11 The stability of four different rock mass models with varying shapes was calculated to analyze the impact of rock mass morphology on stability. The four rock mass models with different shapes are shown below. Figure 11 As shown in (a) to 11(d): Figure 11 (a): The fracture surface at the rear edge of the unstable rock mass is an equilateral triangle; Figure 11 (b): The fracture surface at the rear edge of the unstable rock mass is an isosceles trapezoid; Figure 11 (c): The fracture surface at the rear edge of the unstable rock mass is rectangular; Figure 11 (d): A trapezoid with the same bottom surface on both sides of the unstable rock mass.

[0042] The unstable rock mass has a height (AD) of 20 m and a thickness of 10 m; other dimensions are shown in the figure. When calculating the stability coefficient using the two-dimensional profile model method... Figure 11The unstable rock masses in (a) to 11(d) can all be simplified as follows: Figure 11 (e) shows the two-dimensional profile calculation model.

[0043] The calculation parameters are as follows: rock mass weight is 26.6 kN / m³, internal friction angle of the slip surface is 16°, cohesion is 55.0 kPa, the trailing edge is a single fracture filled with water, and the water filling height is 6.4 m. This was achieved by establishing... Figure 11 The three-dimensional models (a), (b), (c), and (d) are shown in Table 3, which allows for the measurement of the model's volume and sliding surface area. The relevant data are listed in Table 3. The table lists the working conditions... Figure 11 The volume and sliding surface area of ​​(e) are calculated with a width of 1 m. The three-dimensional stability coefficients of the unstable rock mass calculated according to the method proposed in this paper are also shown in Table 3. The stability coefficient calculation results show that: Operating conditions Figure 11 (a), 11(c), and 11(e) are stable; Operating conditions Figure 11 (d) is basically stable; Operating conditions Figure 11 (b) is unstable.

[0044] Among them, except Figure 11 (c) Except for the calculation results of the unstable rock mass (regular cuboid) which are consistent with the calculation results of the two-dimensional profile method (both are 1.237), other working conditions... Figure 11 The results (a), (b), and (d) differ significantly from those calculated using the two-dimensional profile method. This indicates that, under three-dimensional conditions, the morphology of the unstable rock has a significant impact on its stability, while the traditional two-dimensional profile method may not accurately reflect the stability characteristics of unstable rocks with complex shapes.

[0045] 3.2 Engineering Significance Three-dimensional methods can accurately simulate the water pressure distribution after multiple fractures are filled with water, quantifying its impact on the stability of unstable rocks and overcoming the shortcomings of traditional two-dimensional methods. This provides a more accurate tool for stability analysis under complex geological conditions. Furthermore, under extreme conditions such as torrential rain and earthquakes, three-dimensional methods can comprehensively consider the impact of multiple factors on the stability of unstable rocks, providing a more accurate risk assessment. This offers a scientific basis for disaster early warning and emergency response, guides the design of protective engineering projects, and improves the reliability and economy of protective engineering.

[0046] Figure 11 Calculation models of dangerous rocks of different forms Figure 11. Calculation Models of Unstable Rocks of Various Shapes Table 3 Stability Calculation Table for Different Types of Rockfalls

[0047] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions will not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for assessing the stability of sliding rockfalls with steeply dipping fractures at the rear edge, characterized in that, Includes the following steps: S1. Use UAV oblique photography, aerial remote sensing or airborne LiDAR to acquire high-precision point cloud data of the dangerous rock surface and construct a triangular network model of the dangerous rock surface. S2. Construct a three-dimensional solid model based on the boundary conditions of the dangerous rock and the slip surface; S3. Extract the volume, center of gravity, slip surface area, and slip surface spatial orientation information of the dangerous rock from the three-dimensional solid model, and calculate the self-weight of the dangerous rock by combining the unit weight of the rock mass and the additional weight of the water in the fissure. S4. Calculate the resultant force of the hydraulic pressure in the trailing edge fracture and project it onto the local coordinate system x', y', z' where the slip surface is located, where x' is the horizontal direction along the dip of the slip surface, y' is the horizontal direction along the strike of the slip surface, and z' is the vertical upward direction; in the local coordinate system, extract the sliding component and the vertical component of the resultant force of the hydraulic pressure along the slip surface direction; The specific formula is as follows: , ; ； ； In stability calculations, the resultant force needs to be projected onto the plane containing the slip surface, and the dip direction of the plane containing the slip surface should be θ. ,inclination Establish an independent coordinate system x', y', z' in the plane containing the sliding surface. Define the horizontal axis along the dip of the sliding surface as x', the horizontal axis along the direction of the sliding surface as y', and the vertical upward axis as z'. , and After transforming the coordinates to an independent coordinate system x', y', z', the water pressure in the three directions x', y', and z' of this coordinate system is: ， ， ， In the formula: , and The components of the resultant water pressure force along the x', y', and z' directions in the rectangular coordinate system; In stability calculations, the resultant force needs to be projected onto the plane containing the slip surface, and the dip direction of the plane containing the slip surface should be θ. ,inclination Establish an independent coordinate system x', y', z' in the plane containing the sliding surface. Define the horizontal axis along the dip of the sliding surface as x', the horizontal axis along the direction of the sliding surface as y', and the vertical upward axis as z'. , and After transforming the coordinates to an independent coordinate system x', y', z', the water pressure in the three directions x', y', and z' of this coordinate system is: ， ， （11）， In the formula: , and The components of the resultant water pressure force along the x', y', and z' directions in the rectangular coordinate system; S5. Calculate the buoyancy force of the sliding surface by considering the water pressure on the sliding surface in the three-dimensional state as an integral of the water pressure of countless two-dimensional profiles. S6. Based on the limit equilibrium theory, calculate the anti-sliding force and sliding force of the unstable rock, and obtain the three-dimensional sliding stability coefficient.

2. The method for assessing the stability of sliding rockfalls with steeply dipping fractures at the rear edge, as described in claim 1, is characterized in that... The three-dimensional solid model is used to directly derive the geometric characteristic parameters of the dangerous rock, including volume, center of gravity position, bottom slip surface area and outer surface area; The volume is obtained by accumulating three-dimensional space volume elements, the center of gravity is obtained by calculating the three-dimensional centroid integral, and the area parameter is obtained by summing the areas of triangular mesh patches, so as to provide accurate geometric input for self-weight, fracture water pressure and stability analysis.

3. The method for assessing the stability of sliding rockfalls with steeply dipping fractures at the rear edge, as described in claim 2, is characterized in that... Dangerous rock mass self-weight It can be calculated using the following formula: ， In the formula, Due to the weight of the unstable rock mass, The density of the unstable rock mass, This represents the volume of the unstable rock mass.

4. The method for assessing the stability of sliding rockfalls with steeply dipping fractures at the rear edge, as described in claim 3, is characterized in that... Stability coefficient of unstable rock under two-dimensional simplified model The simplified two-dimensional model can be derived from the formula: ， In the formula: The stability coefficient of the unstable rock; For the weight of the unstable rock mass; The height of water filling the trailing edge fissure (m); For fissure water pressure, This represents the horizontal component of the seismic force. This represents the vertical component of the seismic force. The inclination angle (º) of the contact surface between the unstable rock mass and the base. Slip cohesion; Slippage internal friction angle (º); The slip length is in meters (m). The pressure of the slip surface water.

5. The method for assessing the stability of sliding rockfalls with steeply dipping fractures at the rear edge, as described in claim 4, is characterized in that... The trailing fracture water pressure is calculated in differential form in the global rectangular coordinate system x, y, z: ， In the formula, The resultant force of the water pressure in the trailing edge fracture, For the first Each differential unit The density of water, Due to water pressure, For the height of the infinitesimal element, For the first The projected width or equivalent width of the fracture surface.

6. The method for assessing the stability of sliding rockfalls with steeply dipping fractures at the rear edge, as described in claim 5, is characterized in that... The resultant force of the water pressure is projected onto the local coordinate system x', y', z' of the sliding surface through a coordinate transformation matrix, and the sliding component V_w along the sliding surface direction and the vertical component N_w are extracted for subsequent calculation of the anti-slip force and sliding force of the sliding surface.

7. The method for assessing the stability of sliding rockfalls with steeply dipping fractures at the rear edge, as described in claim 6, is characterized in that... The buoyancy force U on the sliding surface is calculated using a three-dimensional integral method, treating the water pressure on the sliding surface in a three-dimensional state as the sum of water pressures from countless two-dimensional profiles. The infinitesimal element of the buoyancy force for any profile is: ， In the formula, For the buoyancy force of a single two-dimensional cross-sectional micro-element, The density of water, For the first The water depth at each cross-section For the first One section width, The water pressure in the three-dimensional state is the sum of the above equations, so we have: ， In the formula, The total buoyancy force of the sliding surface. For the first The buoyancy force of a differential profile For the first The differential length of a cross section along the sliding surface direction.

8. The method for assessing the stability of sliding rockfalls with steeply dipping fractures at the rear edge, as described in claim 7, is characterized in that... In a three-dimensional state, the anti-sliding force of the unstable rock. and downward force They can be represented as: Anti-skid force calculation: , Calculation of glide force: , In the formula, For the anti-sliding force of dangerous rocks, To compensate for the weight of the dangerous rock, This represents the component of the seismic force along the slip surface. The angle of inclination of the smooth surface. The component of water pressure perpendicular to the sliding surface. For the buoyancy of the sliding surface, The internal friction angle of the sliding surface. For smooth surface cohesion, The surface area is the area of ​​the smooth surface. For the sliding force of the unstable rock, To compensate for the weight of the dangerous rock, This represents the vertical force component of the earthquake. The angle of inclination of the smooth surface. For the horizontal force components of the earthquake, This is the component of water pressure along the sliding surface.

9. A method for assessing the stability of sliding rockfalls with steeply dipping fractures at the rear edge, as described in claim 8, is characterized in that... Calculate the three-dimensional sliding stability coefficient of the unstable rock. To determine the stability of unstable rock under different working conditions, including unfilled fissures, single fissure filled with water, and combinations of multiple fissures filled with water, the calculation formula is as follows: ,in For the sliding force of the unstable rock, This refers to the anti-sliding force of unstable rocks.

10. A stability assessment system for rockfalls with steeply dipping fractures at the rear edge, as described in any one of claims 1-9, comprising: The dangerous rock surface acquisition module uses UAV oblique photography, aerial remote sensing or LiDAR to acquire point cloud data of the dangerous rock surface, constructs a triangular mesh model and combines it with the boundary structure surface to generate a three-dimensional solid model, and extracts geometric parameters such as volume, center of gravity and slip surface area. The module for calculating the self-weight of unstable rock and the pressure of water in fissures calculates the self-weight based on a three-dimensional solid model and the unit weight of the unstable rock, and also considers the additional weight formed by water in the fissures at the rear edge; it calculates the resultant force of water pressure in multiple fissures by decomposing the coordinate system. The module for extracting the buoyancy force and water pressure component of the sliding surface divides the water pressure of the sliding surface into the buoyancy force by dividing the water pressure of the sliding surface into the differential section area, and projects the water pressure of the fissure onto the local coordinate system of the sliding surface to extract the components along the sliding surface and the vertical components. The three-dimensional stability calculation module calculates the anti-slip force and sliding force of the sliding surface based on the limit equilibrium theory, and obtains the three-dimensional sliding stability coefficient of the dangerous rock to evaluate the stability under different working conditions. The working condition analysis and result output module supports various working condition analyses and exports the stability calculation results and geometric parameters of dangerous rocks, providing a basis for engineering decision-making and risk assessment.

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