A random fuzzy method for slope stability analysis

Abstract

The present invention provides a random fuzzy slope stability analysis method, comprising the following steps: dividing the slope slip surface into a plurality of strips and obtaining the physical and mechanical parameters of each strip, calculating the fuzzy statistical mean and fuzzy statistical variance of each physical and mechanical parameter; calculating the difference between the fuzzy statistical mean and the conventional statistical mean, calculating the difference between the fuzzy statistical variance and the conventional statistical variance, and judging whether the accuracy of the current fuzzy statistical mean and the fuzzy statistical variance both meet the requirements; establishing the fuzzy state equation of the slope; obtaining the slope membership function according to the fuzzy state equation of the slope, and obtaining the fuzzy failure probability of the slope through the slope membership function and the slope state function, and obtaining the slope stability analysis result in combination with the fuzzy reliability calculation of the slope. Beneficial effects of the present invention: fully considering the many randomnesses in the process of slope engineering safety and stability evaluation.

Description

Technical Field

[0001] The invention belongs to the field of disaster prevention and reduction, and in particular relates to a random fuzzy slope stability analysis method. Background Art

[0002] There are a large number of slope projects in various construction, highway, railway, hydropower, mining and other engineering projects. The rock and soil of the slope has been complex and variable in space and time after a long geological period and various internal and external geological effects. Accurately judging the stability state of the slope is a prerequisite for determining the excavation and maintenance plan of the slope and specifying the control measures. It is an important part of the stability analysis of geotechnical engineering slopes.

[0003] In past engineering construction, most of the slope stability analysis was done using traditional reliability theory. With the development of computer technology, the limit equilibrium method has gradually been applied to slope stability analysis. However, the traditional analysis method has the following problems.

[0004] The complexity and heterogeneity of slope soil lead to the uncertainty of the physical and mechanical properties of slope soil. The uncertainty of the slope mainly includes two aspects: fuzziness and randomness. Among them, the main reason for fuzziness is that some things are not given a clear definition or the boundaries between things are unclear, while randomness is caused by the ambiguity of test results due to unclear cause and effect relationships, such as measurement errors.

[0005] In previous slope stability analysis, the randomness and ambiguity of the slope were not fully considered. Generally, the parameters of the rock and soil mass were regarded as a constant for calculation. However, in the long-term geological structure, the mechanical parameters of the rock and soil mass of the slope show obvious randomness at different positions. In fact, extracting a small number of samples and taking the weighted average as the result of the stability calculation of the rock and soil mass parameters is not scientific and accurate enough.

[0006] In actual engineering practice, due to the limitations of funding scale and site conditions, measured slope data are often difficult to meet the requirements of probability statistics. This is also an important reason why some sites cannot be evaluated using traditional evaluation methods.

[0007] Among the traditional slope stability analysis methods, some methods, such as reliability theory, are based on statistical principles and regard soil parameters as a certain distribution state. This makes up for the problem of neglecting the randomness of rock and soil in previous methods to a certain extent. However, it still does not take into account the ambiguity of slope engineering. The ambiguity of slope soil parameters, failure process and external disaster-prone environment leads to inaccurate results obtained by this method.

[0008] In actual engineering practice, the slope conditions faced by engineering designers are becoming increasingly complex, and higher requirements are also placed on the slope stability evaluation method. In the process of investigation, design, management and maintenance of slope projects by engineering designers, on the one hand, they should fully draw on the valuable experience of their predecessors according to the characteristics of different slopes. However, these experiences cannot be expressed through classical mathematical methods to solve uncertainty problems, which is exactly the advantage of fuzzy mathematics. The fuzzy parameters of soil, as the key to judging slope stability, are often estimated by engineers based on experience in actual projects. Summary of the invention

[0009] In view of this, the present invention aims to propose a random fuzzy slope stability analysis method in order to solve at least one of the above-mentioned technical problems.

[0010] To achieve the above object, the technical solution of the present invention is achieved as follows:

[0011] A random fuzzy slope stability analysis method includes the following steps:

[0012] Divide the slope sliding surface into multiple strips and blocks, obtain the physical and mechanical parameters of each strip and block, and calculate the fuzzy statistical mean and fuzzy statistical variance of each physical and mechanical parameter;

[0013] Determine whether the accuracy of the current fuzzy statistical mean and fuzzy statistical variance meets the requirements; if so, establish the fuzzy state equation of the slope; otherwise, re-acquire the physical and mechanical parameters of each strip and perform corresponding calculations;

[0014] The slope membership function is obtained according to the fuzzy state equation of the slope, and the fuzzy failure probability of the slope is obtained through the slope membership function and the slope state function. The slope stability analysis result is obtained by combining the fuzzy reliability calculation of the slope.

[0015] Furthermore, the sample values ​​of the slope rock and soil mass are taken as the domain and the fuzzy subset of the domain is obtained;

[0016] Calculate the sample value of the slope rock and soil mass, build the membership function according to the core point of the fuzzy subset, and calculate the membership degree between each sample value in the domain and the fuzzy subset through the membership function;

[0017] The fuzzy statistical mean value is obtained by iteratively calculating the membership degree in combination with the conventional statistical mean value; wherein the kernel point is the square of the difference between the sample value and the conventional statistical mean value.

[0018] Furthermore, fuzzy variables are obtained based on the sample values ​​of the slope rock and soil mass, and the set of fuzzy variables is used as the domain and the fuzzy subset of the domain is obtained;

[0019] The membership degree between each sample value and the fuzzy subset in the domain is calculated based on the fuzzy variables and the conventional statistical variance;

[0020] The fuzzy statistical variance is obtained by iteratively calculating the membership degree in combination with the conventional statistical variance.

[0021] Furthermore, a fuzzy state equation of the slope is established, the output of which is the difference between the anti-sliding force and the sliding force, and the current state of the slope is determined based on the difference;

[0022] Wherein, the anti-sliding force and the sliding force are both calculated based on the physical and mechanical parameters of the current slope;

[0023] The slopes include arc slopes and broken line slopes, and two different slopes correspond to two different fuzzy state equations.

[0024] Furthermore, if the difference between the anti-sliding force and the sliding force is greater than zero, the current slope is in a safe state;

[0025] If the difference between the anti-sliding force and the sliding force is equal to zero, the current slope is in a limit state;

[0026] If the difference between the anti-sliding force and the sliding force is less than zero, the current slope is in a damaged state.

[0027] Furthermore, the anti-sliding force of the arc-shaped slope is calculated according to the slope angle and safety factor of the slope, and the calculation process of the safety factor is:

[0028] Perform fuzzy processing on the physical and mechanical parameters, initialize the safety factor to a fixed value and obtain the corresponding verification parameters; substitute the verification parameters into the calculation formula of the safety factor to calculate, obtain the new safety factor and determine whether the safety factor meets the engineering requirements;

[0029] If it does not meet the requirements, the new safety factor is used as a fixed value to obtain the verification parameters again and perform iterative calculations until the safety factor meets the engineering requirements; otherwise, the calculation is stopped.

[0030] Furthermore, the fuzzy failure probability of the slope is obtained by calculating the integral value of the product of the slope membership function and the probability density function of the slope state function;

[0031] The construction process of the probability density function is as follows:

[0032] Set the output value of the fuzzy state equation to the output when the slope is in the limit state;

[0033] The average value and standard deviation of the output values ​​are calculated to obtain the average value and standard deviation of the fuzzy state function under the limit state, and the probability density function is constructed based on the average value and standard deviation.

[0034] Compared with the prior art, the random fuzzy slope stability analysis method described in the present invention has the following beneficial effects:

[0035] The random fuzzy theory is introduced into the safety and stability evaluation process of slope engineering, and the many random factors in the safety and stability evaluation process of slope engineering are fully considered. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The accompanying drawings constituting a part of the present invention are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the accompanying drawings:

[0037] Figure 1 The present invention is a flowchart of a random fuzzy slope stability analysis method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0038] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0039] The present invention will be described in detail below with reference to the accompanying drawings and in conjunction with embodiments.

[0040] A random fuzzy slope stability analysis method includes the following steps:

[0041] Step 1: Divide the slope sliding surface into multiple strips and obtain the physical and mechanical parameters of each strip;

[0042] Step 2: Calculate the fuzzy statistical mean and fuzzy statistical variance of each physical and mechanical parameter;

[0043] Step 3: Determine whether the accuracy of the current fuzzy statistical mean and fuzzy statistical variance meets the requirements; if so, establish the fuzzy state equation of the slope; otherwise, re-acquire the physical and mechanical parameters of each strip and perform corresponding calculations;

[0044] Step 4: Obtain the slope membership function according to the fuzzy state equation of the slope;

[0045] Step 5: Obtain the fuzzy failure probability of the slope through the slope membership function and the slope state function;

[0046] Step 6: Combine the fuzzy reliability calculation of the slope to obtain the slope stability analysis result.

[0047] The process of dividing the slope sliding surface into multiple strips in step 1 is as follows:

[0048] The Swedish strip method is used to divide the slope slip surface into multiple strips.

[0049] Physical and mechanical parameters include the deadweight of each bar ,inclination , length of the strip-block slip surface , Cohesion , internal friction angle wait;

[0050] The specific process of calculating the fuzzy statistical average in step 2 is:

[0051] Take samples of slope rock and soil , is the domain, where n is the sample number, For the sample value, get The fuzzy subset of , domain Elements in The membership degree of A is , the membership function is: ;

[0052] in, yes The kernel point of the fuzzy set is expressed as: ;

[0053] in, is the fuzziness weight: ;

[0054] in, and They are The maximum and minimum values ​​in the sample mean can be obtained as follows: m A x i =EXP[ -2 d il d 1max - d 1min ] ;

[0055] The conventional statistical mean of the slope As the initial mean, the new fuzzy statistical mean is obtained by iterating the following formula: : ;

[0056] Among them, the conventional statistical average is: .

[0057] The specific process of calculating the fuzzy statistical variance in step 2 is:

[0058] Let the initial variance of the sample be ,in, is the normal statistical variance of the sample, let Based on the soil sample value The fuzzy variables are ;

[0059] Take the domain ,set up Domain fuzzy subsets on ;

[0060] The membership function form of the standard deviation is: m B x i =EXP[ -2 x i - s 2 2 d 2max - d 2min ] ;

[0061] in, and They are The maximum and minimum values ​​in ;

[0062] The general statistical variance of the slope As the initial variance, the new fuzzy statistical variance is obtained by iterating the following formula: ;

[0063] Among them, the conventional statistical variance is: .

[0064] The specific process of judging whether the accuracy of the current fuzzy statistical mean and fuzzy statistical variance meets the requirements in step 3 is as follows:

[0065] Calculate the average difference between the fuzzy statistical mean and the conventional statistical mean, and calculate the variance difference between the fuzzy statistical variance and the conventional statistical variance. If the average difference and the variance difference are both less than , the accuracy meets the requirements; otherwise, it does not meet the requirements.

[0066] The specific process of establishing the fuzzy state equation of the slope in step 3 is:

[0067] Substitute the fuzzy mean into the state equation of the slope and calculate the limit state function expressed as a safety reserve ;

[0068] in, is a random variable after fuzzy processing, R is the resistance of the structure (i.e., anti-sliding force), and S is the effect of the structure (i.e., sliding force);

[0069] , which is a safe state; , is the limit state; , is a destroyed state.

[0070] For circular slope, the anti-sliding force is: ;

[0071] in, is the fuzzy cohesion of the slope soil, is the length of the soil bottom, is the internal friction angle, The weight of the soil. is the pore water pressure, To verify the parameters: ;in, is the slope angle, is the safety factor of the slope;

[0072] The sliding force is: ;

[0073] Safety factor of slope for: ;

[0074] initialization , substitute the calibration parameters The calculation formula is obtained ,Will Resubstitution The new ;

[0075] The above process is iterated until the safety factor meets the engineering requirements, and the state equation of the circular slope is obtained: - .

[0076] For broken line slopes, the anti-sliding force ;

[0077] in, , is the transfer coefficient when the residual sliding force of the i-th block is transferred to the i+1 block segment, is the slope angle of the i-th broken line segment of the slope, represents the anti-slip force acting on the i-th segment, represents the anti-slip force acting on the nth segment;

[0078] Sliding force ;

[0079] in, represents the sliding force acting on the i-th sliding surface, It represents the sliding force acting on the nth sliding surface, and the state equation of the broken line slope is calculated as:

[0080] - .

[0081] Step 4 The process of obtaining the slope membership function according to the fuzzy state equation of the slope is as follows:

[0082] The following membership function is selected to perform calculation and analysis on the actual project. The membership function of the fuzzy limit state equation is calculated by the following formula:

[0083] ;

[0084] From the above formula, we can know that when hour, , the slope is in a damaged state;

[0085] when hour, , the slope is in a stable state;

[0086] when hour, , the slope is in a fuzzy state;

[0087] When the above membership function is used, the change of the slope from stable state to damaged state corresponds to the change of the membership function from 1 to 0;

[0088] when When it approaches infinity, the anti-sliding force is much greater than the sliding force, and the membership degree of the slope in the destroyed state is 0, and the slope is safe at this time;

[0089] when When it approaches to infinitesimal, the anti-sliding force is much smaller than the sliding force, and the membership degree of the slope in the destroyed state is 1, at which time the slope is very unsafe.

[0090] Step 5 The process of obtaining the fuzzy failure probability of the slope through the slope membership function and the slope state function is:

[0091] In the slope stability analysis, it is assumed that and All obey the normal distribution, so the limit state function Also obeys the normal distribution, the limit state function The average value is: ;

[0092] Limit state function The standard deviation of is: ;

[0093] Limit state function The probability density function of is: ;

[0094] Based on the fuzziness of the slope transition from a stable state to a damaged state, the membership function is introduced. Indicates the state of the slope;

[0095] Get the random fuzzy failure probability of the slope for: .

[0096] Step 6 The process of obtaining the slope stability analysis result by combining the fuzzy reliability calculation of the slope is as follows:

[0097] make , normalize Z, then we have , substitute the random fuzzy failure probability of the slope The following formula can be obtained:

[0098] = ;

[0099] Then we get the fuzzy reliability: ;

[0100] The output calculation results are used as slope stability analysis results.

[0101] Those of ordinary skill in the art will appreciate that the units and method steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the composition and steps of each example have been generally described in terms of function in the above description. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0102] In the several embodiments provided in the present application, it should be understood that the disclosed methods and systems can be implemented in other ways. For example, the division of the units described above is only a logical function division, and there may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. The above-mentioned units may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the embodiments of the present invention.

[0103] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. These modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be included in the scope of the claims and specification of the present invention.

[0104] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A random fuzzy slope stability analysis method, characterized in that: The steps include: Divide the slope sliding surface into multiple strips and blocks, obtain the physical and mechanical parameters of each strip and block, and calculate the fuzzy statistical mean and fuzzy statistical variance of each physical and mechanical parameter; Determine whether the accuracy of the current fuzzy statistical mean and fuzzy statistical variance meets the requirements; if so, establish the fuzzy state equation of the slope; otherwise, re-acquire the physical and mechanical parameters of each strip and perform corresponding calculations; The slope membership function is obtained according to the fuzzy state equation of the slope, and the fuzzy failure probability of the slope is obtained through the slope membership function and the slope state function, and the slope stability analysis result is obtained by combining the fuzzy reliability calculation of the slope; The specific process of calculating the fuzzy statistical average value is as follows: Take the slope rock and soil sample X = {x1(1),x2(2),…,x i (n)}, is the domain, where n is the sample number, x i For the sample value, get the fuzzy subset A of X, the element x in the domain X i For A, the membership degree is μ A (x i ), the membership function is: Among them, D il is x i The kernel point of the fuzzy set is expressed as: Among them, ω i is the fuzziness weight: Among them, d 1max and d 1min They are The maximum and minimum values ​​in the sample mean can be obtained as follows: μ A (x i )=EXP[-2d il / (d 1max -d 1min )]; The conventional statistical mean of the slope As the initial mean, the new fuzzy statistical mean is obtained by iterating the following formula: Among them, the conventional statistical average is: The specific process of calculating the fuzzy statistical variance is as follows: let the initial variance of the sample σ = σ f , where σ f is the conventional statistical variance of the sample, and ξ is based on the soil sample value X = {x1, x2, …, x i }, let Take the domain R = {ξ1, ξ2, ..., ξ n }, let B be a fuzzy subset on the domain R; The membership function form of the standard deviation is: μ B (ξ i )=ECP[-2(ξ i -σ 2 ) 2 / d 2max -d 2min ]; Among them, d 2max and d 2min They are d il =(ξ i -σ 2 ) 2 The maximum and minimum values ​​in ; The conventional statistical variance of the slope σ f As the initial variance, the new fuzzy statistical variance is obtained by iterating the following formula: Among them, the conventional statistical variance is: The specific process of judging whether the accuracy of the current fuzzy statistical mean and fuzzy statistical variance meets the requirements is as follows: Calculate the average difference between the fuzzy statistical mean and the conventional statistical mean, and calculate the variance difference between the fuzzy statistical variance and the conventional statistical variance. If both the average difference and the variance difference are less than ε = 1e -6 , then the accuracy meets the requirements, otherwise it does not meet the requirements; The process of establishing the fuzzy state equation of the slope is as follows: Substitute the fuzzy mean into the state equation of the slope and calculate the limit state function represented by the safety reserve. in, It is a random variable after fuzzy processing, R is the resistance of the structure, that is, the anti-sliding force, and S is the effect of the structure, that is, the sliding force; Z>0, it is a safe state; Z=0, it is a limit state; Z<0, it is a destructive state; For circular slope, the anti-sliding force is: in, is the fuzzy cohesion of the slope soil, l is the length of the bottom surface of the soil, is the internal friction angle, is the soil weight, u i is the pore water pressure, To verify the parameters: in, is the slope angle, F S is the safety factor of the slope; The sliding force is: Safety factor F of the slope S for: Initialize F S =1, substitute the calibration parameters The calculation formula is obtained Will Substitute F again S The new F is obtained from the calculation formula S ; The above process is iterated until the safety factor meets the engineering requirements, and the state equation of the circular slope is obtained: For broken line slopes, the anti-sliding force in, ψ j is the transfer coefficient when the residual sliding force of the i-th block is transferred to the i+1 block segment, θ i is the slope angle of the i-th broken line segment of the slope, R i represents the anti-slip force acting on the i-th segment, R n represents the anti-slip force acting on the nth segment; Sliding force Among them, T i represents the sliding force acting on the i-th sliding surface, T n It represents the sliding force acting on the nth sliding surface, and the state equation of the broken line slope is calculated as:

2. The random fuzzy slope stability analysis method according to claim 1 is characterized by: The sample values ​​of the slope rock and soil mass are taken as the domain and the fuzzy subset of the domain is obtained; Calculate the sample value of the slope rock and soil mass, build the membership function according to the core point of the fuzzy subset, and calculate the membership degree between each sample value in the domain and the fuzzy subset through the membership function; The fuzzy statistical mean value is obtained by iteratively calculating the membership degree in combination with the conventional statistical mean value; wherein the kernel point is the square of the difference between the sample value and the conventional statistical mean value.

3. The random fuzzy slope stability analysis method according to claim 1 is characterized by: Based on the sample value of the slope rock and soil mass, fuzzy variables are obtained, the set of fuzzy variables is used as the domain and the fuzzy subset of the domain is obtained; The membership degree between each sample value and the fuzzy subset in the domain is calculated based on the fuzzy variables and the conventional statistical variance; The fuzzy statistical variance is obtained by iteratively calculating the membership degree in combination with the conventional statistical variance.

4. The random fuzzy slope stability analysis method according to claim 1 is characterized by: Establish the fuzzy state equation of the slope. The output of the fuzzy state equation is the difference between the anti-sliding force and the sliding force. The current state of the slope is determined based on the difference. Wherein, the anti-sliding force and the sliding force are both calculated based on the physical and mechanical parameters of the current slope; The slopes include arc slopes and broken line slopes, and two different slopes correspond to two different fuzzy state equations.

5. A random fuzzy slope stability analysis method according to claim 4, characterized in that: If the difference between the anti-sliding force and the sliding force is greater than zero, the current slope is in a safe state; If the difference between the anti-sliding force and the sliding force is equal to zero, the current slope is in a limit state; If the difference between the anti-sliding force and the sliding force is less than zero, the current slope is in a damaged state.

6. The random fuzzy slope stability analysis method according to claim 4 is characterized by: The anti-sliding force of the arc-shaped slope is calculated according to the slope angle and safety factor of the slope. The calculation process of the safety factor is: Perform fuzzy processing on the physical and mechanical parameters, initialize the safety factor to a fixed value and obtain the corresponding verification parameters; substitute the verification parameters into the calculation formula of the safety factor to calculate, obtain the new safety factor and determine whether the safety factor meets the engineering requirements; If it does not meet the requirements, the new safety factor is used as a fixed value to obtain the verification parameters again and perform iterative calculations until the safety factor meets the engineering requirements; otherwise, the calculation is stopped.

7. The random fuzzy slope stability analysis method according to claim 1 is characterized by: The fuzzy failure probability of the slope is obtained by calculating the integral value of the product of the slope membership function and the probability density function of the slope state function; The construction process of the probability density function is as follows: Set the output value of the fuzzy state equation to the output when the slope is in the limit state; The average value and standard deviation of the output values ​​are calculated to obtain the average value and standard deviation of the fuzzy state function under the limit state, and the probability density function is constructed based on the average value and standard deviation.

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