A method for calculating the slope safety factor based on stochastic search theory

Abstract

This invention relates to the field of slope stability analysis, and particularly to a method for calculating the slope safety factor based on stochastic search theory. This method searches for a polygonal slip surface based on the stochastic theory of distribution functions and calculates the safety factor. The method mainly includes: structural plane distribution function, crack initiation range division, random number and random variable calculation, structural plane propagation calculation, failure conditions, shearing criterion, and safety factor calculation. This invention fully considers the randomness of structural plane distribution in complex fractured rock masses, utilizes a sufficient number of random variables to realize crack propagation and the generation of polygonal slip surfaces, and closely approximates the application of practical slope engineering.

Description

Technical Field

[0001] This invention relates to the field of slope stability analysis, and in particular to a method for calculating the slope safety factor based on stochastic search theory. Background Technology

[0002] Rock slopes typically fail along fracture surfaces, and their sliding surfaces are generally zigzag-shaped. The circular sliding analysis methods used for soil slopes are no longer applicable to the stability analysis of complex rock slopes. Rock slopes widely develop numerous structural planes of varying grades. Accurate values ​​are usually relatively easy to obtain for faults, bedding planes, and fracture zones. However, for grade III and IV structural planes, which are distributed throughout the rock mass, large-scale, detailed, and definitive investigations are difficult due to limitations in manpower, resources, and funding. Determining the zigzag sliding surface of rock slope failure using limited structural plane information from field outcrop surveys, UAV oblique photography surveys, borehole and adit surveys remains a significant challenge in geotechnical engineering.

[0003] For polygonal slip surfaces, current methods often involve artificially specifying the slip surface through fracture combinations and then calculating its stability coefficient. However, this approach cannot determine whether the specified slip surface is the most unfavorable one and cannot achieve automatic search. Therefore, methods that analyze slope stability by reasonably representing the uncertainty and probability distribution of the geometric parameters of the rock mass structural surfaces are gradually being accepted by scholars both domestically and internationally. Current research mainly focuses on generating rock mass fracture networks using Monte Carlo (MCS), Bayesian statistics, and computer simulation methods, considering the variability of the geometric parameters of the structural surfaces and probabilistic statistical models, and then conducting stability analysis based on reliability theory. However, methods that use probabilistic distribution models of the geometric parameters of the rock mass structural surfaces to calculate and search for polygonal slip surfaces and calculate their safety factors still require further research. Summary of the Invention

[0004] To overcome the shortcomings of the prior art, this invention provides a slope safety factor calculation method based on random search theory. It fully considers the randomness of the distribution of structural surfaces in complex fractured rock masses, and uses a sufficient number of random variables to realize the expansion of fractures and the generation of broken-line slip surfaces, so as to be as close as possible to the application of actual slope engineering.

[0005] This invention provides a method for calculating the slope safety factor based on stochastic search theory, comprising the following steps:

[0006] S1. Obtain the non-standard normal distribution functions of the structural surface tilt angle θ and trace length L respectively;

[0007] S2. At the top of the slope, arbitrarily designate a crack initiation segment of length L0, and divide the crack initiation segment into m equal segments, where m = aL0 / λ. L Where a≥2, λL Given the average length L, m+1 initiation points M are formed on the initiation segment. i ,i=0,1,2,...,i,...,m;

[0008] S3, Select the initial cracking point M on the crack initiation section at the top of the slope. i , starting with i = 0, generate 2 sets of uniformly distributed random numbers N(0, 1) with a size of p × p;

[0009] S4. Select one random number {v} from each of the two sets of random numbers generated in S3. l}、{ul},I=1,2,…,I,...,p,Initially I=1,Each group contains p random numbers;

[0010] S5, take {v} respectively l}、{u l The random variable θ′ is obtained by transforming two adjacent random numbers using a binary function. k L′ k k = 1, 2, ..., k, ..., p, initially k = 1;

[0011] S6. The two random variables θ′ obtained in S5 k L′ k θ is obtained by linear transformation respectively k L k That is, the dip angle and trace length of the k-th fracture, and calculate the coordinates of the tip of the k-th fracture;

[0012] S7. Determine whether the coordinates of the tip of the kth crack meet the failure condition. If the failure condition is met, then I = l + 1 and return to execute S4. If the failure condition is not met, then execute the next step.

[0013] S8. Determine whether the coordinates of the tip of the kth fracture satisfy the shearing criterion. If the shearing criterion is not satisfied, then k = k + 1 and return to execute S5. If the shearing criterion is satisfied, then form a polygonal slip surface based on the obtained k random fracture dip angles and trace lengths, and calculate the safety factor f(s) of the obtained polygonal slip surface.

[0014] S9. Determine whether I ≥ p holds true. If it does, then obtain the safety factors f(s1), f(s2), ..., f(s1), ..., f(s2) for the p polygonal smooth surfaces. p If the condition is met, proceed to the next step; otherwise, I = l + 1 and return to execute S4.

[0015] S10, Screening safety factors f(s1), f(s2), ..., f(s) l ), ..., f(s) p The minimum value in ) is denoted as F(s) i );

[0016] S11. Determine whether i≥m holds true. If true, obtain the safety factors F(s0), F(s1), F(s2), ..., F(s) corresponding to the m+1 crack initiation points, respectively. i ), ..., F(s) m If i is not found, proceed to the next step; otherwise, i = i + 1 and return to execute S3.

[0017] S12, Screening safety factors F(s0), F(s1), F(s2), ..., F(si), ..., F(s m The minimum value in the equation is denoted as F(S), which is the overall safety factor of the slope. The broken-line slip surface corresponding to F(S) is the most dangerous slip surface.

[0018] Preferably, the non-standard normal distribution functions of the structural surface tilt angle θ and the trace length L are respectively:

[0019]

[0020]

[0021] Where, τ θ , λ θ These are the standard deviation and mean of the tilt angle, τ, respectively. L , λ L These are the standard deviation and mean of the trace length, respectively.

[0022] Preferably, p in S3 is represented as:

[0023]

[0024] Where b≥4 and b is even, λ L The mean of the trace length, Let (x1, y1) be the average slope length, and (x1, y1) be the coordinates of the top point of the free slip surface of the slope. n y n () represents the coordinates of the bottom point of the free-slip surface of the slope.

[0025] Preferably, in S4, one random number is randomly selected from each of the two sets of random numbers generated in S3, and the two sets of random numbers are represented as follows:

[0026]

[0027] When υ1, υ2 and u1, u2 are selected as two adjacent random numbers respectively, the formula used for the bivariate function transformation in S5 is...

[0028] for:

[0029]

[0030]

[0031] The formula used for linear transformation in S6 is:

[0032]

[0033]

[0034] Where, τ θ , λ θ These are the standard deviation and mean of the tilt angle, τ, respectively. L , λ L These are the standard deviation and mean of the trace length, respectively.

[0035] Preferably, the formula for calculating the coordinates of the k-th crack tip in S6 is:

[0036]

[0037] Where, θ k L k , respectively, are the dip angle and trace length of the k-th fracture.

[0038] Preferably, the failure condition for the coordinates of the k-th crack tip in S7 is:

[0039]

[0040] Among them, (x n y n () represents the coordinates of the bottom point of the free-slip surface of the slope.

[0041] Preferably, the shearing criterion in S8 is:

[0042]

[0043] Among them, (x j-1 y j-1 ), (x j y j All of these are the coordinates of the inflection point of the slope surface on the free-slip surface of the slope.

[0044] Preferably, the safety factor f(s) of the polygonal sliding surface calculated in S8 using the rigid body limit equilibrium method includes:

[0045] First, the slope above the polygonal sliding surface is divided into multiple sliders by vertically cutting upwards according to the inflection point of the slope. The weight of the k-th slider is Wk, and the length of the bottom structural surface of the slider is Lk. The mechanical parameters of the structural surface include cohesion ck and internal friction angle φk. Then, the residual sliding force generated by each slider on the last slider under the safety factor f(s) is calculated. Finally, the limit equilibrium condition of the last slider is used to solve the linear equation with respect to the safety factor f(s).

[0046] The present invention also provides an electronic device, including a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, it implements the slope safety factor calculation method based on random search theory described in any of the preceding claims.

[0047] The present invention also provides a readable storage medium storing a computer program, which, when executed by a processor, implements the slope safety factor calculation method based on random search theory described in any of the preceding claims.

[0048] In summary, the beneficial effects of this invention are as follows:

[0049] 1. Update the probability distribution of structural surface geometric parameters (tilt angle, trace length) using on-site measured samples, thereby obtaining a structural surface parameter probability distribution model that is closer to the actual engineering situation;

[0050] 2. Without the need to divide the rock mass structural plane network, the structural plane parameters are converted by generating random numbers from a standard normal distribution using a computer, providing an effective method for evaluating the stability of fractured rock mass slopes based on stochastic theory;

[0051] 3. It can effectively solve the problem of global search for polygonal sliding surfaces. At the same time, the safety factor calculation is not limited by the shape and terrain of the polygonal sliding surface, and can integrate multiple safety factor calculation methods, providing a strong basis for slope protection engineering.

[0052] 4. The proposed calculation method is simple and profound, avoids complex and redundant calculations, and has a good prospect of being widely used in engineering design.

[0053] The invention will now be further described with reference to the accompanying drawings. Attached Figure Description

[0054] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0055] Figure 1 This is a schematic diagram illustrating how the crack initiation range at the top of a slope can be arbitrarily specified and segmented according to the present invention.

[0056] Figure 2 This is a schematic diagram illustrating the method for calculating the development and location of cracks according to the present invention;

[0057] Figure 3 This is a schematic diagram illustrating the failure conditions and shearing criteria of a polygonal slip surface according to the present invention;

[0058] Figure 4 This is a schematic diagram illustrating the calculation of the safety factor using the rigid body limit equilibrium method according to the present invention.

[0059] Figure 5 This is a schematic diagram illustrating a process for calculating the slope safety factor according to the present invention. Detailed Implementation

[0060] The following will be based on embodiments of the present invention. Figures 1 to 5 The technical solutions in the embodiments of the present invention are clearly and completely described herein. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0061] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions in the embodiments of this invention will be described in more detail below with reference to the accompanying drawings.

[0062] Current methods for calculating the broken-line sliding surface and its safety factor of rock slopes typically involve manually specifying the sliding surface or calculating the critical safety factor through reliability analysis. For slope engineering projects such as railways and water conservancy, it is crucial to identify the location of the most unfavorable broken-line sliding surface and its safety factor. This invention proposes a method for calculating the broken-line sliding surface and safety factor of rock slopes based on stochastic search theory. Essentially, it provides a search method for the broken-line sliding surface of rock slopes based on stochastic search theory, which can be used to calculate the deformation and failure process of complex rock slopes. It fully considers the randomness of the distribution of structural surfaces in complex fractured rock masses, and uses a sufficient number of random variables to realize the expansion of fractures and the generation of broken-line sliding surfaces, closely approximating the application of actual slope engineering. This provides an effective method for evaluating the stability of fractured rock mass slopes based on stochastic theory.

[0063] This invention proposes a method for searching polygonal slip surfaces on rock slopes based on random search theory.

[0064] like Figures 1 to 5As shown in this embodiment, a method for calculating the slope safety factor based on stochastic search theory is disclosed, which includes the following steps:

[0065] S1. Obtain the non-standard normal distribution functions of the structural surface tilt angle θ and trace length L respectively;

[0066] For rock slopes, the probability distribution of parameters such as the orientation, dip angle, trace length, and spacing of structural surfaces usually follows a normal distribution function. After comprehensive investigation of structural surfaces, statistical functions such as the circumferential direction, dip angle, trace length, and spacing of fractures can be obtained from statistical data. Comprehensive investigation of structural surfaces mainly involves obtaining structural surface information through field surveys, thereby generating a large amount of statistical data.

[0067] This invention is a two-dimensional planar calculation, therefore only the tilt angle θ and trace length L are considered. As a preferred technical solution, this embodiment assumes that the probability distributions of the tilt angle and trace length follow the following normal distribution functions (Equations (1) and (2)):

[0068]

[0069]

[0070] Where, τ θ , λ θ These are the standard deviation and mean of the tilt angle, τ, respectively. L , λ L These are the standard deviation and mean of the trace length, respectively.

[0071] S2. At the top of the slope, arbitrarily designate a crack initiation segment of length L0, and divide the crack initiation segment into m equal segments, where m = aL0 / λ. L Where a≥2, λ L Given the average length L, m+1 initiation points M are formed on the initiation segment. i ,i=0,1,2,...,i,...,m;

[0072] slopes Figure 1-3 As shown, in Figure 1 In this paper, it is assumed that the crack initiation point of the slope is located at the top of the slope (in reality, the crack initiation range can be arbitrarily specified; for the sake of simplifying the calculation, the top of the slope is chosen as the crack initiation range). When it is necessary to obtain the safety factor for the crack initiation point within an arbitrary length L0 range at the top of the slope, L0 is divided into equal parts, assuming they are divided into... If a segment of length L0 forms m+1 initiation points, then 'a' can be set to different values ​​(a≥2) for different calculation conditions with varying precision, establishing a... Figure 3 In the coordinate system shown, any crack initiation point M within the crack initiation range i The coordinates are given by equation (3):

[0073]

[0074] S3, Select the initial cracking point M on the crack initiation section at the top of the slope. i , starting with i = 0, generate 2 sets of uniformly distributed random numbers N(0, 1) with a size of p × p;

[0075] In order to be able to determine any initial cracking point M on the cracking segment at the top of the slope i To form p fracture surfaces, this step generates two sets of uniformly distributed random numbers N(0,1) with a size of p×p.

[0076] As a preferred technical solution, p can be the average trace length λ of the structural surface measured on-site. L The calculation can be expressed as the ratio of the average slope length to the average trace length of the slope. In order to generate enough cracks to ensure that the slip surface can be sheared out from the slope, a multiple of b (b≥4 and b is an even number) can be defined (equation (4)), that is, p in S3 is expressed as:

[0077]

[0078] in, Let (x1, y1) be the average slope length, and (x1, y1) be the coordinates of the top point of the free slip surface of the slope. n y n () represents the coordinates of the bottom point of the free-slip surface of the slope.

[0079] S4. Select one random number {v} from each of the two sets of random numbers generated in S3. l}、{u l}, l = 1, 2, ..., I, ..., p, initially I = 1, each group contains p random numbers;

[0080] In this step, each person randomly selects a set of random numbers {v} l}、{u l This will form a fracture surface, corresponding to a specific value of I. Initially, I = 1. Each time, one random number {v} is randomly selected from the two sets of random numbers generated in S3. l}、{u l}, a total of p times can be selected, therefore based on the selected crack initiation point M i This can form p fracture surfaces, {v l}、{u l} are a set of p random numbers, which can be represented as:

[0081]

[0082] S5, take {v} respectively l}、{u l Two adjacent random numbers in the array are transformed using a binary function to obtain random variables θ′k and L′. kk = 1, 2, ..., k, ..., p, initially k = 1;

[0083] S6. The two random variables θ′ obtained in S5 k L′ k θ is obtained by linear transformation respectively k L k That is, the dip angle and trace length of the k-th fracture, and calculate the coordinates of the tip of the k-th fracture;

[0084] For the two sets of random numbers selected:

[0085] To facilitate the demonstration of the calculation process in steps S5 and S6, this embodiment uses the selection of υ1, υ2 and u1, u2 as two adjacent random numbers as an example. The formula used for the binary function transformation in S5 is:

[0086]

[0087]

[0088] The formula used for linear transformation in S6 is:

[0089]

[0090]

[0091] Where, τ θ , λ θ These are the standard deviation and mean of the tilt angle, τ, respectively. L , λ L These are the standard deviation and mean of the trace length, respectively.

[0092] In the above scheme, to obtain the normal distribution function random variable of the tilt angle θ, two independent random numbers v1 and v2 can be randomly selected from the uniform distribution N(0,1), and then the random variables v1′ and v2′ can be obtained by using the bivariate function (Equation (6)). Then, the normal distribution function random variable of the tilt angle θ can be obtained by the linear transformation (Equation (8)). Similarly, two independent random numbers u1 and u2 can be randomly selected from the uniform distribution N(0,1), and the normal distribution function random variable of the trace length L can be obtained by the transformation by Equations (7) and (9).

[0093] Steps S5 and S6 are mainly used to obtain the dip angles of p random fractures and the trace lengths of p random fractures corresponding to a single polygonal slip surface, respectively taking {v l}、{u l Two adjacent random numbers v in} k v k+1 and u k u k+1By combining these methods, we can obtain the general expressions for the dip angle and trace length of the k-th fracture, as shown in equation (10):

[0094]

[0095] Equation (10) gives a general expression for the dip angle and trace length of two adjacent fractures.

[0096] Establish such as Figure 3 When using the coordinate system shown, as a preferred technical solution, such as... Figure 2 As shown, the formula for calculating the coordinates of the k-th crack tip in S6 is:

[0097]

[0098] Where, θ k L k , respectively, are the dip angle and trace length of the k-th fracture.

[0099] S7. Determine whether the coordinates of the tip of the kth crack meet the failure condition. If the failure condition is met, then I = I + 1 and return to execute S4. If the failure condition is not met, then proceed to the next step.

[0100] S8. Determine whether the coordinates of the tip of the kth fracture satisfy the shearing criterion. If the shearing criterion is not satisfied, then k = k + 1 and return to execute S5. If the shearing criterion is satisfied, then form a polygonal slip surface based on the obtained k random fracture dip angles and trace lengths, and calculate the safety factor f(s) of the obtained polygonal slip surface.

[0101] During the expansion of the structural surface, it is necessary to determine whether the polygonal slip surface formed by the dip angles and trace lengths of k random fractures is stable. The polygonal slip surface formed during the expansion of the structural surface can include a stable slip surface (which will not shear out along the slope) and a through slip surface that shears out along the slope.

[0102] Steps S7 and S8 in this embodiment mainly rely on the coordinates of the tip of the kth crack to determine the stability of the slip surface. If the coordinates of the tip of the kth crack meet the failure condition, it means that the slip surface is in a stable state, that is, it will not shear out along the slope. When the failure condition is met, I = I + 1 and return to execute S4 to regenerate a fracture surface based on the selected initiation point. If the failure condition is not met, it is determined whether the shearing criterion is met. If the coordinates of the tip of the kth crack do not meet the shearing criterion, it means that the slip surface has not sheared out. Then k = k + 1 and return to execute S5. The structural surface continues to extend forward to form the next crack. If the coordinates of the tip of the kth crack meet the shearing criterion, it means that the slip surface has sheared out to form a through slip surface. At this time, a through broken-line slip surface is formed based on the obtained k random crack dip angles and trace lengths. The safety factor f(s) of the obtained broken-line slip surface can be calculated by using the rigid body limit equilibrium method.

[0103] It should be noted that when a polygonal slip surface meets the failure condition and is in a stable state, the polygonal slip surface is safe. The safety factor of this polygonal slip surface is not necessarily the minimum, therefore it does not need to be calculated. To expedite the calculation of the safety factor for p fracture surfaces generated from a single fracture point, this embodiment only calculates the safety factor of the polygonal slip surface that can be sheared to form a continuous slip surface, and selects the minimum value, denoted as F(s). i ), its corresponding crack initiation point M i .

[0104] like Figure 3 As shown, as a preferred technical solution, the failure condition for the coordinates of the k-th crack tip in S7 is:

[0105]

[0106] Among them, (x n y n () represents the coordinates of the bottom point of the free-slip surface of the slope.

[0107] like Figure 3 As shown, as a preferred technical solution, the cut-out criterion in S8 is:

[0108]

[0109] Among them, (x j-1 y j-1 ), (x j y j All of these are the coordinates of the inflection point of the slope surface on the free-slip surface of the slope.

[0110] S9. Determine whether I ≥ p holds true. If it does, then obtain the safety factors f(s1), f(s2), ..., f(s1), ..., f(s2) for the p polygonal smooth surfaces. p If the condition is met, proceed to the next step; otherwise, I = I + 1 and return to execute S4.

[0111] S10, Screening safety factors f(s1), f(s2), ..., f(s) l ), ..., f(s) p The minimum value in ) is denoted as F(s) i );

[0112] Based on any initial cracking point M on the cracking segment at the top of the slope iEach step generates p fracture surfaces. Step S9 is used to determine whether p fracture surfaces have been generated based on a fracture initiation point and to calculate the safety factor of the corresponding slip surface. If I≥p is not true, then I=I+1 and return to execute S4. A fracture surface is regenerated based on the selected fracture initiation point for judgment and calculation. If I≥p is true, then p fracture surfaces have been generated based on a fracture initiation point. At this time, the safety factors f(s1), f(s2), ..., f(s) of the p polygonal slip surfaces are obtained. l ), ..., f(s) p And filter the safety factors f(s1), f(s2), ..., f(s) l ), ..., f(s) p The minimum value in ) is denoted as F(s) i ), its corresponding crack initiation point M i .

[0113] S11. Determine whether i≥m holds true. If true, obtain the safety factors F(s0), F(s1), F(s2), ..., F(s) corresponding to the m+1 crack initiation points, respectively. i ), ..., F(s) m If i is not found, proceed to the next step; otherwise, i = i + 1 and return to execute S3.

[0114] S12, Screening safety factors F(s0), F(s1), F(s2), ..., F(s i ), ..., F(s) m The minimum value in the equation is denoted as F(S), which is the overall safety factor of the slope. The broken-line slip surface corresponding to F(S) is the most dangerous slip surface.

[0115] The slope crest with length L0 forms m+1 initiation points. Step S11 is used to determine whether the fracture surface of m+1 initiation points has been generated. If i≥m is not true, then i=i+1 and return to execute S3, that is, reselect an initiation point M on the slope crest initiation segment. i If i≥m, it indicates that the fracture surface generation and safety factor calculation for m+1 fracture initiation points have been completed. Then, the safety factors F(s0), F(s1), F(s2), ..., F(s) are selected. i ), ..., F(s) m The minimum value in the equation is denoted as F(S), which is the overall safety factor of the slope. The broken-line slip surface corresponding to F(S) is the most dangerous slip surface.

[0116] The above scheme can calculate and generate a polygonal smooth surface through steps S1-S8 and equations (1)-(13). Figure 4The rigid body limit equilibrium method shown can calculate its safety factor f(s). In fact, there are many methods for calculating the safety factor of broken line sliding of rock slopes. This invention mainly provides a sliding surface search method. The safety factor calculation can replace other methods such as unbalanced thrust method, upper limit method, lower limit method and method based on virtual work principle, etc., or use multiple methods to make a comprehensive judgment. The principle is the same as that of this invention. This invention will not elaborate further, but only introduces a simple and fast limit equilibrium method.

[0117] exist Figure 4 In this study, the slope above the polygonal sliding surface is divided into multiple sliding blocks based on the vertical upward division of the slope inflection point. First, the influence of the unit force in each sliding block on the remaining sliding force of the last sliding block is analyzed. Then, the remaining sliding force generated by each sliding block on the last sliding block under the safety factor f(s) is calculated. Finally, using the limit equilibrium condition of the last sliding block, a linear equation about the safety factor f(s) is solved. Figure 4 The weight of the k-th slider is W. k The length of the bottom structural surface of the slider is L. k The structural surface mechanical parameters are c k (cohesion), φ k (Internal friction angle), then when calculating the safety factor, the remaining sliding force of each sliding block on the last sliding block can be considered separately. When the safety factor is f(s), the N1th and N2th sliding blocks on the Nth... p The remaining sliding force of the slider is given by equations (14) and (15). Similarly, the Nth... k Slider for the Nth p The remaining sliding force of the slider is given by equation (16), and so on, until the last slider N... p The remaining sliding force is given by equation (17). The cumulative force N acting on the last slider is obtained through equations (14) to (17). p The remaining sliding force is Ω p Equation (18), when the last slider reaches limit equilibrium (Ω) P =0), the safety factor f(s) is obtained as equation (19). If each structural surface c k If they are the same, then the value of C is used to represent it, and the safety factor f(s) can be obtained in general formulas (20) to (22).

[0118]

[0119]

[0120]

[0121]

[0122]

[0123]

[0124] f(s)=A+C·B (20)

[0125]

[0126]

[0127] In the above scheme, the two sets of uniformly distributed random numbers generated by equation (5) can produce a broken-line sliding surface (or penetrate deep into the slope and cannot be sheared out), while for a certain cracking point M at the top of the slope... i Based on the concept of randomness, the dip angle and trace length of each fracture that develops downwards are randomly distributed. Therefore, equations (23) and (24) represent two sets of random numbers with a size of p×p, randomly selected from a uniform distribution N(0,1), which respectively yield two sets of random variables with a size of p×p corresponding to the two normal distribution functions of equations (1) and (2). Based on equations (23) and (24), any one set of random numbers {v} is selected. l}、{u l},according to Figure 5 Repeating equations (1) to (13) will generate a polygonal slip surface, thus for any crack initiation point M at the top of the slope. i This will generate p fracture surfaces, and their safety factors f(s1), f(s2), ..., f(s) can be obtained respectively. l ), ..., f(s) p The minimum value f(s) and its corresponding polygonal smooth surface are taken as the crack initiation point M. i The most dangerous slip surface and the safety factor F(s) i ).

[0128]

[0129]

[0130] In the above scheme, any cracking point M i The most dangerous slip surface and safety factor F(s) can be obtained from both. i When all crack initiation points are completed, the most dangerous slip surface and the safety factors F(s0), F(s1), ..., F(s) are determined. i ), ..., F(s) m After that, the crack initiation point and the broken-line sliding surface corresponding to the minimum value are taken as the overall safety factor F(S) of the slope and the most dangerous sliding surface.

[0131] The slope polygonal slip surface search method based on random search theory provided in this invention can effectively solve the current problem of difficulty in achieving global search for polygonal slip surfaces. Furthermore, the safety factor calculation is not limited by the shape and terrain of the polygonal slip surface, and can integrate multiple safety factor calculation methods, providing a strong basis for slope protection engineering. The proposed calculation method is simple and insightful, avoiding complex and redundant calculations, and has a promising future for widespread application in engineering design.

[0132] This invention uses statistical probability distribution functions of actual structural surface information and computer-generated random numbers with standard normal distribution to calculate structural surface parameters to obtain the broken-line sliding surface of rock slopes. This provides an effective method for evaluating the stability of fractured rock mass slopes based on stochastic theory, which is more in line with engineering practice and has good social and economic benefits.

[0133] Based on the same inventive concept, this embodiment also discloses an electronic device, including a processor and a memory, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, it implements the slope safety factor calculation method based on random search theory as described above.

[0134] Based on the same inventive concept, this embodiment also discloses a readable storage medium storing a computer program. When the computer program is executed by a processor, it implements the slope safety factor calculation method based on random search theory as described above.

[0135] The parts not covered in this embodiment are the same as or can be implemented using existing technologies, and will not be further described here.

[0136] Please note to all technical personnel: Although the present invention has been described according to the specific embodiments above, the inventive concept of the present invention is not limited to this invention. Any modifications that utilize the inventive concept will be included within the scope of protection of this patent.

Claims

1. A method for calculating the slope safety factor based on stochastic search theory, characterized in that, Includes the following steps: S1. Obtain the non-standard normal distribution functions of the structural surface tilt angle θ and trace length L respectively; S2. At the top of the slope, arbitrarily specify a crack initiation segment of length L0, and divide the crack initiation segment into m equal segments, where m = aL0 / λ. L Where a≥2, Given the average length L, m+1 initiation points M are formed on the initiation segment. i , i = 0, 1, 2, ..., m; S3, Select the initial cracking point M on the crack initiation section at the top of the slope. i Starting with i=0, generate two sets of uniformly distributed random numbers U(0,1) with a count of p×p; S4. Select one random number from each of the two sets of random numbers generated in S3. l=1, 2, ..., p, initially l=1, each group contains p random numbers; where {v l } represents the first set of random numbers; {u l } represents the second set of random numbers; S5, take respectively The random variable θ' is obtained by transforming two adjacent random numbers using a binary function. k L' k k=1,2,...,p, initially k=1; S6. The two random variables θ' obtained in S5 k L' k θ is obtained by linear transformation respectively k L k That is, the dip angle and trace length of the k-th fracture, and calculate the coordinates of the tip of the k-th fracture; S7. Determine whether the coordinates of the tip of the kth crack meet the failure condition. If the failure condition is met, then l = l + 1 and return to execute S4. If the failure condition is not met, then execute the next step. S8. Determine whether the coordinates of the tip of the kth fracture satisfy the shearing criterion. If the shearing criterion is not satisfied, then k = k + 1 and return to execute S5. If the shearing criterion is satisfied, then form a polygonal slip surface based on the obtained k random fracture dip angles and trace lengths, and calculate the safety factor fs of the obtained polygonal slip surface. S9. Determine whether l≥p holds true. If it does, obtain the safety factors fs(1), fs(2), ..., fs(l), ..., fs(p) of the p-shaped sliding surfaces, and proceed to the next step. Otherwise, l=l+1 and return to execute S4. S10. Select the minimum value among the safety factors fs(1), fs(2), ..., fs(l), ..., fs(p) and denote it as Fs(i); S11. Determine whether i≥m holds true. If it holds true, obtain the safety factors Fs(0), Fs(1), Fs(2), ..., Fs(i), ..., Fs(m) corresponding to m+1 crack initiation points respectively, and then proceed to the next step. Otherwise, i=i+1 and return to execute S3. S12. Select the minimum value among the safety factors Fs(0), Fs(1), Fs(2), ..., Fs(i), ..., Fs(m) and record it as FS. FS is the overall safety factor of the slope, and the broken-line slip surface corresponding to FS is the most dangerous slip surface. The formula for calculating the coordinates of the k-th crack tip in S6 is as follows: ； Where, θ q L q These are the dip angle and trace length of the q-th fracture, respectively; The failure condition for the coordinates of the k-th crack tip in S7 is: ； Among them, (x) n y n () represents the coordinates of the bottom point of the free-slip surface of the slope; The cut-out criterion in S8 is: ； Among them, (x) j-1 ,y j-1 ), (x j ,y j All of these are the coordinates of the inflection point of the slope surface on the free-slip surface of the slope.

2. The method for calculating the slope safety factor based on stochastic search theory according to claim 1, characterized in that, The non-standard normal distribution functions of the structural surface tilt angle θ and the trace length L are respectively: ； ； in, , These are the standard deviation and mean of the tilt angle, respectively. , These are the standard deviation and mean of the trace length, respectively.

3. The method for calculating the slope safety factor based on stochastic search theory according to claim 1, characterized in that, p in S3 is represented as: ； Where b ≥ 4 and b is an even number. The mean of the trace length, Let (x1, y1) be the average slope length, and (x1, y1) be the coordinates of the top point of the free slip surface of the slope. n y n () represents the coordinates of the bottom point of the free-slip surface of the slope.

4. The method for calculating the slope safety factor based on stochastic search theory according to claim 1, characterized in that, In S4, one random number is randomly selected from each of the two sets of random numbers generated in S3. The two sets of random numbers are represented as follows: ； Select respectively and When the numbers are two adjacent random numbers, the formula used for the bivariate function transformation in S5 is: ； ； The formula used for linear transformation in S6 is: ； ； in, The result of the bivariate function transformation ; The result of the bivariate function transformation ; , The dip angle and trace length of the first fracture; , The dip angle and trace length of the second fracture; , These are the standard deviation and mean of the tilt angle, respectively. , These are the standard deviation and mean of the trace length, respectively.

5. The method for calculating the slope safety factor based on stochastic search theory according to claim 1, characterized in that, The safety factor f(s) of the polygonal sliding surface calculated in S8 using the rigid body limit equilibrium method includes: First, the slope above the polygonal sliding surface is divided into multiple sliders by vertically cutting upwards according to the inflection point of the slope. The weight of the k-th slider is Wk, and the length of the bottom structural surface of the slider is Lk. The mechanical parameters of the structural surface include cohesion ck and internal friction angle φk. Then, the residual sliding force generated by each slider on the last slider under the safety factor f(s) is calculated. Finally, the limit equilibrium condition of the last slider is used to solve the linear equation with respect to the safety factor f(s).

6. An electronic device, characterized in that, It includes a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, it implements the slope safety factor calculation method based on random search theory as described in any one of claims 1 to 5.

7. A readable storage medium, characterized in that, The readable storage medium stores a computer program, which, when executed by a processor, implements the slope safety factor calculation method based on random search theory as described in any one of claims 1 to 5.

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