A hidden dip rock slope grading and collaborative anchoring prevention method

Abstract

The application discloses a kind of hidden order to dip rock slope grading collaborative anchoring prevention and control methods, it is related to the technical field of hidden order to dip rock slope grading collaborative anchoring prevention and control, comprising the following steps: obtaining the geological survey data of target slope, and generate the digital model of slope by multiple grid nodes;Strength reduction is carried out to the digital model of slope, simulates the process that target slope evolves from steady state to non-steady state, and obtains each grid node data in simulation process, and calculates the shear strain value of each grid node, generates initial slope stress field data.The application accurately tracks the dynamic evolution path of shear zone by strength reduction simulation and space-time sequence reconstruction, can accurately identify shear evolution characteristics, so as to effectively avoid the position of reinforcement and actual disaster domain misplacement, so as to effectively avoid the reinforcement failure caused by shear failure of slope, effectively improve the prevention and control effect.

Description

Technical Field

[0001] This invention relates to the field of graded and coordinated anchoring control technology for concealed dip-sloping rock slopes, specifically a graded and coordinated anchoring control method for concealed dip-sloping rock slopes. Background Technology

[0002] Mountainous areas account for approximately two-thirds of my country's total land area. With the advancement of infrastructure construction such as water conservancy and hydropower projects, transportation networks, and open-pit mines, a large number of dipping rock slopes have been created through engineering excavation. Under external loads such as gravity, earthquakes, and rainfall, these slopes are highly susceptible to instability and failure, making their stability control a key challenge in engineering construction.

[0003] Based on the geometric relationship between the dip angle of the rock strata and the slope angle, dip-parallel rock slopes are mainly divided into two categories: one is the cut-bedding rock slope, which is a bedding slope with a bedding angle smaller than the slope angle, and the bedding plane is directly exposed on the slope surface; the other is the concealed dip-parallel rock slope, which is a steep slope with a bedding angle greater than or equal to the slope angle, and the bedding plane is recessed downwards into the slope toe. The stability of concealed dip-parallel rock slopes is particularly complex. These slopes have poor rock strata exposure conditions, and potential slip surfaces are often concealed. During deformation and failure, they often exhibit localized tensile cracking and bending deformation, gradually evolving towards overall instability. The failure mechanism is characterized by obvious gradualism, concealment, and suddenness. Furthermore, concealed dip-parallel rock slopes are often steep slopes with large slope height and strong structural control, making them highly susceptible to large-scale instability under adverse factors such as rainfall, earthquakes, and engineering disturbances. Their stability is also constrained by factors such as construction conditions, stress mechanisms, and reinforcement effectiveness.

[0004] In existing technologies, the prevention and control effect is improved by using a combination of fixed foot and strong waist reinforcement. However, in the implementation process, the geometric center of the slope surface is often equated with the stress concentration waist. In fact, the peak area of ​​shear stress migration is not a fixed geometric location, but a stress concentration disaster area that dynamically migrates with the localization evolution of shear deformation. Equating the geometric center of the slope surface with the stress concentration waist cannot quantify the secondary redistribution mechanism of shear stress after the slope foot constraint, and lacks accurate identification of this shear evolution characteristic. As a result, the reinforcement location is misaligned with the actual disaster area. Even if strong waist measures are implemented, the slope will still experience shear failure, causing the reinforcement to fail. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a graded and coordinated anchoring method for the prevention and control of hidden, dip-sloping rock slopes.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] A graded and coordinated anchoring method for the prevention and control of concealed dip-sloping rock slopes includes the following steps:

[0008] Obtain geological survey data of the target slope and generate a digital model of the slope consisting of multiple grid nodes;

[0009] Strength reduction is applied to the digital model of the slope to simulate the evolution of the target slope from steady state to unsteady state. Data of each grid node is obtained during the simulation, and the shear strain value of each grid node is calculated to generate the initial slope stress field data.

[0010] Extract the grid nodes in the initial slope stress field data where the shear stress value is greater than the shear deformation threshold to obtain the initial shear deformation localization region data;

[0011] Based on the initial shear deformation localization region data, the first-level anchorage region is determined. In the slope digital model, the first-level anchorage region is subjected to first-level anchorage constraints, and the strength reduction is re-executed to simulate and generate the first slope stress field data and the first shear deformation localization region data.

[0012] Spatiotemporal sequence reconstruction of the data from the first localized shear deformation region yields evolution path data characterizing the dynamic expansion trajectory of the shear band.

[0013] The difference between the initial slope stress field data and the first slope stress field data is calculated to obtain the stress migration increment field data.

[0014] Overlay analysis of stress migration increment field data and evolution path data is performed to identify extreme points of stress migration increment, and extreme points located in the primary anchorage region are removed. The coordinates of the first extreme point located at the rear edge of the primary anchorage region are determined as the geometric center coordinates of the secondary anchorage region.

[0015] Based on the geometric center coordinates, determine the secondary anchorage area data and generate secondary anchorage design parameters;

[0016] Based on the data of the primary and secondary anchorage areas and the design parameters of the secondary anchorage, a graded and coordinated anchorage project was implemented on the target slope.

[0017] Preferably, the spatiotemporal sequence reconstruction of the data from the first localized shear deformation region yields evolution path data characterizing the dynamic expansion trajectory of the shear band, specifically including:

[0018] Based on the time series of strength reduction, extract the data of the first localized region of shear deformation corresponding to each reduction coefficient;

[0019] Extract the shear strain value of the first shear deformation localization region data corresponding to each reduction factor, and identify the maximum peak point set of the shear strain value under the corresponding factor;

[0020] Interpolate and fit the set of maximum peak points corresponding to different reduction coefficients in chronological order to generate continuous evolution path data that characterizes the gradual expansion of the shear band as the intensity decreases.

[0021] Preferably, the stress migration increment field data and evolution path data are overlaid and analyzed to identify extreme points of stress migration increments, and extreme points located within the primary anchorage region are removed. Specifically, this includes:

[0022] Map the evolution path data to the stress migration increment field data;

[0023] Along the direction of the evolution path, extract the stress migration increment of each grid node on the evolution path;

[0024] Construct a distribution curve of stress migration increment along the evolution path and identify the extreme points on the curve;

[0025] Exclude all extreme points located within the geometric boundary of the primary anchorage zone.

[0026] Preferably, the secondary anchorage area data is determined based on the geometric center coordinates, specifically including:

[0027] Using the geometric center coordinates as a reference, contour analysis is performed on the stress migration increment field data along the direction of the hidden structural surface to determine the contour range of the stress migration increment attenuating to the proportion of the first peak value, which serves as the longitudinal boundary of the secondary anchorage area.

[0028] In the profile corresponding to the geometric center coordinates, extract the shear strain distribution data perpendicular to the hidden structure plane, and determine the width of the region where the shear strain value is greater than or equal to the shear deformation threshold, as the shear deformation localization bandwidth.

[0029] Based on the sum of the localized bandwidth of shear deformation and the preset stable bedrock anchorage length, the normal anchorage depth required for secondary anchorage is calculated.

[0030] The anchoring length in the stable bedrock is a length of 3-5 meters extending into the stable bedrock of both the upper and lower plates.

[0031] Preferably, the secondary anchorage design parameters are generated, specifically including:

[0032] Based on the stress migration increment field data corresponding to the geometric center coordinates, the direction of the corresponding shear stress resultant force vector is calculated.

[0033] The placement angle of the secondary anchor body is determined based on the direction of the resultant shear stress vector, so that the direction of the anchor body forms a reverse shear angle with the shear slip direction;

[0034] Obtain the first design prestress value of the primary anchorage structure, multiply the first design prestress value by a preset proportional coefficient, and calculate the second prestress design value of the secondary anchorage.

[0035] The length of the anchorage section of the secondary anchor body is determined based on the normal anchorage depth.

[0036] Preferably, a graded and coordinated anchoring project is implemented on the target slope, specifically including:

[0037] Within the primary anchorage area, the primary anchorage structure is constructed and tensioned according to the high stiffness design requirements, and the first design prestress value is applied.

[0038] The displacement rate of the target slope is monitored. When the displacement rate converges to the stability threshold, it is determined that the stress redistribution inside the slope tends to be stable.

[0039] Within the range specified by the secondary anchorage area data, construct and tension the secondary anchorage structure, and apply the second prestress design value;

[0040] The secondary anchoring structure adopts an anchor cable structure with constant resistance and large deformation characteristics, and a flexible buffer pad layer is set between the anchor pier and the slope.

[0041] Preferably, after implementing the graded and coordinated anchoring project, a dynamic feedback control step is also included, specifically including:

[0042] Establish a monitoring system linking deep stress and surface deformation in the secondary anchorage area;

[0043] Continuously acquire monitoring data on anchor cable axial force and slope surface displacement of the secondary anchorage structure;

[0044] The axial force monitoring data of the anchor cable is subjected to real-time differential processing to obtain the axial force change rate data;

[0045] The slope displacement monitoring data is processed by real-time differentiation to obtain the displacement change rate data;

[0046] In response to the simultaneous detection that the axial force change rate data is lower than a preset negative threshold and the displacement change rate data is higher than a preset positive threshold, a dynamic reinforcement early warning signal is generated.

[0047] Based on the warning signal, supplementary anchoring or targeted reinforcement measures are implemented at the locations where abnormal stress concentration is detected.

[0048] Preferably, the construction of the digital model of the slope specifically includes:

[0049] Based on the rock strata attitude, spatial location of hidden weak interlayers and rock and soil mechanical parameters in geological exploration data, a numerical calculation model reflecting the characteristics of hidden dip-side structures is constructed.

[0050] In the numerical calculation model, the rock strata dip is consistent with the slope dip, and the rock strata dip angle is greater than or equal to the slope dip angle.

[0051] In the model, contact surface elements or weak interlayer materials are set along the rock layer interface to simulate interlayer slip, debonding and shear softening behavior.

[0052] Elastoplastic solid elements were set up in the rock bridge area at the foot of the slope to simulate potential shear failure paths.

[0053] Preferably, the primary anchorage region is the concentrated distribution area with the largest shear strain value in the initial shear deformation localization region data, and the primary anchorage region is located in the stress concentration area at the toe of the slope.

[0054] Preferably, the shear deformation threshold is 1.5 to 2.0 times the peak shear strain value of the target slope rock mass obtained through rock mass testing.

[0055] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0056] This invention accurately tracks the dynamic evolution path of the shear zone through strength reduction simulation and spatiotemporal sequence reconstruction. Combined with stress migration increment field and path superposition analysis, it quantifies the stress redistribution law after slope toe anchoring, and finally locks the primary and secondary anchoring zones. This ensures that the anchoring range highly overlaps with the risk domain, enabling the anchoring system to withstand the impact of instantaneous loads and accommodate long-term rheological deformation. The disaster resistance toughness is significantly improved compared to traditional single stiffness anchoring. It can accurately identify shear evolution characteristics, thereby effectively avoiding the misalignment of the reinforcement location with the actual disaster-causing domain, thus effectively preventing shear failure of the slope and reinforcement failure, and effectively improving the prevention and control effect. Attached Figure Description

[0057] The disclosure of this invention is illustrated with reference to the accompanying drawings. It should be understood that the drawings are for illustrative purposes only and are not intended to limit the scope of protection of this invention. In the drawings, the same reference numerals are used to refer to the same parts. Wherein:

[0058] Figure 1 This is a flowchart of the method of the present invention;

[0059] Figure 2 This is a schematic cross-sectional view of the slope graded collaborative prevention and control principle of the present invention;

[0060] Figure 3 This is a schematic diagram of the secondary anchoring rigidity-toughness matching structure of the present invention;

[0061] Figure 4 This is a schematic diagram illustrating the shear band evolution and stress migration positioning principle in an example of the present invention.

[0062] Figure 5 This is a distribution diagram of the shear stress migration increment after applying the first-level anchoring measure in an example of the present invention;

[0063] Figure 6This is a distribution diagram of the shear stress migration increment after applying primary and secondary anchoring reinforcement measures in an example of the present invention;

[0064] Figure 7 This is a diagram of the graded collaborative anchoring combination in an example of the present invention. Detailed Implementation

[0065] It is readily understood that, based on the technical solution of this invention, those skilled in the art can propose various interchangeable structural methods and implementations without altering the essential spirit of the invention. Therefore, the following detailed embodiments and accompanying drawings are merely illustrative examples of the technical solution of this invention and should not be considered as the entirety of the invention or as limitations or restrictions on the technical solution of this invention.

[0066] like Figure 1-7 As shown, a graded and coordinated anchoring method for the prevention and control of concealed dip-sloping rock slopes includes the following steps:

[0067] Obtain geological survey data of the target slope and generate a digital model of the slope consisting of multiple grid nodes;

[0068] Specifically, the failure of concealed dip-sloping rock slopes is essentially a progressive shear failure controlled by concealed structural planes. Therefore, digital models must accurately reproduce their geometric structure, material composition, and mechanical parameters in order to simulate the deformation and stress evolution laws consistent with those of actual slopes.

[0069] The geological survey data collected for the target slope includes:

[0070] Geometric feature data:

[0071] Overall dimensions of the slope, including slope height, bottom width, and slope angle;

[0072] The attitude of rock strata, including the dip direction and dip angle of the rock strata;

[0073] The data collection must meet the definition of concealed dip: the dip direction of the rock strata is consistent with the dip direction of the slope, and the dip angle of the rock strata is greater than or equal to the dip angle of the slope; the slope height and bottom width must be combined with the actual engineering scenario, and the dip angle accuracy must be controlled within ±1° to ensure accurate geometric relationships.

[0074] Structural feature data:

[0075] The spatial location of the hidden weak interlayer, including its burial depth, extent of extension, and thickness;

[0076] Distribution range and thickness of rock bridges at the toe of slopes;

[0077] Rock mass fracture development, including density, orientation, and continuity;

[0078] Hidden weak interlayers are the core channels for the evolution of shear zones and need to be accurately located through drilling exploration or geophysical exploration, such as ground-penetrating radar; the slope toe anti-slide rock bridge is the key object of primary anchorage and the spatial relationship between the slope toe anti-slide rock bridge and the weak interlayer needs to be clarified.

[0079] Mechanical parameter data:

[0080] Bedrock mechanical parameters, including elastic modulus, Poisson's ratio, cohesion, and internal friction angle;

[0081] Mechanical parameters of weak interlayers or structural surfaces, including normal stiffness, tangential stiffness, cohesion, and internal friction angle;

[0082] Peak shear strain of the rock mass;

[0083] The parameters need to be obtained through indoor tests, such as uniaxial compression and direct shear tests of rocks, or in-situ tests. For weak interlayer parameters, the shear softening characteristics should be the focus, reflecting the strength decay law during deformation.

[0084] Furthermore, based on geological exploration data, a digital model containing finely detailed grid nodes is constructed using numerical simulation software, such as FLAC3D, Phase2, and MidasGTS, as detailed below:

[0085] Numerical calculation model: Two-dimensional or three-dimensional models are constructed using software, with mesh nodes as the basic units of calculation, and the stress, strain, and displacement data of each node can be accurately output;

[0086] Strictly adhere to the hidden dip-slope characteristic where the rock strata dip angle is greater than or equal to the slope dip angle, ensuring that the rock strata penetrate downward into the bedrock at the toe of the slope to form a rock bridge that prevents sliding at the toe of the slope.

[0087] Grid node design:

[0088] Mesh generation principles: refine the mesh in critical areas and coarse the mesh in non-critical areas. Fine meshing is required in areas such as the toe of the slope, weak interlayers, and potential shear paths. The mesh node density should be high to ensure that local shear deformation can be captured. The mesh can be appropriately coarsened in the stable upper part of the slope to balance computational efficiency and accuracy.

[0089] Mesh nodes: Each mesh node is the calculation carrier of stress, strain, and displacement, providing a basis for identifying localized regions of shear deformation;

[0090] After the model is built, its rationality needs to be verified through gravity equilibrium calculations: After applying self-weight load, the initial stress field of the model is calculated. If the shear stress concentration area at the slope toe is consistent with the theoretical law and there are no abnormal stress abrupt changes, then the model is valid; otherwise, the mesh generation or mechanical parameters need to be adjusted. Specifically:

[0091] Only the self-weight load is applied to the completed slope digital model, without additional external loads such as earthquakes or rainfall, to restore the natural initial state of the slope. The stress-displacement field of the slope digital model is iteratively calculated using the mechanical equilibrium algorithm of numerical simulation software, such as FLAC3D and Phase2, until the slope digital model reaches a force equilibrium state, that is, the unbalanced force converges to a set threshold, usually 1e-5 to 1e-6. After the calculation is completed, the initial shear stress field and initial displacement field data of the model are extracted, with a focus on the stress distribution and deformation values ​​of key areas such as the slope toe, hidden weak interlayers, and the upper and middle parts of the slope.

[0092] A slope digital model can only be deemed reasonably constructed if all of the following conditions are met:

[0093] The stress distribution conforms to theoretical laws:

[0094] The shear stress concentration zone is consistent with the theory: the toe of the slope is the peak shear stress zone, and the shear stress value gradually decreases from the toe of the slope to the top of the slope.

[0095] The shear stress of the hidden weak interlayer is higher than that of the surrounding bedrock: because the weak interlayer has low shear strength, stress tends to accumulate here, which is consistent with the mechanical mechanism of the structural surface controlling slope instability;

[0096] Vertical stress increases linearly with depth: This conforms to the basic law of calculating the self-weight stress of soil and rock masses.

[0097] The deformation state is within the elastic range:

[0098] The overall displacement of the model is extremely small, with no obvious plastic deformation or large displacement area;

[0099] The displacement direction conforms to the trend of gravity: the slope has a slight downward sliding tendency along the slope surface, and there is no obvious shear deformation at the toe of the slope, which is consistent with the stable state of a natural slope.

[0100] No abnormal stress or sudden displacement:

[0101] The stress and displacement values ​​of adjacent grid nodes transition continuously without any abrupt increases or decreases.

[0102] The stress connection between different element types (bedrock solid element and weak interlayer contact surface element) is smooth and there is no stress abrupt change, avoiding stress distortion caused by improper element setting.

[0103] By eliminating defects in the model construction through gravity balance calculations, we can avoid the failure of engineering reinforcement caused by positioning deviations in the anchorage area and unreasonable design of anchorage parameters due to model distortion.

[0104] Strength reduction is applied to the digital model of the slope to simulate the evolution of the target slope from steady state to unsteady state. Data of each grid node is obtained during the simulation, and the shear strain value of each grid node is calculated to generate the initial slope stress field data.

[0105] Extract the grid nodes in the initial slope stress field data where the shear stress value is greater than the shear deformation threshold to obtain the initial shear deformation localization region data;

[0106] Specifically, the instability of a hidden dip slope is essentially due to insufficient shear strength to resist the sliding force. The strength reduction method artificially reduces the shear strength parameters of the rock mass and weak surfaces, including cohesion. and internal friction angle Simulate the strength deterioration process of a slope under gravity and external loads:

[0107] Each reduction factor That is, each reduction in cohesion and internal friction angle Each time the slope's anti-sliding capacity is reduced, as the reduction factor increases, the slope gradually transitions from stress equilibrium to stress imbalance, that is, from steady state to unsteady state, eventually resulting in large deformation or non-convergence of calculations, which means reaching the critical state of instability. This process is highly consistent with the gradual evolution law of actual slopes from long-term deformation to local failure and then to overall instability.

[0108] Furthermore, the details are as follows:

[0109] Set reduction parameters and termination conditions:

[0110] The reduction targets are the shear strength parameters of bedrock and concealed weak interlayers. Among them, the parameters of weak interlayers are given higher priority for reduction because they are the main development areas of shear zones.

[0111] Reduction range: Gradually reduce cohesion by 5%-10% per level. internal friction angle For example, the initial After the first level of reduction Level 2 wait;

[0112] Termination condition: The reduction will cease when any of the following conditions are met:

[0113] The numerical model calculations do not converge, meaning that the stress and displacement cannot be balanced;

[0114] The model exhibits significant deformation, such as the slope toe displacement exceeding the warning threshold.

[0115] The shear band extending to the top of the slope simulates the evolution of the slope from a steady state to an unsteady state.

[0116] Graded reduction and equilibrium calculation: According to the set reduction range, strength degradation loading is applied to the model in stages. After each loading stage, the equilibrium algorithm of the numerical simulation software is started to iteratively calculate the stress of each grid node, such as normal stress and shear stress, and the displacement, such as horizontal displacement and vertical displacement, until the model reaches force equilibrium. After each reduction equilibrium stage, the current reduction coefficient is recorded synchronously. The original data for all corresponding mesh nodes, namely stress tensors and displacement vectors.

[0117] Grid node data extraction and preprocessing:

[0118] Extraction scope: All grid nodes in the model, with a focus on key areas such as the slope toe, hidden weak interlayers, and the upper and middle parts of the slope;

[0119] Core extracted data:

[0120] Stress tensor: , , This reflects the normal stress and shear stress state of the node;

[0121] Data preprocessing: Remove outlier data, such as nodes with sudden stress changes caused by improper meshing, to ensure data continuity and authenticity.

[0122] Shear strain It is a core indicator characterizing the shear deformation strength of rock mass, and needs to be calculated based on the extracted stress tensor or nodal displacement. The specific method is as follows:

[0123] Based on the principles of elasticity, the maximum shear strain is derived using the stress tensor of the nodes, and the formula is simplified as follows:

[0124] ;

[0125] in, For the maximum principal stress, The minimum principal stress is calculated from the stress tensor.

[0126] The rock mass shear modulus is derived from the elastic modulus. Compared to Poisson Derivation: ;

[0127] The larger the value, the more severe the shear deformation at that node, and the closer it is to yield failure.

[0128] Shear deformation localization threshold screening: Set the shear deformation localization threshold The shear strain value of each grid node is 1.5 to 2.0 times the peak shear strain of the rock mass. contrast:

[0129] This indicates that the grid nodes are located in the localized shear deformation zone, meaning the rock mass has yielded and belongs to the potential shear zone.

[0130] This indicates that the grid nodes are in the elastic deformation zone, meaning the rock mass has not yielded and its stability is good.

[0131] Furthermore, the stress data of all grid nodes and the calculated shear strain data are processed through the visualization module of the numerical software to generate continuous stress distribution cloud maps and shear strain distribution cloud maps across the entire field, collectively referred to as the initial slope stress field data, which specifically includes:

[0132] Shear stress field: Clearly shows the spatial distribution of shear stress, with obvious red high value areas, i.e. stress concentration areas, at the toe of the slope and in weak interlayers;

[0133] Shear strain field: all marked The grid nodes form a continuous shear deformation localization zone, i.e. the initial potential shear zone, and the initial shear deformation localization region data is obtained.

[0134] Displacement field: reflects the overall deformation trend of the slope in the unanchored state, usually manifested as slight outward slippage at the toe of the slope and small settlement in the middle and upper part of the slope.

[0135] In the above-mentioned technology, by gradually reducing the shear strength of the rock mass, the gradual evolution of the slope from steady state to unsteady state is restored. The stress and displacement data of all grid nodes are extracted and the shear strain is calculated. Finally, stress field data that can accurately reflect the initial risk distribution is generated, which solves the defect of traditional technology that cannot quantify the initial shear deformation distribution. This allows the positioning of the first-level anchorage zone to change from experience-based judgment to data-driven, and provides benchmark data for subsequent stress migration analysis after first-level anchorage.

[0136] Based on the initial shear deformation localization region data, the first-level anchorage region is determined. In the slope digital model, the first-level anchorage region is subjected to first-level anchorage constraints, and the strength reduction is re-executed to simulate and generate the first slope stress field data and the first shear deformation localization region data.

[0137] Specifically, from the initial localized shear deformation area, the core risk area with the largest and most concentrated shear strain at the slope toe is precisely selected as the primary anchorage area. This area must ensure complete coverage of the initial high-risk domain while avoiding excessive scope that would lead to engineering waste. It provides a precise spatial basis for subsequent application of high-stiffness constraints and prevention of slope toe shearing. The initial localized shear deformation area is a natural high-risk warning zone for the slope, but not all of this area needs to be used as the primary anchorage area. The core objective of primary anchorage is to quickly prevent slope toe shearing failure. The slope toe is the starting point where the hidden dip slope shear stress is most concentrated and yielding occurs earliest. Therefore, it is necessary to focus on the core part with the highest risk and the greatest possibility of failure within this area.

[0138] Obtain the following data:

[0139] Initial data on the localized region of shear deformation;

[0140] Slope geological data, including the location of the anti-slide rock bridge at the toe of the slope and the depth of the hidden weak interlayers, ensures that the anchorage zone matches the key geological structures.

[0141] Furthermore, the shear strain values ​​extracted from the initial shear deformation localization region data are significantly higher than the shear deformation localization threshold. The set of grid nodes represents the core location where the slope is most prone to shear failure. Node clusters that are continuously distributed and without scattered discontinuities are selected. Small, scattered edge areas have lower risk and do not need to be included in the primary anchorage zone. The focus is on the stress concentration area at the slope toe. According to slope mechanics theory, the slope toe is the peak shear stress area. Scattered areas that may appear in the upper part of the slope in the localized area of ​​initial shear deformation are excluded, thus determining the core risk area.

[0142] Furthermore, based on the identified core risk areas, the specific boundaries of the primary anchorage zone are defined according to the following rules:

[0143] Along the longitudinal boundary of the slope height: cover upwards to the uppermost part of the core risk area and downwards to the bedrock surface at the toe of the slope, ensuring complete coverage of the shear concentration area at the toe of the slope;

[0144] The transverse boundary in the direction perpendicular to the slope: extending 1-2 grid nodes to the outside of the shear deformation localization bandwidth into the slope as a buffer zone to avoid edge leakage due to the boundary being too narrow, and to ensure that the anchoring force can completely cover the shear zone.

[0145] Geological adaptation adjustment: If there is a rock bridge that prevents sliding at the toe of the slope, the boundary must include the key stress section of the entire rock bridge to ensure that the anchorage constraint can directly act on the locking structure and enhance the shear resistance.

[0146] Furthermore, the defined boundaries are verified:

[0147] The shear strain of all grid nodes within the primary anchorage zone is greater than or equal to And the core area Ensure coverage of high-risk areas;

[0148] The boundary of the anchorage zone completely coincides with the high-value area of ​​the initial shear stress field, which conforms to the mechanical law of shear stress concentration at the toe of the slope.

[0149] Furthermore, the key principles for boundary delineation are as follows:

[0150] The core focus priority principle is to focus on the sub-regions with the highest peak shear strain and the densest distribution of mesh nodes, rather than pursuing full coverage of the initial shear deformation region.

[0151] Spatial matching principle:

[0152] Range matching: The anchorage zone must completely cover the core part of the initial shear zone, and it cannot be smaller than the core risk zone, nor can it be much larger than the core risk zone;

[0153] Direction matching: The extension direction of the anchorage zone must be consistent with the direction of the hidden weak interlayer to ensure that the anchorage force can act perpendicularly on the potential slip surface and be effectively converted into normal compressive stress.

[0154] Geological adaptation principle: If there are multiple weak interlayers or fracture zones at the toe of the slope, all geologically weak structures that pass through the initial shear core zone should be included in the anchorage range to avoid constraint failure due to omission of key weak links.

[0155] The following is an example:

[0156] Given conditions: The initial shear deformation localization region is the slope toe region with a relative elevation of 0-15m;

[0157] Core filtering: Extract from this area The core area, which is above the threshold and is a continuously distributed set of nodes, was found to be concentrated in the relative elevation range of 0-10m.

[0158] Boundary adjustment: retain a range of 0-10m longitudinally, and extend one grid node into the slope laterally, about 1-2m as a buffer zone;

[0159] Final definition: The primary anchorage zone is the slope toe area with a relative elevation of 0-10m and a transverse shear deformation localization bandwidth + 1m buffer zone.

[0160] The aforementioned technology addresses the blindness of traditional methods that rely on experience to draw the slope toe anchorage zone. By using quantitative data to identify core risks, it ensures that anchorage constraints are precisely matched to risks. The precise primary anchorage zone ensures that high-rigidity constraints are effectively applied to key areas, thereby triggering significant stress migration and creating the necessary conditions for subsequent location of secondary critical disaster-causing areas.

[0161] Furthermore, in the slope digital model, a first-level anchorage constraint is applied to the first-level anchorage region, and strength reduction is re-executed to simulate and generate the first slope stress field data and the first shear deformation localization region data. By applying high-stiffness anchorage constraints to the precisely defined first-level anchorage region, the risk of shearing out at the slope toe is forcibly suppressed. Then, through repeated strength reduction simulations, the stress redistribution and shear zone migration characteristics of the slope after anchorage are captured, generating the first slope stress field and the first shear deformation localization region data, which serve as a benchmark for subsequent quantification of stress migration and location of secondary key disaster-causing areas. Specifically:

[0162] Apply first-level anchorage constraint in the slope digital model: the structural stiffness must be significantly higher than that of the surrounding rock mass to ensure effective suppression of slope toe displacement and avoid insignificant stress migration due to insufficient stiffness. Prestressed anchor cables are preferred, but anti-slide piles, rigid concrete retaining walls, or grouting reinforcement can also be used, as long as the high stiffness requirement is met, the choice can be made according to the site construction conditions.

[0163] Key parameters:

[0164] Scope of deployment: Completely covers the primary anchorage zone, with denser coverage in the core area and evenly distributed coverage in the edge area, and no constrained breakpoints;

[0165] Anchoring direction: orthogonal to the potential slip surface (hidden weak interlayer), or forming a reverse shear angle of 15°-30°;

[0166] Anchoring depth: The anchoring section needs to penetrate 3-5m into the stable bedrock at the toe of the slope. The total length = anchoring section + free section, which meets the pull-out resistance requirements.

[0167] Prestress value: 100% prestress tensioning is applied to ensure active application of normal pressure and enhance interlayer friction resistance;

[0168] Furthermore, using numerical software such as the structural element module of FLAC3D, prestressed anchor cables or anti-slide pile elements are added within the boundary of the primary anchorage zone. The layout parameters are input, and the axial stiffness and bending stiffness of the anchorage structure are set to high values ​​to match the high-stiffness, strong-constraint design. This ensures that the contact elements between the anchorage structure and the slope rock mass are reasonably set, avoiding contact slippage that could lead to constraint failure. After applying the primary anchorage constraint, the boundary mechanical conditions of the slope have changed. Repeated strength reduction is required to simulate the evolution of the slope from steady-state to unsteady-state after anchorage. The core requirement is to maintain consistency with the initial simulation parameters to ensure data comparability. Specifically:

[0169] The reduction targets are still the shear strength parameters of bedrock and concealed weak interlayers, with the reduction priority of parameters for weak interlayers being higher than that for bedrock;

[0170] Reduction range: Maintain a gradient of 5%-10% per level to avoid distortion of the evolutionary process due to changes in the magnitude;

[0171] Shear deformation threshold: The criteria for identifying localized shear deformation regions remain consistent;

[0172] Termination conditions: Same as the initial simulation, calculation fails to converge, large deformation occurs, and the shear band extends to the top of the slope.

[0173] After each reduction equilibrium stage, the full-field mesh node data corresponding to the current reduction coefficient is recorded synchronously, including stress tensor, displacement vector, and shear strain value. The location changes of the shear band and the transfer law of the peak shear stress are observed. The following data are obtained through visualization processing and data filtering of the simulation results:

[0174] Stress field data of the first slope This is a continuous full-field contour map containing the shear stress field, normal stress field, and stress tensor distribution. A key feature is that, due to the high stiffness constraint suppressing stress concentration at the slope toe, the peak shear stress migrates towards the upper and middle parts of the slope, forming... The stress migration response region, and the initial shear stress field By comparison, the range, intensity, and peak location of stress migration can be directly quantified.

[0175] The first shear deformation localization region data is still based on Using this as a standard, all grid nodes were screened. The key feature was the disappearance of the shear band initially concentrated at the slope toe. The new localized shear deformation region extended along the hidden weak surface to the upper part of the slope, forming an upward shear band trajectory. This directly reflects the migration path of the shear band after the fixed foot constraint, providing spatial trajectory basis for the subsequent superposition of stress migration increment field and the location of secondary key disaster-causing domains.

[0176] In the above-mentioned technology, the high-stiffness constraint directly addresses the core risk of the slope toe, solving the defects of inaccurate range and insufficient constraint in traditional slope toe reinforcement. The two sets of data generated form a complete data chain before and after anchoring with the initial state, which is the only basis for subsequent quantification of stress migration and identification of secondary disaster-causing domains. The simulation of the disappearance of the shear zone and the migration of the peak shear stress at the slope toe after anchoring shows that the primary anchoring constraint design is effective; otherwise, the anchoring parameters need to be adjusted.

[0177] Spatiotemporal sequence reconstruction of the data from the first localized shear deformation region yields evolution path data characterizing the dynamic expansion trajectory of the shear band.

[0178] Specifically, after primary anchoring, the shear band is no longer fixed at the slope toe but gradually rises along the hidden weak surface towards the slope crest, its position and shape constantly changing with increasing load. Traditional techniques can only obtain the shear band distribution at a single stage and cannot reconstruct its dynamic evolution process. The core of spatiotemporal sequence reconstruction is to integrate spatial deformation data from different time points, reconstructing the dynamic trajectory from static slices, and accurately capturing the expansion direction, velocity, and leading edge position of the shear band. Through spatiotemporal sequence reconstruction technology combining time-series slicing and spatial peak fitting, the discrete, localized data of the first shear deformation at different stages after primary anchoring are transformed into continuous trajectory data representing the dynamic expansion of the shear band from the slope toe to the upper part of the slope. Details are as follows:

[0179] From the simulation results of re-executing strength reduction, several key time nodes were selected, corresponding to different loading steps with different strength reduction coefficients. For each node, a shear strain contour map of the first shear deformation localization region was extracted. Each time node corresponds to a stage of slope deformation; the larger the reduction coefficient, the more fully the shear zone evolves. For each time-series slice, the focus was... The shear deformation localization region is identified by determining the set of points with the largest shear strain along the width of the shear band, i.e., the peak point set. These points are the core stress area of ​​the shear band and determine the direction of expansion. The line connecting the peak point sets is the trajectory of the shear band most likely to expand preferentially. The fitted main axis path can eliminate local discrete noise and reflect the overall expansion direction of the shear band. Using the least squares method or spline interpolation algorithm, the discrete peak point set is fitted into a smooth and continuous curve, which is the main axis path of shear band evolution.

[0180] Furthermore, by searching along the main axis of shear zone evolution from the slope to the slope crest, the shear strain value was found to drop to... The following are the critical points, and their coordinates. This refers to the shear zone evolution front at the current time point. The evolution front is the very beginning of the shear zone and also the slope yield zone. ) and elastic zone ( The mechanical critical boundary of the shear band directly reflects the current evolution progress of the shear band.

[0181] Furthermore, the evolutionary coordinates of all key time points... Arranged in chronological order or by reduction factor from smallest to largest, the data is then fitted again using an interpolation algorithm, such as linear interpolation or spline interpolation, to generate a continuous and smooth shear damage evolution path map. This path map visually presents the complete trajectory of the shear zone starting from the toe of the slope, i.e., the rear edge of the primary anchorage zone, and gradually expanding along the hidden weak surface to the top of the slope. It includes core information such as the direction and speed of expansion and key turning points, thus obtaining evolution path data that characterizes the dynamic expansion trajectory of the shear zone.

[0182] The aforementioned technology addresses the limitation of existing technologies in identifying the dynamic evolution path of shear bands, enabling full-process tracking of concealed shear bands from their origin to their leading edge. The generated evolution path is a key carrier for the subsequent superimposed stress migration increment field. Only by clearly identifying the expansion trajectory of the shear band can the peak point of stress migration on the trajectory, i.e. the center of the secondary disaster-causing domain, be accurately located. By observing the changes in the leading edge position at different nodes, the evolution speed and trend of the shear band can be quantified, providing a quantitative basis for targeted blocking of secondary anchorage.

[0183] The difference between the initial slope stress field data and the first slope stress field data is calculated to obtain the stress migration increment field data.

[0184] Specifically, by calculating the node-by-node difference between the shear stress field after primary anchoring and the initial shear stress field without anchoring, the shear stress migration law induced by strong constraints at the slope toe is quantified. This yields incremental field data that reflects only the stress migration effect. The region where the shear stress increment is greater than 0 represents the secondary risk zone where the slope toe is constrained, leading to thrust transfer and stress accumulation. Details are as follows:

[0185] Initial slope stress field In the unanchored state, the shear stress field generated by strength reduction simulation reflects the natural shear stress distribution of the slope, with the slope toe being a high stress concentration area.

[0186] Stress field of the first slope After the first-level anchorage is applied, the shear stress field generated by the strength reduction simulation is re-executed to reflect the shear stress redistribution state of the slope after the high-stiffness anchorage.

[0187] The formula for calculating the shear stress migration increment field is:

[0188] ;

[0189] The shear stress in this area is greater than that without anchorage. It is a stress accumulation zone formed after the transfer of sliding thrust, i.e., the stress migration response zone.

[0190] The shear stress in this area has not increased or decreased, and it is mostly a direct constraint area of ​​primary anchorage, where stress concentration is suppressed.

[0191] Extracting Shear Stress Field Data from the Same Source: Only shear stress data is extracted because shear stress directly determines the likelihood of slope shear failure, requiring the initial slope stress field... and the stress field of the first slope The mesh node positions are completely consistent, i.e., the same model and the same mesh division, to ensure that the node-by-node difference calculation is meaningful. They all correspond to the same strength reduction stage, avoiding the distortion of the difference due to different evolution stages. They are all exported in the form of a matrix of mesh node coordinates and shear stress values, such as Excel or TXT format, for convenient subsequent calculations.

[0192] Furthermore, for each grid node The shear stress increment values ​​for all nodes in the entire field are calculated one by one according to the formula. No manual calculation is required. In software such as FLAC3D or Phase2, the original data of the incremental field can be automatically generated by directly importing two shear stress field files using the stress field subtraction function. For example:

[0193] Slope toe node: of , Calculated The stress decreases, forming a constrained region;

[0194] Upper and middle nodes of the slope: of , Calculated As stress increases, the migration response zone begins.

[0195] Furthermore, focusing on areas where shear stress is newly concentrated, low-stress areas directly constrained by primary anchorages are excluded to avoid irrelevant data interfering with subsequent disaster-causing domain location; only those areas are retained. Remove node data The area, free from stress accumulation and not a secondary risk zone, will be selected... The node data is interpolated through the visualization module of numerical software to generate a continuous shear stress migration increment distribution cloud map, which is the final stress migration increment field data.

[0196] The above-mentioned technology addresses the shortcomings of existing technologies that only know stress will migrate but cannot quantify the migration range and intensity. It clarifies the secondary risk boundary, provides a quantitative boundary basis for the subsequent delineation of the secondary anchorage zone, and avoids the blindness of traditional experience-based range drawing. The generated incremental field data needs to be superimposed with the shear zone evolution path to find the stress peak point on the shear zone trajectory, that is, the geometric center of the secondary key disaster-causing domain.

[0197] Overlay analysis of stress migration increment field data and evolution path data is performed to identify extreme points of stress migration increment, and extreme points located in the primary anchorage region are removed. The coordinates of the first extreme point located at the rear edge of the primary anchorage region are determined as the geometric center coordinates of the secondary anchorage region.

[0198] Specifically, by superimposing the shear band evolution path and the stress migration increment field, the stress concentration points on the dynamic trajectory of the shear band are focused, and invalid peaks within the primary anchorage zone are eliminated. Finally, the first secondary peak point of stress migration located at the rear edge of the primary anchorage is identified. This point represents the true mechanical waist after stress migration, rather than the geometric center based on traditional experience, providing a precise central target for secondary anchorage. The shear band evolution path is the dynamic channel where slopes are most prone to shear failure, and the stress migration increment field is the risk area where shear stress accumulates. Superimposing these two points allows for dual focusing on both the channel and the risk. The primary anchorage zone has already suppressed stress concentration through high-stiffness constraints, and its internal extreme points (the first peak) are not worth reinforcing and must be eliminated. The first secondary peak point at the rear edge of the primary anchorage is the most concentrated disaster-causing core after the transfer of sliding thrust. Using this as the geometric center of the secondary anchorage ensures that reinforcement directly targets the high-risk area after stress migration. Details are as follows:

[0199] Input data:

[0200] Stress migration increment field data, The shear stress increment distribution cloud map has been used to screen out the stress migration response zone;

[0201] Evolution path data: The continuous evolution path of the shear band generated by spatiotemporal sequence reconstruction clarifies the dynamic expansion trajectory of the shear band;

[0202] Key auxiliary data: Boundary coordinates of the primary anchorage area, used for subsequent extreme point selection.

[0203] Furthermore, in numerical software (such as FLAC3D or Origin), the vector map of the shear zone evolution path is overlaid on the cloud map of shear stress migration increment, ensuring that the coordinate system and model scale of the two are completely consistent. Along the direction of the overlaid evolution path, the shear stress increment value corresponding to each node is extracted to form the distribution curve of shear stress increment value and path length. All maximum points (extreme points) in the curve are identified. These points are the locations where shear stress accumulates most significantly on the path and are also potential disaster cores. The shear zone is the weakest area of ​​the slope, and the shear stress after stress migration will preferentially accumulate on the path. The extreme points are the stress peak center of this area.

[0204] Furthermore, peak values ​​within the primary anchorage zone are removed. By comparing the boundary coordinates of the primary anchorage zone, it is determined whether each extreme point is located within the anchorage zone. Extreme points located within the primary anchorage zone are removed because the stress concentration of the peak values ​​has been suppressed by the primary high-stiffness constraint and no further reinforcement is needed. Extreme points outside the anchorage zone are retained. The first extreme point located at the rear edge of the primary anchorage zone is selected, which is the first high-risk core formed after stress migration, i.e., the secondary peak point. The spatial coordinates of the selected secondary peak point are extracted and directly determined as the geometric center coordinates of the secondary anchorage zone. These coordinates correspond to the stress on the shear band trajectory. The peak center of force migration, i.e. the true mechanical waist of the slope, is fundamentally different from the traditional technique of locating it according to the geometric center of the slope surface. It breaks through the misconception of equating the geometric center with the mechanical waist in existing technologies. It achieves quantitative positioning of the true mechanical waist through data superposition, avoiding misalignment of reinforcement positions. The geometric center is the core target point of the secondary anchorage zone. The longitudinal and normal ranges of the subsequent secondary anchorage layout are all centered around this center, ensuring that the reinforcement can directly act on the stress concentration core. It directly links the dynamic evolution of the shear zone with the stress migration increment, transforming the positioning of the secondary anchorage from experience-based judgment to data-driven, making anchorage control more scientific.

[0205] Based on the geometric center coordinates, determine the secondary anchorage area data and generate secondary anchorage design parameters;

[0206] Specifically, the secondary anchorage zone must completely encompass the secondary critical disaster-causing area. Design parameters must match the mechanical properties of the disaster-causing area. In terms of scope, it should longitudinally cover the core area of ​​stress migration increments, and normally penetrate the potential shear zone and extend into stable bedrock. Parameters such as anchorage angle, prestress, and structural type should all serve the goals of blocking shear zones and accommodating large deformations, complementing the high stiffness of the primary anchorage. Details are as follows:

[0207] Using the geometric center as a reference, and combining data on stress migration increment field and shear strain distribution, the extent is defined in two dimensions: longitudinal along the concealed structural plane and normal to the concealed structural plane.

[0208] Longitudinal boundary delineation: Along the direction of the concealed structural plane, contour analysis is performed on the stress migration increment field data to determine the contour range where the stress migration increment decays to the proportion of the first peak value. This range serves as the longitudinal boundary of the secondary anchorage region, with the first peak value typically taken as 80%. The region where stress decays to 80% of its peak value is the core area of ​​stress accumulation. Stress increments beyond this range have minimal impact on shear failure and do not need to be included in the anchorage range, thus avoiding engineering waste.

[0209] Normal depth delineation: Extract the shear strain distribution curve of the section corresponding to the geometric center, and select the width of the region where the shear strain value is greater than or equal to the shear deformation threshold as the shear deformation localization bandwidth. This width is the actual thickness of the potential shear band, and the anchoring structure must completely pass through it.

[0210] Normal anchorage depth = shear deformation localization bandwidth + stable bedrock anchorage length;

[0211] The anchorage length in stable bedrock is fixed at 3-5m to ensure that the anchorage section penetrates deep into the stable rock mass and avoids failure due to anchoring in weak zones.

[0212] Furthermore, based on the stress characteristics and shear band parameters of the secondary anchorage region, key parameters such as anchorage angle, prestress, length, and structural type are generated:

[0213] Anchoring angle design: Based on the direction of the resultant shear stress vector in the geometric center region, the anchor body forms a reverse shear angle with the shear slip direction, thereby ensuring that the anchoring force can be effectively converted into normal compressive stress, increasing interlayer friction resistance, rather than being parallel to the slip direction.

[0214] Prestress value design: Secondary anchorage prestress = Primary anchorage prestress × Preset proportional coefficient. The preset proportional coefficient ranges from 60% to 80%, reserving space for deformation and resistance conversion. If the prestress is too high, the secondary anchorage stiffness will be too large, and it is easy to yield too early in the early stage of shear zone evolution. A gradient of 60% to 80% allows the secondary anchorage to gradually exert its maximum shear resistance through moderate deformation, forming a stepped resistance with the primary anchorage.

[0215] Anchorage length design: Total anchorage length = Free segment length + Anchorage segment length, where the anchorage segment length must completely pass through the shear deformation localization bandwidth and penetrate deep into stable bedrock.

[0216] Anchorage structure design: Prioritize the use of high elongation anchor cables or add constant resistance large deformation devices to the anchor head to accommodate large deformation of the surrounding rock and avoid brittle shearing. Set flexible pads between the anchor pier and the slope to adapt to the non-coordinated deformation of the surface rock mass and prevent the anchor from being pulled out due to the expansion of the rock mass.

[0217] Layout density design: the core area is densely packed and the edge area is evenly distributed to ensure that the anchoring force continuously covers the secondary anchoring area without any constraint breaks.

[0218] The aforementioned technologies achieve a high degree of overlap between the regional scope and the secondary critical disaster-causing zone, and the design parameters match the stress level and deformation characteristics of the disaster-causing zone. This solves the defects of the traditional blind scope and one-size-fits-all parameter approach. The high toughness design of the secondary anchor and the high stiffness of the primary anchor complement each other, avoiding the problem of failure caused by strong foot and weak waist or excessive stiffness mismatch. All parameters (length, angle, prestress) are quantifiable and can be directly guided for on-site construction, ensuring that the secondary anchor can physically cut off the shear zone.

[0219] Based on the data of the primary and secondary anchorage areas and the design parameters of the secondary anchorage, a graded and coordinated anchorage project was implemented on the target slope.

[0220] Specifically, the boundary coordinates and design parameters of the primary or secondary anchorage area are converted into measurable construction coordinates on site, detailed construction layout diagrams are drawn, the actual locations of the slope toe anti-slide rock bridge and hidden weak interlayers are verified, and the anchorage point coordinates are fine-tuned by comparing them with the digital model to avoid drilling through fractured zones or obstacles.

[0221] Primary anchoring: Prepare high-rigidity components, such as prestressed anchor cables or anti-slide piles, and matching tensioning equipment;

[0222] Secondary anchoring: Prepare high-toughness components, such as constant resistance large deformation anchor cables or pressure relief anchors, flexible pads, and tensioning equipment for precise force control.

[0223] Furthermore, boreholes are drilled according to the arrangement density and anchoring angle of the primary anchoring area. The drilling depth must meet the design requirements. After drilling, the rock powder inside the hole is cleaned to ensure that the anchoring section is tightly bonded to the rock mass. Anchor cable rods are then inserted (high-rigidity steel strands are selected for the primary anchoring section), ensuring that the anchoring section is located in stable bedrock and that the free section is smooth and free of twisting. Anchoring agent, such as cement grout or resin, is injected into the hole, ensuring full injection without voids. After the anchoring agent reaches the design strength, the prestress is applied in stages according to 100% of the design. Each stage of tensioning is held for 5-10 minutes, and locked after stabilization. After tensioning, excess rods are cut off, and the anchor is sealed with concrete to form a complete rigid constraint structure. The anchoring force is tested through an anchor cable pull-out test to ensure that the actual anchoring force of each anchor cable is not less than 95% of the design value, and there are no constraint breaks in the primary anchoring area.

[0224] Furthermore, secondary anchoring should be implemented after the stress redistribution of primary anchoring has stabilized to avoid interference between the two levels of stress. Monitoring points are set up in the primary anchoring area and the upper part of the slope to monitor the displacement rate in real time. When the displacement rate converges to the stability threshold, it is determined that the stress redistribution inside the slope tends to stabilize, and secondary anchoring construction is initiated. Holes are drilled according to the boundary and density of the secondary anchoring area. The holes must accurately pass through the localized shear deformation zone. The anchoring section penetrates 3-6m into the stable bedrock. NPR anchor rods are installed, and flexible pads are laid between the anchor and the slope to ensure fit with the slope and adapt to rock deformation. Prestressing is performed in stages according to the design, and the staged load holding method is also used to avoid stress abrupt changes. After tensioning, the anchors are locked and sealed to ensure that the secondary anchoring structure fits tightly with the slope without loosening.

[0225] In the aforementioned technologies, the dynamic evolution path of the shear zone is accurately tracked through strength reduction simulation and spatiotemporal sequence reconstruction. Combined with stress migration increment field and path superposition analysis, the stress secondary redistribution law after slope toe anchoring is quantified, and the primary and secondary anchoring zones are finally identified. This ensures that the anchoring range highly overlaps with the risk domain, enabling the anchoring system to withstand the impact of instantaneous loads and accommodate long-term rheological deformation. The disaster resistance toughness is significantly improved compared to traditional single stiffness anchoring. It can accurately identify shear evolution characteristics, thereby effectively avoiding misalignment between the reinforcement location and the actual disaster-causing domain, thus effectively preventing shear failure of the slope and reinforcement failure, and effectively improving the prevention and control effect.

[0226] Spatiotemporal sequence reconstruction of the data from the first localized shear deformation region yields evolution path data characterizing the dynamic expansion trajectory of the shear band, specifically including:

[0227] Based on the time series of strength reduction, extract the data of the first localized region of shear deformation corresponding to each reduction coefficient;

[0228] Extract the shear strain value of the first shear deformation localization region data corresponding to each reduction factor, and identify the maximum peak point set of the shear strain value under the corresponding factor;

[0229] Interpolate and fit the set of maximum peak points corresponding to different reduction coefficients in chronological order to generate continuous evolution path data that characterizes the gradual expansion of the shear band as the intensity decreases.

[0230] Specifically, the core methods for interpolation fitting to generate continuous evolution paths are spline interpolation and linear interpolation. Spline interpolation can best fit the smooth and continuous evolution characteristics of the shear band, making it the preferred method for engineering simulation. Linear interpolation is simple to operate and suitable for scenarios with dense nodes. Taking spline interpolation as an example, the details are as follows:

[0231] Spline interpolation divides the discrete evolution front coordinates into segments in chronological order, and connects each two segments with a cubic polynomial to ensure that the curves between adjacent segments are smooth and continuous, that is, the first and second derivatives are continuous, perfectly restoring the smooth trajectory of the shear band's gradual ascent.

[0232] Input data: Coordinates of the evolution front at all key time points, sorted chronologically or by reduction factor from smallest to largest, denoted as the data point set. n is the number of time points, for example:

[0233] 4 node coordinates and reduction coefficients correspond:

[0234] ;

[0235] ;

[0236] ;

[0237] .

[0238] For two adjacent data points, for example and , and Construct cubic polynomials respectively:

[0239] ;

[0240] Constraints:

[0241] Each polynomial passes through corresponding data points, such as: , ;

[0242] Adjacent polynomials have the same first derivative at the junction point, such as: The second derivatives are equal. Ensure the curve is smooth;

[0243] Two endpoints The second derivative is set to 0 (natural spline) to avoid boundary distortion.

[0244] Furthermore, based on the above constraints, a system of linear equations is established, and the coefficients of each piecewise polynomial are solved. , , ᵢ、 Without manual calculation, the sorted coordinate data can be exported and imported into Origin, Matlab, or numerical simulation software (such as FLAC3D). The cubic spline interpolation function can be called to automatically generate a continuous curve. The interpolated curve must pass through all the original data points, and the curve between any two points must not deviate significantly from the shear band evolution direction.

[0245] Overlay analysis of stress migration increment field data and evolution path data is performed to identify extreme points of stress migration increments, and extreme points located within the primary anchorage region are removed. Specifically, this includes:

[0246] Map the evolution path data to the stress migration increment field data;

[0247] Along the direction of the evolution path, extract the stress migration increment of each grid node on the evolution path;

[0248] Construct a distribution curve of stress migration increment along the evolution path and identify the extreme points on the curve;

[0249] Exclude all extreme points located within the geometric boundary of the primary anchorage zone.

[0250] The secondary anchorage zone data is determined based on the geometric center coordinates, specifically including:

[0251] Using the geometric center coordinates as a reference, contour analysis is performed on the stress migration increment field data along the direction of the hidden structural surface to determine the contour range of the stress migration increment attenuating to the proportion of the first peak value, which serves as the longitudinal boundary of the secondary anchorage area.

[0252] In the profile corresponding to the geometric center coordinates, extract the shear strain distribution data perpendicular to the hidden structure plane, and determine the width of the region where the shear strain value is greater than or equal to the shear deformation threshold, as the shear deformation localization bandwidth.

[0253] Based on the sum of the localized bandwidth of shear deformation and the preset stable bedrock anchorage length, the normal anchorage depth required for secondary anchorage is calculated.

[0254] The anchoring length in the stable bedrock is 3-5 meters deep into the stable bedrock of both the upper and lower plates.

[0255] Generate secondary anchorage design parameters, specifically including:

[0256] Based on the stress migration increment field data corresponding to the geometric center coordinates, the direction of the corresponding shear stress resultant force vector is calculated.

[0257] The placement angle of the secondary anchor body is determined based on the direction of the resultant shear stress vector, so that the direction of the anchor body forms a reverse shear angle with the shear slip direction;

[0258] Obtain the first design prestress value of the primary anchorage structure, multiply the first design prestress value by a preset proportional coefficient, and calculate the second prestress design value of the secondary anchorage.

[0259] The length of the anchorage section of the secondary anchor body is determined based on the normal anchorage depth.

[0260] Implement graded and coordinated anchoring engineering on the target slope, specifically including:

[0261] Within the primary anchorage area, the primary anchorage structure is constructed and tensioned according to the high stiffness design requirements, and the first design prestress value is applied.

[0262] The displacement rate of the target slope is monitored. When the displacement rate converges to the stability threshold, it is determined that the stress redistribution inside the slope tends to be stable.

[0263] Within the range specified by the secondary anchorage area data, construct and tension the secondary anchorage structure, and apply the second prestress design value;

[0264] The secondary anchoring structure adopts an anchor cable structure with constant resistance and large deformation characteristics, and a flexible buffer pad layer is set between the anchor pier and the slope.

[0265] Following the implementation of the graded and coordinated anchoring project, a dynamic feedback control step is also included, specifically:

[0266] Establish a monitoring system linking deep stress and surface deformation in the secondary anchorage area;

[0267] Continuously acquire monitoring data on anchor cable axial force and slope surface displacement of the secondary anchorage structure;

[0268] Real-time differential processing is performed on the axial force monitoring data of the anchor cable to obtain the axial force change rate data;

[0269] Real-time differential processing is performed on the slope surface displacement monitoring data to obtain displacement change rate data;

[0270] In response to the simultaneous detection that the axial force change rate data is lower than a preset negative threshold and the displacement change rate data is higher than a preset positive threshold, a dynamic reinforcement early warning signal is generated.

[0271] Based on the early warning signal, supplementary anchoring or targeted reinforcement measures are implemented at the locations where abnormal stress concentration is detected.

[0272] Specifically, by establishing a closed-loop mechanism that links deep stress and surface deformation monitoring, analyzes data change rates in real time, and triggers precise reinforcement, the shortcomings of traditional anchoring projects—one-time construction and lack of subsequent intervention—are addressed. This ensures slope stability under extreme loads or long-term deformation, extending from active blocking to continuous protection. Details are as follows:

[0273] Establish a monitoring system linking deep stress and surface deformation: Focusing on the secondary anchorage area, achieve "dual coverage of internal stress and external deformation" to avoid misjudgment from a single monitoring dimension. Select 10%-15% of the anchors in each row of secondary anchors and install axial force sensors, such as vibrating wire anchor cable force gauges, at the junction of the anchorage section and the free section to collect anchor cable axial force data in real time. On the slope surface corresponding to the secondary anchorage area, deploy displacement gauges, such as GPS positioning devices or inclinometers, at intervals of 5-8m to simultaneously collect horizontal and vertical displacement data of the slope surface. Each deep axial force monitoring point corresponds to 1-2 surface displacement monitoring points to ensure that the data can form a correspondence between stress and deformation, which is convenient for subsequent analysis.

[0274] Data is collected once a week under normal operating conditions to ensure data continuity. Under special operating conditions (after heavy rain or strong earthquakes), the frequency is increased to once a day, or even in real time, to capture short-term abnormal changes, eliminate abnormal data caused by sensor drift and environmental interference, ensure the authenticity of the original data, and unify the data format before importing it into the background analysis system.

[0275] Furthermore, since the raw monitoring values ​​only reflect the current state, the rate of change obtained after differential processing can identify trend anomalies earlier. For example, a slow decrease in axial force may be due to normal stress, but a sudden drop is a risk signal.

[0276] Axial force change rate: The axial force change rate is obtained by real-time differentiation of continuously collected axial force data, which characterizes how fast the axial force of the anchor cable changes.

[0277] Displacement change rate: The displacement change rate is obtained by real-time differentiation of continuously acquired displacement data, which characterizes the development rate of slope deformation.

[0278] Using Matlab or Excel, no manual operation is required, ensuring processing efficiency and accuracy.

[0279] Furthermore, based on the results of slope digital model simulations, similar engineering experience, and the determination of rock mechanics parameters, it is necessary to pre-set the following parameters in the system:

[0280] Preset negative threshold (abnormal axial force): such as the rate of change of axial force < -10kN / d. The specific value can be adjusted according to the prestress of the anchor cable. The core is an abnormal sudden drop, which indicates that the anchor cable anchorage section may have local slippage and reduced shear resistance.

[0281] Preset positive threshold (displacement anomaly): For example, the specific value is adjusted according to the slope stability requirements, indicating that the shear zone is breaking through the secondary anchorage defense line and the slope deformation is accelerating.

[0282] A warning signal is only generated when both the rate of change of axial force are less than a preset negative threshold and the rate of change of displacement are greater than a preset positive threshold, thus avoiding false warnings caused by a single abnormal indicator and ensuring the accuracy of the warning.

[0283] Furthermore, dynamic reinforcement measures will be implemented, as follows:

[0284] Based on the coordinates of the monitoring points used for early warning, combined with the previously generated shear zone evolution path and stress migration increment field data, the specific location of abnormal stress concentration is deduced, i.e., the area where the shear zone is attempting to break through. Secondary high-toughness anchor cables are added at the abnormal location, with parameters consistent with the original secondary anchor cables, to cut off the shear zone expansion path. If stress concentration caused by rock mass fracturing is detected, grouting reinforcement can be carried out first to improve the integrity of the rock mass, followed by additional anchoring. After the reinforcement construction is completed, the monitoring frequency is increased until the axial force change rate converges and the displacement change rate falls back to the stable threshold, confirming that the risk has been eliminated.

[0285] The aforementioned technologies address the problem of prioritizing construction over monitoring in existing anchoring projects, upgrading prevention and control from a one-time design and construction approach to dynamic management throughout the entire lifecycle. This significantly improves the long-term safety of slopes. Through dual-threshold and correlated monitoring, misjudgments based on single indicators are avoided, ensuring that early warning signals accurately reflect the risk of shear zone breaches and allowing time for reinforcement. Based on monitoring data, abnormal areas are accurately located, and targeted reinforcement is implemented only at risk points, eliminating the need for comprehensive rework and significantly reducing subsequent maintenance costs. These technologies can effectively cope with unforeseen factors such as long-term rheological deformation and extreme loads, enabling the anchoring system to have self-adjustment capabilities and further enhancing disaster resilience.

[0286] The construction of a digital model of a slope specifically includes:

[0287] Based on the rock strata attitude, spatial location of hidden weak interlayers and rock and soil mechanical parameters in geological exploration data, a numerical calculation model reflecting the characteristics of hidden dip-side structures is constructed.

[0288] In the numerical calculation model, the rock strata dip is consistent with the slope dip, and the rock strata dip angle is greater than or equal to the slope dip angle;

[0289] In the model, contact surface elements or weak interlayer materials are set along the rock layer interface to simulate interlayer slip, debonding and shear softening behavior.

[0290] Elastoplastic solid elements were set up in the rock bridge area at the foot of the slope to simulate potential shear failure paths.

[0291] The primary anchorage region is the concentrated distribution area with the largest shear strain value in the initial localized shear deformation region data, and the primary anchorage region is located in the stress concentration area at the toe of the slope.

[0292] The shear deformation threshold is 1.5 to 2.0 times the peak shear strain value of the target slope rock mass obtained through rock mass testing.

[0293] Based on a two-dimensional plane strain numerical model of a typical concealed dip-sloping rock slope, a complete implementation process example of graded coordinated anchoring control using primary toe anchorage and secondary strong waist anchorage is presented:

[0294] Slope geometric characteristics:

[0295] Model bottom width Relative slope height ;

[0296] The dip of the rock strata is consistent with the dip of the slope, and the dip angles of the rock strata and the slope are both 1. The condition is met that the dip angle of the hidden slope strata is greater than or equal to the slope dip angle.

[0297] The slope toe features a sliding rock bridge structure, with the rock strata disappearing downwards and cutting into the bedrock at the slope toe.

[0298] Rock and soil mechanical parameters:

[0299] Bedrock (harder sandstone): Elastic modulus Poisson's ratio ;

[0300] Interlayer weak structural plane (mud-like interlayer): Normal stiffness Tangential stiffness Cohesion internal friction angle ;

[0301] Shear deformation localization threshold ;

[0302] Step 1: Perform gravity equilibrium calculations on the model under unanchored conditions to restore the initial state of natural stress on the slope. Use the strength reduction method to simulate the progressive failure of the slope: gradually reduce the shear strength parameters of the bedrock and weak structural surfaces until the model shows a non-convergence trend.

[0303] Extracting the shear strain contour plot under the unanchored state reveals the shear strain... The area is concentrated at the toe of the slope, with a relative elevation of 0-10m, and exhibits typical toe shear failure characteristics. Based on this, the area is defined as a first-level anchorage constraint zone.

[0304] High-stress prestressed anchor cables are applied in the primary anchorage zone: the total length of the anchor cables is 30m, the anchorage section is 10m, and they penetrate deep into the stable bedrock, forming a reverse shear angle of 20° with the rock strata, and 100% design prestress is applied. Construct rigid boundary constraints at the toe of the slope.

[0305] Step 2: For the model after applying the first-level anchorage, maintain the shear deformation threshold. The intensity reduction evolution simulation remains unchanged and is repeated.

[0306] Monitoring revealed: High shear strain zone at the toe of the slope The localized shear deformation region disappears and migrates along the concealed weak surface to the upper part of the slope.

[0307] The evolution path is extracted using spatiotemporal sequence reconstruction technology: shear strain cloud maps corresponding to different reduction coefficients are selected, strain peak points are fitted to obtain the main axis path of shear band evolution, and the position of the evolution front is tracked;

[0308] When the reduction factor At that time, the evolutionary vane had reached a relative elevation of 30m, but had not yet penetrated to the top of the slope, clearly demonstrating the dynamic characteristics of the shear zone gradually climbing from the foot of the slope to the top.

[0309] Step 3: Calculate the shear stress migration increment field: Extract the shear stress field after first-stage anchoring. With unanchored initial shear stress field According to the formula Calculate and filter The stress migration response region;

[0310] Extracting the peak coordinates of shear stress migration: Superimpose the shear band evolution path onto the stress migration response region, and search along the path. After removing the first peak value within the primary anchorage zone, the second peak value is determined at a relative elevation of 32m, and its coordinates are the geometric center of the secondary critical disaster-causing zone.

[0311] Delineate the secondary anchorage range:

[0312] Longitudinal boundary: along the direction of the hidden structural plane, take The contour range attenuated to 80% of the peak value was determined to be a relative elevation of 22-42m (with a longitudinal coverage length of approximately 20m).

[0313] Normal depth: Extract the shear strain distribution curve perpendicular to the structural surface and measure the shear deformation localization bandwidth. Set the depth to stable bedrock length The normal penetration anchorage depth of the secondary anchor cable was calculated. .

[0314] Step Four:

[0315] Design and layout of secondary anchorage structure:

[0316] Scope of deployment: Within the secondary disaster-causing zone with a relative elevation of 22~42m, three rows of secondary anchoring structures will be deployed;

[0317] Structure type: NPR constant resistance large deformation anchor cable is adopted, and a 50mm thick rubber flexible pad is set at the anchor head to adapt to non-coordinated deformation of rock mass;

[0318] Prestress setting: secondary anchor cable prestress (70% of the first-level prestress), reserving space for deformation and resistance transformation;

[0319] Construction sequence: A step-by-step activation strategy is adopted, first activating the primary anchor cables until the unbalanced force converges, and then activating the secondary anchor cables.

[0320] The technical scope of this invention is not limited to the content described above. Those skilled in the art can make various modifications and variations to the above embodiments without departing from the technical concept of this invention, and all such modifications and variations should fall within the protection scope of this invention.

Claims

1. A method for graded and coordinated anchoring control of concealed dip-sloping rock slopes, characterized in that, Includes the following steps: Obtain geological survey data of the target slope and generate a digital model of the slope consisting of multiple grid nodes; Strength reduction is applied to the digital model of the slope to simulate the evolution of the target slope from steady state to unsteady state. Data of each grid node is obtained during the simulation, and the shear strain value of each grid node is calculated to generate the initial slope stress field data. Extract the grid nodes in the initial slope stress field data where the shear stress value is greater than the shear deformation threshold to obtain the initial shear deformation localization region data; Based on the initial shear deformation localization region data, the first-level anchorage region is determined. In the slope digital model, the first-level anchorage region is subjected to first-level anchorage constraints, and the strength reduction is re-executed to simulate and generate the first slope stress field data and the first shear deformation localization region data. Spatiotemporal sequence reconstruction of the data from the first localized shear deformation region yields evolution path data characterizing the dynamic expansion trajectory of the shear band. The difference between the initial slope stress field data and the first slope stress field data is calculated to obtain the stress migration increment field data. Overlay analysis of stress migration increment field data and evolution path data is performed to identify extreme points of stress migration increment, and extreme points located in the primary anchorage region are removed. The coordinates of the first extreme point located at the rear edge of the primary anchorage region are determined as the geometric center coordinates of the secondary anchorage region. Based on the geometric center coordinates, determine the secondary anchorage area data and generate secondary anchorage design parameters; Based on the data of the primary anchorage area and the secondary anchorage area, as well as the design parameters of the secondary anchorage, a graded and coordinated anchorage project was implemented on the target slope. The secondary anchorage zone data is determined based on the geometric center coordinates, specifically including: Using the geometric center coordinates as a reference, contour analysis is performed on the stress migration increment field data along the direction of the hidden structural surface to determine the contour range of the stress migration increment attenuating to the proportion of the first peak value, which serves as the longitudinal boundary of the secondary anchorage area. In the profile corresponding to the geometric center coordinates, extract the shear strain distribution data perpendicular to the hidden structure plane, and determine the width of the region where the shear strain value is greater than or equal to the shear deformation threshold, as the shear deformation localization bandwidth. Based on the sum of the localized bandwidth of shear deformation and the preset stable bedrock anchorage length, the normal anchorage depth required for secondary anchorage is calculated. The anchorage length in the stable bedrock is a length of 3-5 meters extending into the stable bedrock of the upper and lower plates. Generate secondary anchorage design parameters, specifically including: Based on the stress migration increment field data corresponding to the geometric center coordinates, the direction of the corresponding shear stress resultant force vector is calculated. The placement angle of the secondary anchor body is determined based on the direction of the resultant shear stress vector, so that the direction of the anchor body forms a reverse shear angle with the shear slip direction; Obtain the first design prestress value of the primary anchorage structure, multiply the first design prestress value by a preset proportional coefficient, and calculate the second prestress design value of the secondary anchorage. Based on the normal anchorage depth, determine the length of the anchorage section of the secondary anchorage body; Implement graded and coordinated anchoring engineering on the target slope, specifically including: Within the primary anchorage area, the primary anchorage structure is constructed and tensioned according to the high stiffness design requirements, and the first design prestress value is applied. The displacement rate of the target slope is monitored. When the displacement rate converges to the stability threshold, it is determined that the stress redistribution inside the slope tends to be stable. Within the range specified by the secondary anchorage area data, construct and tension the secondary anchorage structure, and apply the second prestress design value; The secondary anchoring structure adopts an anchor cable structure with constant resistance and large deformation characteristics, and a flexible buffer pad layer is set between the anchor pier and the slope.

2. The method for graded and coordinated anchoring control of concealed dip-side rock slopes according to claim 1, characterized in that: Spatiotemporal sequence reconstruction of the data from the first localized shear deformation region yields evolution path data characterizing the dynamic expansion trajectory of the shear band, specifically including: Based on the time series of strength reduction, extract the data of the first localized region of shear deformation corresponding to each reduction coefficient; Extract the shear strain value of the first shear deformation localization region data corresponding to each reduction factor, and identify the maximum peak point set of the shear strain value under the corresponding factor; Interpolate and fit the set of maximum peak points corresponding to different reduction coefficients in chronological order to generate continuous evolution path data that characterizes the gradual expansion of the shear band as the intensity decreases.

3. The method for graded and coordinated anchoring control of concealed dip-side rock slopes according to claim 2, characterized in that: Overlay analysis of stress migration increment field data and evolution path data is performed to identify extreme points of stress migration increments, and extreme points located within the primary anchorage region are removed. Specifically, this includes: Map the evolution path data to the stress migration increment field data; Along the direction of the evolution path, extract the stress migration increment of each grid node on the evolution path; Construct a distribution curve of stress migration increment along the evolution path and identify the extreme points on the curve; Exclude all extreme points located within the geometric boundary of the primary anchorage zone.

4. The method for graded and coordinated anchoring control of concealed dip-side rock slopes according to claim 1, characterized in that: Following the implementation of the graded and coordinated anchoring project, a dynamic feedback control step is also included, specifically: Establish a monitoring system linking deep stress and surface deformation in the secondary anchorage area; Continuously acquire monitoring data on anchor cable axial force and slope surface displacement of the secondary anchorage structure; The axial force monitoring data of the anchor cable is subjected to real-time differential processing to obtain the axial force change rate data; The slope displacement monitoring data is processed by real-time differentiation to obtain the displacement change rate data; In response to the simultaneous detection that the axial force change rate data is lower than a preset negative threshold and the displacement change rate data is higher than a preset positive threshold, a dynamic reinforcement early warning signal is generated. Based on the warning signal, supplementary anchoring or targeted reinforcement measures are implemented at the locations where abnormal stress concentration is detected.

5. The method for graded and coordinated anchoring control of concealed dip-sloping rock slopes according to claim 1, characterized in that: The construction of a digital model of a slope specifically includes: Based on the rock strata attitude, spatial location of hidden weak interlayers and rock and soil mechanical parameters in geological exploration data, a numerical calculation model reflecting the characteristics of hidden dip-side structures is constructed. In the numerical calculation model, the rock strata dip is consistent with the slope dip, and the rock strata dip angle is greater than or equal to the slope dip angle. In the model, contact surface elements or weak interlayer materials are set along the rock layer interface to simulate interlayer slip, debonding and shear softening behavior. Elastoplastic solid elements were set up in the rock bridge area at the foot of the slope to simulate potential shear failure paths.

6. The method for graded and coordinated anchoring control of concealed dip-side rock slopes according to claim 1, characterized in that: The primary anchorage region is the concentrated distribution area with the largest shear strain value in the initial shear deformation localization region data, and the primary anchorage region is located in the stress concentration area at the toe of the slope.

7. The method for graded and coordinated anchoring control of concealed dip-sloping rock slopes according to claim 1, characterized in that: The shear deformation threshold is 1.5 to 2.0 times the peak shear strain value of the target slope rock mass obtained through rock mass testing.

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