Shear strength parameter design point iteration method based on imprecise search

Abstract

The invention relates to the field of geotechnical engineering reliability design, and particularly discloses a shear strength parameter design point iteration method based on imprecise search, and the method comprises the following steps: building an expression of a safety coefficient of a double-slip-surface rock slope; constructing an expression of a performance function of the double-slip-surface rock slope; determining probability distribution information of shear strength parameters; converting the shear strength parameter into an independent standard normal random variable; iteratively solving a shear strength parameter design point; and calculating the failure probability of the double-slip-surface rock slope. According to the method, the actual requirements of slope engineering design are closely met, more reliable technical support is provided for designers, the key effect is achieved in safety evaluation and stable operation of geotechnical engineering, the safety and economical efficiency of engineering are protected, and contribution is made to disaster prevention and reduction work of slopes.

Description

Technical Field

[0001] The present application relates to the field of geotechnical engineering reliability design, and in particular to a shear strength parameter design point iteration method based on non-exact search. Background Art

[0002] As a frequent type of natural disaster, landslides pose a serious challenge to the safety of life and property of human society. Their sudden outbreak mode and strong destructive power highlight the importance of in-depth analysis and accurate risk assessment of slope stability. In recent decades, thanks to the rapid development of engineering technology and the continuous deepening of scientific research, treating shear strength parameters as random variables and using advanced probability statistics theory and methods to quantitatively evaluate slope stability have become widely adopted and highly recognized scientific practices in the industry. However, despite the remarkable progress made in the field of probabilistic slope stability assessment, researchers still face many challenges in their long-term practical exploration, which is mainly due to the extreme complexity and diversity of factors covered by the slope stability assessment system, including the great differences in geological structures, the ever-changing climate conditions, and the profound impact of human activities on the slope environment. The interweaving and joint action of these factors make the slope stability assessment process full of uncertainty and challenges, requiring researchers to continuously innovate ideas and optimize methods to develop more efficient, accurate and adaptable probabilistic assessment procedures.

[0003] In recent years, the innovative integration of Copula theory and first-order reliability method has attracted wide attention and in-depth research in the field of geotechnical engineering reliability design. Copula theory, with its unique advantages, has been widely used to construct accurate models of complex multidimensional joint distribution functions between random variables. This theory can decompose the multidimensional joint distribution function into a series of independent marginal distribution functions and a core Copula function, thereby achieving an intuitive characterization and quantification of the correlation between random variables. More importantly, different types of Copula functions carry different correlation structural characteristics, providing a rich selection space for analyzing the correlation between random variables in different scenarios. At the same time, the first-order reliability method has become a powerful tool for dealing with the reliability assessment of nonlinear functional functions due to its high efficiency and practicality. This method uses the first-order approximation of the functional function near the design point to transform the originally cumbersome nonlinear functional function into a more concise and intuitive linear expression, which greatly simplifies the calculation process of reliability assessment, reduces the calculation cost, and maintains a high assessment accuracy. Combining the Copula theory with the first-order reliability method breaks through the limitations of traditional reliability analysis methods, especially showing excellent performance in dealing with non-Gaussian correlation problems between parameters such as shear strength. This technical innovation not only fully considers the complex and changeable nonlinear relationship between variables, but also realizes the rapid and accurate evaluation of the reliability of geotechnical structures through efficient algorithm design.

[0004] However, when dealing with complex scenarios with multivariable and highly nonlinear functional functions, a problem that cannot be ignored is the potential instability of the design point iteration process, which is manifested in a significant slowdown in convergence speed, and even divergence in some cases, causing the iteration process to fall into a periodic oscillation or chaotic state of solution concentration. Such problems have greatly restricted the widespread application and in-depth development of the first-order reliability method based on Copula theory in the field of geotechnical engineering reliability analysis, making this method face severe challenges between accuracy and practicality. In view of this, the field of geotechnical engineering urgently needs a new method for iterating the design point of shear strength parameters that is both robust and efficient. This method aims to effectively overcome the convergence problems existing in the existing iteration process through innovative algorithm design, ensure the stable and rapid convergence of the design point in the multidimensional nonlinear space, and thus significantly improve the accuracy and efficiency of reliability assessment. Summary of the invention

[0005] In view of the deficiencies of the prior art, the present application provides a shear strength parameter design point iteration method based on non-exact search.

[0006] The present application provides a shear strength parameter design point iteration method based on non-exact search, which adopts the following technical solution: A shear strength parameter design point iteration method based on non-exact search includes the following steps: According to the parameters of the double sliding surface rock slope, a safety factor expression of the double sliding surface rock slope is established; the double sliding surface rock slope includes sliding surface 1 and sliding surface 2; According to the safety factor of the double sliding surface rock slope, the functional expression of the double sliding surface rock slope is constructed; Determine the probability distribution information of shear strength parameters; Transform shear strength parameters into independent standard normal random variables; Iteratively solve the design points of independent standard normal random variables and obtain the design points of shear strength parameters; The failure probability of a rock slope with two sliding surfaces is calculated based on the design points of independent standard normal random variables.

[0007] Furthermore, the functional function of the double sliding surface rock slope G The expression is: , where FS is the safety factor of the double sliding surface rock slope.

[0008] Furthermore, the shear strength parameter Including the cohesion on the sliding surface 1 c 1 and friction coefficient f 1, and the cohesion on the sliding surface 2 c 2 and friction coefficient f 2, , where the superscript T is the transpose of the vector.

[0009] Furthermore, the probability distribution information of the shear strength parameter includes: Cohesion on sliding surface 1 c Cumulative distribution function of 1 F 11 ( c 1); Friction coefficient on sliding surface 1 f Cumulative distribution function of 1 F 12 ( f 1); Cohesion on sliding surface 2 c Cumulative distribution function of 1 F 21 ( c 2); Friction coefficient on sliding surface 2 f Cumulative distribution function of 2 F 22 ( f 2); Cohesion on sliding surface 1 c1 and friction coefficient f Copula function between 1 C 1( F 11 ( c 1), F 12 ( f 1); i 1); Cohesion on sliding surface 2 c 2 and friction coefficient f Copula function between 2 C 2( F 21 ( c 2), F 22 ( f 2); i 2); in i 1 is the first Copula parameter, which is the cohesion on sliding surface 1. c 1 and friction coefficient f Kendall rank correlation coefficient between 1 t 1. Obtained by reverse solution; i 2 is the second Copula parameter, which is calculated by the cohesion on sliding surface 2. c 2 and friction coefficient f Kendall rank correlation coefficient between 2 t 2 Obtained by inverse solution.

[0010] Furthermore, the method of converting the shear strength parameter into an independent standard normal random variable includes: Converting the cohesive force on sliding surface 1 c 1 is the first independent standard normal random variable u 1; Convert the friction coefficient on sliding surface 1 f 1 is the second independent standard normal random variable u 2; Convert the cohesion on sliding surface 2 c 2 is the third independent standard normal random variable u 3; Convert the friction coefficient on sliding surface 2 f 2 is the fourth independent standard normal random variable u 4.

[0011] Furthermore, the method of iteratively solving the design points of independent standard normal random variables and obtaining the design points of shear strength parameters includes: Set the maximum number of iterations N and allowable design point error e; Iteration 1: Set the number of iterations k is 1, and the design point of the independent standard normal random variable of the first iteration is ; No. k Iteration: Calculate the k The function of the iteration and k The gradient of the iteration ,in For the k independent standard normal random variable design points for iterations; No. k +1 iteration: Calculate the k +1 iteration of independent standard normal random variable design points ; The expression is: ; In the formula, is the iteration step length, is the iteration direction, and its expression is: ; Design point error determination: If it satisfies , then let k +1 iteration of independent standard normal random variable design points Design points for independent standard normal random variables , and enter the result conversion step; if it satisfies , then enter the step of determining the number of iterations; where, is the two-norm of the vector, is the absolute value symbol; Iteration number determination: If the iteration number k Greater than or equal to the maximum number of iterations N , then let k +1 iteration of independent standard normal random variable design points Design points for independent standard normal random variables , and enter the result conversion step; if the number of iterations k Less than the maximum number of iterations N , then let the number of iterations k = k +1 and return k Iteration steps; Result transformation: Transform independent standard normal random variable design points is the shear strength parameter design point , ,in is the cohesion design point on sliding surface 1, is the friction coefficient design point on sliding surface 1, is the cohesion design point on sliding surface 2, Design point for the coefficient of friction on sliding surface 2.

[0012] Furthermore, the iteration step length The calculation method is: Set the maximum number of iterations to reduce the step size M ; Calculate target descent D goal , whose expression is: ; In the formula, a is the first inexact search parameter, b is the second inexact search parameter, m To reduce the number of times, is a symbolic function; Calculating True Descent D real , whose expression is: ; Determination of the amount of decline: If the actual amount of decline D real Greater than or equal to the target drop D goal , then let the iteration step length On the contrary, if the actual decrease D real Less than target drop D goal , then enter the reduction number determination step; Reduction times judgment: If the reduction times m Greater than or equal to the maximum number of iterations to reduce the step size M , then let the iteration step length On the contrary, if the number of times is reduced m Less than the maximum number of iteration step reductions M , then reduce the number of m = m +1, and return to the step of calculating the target descent amount.

[0013] Furthermore, the failure probability of the double sliding surface rock slope is P f The expression is: .

[0014] The present application provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, a shear strength parameter design point iteration method based on non-exact search is implemented.

[0015] The present application also provides a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, a shear strength parameter design point iteration method based on inexact search is implemented.

[0016] In summary, the present application includes the following beneficial technical effects: This application aims at the problem of insufficient iterative stability of shear strength parameter design points in slope reliability analysis in geotechnical engineering, and proposes an iterative method for shear strength parameter design points based on non-exact search. Specifically, the expression of the safety factor and the functional function of the double sliding surface rock slope is first constructed, and then the probability distribution information of the shear strength parameter is determined, and then the shear strength parameter is converted into an independent standard normal random variable and the shear strength parameter design point is iteratively solved, and finally the failure probability of the double sliding surface rock slope is calculated. In the process of iteratively solving the shear strength parameter design point, the iteration step is calculated by using the non-exact search theory with low computational cost, which makes the actual descent of the performance function created based on the functional function greater than or equal to the target descent, so that the design point gradually approaches the true solution, effectively overcomes the convergence problem existing in the existing iterative process, and ensures the stable and rapid convergence of the design point in the multi-dimensional nonlinear space, thereby significantly improving the accuracy and efficiency of reliability evaluation. Therefore, this application provides a solid technical support for slope reliability analysis and risk assessment, and contributes to the disaster prevention and mitigation work of slopes. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flow chart of a shear strength parameter design point iteration method based on non-exact search provided in an embodiment of the present application; Figure 2 Schematic diagram of a double sliding surface rock slope in an embodiment of the present application; Figure 3 It is a design point iteration diagram in an embodiment of the present application; Figure 4 is the first independent standard normal random variable in the embodiment of the present application u 1 and a second independent standard normal random variable u 2 design point iteration cloud diagram; Figure 5 is the first independent standard normal random variable in the embodiment of the present application u 1 and a third independent standard normal random variable u 3. Design point iteration cloud diagram; Figure 6is the first independent standard normal random variable in the embodiment of the present application u 1 and the fourth independent standard normal random variable u 4 design point iteration cloud diagram; Figure 7 is the second independent standard normal random variable in the embodiment of the present application u 2 and a third independent standard normal random variable u 3. Design point iteration cloud diagram; Figure 8 is the second independent standard normal random variable in the embodiment of the present application u 2 and a fourth independent standard normal random variable u 4 design point iteration cloud diagram; Figure 9 is the third independent standard normal random variable in the embodiment of the present application u 3 and the fourth independent standard normal random variable u 4 Design point iteration cloud diagram. DETAILED DESCRIPTION

[0018] The following is combined with Figure 1-9 This application is described in further detail.

[0019] The present application embodiment discloses a shear strength parameter design point iteration method based on non-exact search. Figure 1 , the iterative method of shear strength parameter design point based on non-exact search includes the following steps: S100. Based on the parameters of the double sliding surface rock slope, the expression of the safety factor of the double sliding surface rock slope is established as follows: ; In the formula, FS is the safety factor of the double sliding surface rock slope, c 1 is the cohesive force on sliding surface 1, f 1 is the friction coefficient on sliding surface 1, c 2 is the cohesive force on sliding surface 2, f 2 is the friction coefficient on sliding surface 2, α 1 is the inclination angle of sliding surface 1, α 2 is the inclination angle of sliding surface 2, l 1 is the length of sliding surface 1, l 2 is the length of sliding surface 2, G 1 is the weight of slider 1, G 2 is the weight of slider 2.

[0020] In the embodiments of the present application, Figure 2The figure is a schematic diagram of a double-sliding-surface rock slope, in which the rock mass of the slope mainly includes Sinian siliceous dolomite (SLS), red clay layer (SC) and purple-red siliceous rock (SQ). The rock mass of the slope presents a layered structure along the slope and has a group of gently dipping joints along the slope. The average dip is N70°E / SE∠30. It can be seen that the interpenetration of the layers is not very significant. The clay layer and the group of joints may jointly constitute a double-sliding-surface shear failure mode, in which the clay layer serves as the active sliding surface and the joint surface serves as the passive sliding surface. The dip angle of sliding surface 1 is α 1 = 30°, inclination of sliding surface 2 α 2 = 59.133°, the length of sliding surface 1 l 1 = 67.2 m, length of sliding surface 2 l 2 = 96.8 m, the weight of slide 1 G 1 = 46669 kN, the weight of slide 2 G 2 = 34274 kN.

[0021] S200. According to the safety factor of the double sliding surface rock slope, the expression of the functional function of the double sliding surface rock slope is constructed as follows: ; In the formula, G It is the functional function of the double sliding surface rock slope.

[0022] S300, determining probability distribution information of shear strength parameters, the specific steps are: S310, shear strength parameters Including the cohesion on the sliding surface 1 c 1. Friction coefficient on sliding surface 1 f 1. Cohesion on sliding surface 2 c 2. Friction coefficient on sliding surface 2 f 2, , where the superscript T is the transpose of the vector.

[0023] S320, the probability distribution information of shear strength parameters includes the cohesion on the sliding surface 1 c Cumulative distribution function of 1 F 11 ( c 1) Friction coefficient on sliding surface 1 f Cumulative distribution function of 1 F 12 ( f 1) Cohesion on sliding surface 2 c Cumulative distribution function of 1 F 21 ( c 2) Friction coefficient on sliding surface 2 fCumulative distribution function of 2 F 22 ( f 2) Cohesion on sliding surface 1 c 1 and friction coefficient f Copula function between 1 C 1( F 11 ( c 1), F 12 ( f 1); i 1) Cohesion on sliding surface 2 c 2 and friction coefficient f Copula function between 2 C 2( F 21 ( c 2), F 22 ( f 2); i 2), where i 1 is the first Copula parameter, i 2 is the second Copula parameter.

[0024] First Copula Parameters i 1Through the cohesive force on the sliding surface 1 c 1 and friction coefficient f Kendall rank correlation coefficient between 1 t 1 is inversely solved and the calculation expression is: ; Second Copula Parameter i 2Through the cohesive force on the sliding surface 2 c 2 and friction coefficient f Kendall rank correlation coefficient between 2 t 2 Inverse solution is obtained, and the calculation expression is: .

[0025] In the embodiment of the present application, the statistical information of the shear strength parameters is shown in Table 1. The cohesion on the sliding surface 1 c Cumulative distribution function of 1 F 11 ( c 1) Friction coefficient on sliding surface 1 f Cumulative distribution function of 1 F 12 ( f 1) Cohesion on sliding surface 2 c Cumulative distribution function of 1 F21 ( c 2) Friction coefficient on sliding surface 2 f Cumulative distribution function of 2 F 22 ( f 2) Can be uniquely determined by statistical information.

[0026] Table 1 Statistical information of shear strength parameters

[0027] Cohesion on sliding surface 1 c 1 and friction coefficient f Copula function between 1 C 1( F 11 ( c 1), F 12 ( f 1); i 1) Considering the No.16 Copula function, the cohesion on sliding surface 1 c 1 and friction coefficient f Kendall rank correlation coefficient between 1 t 1=-0.3, so the first Copula parameter i 1= 0.0413.

[0028] Cohesion on sliding surface 2 c 2 and friction coefficient f Copula function between 2 C 2( F 21 ( c 2), F 22 ( f 2); i 2) Considering the Frank Copula function, the cohesion on the sliding surface 2 is c 2 and friction coefficient f Kendall rank correlation coefficient between 2 t 2=-0.5, so the second Copula parameter i 2 = -7.9296.

[0029] S400, convert the shear strength parameters into independent standard normal random variables, the specific steps are: First, convert the cohesive force on sliding surface 1 c 1 is the first independent standard normal random variable u 1, its calculation expression is: ; In the formula, is the inverse function of the standard normal distribution function; Then, convert the friction coefficient on sliding surface 1 f 1 is the second independent standard normal random variable u 2, its calculation expression is: ; In the formula, h 1( F 11 ( c 1), F 12 ( f 1); i 1) is the first conditional Copula function, and its expression is: ; Next, the cohesive force on the sliding surface 2 is converted c 2 is the third independent standard normal random variable u 3, its calculation expression is: ; Finally, convert the friction coefficient on sliding surface 2 f 2 is the fourth independent standard normal random variable u 4, its calculation expression is: ; In the formula, h 2( F 21 ( c 2), F 22 ( f 2); i 2) is the second conditional Copula function, and its expression is: .

[0030] S500, iteratively solving the independent standard normal random variable design point, and obtaining the shear strength parameter design point, the specific steps are: S510, set the maximum number of iterations N and allowable design point error Yes.

[0031] S520, 1st iteration: set the number of iterations k = 1, the design point of the independent standard normal random variable of the first iteration , ,in u 1 1is the design point of the first independent standard normal random variable for iteration 1, u 2 1 Design points for the second independent standard normal random variable for iteration 1, u 3 1 is the design point of the third independent standard normal random variable for iteration 1, u 4 1 Design points for the fourth independent standard normal random variable for iteration 1.

[0032] S530, No. k Iteration: Calculate the k The function of the iteration and k The gradient of the iteration ,in For the k independent standard normal random variable design points for iterations, ,in u 1 k For the k The first independent standard normal random variable design point of the iteration, u 2 k For the k The second independent standard normal random variable design point for iterations, u 3 k For the k The third independent standard normal random variable design point for the iteration, u 4 k For the k The fourth independent standard normal random variable design point for iteration .

[0033] S540, No. k +1 iteration: Calculate the k +1 iteration of independent standard normal random variable design points , ,in u 1 k+1 For the k +1 iteration of the first independent standard normal random variable design point, u 2 k+1 For the k +1 second independent standard normal random variable design point for iteration, u 3 k+1 For the k +1 iteration of the third independent standard normal random variable design point, u 4 k+1 For the k +1 iteration of the fourth independent standard normal random variable design point, The expression is: ; In the formula, is the iteration step length, is the iteration direction, and its expression is: .

[0034] Iteration step The calculation method is: S541, set the maximum number of times the iterative step size is reduced M ; S542, calculate the target descent amount D goal , whose expression is: ; In the formula, a is the first inexact search parameter, b is the second inexact search parameter, m To reduce the number of times, is the two-norm of the vector, is a symbolic function; S543, calculate the actual descent D real , whose expression is: ; In the formula, is the absolute value symbol; S544, descent amount determination: If the actual descent amount D real Greater than or equal to the target drop D goal , then let the iteration step length On the contrary, if the actual decrease D real Less than target drop D goal , then proceed to step S545; S545, reduction times determination: if the reduction times m Greater than or equal to the maximum number of iterations to reduce the step size M , then let the iteration step length On the contrary, if the number of times is reduced m Less than the maximum number of iteration step reductions M , then reduce the number of m = m +1, and return to step S542.

[0035] S550, Design point error judgment: If it satisfies , then let k+1 iteration of independent standard normal random variable design points Design points for independent standard normal random variables , ,in Design point for the first independent standard normal random variable, Design points for a second independent standard normal random variable, Design points for the third independent standard normal random variable, Design point for the fourth independent standard normal random variable and proceed to step S570; otherwise, if , then go to step S560.

[0036] S560, iterative number determination: If the number of iterations k Greater than or equal to the maximum number of iterations N , then let k +1 iteration of independent standard normal random variable design points Design points for independent standard normal random variables , and proceed to step S570; otherwise, if the number of iterations is k Less than the maximum number of iterations N , then let the number of iterations k = k +1, and return to step S530.

[0037] S570, Result transformation: Transform independent standard normal random variable design points is the shear strength parameter design point , ; in is the cohesion design point on sliding surface 1, and its expression is: ; In the formula, is the cohesive force on sliding surface 1 c The inverse of the cumulative distribution function of 1, is the standard normal distribution function; is the friction coefficient design point on sliding surface 1, and its expression is: ; In the formula, is the inverse function of the first conditional Copula function, is the friction coefficient on sliding surface 1 f The inverse of the cumulative distribution function of 1; is the cohesion design point on sliding surface 2, and its expression is: ; In the formula, is the cohesive force on sliding surface 2 c The inverse of the cumulative distribution function of 2; is the design point of the friction coefficient on sliding surface 2, and its expression is: ; In the formula, is the inverse function of the second conditional Copula function, is the friction coefficient on sliding surface 2 f The inverse of the cumulative distribution function of 2.

[0038] In the embodiment of the present application, the maximum number of iterations N = 50, allowable design point error e = 0.001, the maximum number of iterations to reduce the step size M = 5, the first inexact search parameter a = 0.25, the second inexact search parameter b = 0.5, design point iteration diagram see Figure 3 , the first independent standard normal random variable u 1 and a second independent standard normal random variable u The design point iteration cloud diagram of 2 is shown in Figure 4 , the first independent standard normal random variable u 1 and a third independent standard normal random variable u The design point iteration cloud diagram of 3 is shown in Figure 5 , the first independent standard normal random variable u 1 and the fourth independent standard normal random variable u The design point iteration cloud diagram of 4 is shown in Figure 6 , the second independent standard normal random variable u 2 and a third independent standard normal random variable u The design point iteration cloud diagram of 3 is shown in Figure 7 , the second independent standard normal random variable u 2 and a fourth independent standard normal random variable u The design point iteration cloud diagram of 4 is shown in Figure 8 , a third independent standard normal random variable u 3 and the fourth independent standard normal random variable u The design point iteration cloud diagram of 4 is shown in Figure 9 , independent standard normal random variable design points = [-2.4235 -0.7752 -0.0509 -0.0147] T , shear strength parameter design point = [106.18 0.680 38.67 0.277] T .

[0039] S600, calculate the failure probability of a double sliding surface rock slope based on the design points of independent standard normal random variables; Failure probability of rock slope with double sliding surfaces P f The expression is: .

[0040] In the embodiment of the present application, the failure probability of the double sliding surface rock slope is P f = 5.464 × 10 -3 .

[0041] It can be seen that the iterative method of shear strength parameter design point based on non-precise search of the present invention converges to the correct design point on the limit state curve after 8 iterations. This process shows good stability and efficiency when facing extremely complex and highly nonlinear functional function challenges, reflecting the excellent advantages and strong adaptability of non-precise search theory in iterative algorithms. The present invention closely meets the core requirements of slope engineering design and provides a more solid and reliable technical solution, which not only significantly improves the design accuracy and efficiency, but also further enhances the scientificity and credibility of design decisions. At the same time, the present invention builds a double guarantee for the safety and economy of engineering projects in the wide field of geotechnical engineering, especially in safety assessment and long-term stable operation and maintenance, effectively reduces potential risks and costs, and improves the sustainability and environmental friendliness of the overall project. For the disaster prevention and mitigation work of slope engineering, the present invention provides strong technical support for preventing geological disasters and reducing disaster losses through precise design and evaluation.

[0042] On the other hand, the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the above-mentioned iterative method for shear strength parameter design points based on inexact search is implemented.

[0043] The present invention also provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the above-mentioned shear strength parameter design point iteration method based on inexact search is implemented.

[0044] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A shear strength parameter design point iteration method based on non-exact search, characterized by: The following steps are involved: According to the parameters of the double sliding surface rock slope, the safety factor expression of the double sliding surface rock slope is established; The double sliding surface rock slope includes sliding surface 1 and sliding surface 2; According to the safety factor of the double sliding surface rock slope, the functional expression of the double sliding surface rock slope is constructed; Determine the probability distribution information of shear strength parameters; Transform shear strength parameters into independent standard normal random variables; Iteratively solve the design points of independent standard normal random variables and obtain the design points of shear strength parameters; The failure probability of a rock slope with two sliding surfaces is calculated based on the design points of independent standard normal random variables.

2. The method for iterating shear strength parameter design points based on inexact search according to claim 1, characterized in that: The functional function of the double sliding surface rock slope G The expression is: , where FS is the safety factor of the double sliding surface rock slope.

3. The method for iterative design point of shear strength parameters based on non-exact search according to claim 1, characterized in that: The shear strength parameter Including the cohesion on the sliding surface 1 c 1 and friction coefficient f 1, and the cohesion on the sliding surface 2 c 2 and friction coefficient f 2, , where the superscript T is the transpose of the vector.

4. The shear strength parameter design point iteration method based on non-exact search according to claim 3 is characterized in that: The probability distribution information of the shear strength parameter includes: Cohesion on sliding surface 1 c Cumulative distribution function of 1 F 11 ( c 1); Friction coefficient on sliding surface 1 f Cumulative distribution function of 1 F 12 ( f 1); Cohesion on sliding surface 2 c Cumulative distribution function of 1 F 21 ( c 2); Friction coefficient on sliding surface 2 f Cumulative distribution function of 2 F 22 ( f 2); Cohesion on sliding surface 1 c 1 and friction coefficient f Copula function between 1 C 1( F 11 ( c 1), F 12 ( f 1); θ 1); Cohesion on sliding surface 2 c 2 and friction coefficient f Copula function between 2 C 2( F 21 ( c 2), F 22 ( f 2); θ 2); in θ 1 is the first Copula parameter, which is the cohesion on sliding surface 1. c 1 and friction coefficient f Kendall rank correlation coefficient between 1 τ 1. Obtained by reverse solution; θ 2 is the second Copula parameter, which is calculated by the cohesion on sliding surface 2. c 2 and friction coefficient f Kendall rank correlation coefficient between 2 τ 2 Obtained by inverse solution.

5. The shear strength parameter design point iteration method based on non-exact search according to claim 4 is characterized in that: Methods for transforming shear strength parameters into independent standard normal random variables include: Converting the cohesive force on sliding surface 1 c 1 is the first independent standard normal random variable u 1; Convert the coefficient of friction on sliding surface 1 f 1 is the second independent standard normal random variable u 2; Converting the cohesive force on sliding surface 2 c 2 is the third independent standard normal random variable u 3; Convert the friction coefficient on sliding surface 2 f 2 is the fourth independent standard normal random variable u 4.

6. The shear strength parameter design point iteration method based on non-exact search according to claim 1, characterized in that: The method of iteratively solving the design points of independent standard normal random variables and obtaining the design points of shear strength parameters includes: Set the maximum number of iterations N and allowable design point error ε; Iteration 1: Set the number of iterations k is 1, and the design point of the independent standard normal random variable of the first iteration is ; No. k Iteration: Calculate the k The function of the iteration and k The gradient of the iteration ,in For the k independent standard normal random variable design points for iterations; No. k +1 iteration: Calculate the k +1 iteration of independent standard normal random variable design points ; The expression is: ； In the formula, is the iteration step length, is the iteration direction, and its expression is: ； Design point error determination: If it satisfies , then let k +1 iteration of independent standard normal random variable design points Design points for independent standard normal random variables , and enter the result conversion step; if it satisfies , then enter the step of determining the number of iterations; where, is the bi-norm of the vector, is the absolute value symbol; Iteration number determination: If the iteration number k Greater than or equal to the maximum number of iterations N , then let k +1 iteration of independent standard normal random variable design points Design points for independent standard normal random variables , and enter the result conversion step; if the number of iterations k Less than the maximum number of iterations N , then let the number of iterations k = k +1 and return k Iteration steps; Result transformation: Transform independent standard normal random variable design points is the shear strength parameter design point , ,in is the cohesion design point on sliding surface 1, is the friction coefficient design point on sliding surface 1, is the cohesion design point on sliding surface 2, Design point for the coefficient of friction on sliding surface 2.

7. The method for iterating shear strength parameter design points based on non-exact search according to claim 6, characterized in that: The iteration step size The calculation method is: Set the maximum number of iterations to reduce the step size M ; Calculate target descent D goal , whose expression is: ； In the formula, a is the first inexact search parameter, b is the second inexact search parameter, m To reduce the number of times, is a symbolic function; Calculating True Descent D real , whose expression is: ； decline Quantity determination: If the actual drop D real Greater than or equal to the target drop D goal , then let the iteration step length ; On the contrary, if the actual decline D real Less than target drop D goal , then enter the reduction number determination step; Reduction times judgment: If the reduction times m Greater than or equal to the maximum number of iterations to reduce the step size M , then let the iteration step length ; On the contrary, if the number of times is reduced m Less than the maximum number of iteration step reductions M , then reduce the number of m = m +1, and return to the step of calculating the target descent amount.

8. The shear strength parameter design point iteration method based on non-exact search according to claim 7, characterized in that: The failure probability of the double sliding surface rock slope P f The expression is: 。 9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the iterative method for shear strength parameter design points based on non-exact search as described in any one of claims 1 to 8 is implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for iterating shear strength parameter design points based on non-exact search as described in any one of claims 1 to 8 is implemented.

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