CN-115879193-B - Slope safety coefficient calculation method based on random search theory

CN115879193BCN 115879193 BCN115879193 BCN 115879193BCN-115879193-B

Abstract

The invention relates to the field of slope stability analysis, in particular to a slope safety coefficient calculation method based on a random search theory, which searches a broken line sliding surface and realizes safety coefficient calculation based on a distribution function random theory, and mainly comprises the following steps: structural plane distribution function, cracking range division, random number and random variable calculation, structural plane expansion calculation, failure condition, clipping criterion and safety coefficient calculation. The invention fully considers the randomness of structural surface distribution in the complex fractured rock mass, realizes the expansion of the fracture and the generation of the broken line type sliding surface by utilizing a sufficient number of random variables, and is as close to the application of the actual slope engineering as possible.

Inventors

ZHANG ZHANRONG
ZHANG TAO
LIU QIANG
LI WEI
ZHANG LIANGLIANG
GAO YANG
YANG CHUANG
SUN HONGLIN
LI SHILIANG
HUANG GUOLIANG
ZHAO JINQIAN
YUAN CONGJUN
LIU HUAJI
YANG HUIJIAN

Assignees

中铁第四勘察设计院集团有限公司

Dates

Publication Date: 20260505
Application Date: 20221116

Claims (7)

1. The slope safety coefficient calculation method based on the random search theory is characterized by comprising the following steps of: S1, respectively obtaining nonstandard normal distribution functions of a structural plane inclination angle theta and a trace length L; s2, arbitrarily designating a cracking section with the length L 0 at the top of the slope, equally dividing the cracking section into m sections, taking m=aL 0 /λ L , wherein a is more than or equal to 2, Forming m+1 initiation points M i on the initiation section, i=0, 1,2, M, as the mean of the trace length L; S3, selecting a starting point M i on the jack-up cracking section of the slope, starting i=0, and generating 2 groups of random numbers of uniformly distributed U (0, 1) with the number of p multiplied by p; S4, selecting one random number from 2 random numbers generated in S3 L=1, 2,..p, starting l=1, p numbers per set of random numbers, wherein { v l } is a first set of random numbers } { u l } is a second set of random numbers; S5, respectively taking The random variable θ' k 、L' k , k=1, 2,..p, starting k=1; S6, respectively carrying out linear transformation on the two random variables theta' k 、L' k obtained in the S5 to obtain theta k 、L k , namely the dip angle and the trace length of the kth crack, and calculating the coordinates of the tip of the kth crack; S7, judging whether the coordinates of the tip of the kth crack meet the failure condition, if so, l=l+1 and returning to the step S4, and if not, executing the next step; S8, judging whether the coordinates of the tip of the kth crack meet a cutting criterion, if not, k=k+1 and returning to S5, if so, forming 1 broken line type sliding surface according to the obtained k random crack dip angles and trace lengths, and calculating the safety coefficient fs of the obtained broken line type sliding surface; S9, judging whether l is more than or equal to p is met, if yes, obtaining safety coefficients fs (1), fs (2), fs (l), fs (p) of the p folding line type sliding surfaces, executing the next step, otherwise, carrying out l=l+1, and returning to execute S4; S10, screening the minimum values of the safety coefficients Fs (1), fs (2), fs (l), fs (p) and recording as Fs (i); S11, judging whether i is equal to or greater than m is met, if so, obtaining safety coefficients Fs (0), fs (1), fs (2), fs (i), fs (m) corresponding to m+1 starting points respectively, executing the next step, otherwise, i=i+1, and returning to execute S3; S12, screening safety factors Fs (0), fs (1), fs (2), fs (i), fs (m) and marking the minimum value of the safety factors Fs (0), fs (1), fs (2), fs (i) and Fs (m) as FS, namely the overall safety factor of the side slope, wherein a broken line type sliding surface corresponding to the FS is the most dangerous sliding surface; wherein, the formula for calculating the tip coordinates of the kth slot in S6 is: ; wherein, theta q 、L q is the inclination angle and trace length of the q-th crack respectively; wherein, the failure condition of the kth crack tip coordinate in S7 is: ; Wherein, (x n ,y n ) is the bottom point coordinate of the slope temporary sliding surface; The clipping criterion in S8 is: ; wherein (x j-1 ,y j-1 ）、（x j ,y j ) is the coordinates of the slope turning point on the slope critical sliding surface.
2. The slope safety coefficient calculation method based on the random search theory according to claim 1, wherein the nonstandard normal distribution functions of the structural surface inclination angle θ and the trace length L are respectively: ; ; Wherein, the 、 The standard deviation and the average value of the inclination angle are respectively, 、 Standard deviation and mean of trace lengths, respectively.
3. The slope safety coefficient calculation method based on the random search theory according to claim 1, wherein p in S3 is expressed as: ; wherein b is greater than or equal to 4 and b is an even number, Is the average value of the trace length, The average slope length of the slope is (x 1 ,y 1 ) the top point coordinate of the slope critical sliding surface, and the bottom point coordinate of the slope critical sliding surface is (x n ,y n ).
4. The slope safety coefficient calculation method based on the random search theory according to claim 1, wherein in S4, each of the 2 sets of random numbers generated in S3 is selected from one set of random numbers, and the two selected sets of random numbers are expressed as: ; respectively select And When two adjacent random numbers are used, the binary function transformation in S5 adopts the following formula: ; ; the linear transformation in S6 adopts the following formula: ; ; Wherein, the Transformed for binary function ; Transformed for binary function ; 、 The dip angle and trace length of the 1 st crack; 、 Inclination angle and trace length of the 2 nd crack; 、 the standard deviation and the average value of the inclination angle are respectively, 、 Standard deviation and mean of trace lengths, respectively.
5. The slope safety coefficient calculation method based on the random search theory according to claim 1, wherein the safety coefficient f (S) of the broken line type sliding surface is calculated in S8 by using a rigid body limit balance method, and the rigid body limit balance method comprises: Firstly dividing a slope above a broken line type sliding surface into a plurality of sliding blocks according to vertical upward segmentation of a slope inflection point, wherein the weight of a kth sliding block is Wk, the length of a structural surface at the bottom of the sliding block is Lk, mechanical parameters of the structural surface comprise cohesive force ck and an internal friction angle phi k, then calculating the residual sliding force of each sliding block on the last sliding block under a safety coefficient f(s), and finally solving a primary equation about the safety coefficient f(s) by utilizing the limit balance condition of the last sliding block.
6. An electronic device comprising a processor and a memory, the memory having stored thereon a computer program which, when executed by the processor, implements the random search theory based slope safety factor calculation method of any of claims 1 to 5.
7. A readable storage medium, wherein a computer program is stored in the readable storage medium, and when the computer program is executed by a processor, the method for calculating a slope safety coefficient based on the random search theory according to any one of claims 1 to 5 is implemented.

Description

Slope safety coefficient calculation method based on random search theory Technical Field The invention relates to the field of slope stability analysis, in particular to a slope safety coefficient calculation method based on a random search theory. Background Rock slopes are usually broken along fracture surfaces, sliding surfaces of the rock slopes are generally broken line-type sliding surfaces, and the arc-shaped sliding analysis method for the soil slopes is not suitable for stability analysis of complex rock slopes. The rock slope widely develops a large number of structural surfaces, the structural surface grades are also different, accurate values are usually easy to obtain for faults, rock stratum layers and fracture zones, and for III and IV structural surfaces, the structural surfaces are spread in rock mass and are influenced by manpower, material resources, financial resources and the like, the difficulty of large-scale detailed deterministic investigation on the structural surfaces is high, and how to determine a broken folded line type sliding surface of the rock slope by using a small amount of structural surface information of field outcrop investigation, unmanned aerial vehicle oblique photography investigation, drilling and footrill investigation is still an important difficulty in geotechnical engineering. For broken line type sliding, at present, a broken line type sliding surface is manually specified through crack combination, so that the stability coefficient of the broken line type sliding surface is calculated, and the method cannot determine whether the specified sliding surface is the most unfavorable sliding surface or not, and automatic searching cannot be realized, so that the method for analyzing the stability of the side slope is gradually accepted by students at home and abroad through reasonably displaying the uncertainty of geometric parameters of a rock mass structural surface and probability distribution of the geometric parameters. At present, the research direction is mainly focused on the condition of considering structural plane geometric parameter variability and probability statistical models, a rock mass fracture network is generated by utilizing Monte Carlo (MCS), bayesian statistics, a computer simulation method and the like, stability analysis is further carried out based on reliability theory and the like, and a method for searching a broken line type sliding surface and calculating a safety coefficient of the broken line type sliding surface by utilizing random variable calculation based on a probability distribution model of the structural plane geometric parameters of the rock mass is still to be further researched. Disclosure of Invention In order to overcome the defects of the background technology, the invention provides a slope safety coefficient calculation method based on a random search theory, which fully considers the randomness of structural surface distribution in complex fractured rock mass, and utilizes a sufficient number of random variables to realize the expansion of the fracture and the generation of a broken line type sliding surface, so as to be as close to the application of actual slope engineering as possible. The invention provides a slope safety coefficient calculation method based on a random search theory, which comprises the following steps: S1, respectively obtaining nonstandard normal distribution functions of a structural plane inclination angle theta and a trace length L; s2, a cracking section with the length L0 is arbitrarily designated at the top of a slope, the cracking section is equally divided into M sections, m=aL 0/λL is taken, wherein a is more than or equal to 2, lambda L is the average value of trace length L, and m+1 cracking points M i, i=0, 1,2 are formed on the cracking section; S3, selecting a starting point M i on the jack-up cracking section of the slope, starting i=0, and generating 2 groups of random numbers with the number p multiplied by p and uniformly distributed N (0, 1); S4, selecting a set of random numbers { v l }, { ul }, i=1, 2, & gt, I, & gt, p, starting i=1, each set of random numbers being p; s5, respectively taking two adjacent random numbers in { v l}、{ul } and utilizing a binary function to transform to obtain a random variable theta' k、L′k, wherein k=1, 2, & gt, k, & gt, p, and starting k=1; S6, respectively carrying out linear transformation on the two random variables theta' k、L′k obtained in the S5 to obtain theta k、Lk, namely the dip angle and the trace length of the kth crack, and calculating the coordinates of the tip of the kth crack; S7, judging whether the coordinates of the tip of the kth crack meet the failure condition, if so, I=l+1 and returning to the step S4, and if not, executing the next step; s8, judging whether the coordinates of the tip of the kth crack meet a cutting criterion, if not, k=k+1 and returning to S5, if so, forming 1 broken line type sliding surface accord