Stability analysis method for random wedge body of rock slope based on structural surface statistics

Abstract

The invention relates to the technical field of rock slopes, in particular to a stability analysis method for a random wedge body of a rock slope based on structural plane statistics. According to the method disclosed by the invention, on the basis of measuring a random structural plane developed in a slope rock mass on site and counting obtained distribution probabilities and statistical parameters of the tendency, the dip angle and the trace length of a dominant structural plane, a structural plane combination of a potential unstable block possibly formed on a free face of a slope is judged by adopting a stereographic projection pole analysis method; and aiming at each structural surface combination, a series of operations such as multiple random sampling, surface-to-surface intersection, branch cutting and surface combination forming are carried out by adopting a Monte-Carlo method to obtain a series of wedge bodies which are possibly unstable, so that the exposure depth, the scale and the stability of the wedge bodies are obtained, and a basis can be provided for systematic anchor rod support and shotcrete support design of the shallow surface layer of the rock slope.

Description

Technical Field

[0001] The present invention relates to the technical field of rock slopes, and particularly relates to a stability analysis method for random wedges of rock slopes based on structural plane statistics. Background Art

[0002] Wedge sliding is a very common failure mode of rock slopes. According to the characteristics of the structural planes composing the wedge, wedge sliding can be divided into two types: located wedges and random wedges. Generally, wedges formed by the cutting and combination of faults or long and large fissures are called located wedges. Such wedges have clear outcrop positions and volumes, and their calculation and analysis methods are relatively mature. Random wedges are divided into two categories. Wedges formed by the combination of part of faults and long and large fissures and part of random structural planes are called semi-located and semi-random wedges, while wedges formed entirely by the cutting and combination of random wedges are called fully random wedges. Random wedges have the characteristics of uncertainty in the outcrop position on the slope surface, randomness in attitude and development law, which bring a series of challenges to the stability of random wedges.

[0003] Most of the currently proposed search and calculation methods for random wedges are based on three-dimensional structural plane network simulation. The specific approach is to generate a three-dimensional rock mass structural plane network in the rock slope according to the statistical probability model of random structural planes, and carry out the cutting and combination between groups of structural planes and between structural planes and free faces to search for key blocks that may be formed on the free face. Since this method requires obtaining the volume density according to the spacing of random structural planes and generating a three-dimensional structural plane network diagram in the simulation area. When the simulation space is large or the structural planes are dense, thousands of groups of random structural planes will be generated inside the simulation space. On this basis, a series of operations such as structural plane cutting, pruning, and searching for random blocks are required, which requires a large amount of redundant and ineffective block cutting and searching work. Not only is the calculation amount large and the calculation efficiency very low, but also due to the influence of floating-point precision, the error probability is very high. Summary of the Invention

[0004] Aiming at the above deficiencies in the prior art, the purpose of the present invention is to provide a stability analysis method for random wedges of rock slopes based on structural plane statistics, which can provide reference for the system bolt support of rock slopes, the design of shotcrete thickness, etc.

[0005] In order to achieve the above invention purpose, the technical solution adopted by the present invention is as follows:

[0006] Provide a stability analysis method for random wedges of rock slopes based on structural plane statistics, which includes the following steps:

[0007] S1: On-site measurement and statistical analysis of the dip direction, dip angle, and trace length of the dominant structural planes developed in the slope rock mass are carried out using the traverse method or the statistical window method to obtain the distribution models and statistical parameters of the dip direction, dip angle, and trace length of the dominant structural planes developed in the slope rock mass;

[0008] S2: The slope instability mode analysis and judgment are carried out using the pole analysis method to obtain the structural plane combinations of potential unstable wedges that may be formed on the free face;

[0009] S3: For each structural plane combination mode, the Monte-Carlo method is used for random sampling to obtain the closed loops representing the structural planes. Through a series of operations such as mutual cutting, pruning, and surface combination to form a body between the structural planes and between the structural planes and the free face, finite blocks are combined, and the scale, outcrop depth, and safety factor of the wedge are calculated;

[0010] S4: Step S3 is repeatedly executed multiple times to obtain samples of random wedges that may develop in the slope, and the geometric characteristics and instability probability of the wedges are analyzed statistically.

[0011] Further, the specific implementation process of the Monte-Carlo method random sampling for each structural plane combination mode in step S3 is as follows:

[0012] For semi-positioned and semi-random wedges, specifically as follows:

[0013] S3-1-1: According to the position and attitude of the positioned structural plane, a closed loop representing the positioned structural plane is generated, and the intersection line between the positioned structural plane and the free face is calculated;

[0014] S3-1-2: Randomly select 1 point on the intersection line obtained in step S3-1-1 as the point on the random structural plane, and according to the distribution model of the geometric information of the random structural plane, randomly sample once to calculate the dip direction, dip direction and diameter of the structural plane, and obtain the closed loop representing the random structural plane;

[0015] S3-1-3: Calculate the intersection lines between the structural planes and between the structural planes and the excavation face and the boundary face, and through a series of operations such as pruning and surface combination to form a body, judge whether a finite block can be generated on the free face only by the combination of the structural planes and the free face;

[0016] For fully random wedges, specifically as follows:

[0017] S3-2-1: Randomly generate 1 point on the free face as the intersection point of the intersection line of the left and right sliding surfaces of the wedge and the free face;

[0018] S3-2-2. Randomly sample once using the Monte-Carlo method to obtain a sample of the dip direction, dip direction and diameter of the random structural plane, and combine with the coordinates of the points obtained in step S3-2-1 to generate a closed loop representing the random structural plane.

[0019] S3-2-3. According to a series of operations such as intersection of surfaces, pruning, and combination of surfaces to form a solid, determine whether it is possible to generate a finite block formed only by the combination of the structural plane and the free face on the free face.

[0020] Furthermore, if the wedge obtained in step S3-1-3 or S3-2-3 is a finite block, calculate the volume, buried depth of the wedge, and calculate the anti-sliding stability safety factor of the wedge using the conventional three-dimensional wedge stability analysis method; if the wedge obtained in step S3-1-3 or S3-2-3 is an infinite block, a group of random structural planes needs to be introduced as the trailing-edge cutting plane of the wedge, and determine whether it is possible to form a finite block through cutting combination. The calculation steps are as follows:

[0021] S3-3-1. Randomly select a group of random structural planes that are not left and right sliding planes as the trailing-edge cutting plane of the wedge.

[0022] S3-3-2. Calculate the intersection line of the closed loops representing the left and right sliding planes of the wedge, and randomly select 1 point on the intersection line as the point on the trailing-edge cutting plane; randomly sample once using the Mont-Carlo method to obtain a sample of the dip direction, dip angle, and diameter of the trailing-edge cutting plane, and generate a closed loop representing the trailing-edge cutting plane.

[0023] S3-3-3. According to a series of operations such as intersection of surfaces, pruning, and combination of surfaces to form a solid, determine whether it is possible to generate a finite block formed only by the combination of the structural plane and the free face on the free face.

[0024] The beneficial effects of the present invention are as follows:

[0025] Based on the distribution probability models and statistical parameters of the dip direction, dip angle, and trace length of the dominant structural planes obtained by measuring and statistically analyzing the random structural planes developed in the slope rock mass on site using the present invention method, the pole analysis method of stereographic projection is used to judge the structural plane combinations of potential unstable blocks that may be formed on the slope free face. For each structural plane combination, a series of operations such as multiple random samplings using the Monte-Carlo method, intersection of surfaces, pruning, and combination of surfaces to form a solid are carried out to obtain a series of possible unstable wedges, and then the outcrop depth, scale, and stability of the wedges are obtained, which can provide a basis for the design of systematic bolt support and shotcrete support for the shallow surface layer of rock slopes. Description of the Drawings

[0026] Figure 1 It is the overall method flow chart of the embodiment;

[0027] Figure 2 It is a flow chart for carrying out stability analysis and evaluation by randomly sampling each group of structural plane combinations using the Monte-Carlo method in the embodiment;

[0028] Figure 3 It is a schematic diagram for analyzing and judging the instability mode of a rock slope using the pole analysis method in the embodiment;

[0029] Figure 4 It is a schematic diagram of a three-dimensional terrain generalization model of an engineering excavation slope in the embodiment;

[0030] Figure 5 It is a schematic diagram of a semi-positioned and semi-random wedge formed by the cutting and combination of a positioned structural plane and a random structural plane in the embodiment;

[0031] Figure 6 It is a schematic diagram of a fully random wedge formed by the cutting and combination of random structural planes in the embodiment;

[0032] Figure 7 It is a schematic diagram of some random wedges obtained by searching in the embodiment. Specific embodiments

[0033] The following describes the specific embodiments of the present invention to facilitate those skilled in the art of the present technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art of the present technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are within the scope of protection.

[0034] Embodiment

[0035] For the analysis method of the three-dimensional random wedge stability of a rock slope based on the statistics of structural planes, the following assumptions are introduced:

[0036] The shape of the structural plane is the Baecher disk model without thickness, ignoring the bending and undulation of the joint surface;

[0037] The distribution of the diameter of the structural plane is independent of the dip distribution and position;

[0038] The probability of the position where the random structural planes forming the left and right sliding surfaces of the wedge appear within the given free face range follows a uniform distribution, that is, the probability of appearing at a position on the free face is equal;

[0039] Only wedges formed by the cutting and combination of two or three groups of structural planes and the free face are considered, and wedges formed by the cutting and combination of four or more groups of structural planes are not considered.

[0040] For a wedge formed by the combination of three sets of structural planes (i.e., in the case where there is a trailing cutting plane), the intersection position of the random structural plane serving as the trailing cutting plane and the intersection edge line formed by the cutting of the left and right sliding planes follows a uniform distribution, that is, the probability of passing through any point on the intersection edge line is equal.

[0041] Refer to Figure 1 , which mainly includes the following steps:

[0042] Step 1: Adopt the survey line method or the statistical window method to conduct structural plane measurement and statistical analysis on the slope exploration adit and surface outcrop in the field, and obtain the distribution probability model and statistical parameters (referring to the mean μ and standard deviation σ) of the geometric parameters (dip direction α, dip angle β, trace length l) of the dominant structural planes developed in the slope rock mass of the study area;

[0043] Step 2: Determine the statistical parameters (including the mean μ and standard deviation σ) of the structural plane diameter D according to the statistical parameters of the structural plane trace length l.

[0044] According to the existing research results and a large number of engineering practices, the trace lengths of structural planes are mainly distributed in negative exponential distribution and lognormal distribution, and the distribution probability model of the structural plane diameter is consistent with that of the trace length. The statistical parameters of the diameter distribution probability model can be estimated by using the measured trace lengths.

[0045] (1) If the structural plane diameter D follows a negative exponential distribution, then there is

[0046]

[0047] In the formula, μ D , σ D respectively represent the mean and standard deviation of the structural plane diameter, and μ L represents the mean of the structural plane trace length obtained by the survey line method.

[0048] (2) If the structural plane diameter D follows a lognormal distribution, then there is

[0049]

[0050] In the formula: μ L , σ L are respectively the mean and standard deviation of the structural plane trace length obtained by the survey line method, and μ, σ are respectively the statistical parameters of the diameter D in the lognormal distribution.

[0051] Step 3: Generate a three-dimensional terrain generalization model (including the free face and the model boundary surface) of the engineering excavation slope according to the excavation topographic map of the engineering slope;

[0052] Step 4: Use the stereographic projection analysis method to conduct the analysis and judgment of the slope instability mode, and preliminarily determine the combination of structural planes that may form a potential unstable wedge on the free face (that is, judge which two groups of structural planes may form the left and right sliding faces of the potential unstable wedge);

[0053] A large number of engineering practices have shown that for two groups of structural planes to form a potential unstable wedge on the slope, the conditions to be met are: the apparent dip angle β of the intersection edge line of the two groups of structural planes on the slope should not be greater than the dip angle β of the slope p , that is, β ≤ β p .

[0054] The pole analysis method of stereographic projection can be used for quick judgment. Specifically, first, draw the failure area where sliding may occur on the stereographic projection plane according to the occurrence of the free face, and then judge whether there is a possibility of wedge sliding failure according to whether the pole of the intersection line of the two groups of structural planes falls within the sliding failure area.

[0055] Step 5: For each combination of structural planes, conduct N times of Monte-Carlo method random sampling, and the calculation steps for each random sampling are as follows.

[0056] Step 5.1: For the semi-positioned and semi-random wedge (in the left and right sliding faces that make up the wedge, one group is a positioned structural plane and the other group is a random structural plane), the calculation steps are as follows:

[0057] Step 5.1.1: According to the occurrence and position of the positioned structural planes (faults and long fractures), generate a closed loop representing the positioned structural planes within the range of the terrain model, and calculate the intersection line of the closed loop and the free face;

[0058] Step 5.1.2: Randomly select 1 point on the intersection line obtained in Step 5.1.1 as the point on the random structural plane, and use the Monte-Carlo method to conduct 1 random sampling according to the distribution probability model of the geometric information of the random structural plane, calculate 1 sample of the dip direction and the dip direction and diameter of the randomly generated structural plane, and obtain the closed loop representing the random structural plane;

[0059] Generally, the intersection line of the positioned structural plane and the free face is a three-dimensional polyline composed of multiple line segments. The steps to randomly generate 1 point on the three-dimensional polyline composed of n line segments are as follows:

[0060] ① Calculate the total length l of the three-dimensional polyline and the length l of the i-th line segment i (0 ≤ i < n), and calculate the relative cumulative length λ of the i-th line segment i , and the calculation formula is:

[0061]

[0062] ② Generate a uniformly distributed random number r between [0, 1] 1 , and calculate λ i-1 ≤r 1 <λ i of the line segment i as the line segment number for generating random points;

[0063] ③ Let (x 1 , y 1 , z 1 ), (x 2 , y 2 , z 2 ) represent the starting and ending coordinates of the line segment i respectively, and generate a uniformly distributed random number r between [0, 1] 2 , then the calculation formula for the coordinates (x, y, z) of the generated random point is:

[0064] x = x 1 +r 2 (x 2 -x 1 )(8)

[0065] y = y 1 +r 2 (y 2 -y 1 )(9)

[0066] z = z 1 +r 2 (z 2 -z 1 )(10)

[0067] According to the distribution probability model and statistical parameters of random variables (dip, dip angle, and diameter), the Monte-Carlo method is used for random sampling, and generally, it can be indirectly calculated using uniformly distributed random numbers in the [0, 1] interval.

[0068] Step 5.1.3: Calculate the intersection lines between each structural plane and between the structural plane and the excavation surface and the boundary surface, and through a series of operations such as pruning and surface combination to form a solid, and judge whether a finite block can be generated on the free surface only composed of the combination of the structural plane and the free surface;

[0069] Step 5.2: For a fully random wedge (i.e., all the structural planes forming the wedge are random structural planes), the calculation steps are as follows:

[0070] Step 5.2.1: Randomly generate 1 point on the free surface as the intersection point of the intersection line of the left and right sliding surfaces of the wedge and the free surface;

[0071] Generally, the free surface of a slope can be a complex surface composed of multiple triangles or quadrilaterals. The steps for generating uniformly distributed random points on the free surface are as follows:

[0072] ① Decompose the free face into n triangles using the Delaunay method, and calculate the area S of each triangle i (0 ≤ i < n - 1) and the total area S of the free face. At the same time, calculate the relative cumulative area λ of each triangle i . The calculation formula is as follows:

[0073]

[0074] ② Generate a uniformly distributed random number r between [0, 1] 1 , and calculate λ i-1 ≤ r 1 < λ i of triangle i as the triangle number for generating the random point;

[0075] ③ Generate a uniformly distributed random number u between [0, 1], and generate a uniformly distributed random number v between [0, u]. Let w = 1 - u - v, then the coordinates (x, y, z) of the random point are:

[0076] x = u · x 1 + v · x 2 + w · x 3 (13)

[0077] y = u · y 1 + v · y 2 + w · y 3 (14)

[0078] z = u · z 1 + v · z 2 + w · z 3 (15)

[0079] In the formula, (x 1 , y 1 , z 1 ), (x 2 , y 2 , z 2 ) and (x 3 , y 3 , z 3 ) are the coordinates of the three vertices of triangle i respectively.

[0080] Step 5.2.2: Generate a closed loop representing a random structural plane according to the distribution probability model of the geometric parameters of the structural plane and the coordinates of the points obtained in Step 5.2.1;

[0081] Step 5.2.3: Determine whether a finite block can be generated on the free face only by the combination of the structural plane and the free face through a series of operations such as surface intersection, pruning, and surface combination to form a volume;

[0082] Step 6: If the wedge obtained in Step 5 is a finite block, calculate the volume and burial depth of the wedge, and use the three-dimensional wedge stability analysis method to calculate the anti-sliding stability safety factor of the wedge; otherwise, go to Step 7;

[0083] Step 7: If the wedge obtained in Step 5 is an infinite block, a set of random structural planes needs to be introduced as the trailing-edge cutting plane of the wedge. The calculation steps are as follows:

[0084] Step 7.1: Randomly select a set of random structural planes that are not the left and right sliding planes as the trailing-edge cutting plane of the wedge;

[0085] Step 7.2: Calculate the intersection line of the finite loop representing the left and right sliding planes of the wedge, and randomly select 1 point on the intersection line as the point on the trailing-edge cutting plane. Then, according to the distribution probability model and statistical parameters of the dip, dip angle, and diameter of the trailing-edge cutting plane, randomly generate a finite loop representing the trailing-edge cutting plane;

[0086] Step 7.3: According to a series of operations such as plane intersection, pruning, and plane combination to form a body, judge whether it is possible to generate a finite block formed only by the combination of structural planes and the free face on the free face.

[0087] Step 8: If the wedge formed in Step 7 is a finite block, use the block theory analysis to judge the mobility and the corresponding sliding mode, and use the three-dimensional wedge stability analysis method to calculate the anti-sliding stability safety factor of the wedge;

[0088] Step 9: Repeat Steps 5 to 8 to obtain samples of random wedges that may develop in the slope, and analyze the geometric characteristics and instability probability of the wedges from a statistical perspective.

[0089] Based on the distribution probability model and statistical parameters of the dip, dip angle, and trace length of the dominant structural planes obtained by measuring and statistically analyzing the random structural planes developed in the slope rock mass on-site, the proposed method uses the pole analysis method of stereographic projection to judge the structural plane combinations of potential unstable blocks that may be formed on the slope free face. For each structural plane combination, a series of operations such as multiple random sampling using the Monte-Carlo method, plane intersection, pruning, and plane combination to form a body are carried out to obtain a series of wedges that may be unstable, and then the outcrop depth, scale, and stability of the wedges are obtained, which can provide a basis for the design of systematic bolt support and shotcrete support for the shallow surface layer of rock slopes.

[0090] It is obvious to those skilled in the art that the present invention is not limited to the details of the above-described exemplary embodiments, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the present invention. Therefore, in all respects, the embodiments should be regarded as exemplary and non-restrictive. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be embraced within the present invention.

[0091] In addition, it should be understood that although this specification is described in terms of embodiments, not every embodiment only contains an independent technical solution. This narrative manner of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A stability analysis method for random wedges in rock slopes based on structural surface statistics, characterized in that: The following steps are involved: S1: Use the line method or statistical window method to measure and statistically analyze the inclination, dip angle and trace length of the dominant structural surface of the slope rock mass on site, and obtain the distribution pattern and statistical parameters of the inclination, dip angle and trace length of the dominant structural surface of the slope rock mass; S2: Use the extreme point analysis method to analyze and judge the slope instability mode and obtain the structural surface combination of the potential unstable wedge that may be formed on the free surface; S3: For each structural surface combination mode, the Monte-Carlo method is used to randomly sample and obtain a closed loop representing the structural surface. Through a series of operations such as cutting and cutting between structural surfaces and between structural surfaces and free-surface surfaces, and combining surfaces to form a body, a finite block is formed, and the scale, exposure depth and safety factor of the wedge are calculated. S4: Repeat step S3 for multiple times to obtain samples of random wedges that may develop in the slope, and analyze the geometric characteristics and instability probability of the wedges in a statistical sense.

2. The stability analysis method of random wedges of rock slopes based on structural surface statistics according to claim 1 is characterized in that: The specific implementation process of the Monte-Carlo random sampling for each structural surface combination mode in step S3 is as follows: For semi-positioned and semi-random wedges, the details are as follows: S3-1-1. Generate a closed loop representing the positioning structure surface according to the position and occurrence of the positioning structure surface, and calculate the intersection line between the positioning structure surface and the free surface; S3-1-2, randomly selecting a point on the intersection line obtained in step S3-1-1 as a point on the random structural surface, and according to the distribution probability of the geometric information of the random structural surface, randomly sampling once to calculate the inclination, inclination and diameter of the structural surface, and obtaining a closed loop representing the random structural surface; S3-1-3. Calculate the intersection lines between each structural surface and between the structural surface and the excavation surface and boundary surface, and through a series of operations such as cutting branches and combining surfaces to form a body, determine whether a finite block formed by only the combination of the structural surface and the free surface can be generated on the free surface; For a fully random wedge, the details are as follows: S3-2-1. Generate a point randomly on the free surface as the intersection point of the intersection line of the left and right sliding surfaces of the wedge and the free surface; S3-2-2, using the Monte-Carlo method to randomly sample once, obtain a sample of the inclination, tendency and diameter of the random structural surface, and combine the coordinates of the points obtained in step S3-2-1 to generate a closed loop representing the random structural surface; S3-2-3. Based on a series of operations such as intersecting faces, cutting branches, and combining faces to form a body, determine whether a finite block can be generated on the free-facing surface that is formed only by the combination of structural faces and free-facing faces.

3. The stability analysis method of random wedges of rock slopes based on structural surface statistics according to claim 2 is characterized in that: If the wedge obtained in step S3-1-3 or S3-2-3 is a finite block, calculate the volume and burial depth of the wedge, and use the conventional three-dimensional wedge stability analysis method to calculate the anti-sliding stability safety factor of the wedge; if the wedge obtained in step S3-1-3 or S3-2-3 is an infinite block, it is necessary to introduce a set of random structural surfaces as the trailing edge cutting surfaces of the wedge to determine whether it is possible to form a finite block through cutting combination. The calculation steps are as follows: S3-3-1. Randomly select a set of random structural surfaces that are not left or right sliding surfaces as the trailing edge cutting surfaces of the wedge; S3-3-2. Calculate the intersection line of the closed loop representing the left and right sliding surfaces of the wedge, and randomly select a point on the intersection line as a point on the trailing edge cutting surface; use the Mont-Carlo method to randomly sample once to obtain a sample of the inclination, dip angle, and diameter of the trailing edge cutting surface, and generate a closed loop representing the trailing edge cutting surface; S3-3-3. Based on a series of operations such as intersecting faces, cutting branches, and combining faces to form a body, determine whether a finite block can be generated on the free-facing surface that is formed only by the combination of structural faces and free-facing faces.

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