Iterative method for design points of shear strength parameters based on inexact search

Abstract

This application relates to the field of geotechnical engineering reliability design and specifically discloses an iterative method for shear strength parameter design points based on non-exact search, which includes the following steps: establishing an expression for the safety factor of a double-sliding-surface rock slope; constructing an expression for the functional function of a double-sliding-surface rock slope; determining the probability distribution information of the shear strength parameter; converting the shear strength parameter into an independent standard normal random variable; iteratively solving the shear strength parameter design point; and calculating the failure probability of the double-sliding-surface rock slope. This application not only closely meets the actual needs of slope engineering design and provides designers with more reliable technical support, but also strives to play a key role in the safety assessment and stable operation of geotechnical engineering, safeguarding the safety and economy of the project, and contributing to slope disaster prevention and mitigation.

Description

Technical Field

[0001] This application relates to the field of reliability design in geotechnical engineering, and in particular to an iterative method for designing shear strength parameters based on inaccurate search. Background Technology

[0002] Landslides, as a frequent type of natural disaster, pose a significant and serious challenge to the safety of life and property in human society. Their sudden onset and powerful destructive force 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 probabilistic statistical theories and methods to quantitatively assess slope stability has become a widely adopted and highly recognized scientific practice in the industry. However, despite remarkable progress in the field of probabilistic slope stability assessment, researchers still face numerous challenges in their long-term practical exploration. This is mainly due to the extreme complexity and diversity of factors encompassed by the slope stability assessment system, including the vast differences in geological structures, the rapid changes in climate conditions, and the profound impact of human activities on the slope environment. The interplay and interaction of these factors make the slope stability assessment process full of uncertainty and challenges, requiring researchers to continuously innovate their thinking and optimize their 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 methods has attracted widespread attention and in-depth research in the field of reliability design in geotechnical engineering. Copula theory, with its unique advantages, has been widely used to construct accurate models of complex multidimensional joint distribution functions among 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 each carry different correlation structure characteristics, providing a rich selection space for analyzing the correlation between random variables in different scenarios. Meanwhile, the first-order reliability method, with its efficiency and practicality, has become a powerful tool for handling the reliability assessment problem of nonlinear function performance. This method utilizes the first-order approximation of the function performance near the design point, transforming the originally computationally cumbersome nonlinear function performance into a more concise and intuitive linear expression, greatly simplifying the reliability assessment calculation process, reducing computational costs, and maintaining high assessment accuracy. By combining Copula theory with first-order reliability methods, this approach overcomes the limitations of traditional reliability analysis methods, demonstrating superior performance, particularly in handling non-Gaussian correlations between parameters such as shear strength. This technological innovation not only fully considers the complex and variable nonlinear relationships between variables but also achieves rapid and accurate assessment of the reliability of geotechnical structures through efficient algorithm design.

[0004] However, when dealing with complex scenarios involving multivariable and highly nonlinear functional functions, a significant challenge lies in the potential instability of the design point iteration process. This manifests as a significantly slower convergence rate, and in some cases, even divergence, leading the iteration process into periodic oscillations or chaotic solution sets. Such problems severely restrict the widespread application and in-depth development of first-order reliability methods based on Copula theory in geotechnical engineering reliability analysis, posing a serious challenge to the balance between accuracy and practicality. Therefore, the geotechnical engineering field urgently needs a new design point iteration method for shear strength parameters that combines robustness and efficiency. This method aims to effectively overcome the convergence difficulties in existing iteration processes through innovative algorithm design, ensuring stable and rapid convergence of the design point in a multidimensional nonlinear space, thereby significantly improving the accuracy and efficiency of reliability assessment. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this application provides an iterative method for designing shear strength parameters based on inaccurate search.

[0006] This application provides an iterative method for designing shear strength parameters based on inaccurate search, which employs the following technical solution:

[0007] An iterative method for designing shear strength parameters based on inexact search includes the following steps:

[0008] Based on the parameters of the double-slip surface rock slope, an expression for the safety factor of the double-slip surface rock slope is established; the double-slip surface rock slope includes sliding surface 1 and sliding surface 2.

[0009] Based on the safety factor of the double-slip surface rock slope, construct the functional expression of the double-slip surface rock slope;

[0010] Determine the probability distribution information of shear strength parameters;

[0011] Transform the shear strength parameters into independent standard normal random variables;

[0012] The design points of independent standard normal random variables are solved iteratively, and the design points of shear strength parameters are obtained.

[0013] The failure probability of a double-slip surface rock slope is calculated based on the design points of independent standard normal random variables.

[0014] Furthermore, the functional function of the double-slip surface rock slope G The expression is: In the formula, FS The safety factor is the factor for a double-slip surface rock slope.

[0015] Furthermore, the shear strength parameter Including the cohesion on sliding surface 1 c 1 and coefficient of friction f 1, and the cohesion on the sliding surface 2. c 2 and coefficient of friction f 2, , where the superscript T is the transpose of the vector.

[0016] Furthermore, the probability distribution information of the shear strength parameters includes:

[0017] Cohesion on sliding surface 1 c Cumulative distribution function of 1 F 11 ( c 1);

[0018] coefficient of friction on sliding surface 1 f Cumulative distribution function of 1 F 12 ( f 1);

[0019] Cohesion on sliding surface 2 c Cumulative distribution function of 1 F 21 ( c 2);

[0020] coefficient of friction on sliding surface 2 f Cumulative distribution function of 2 F 22 ( f 2);

[0021] Cohesion on sliding surface 1 c 1 and coefficient of friction f Copula functions between 1 C 1( F 11 ( c 1), F 12 ( f 1); i 1);

[0022] Cohesion on sliding surface 2 c 2 and coefficient of friction f Copula functions between 2 C 2( F 21 ( c 2), F 22 ( f 2); i 2);

[0023] in i 1 is the first Copula parameter, determined by the cohesion on sliding surface 1. c 1 and coefficient of friction f Kendall rank correlation coefficient between 1 and 1 t 1. Obtained by inverse solution; i 2 is the second Copula parameter, determined by the cohesion on sliding surface 2. c 2 and coefficient of friction f Kendall rank correlation coefficient between 2 t 2. Obtained by inverse solution.

[0024] Furthermore, methods for converting shear strength parameters into independent standard normal random variables include:

[0025] Conversion of cohesion on sliding surface 1 c 1 is the first independent standard normal random variable u 1;

[0026] Convert the coefficient of friction on sliding surface 1 f 1 is the second independent standard normal random variable u 2;

[0027] Conversion of cohesion on sliding surface 2 c2 is the third independent standard normal random variable u 3;

[0028] Convert the coefficient of friction on sliding surface 2 f 2 is the fourth independent standard normal random variable u 4.

[0029] Furthermore, methods for iteratively solving for the design points of independent standard normal random variables and obtaining the design points of shear strength parameters include:

[0030] Set the maximum number of iterations. N and allowable design point error e;

[0031] First iteration: Set the number of iterations. k The design point for the independent standard normal random variable in the first iteration is 1. ;

[0032] No. k The iteration: calculate the... k The function of the next iteration and the k gradient of the next iteration ,in For the first k Design points for independent standard normal random variables in each iteration;

[0033] No. k +1 iteration: Calculate the... k +1 iterations of independent standard normal random variable design points ; The expression is:

[0034] ;

[0035] In the formula, The iteration step size, For the iteration direction, its expression is:

[0036] ;

[0037] Design point error judgment: If the following conditions are met... Then let the first k +1 iterations of independent standard normal random variable design points Design points for independent standard normal random variables And proceed to the result transformation step; if the conditions are met... Then proceed to the iteration count determination step; where, Let L be the L2 norm of the vector. It is the absolute value symbol;

[0038] Iteration count determination: If the iteration count is... k Greater than or equal to the highest number of iterations N Then let the first k +1 iterations of independent standard normal random variable design points Design points for independent standard normal random variables Then proceed to the result transformation step; if the number of iterations... k Less than the highest number of iterations N Then let the number of iterations be... k = k +1, and return the first k The next iteration step;

[0039] Result Transformation: Transform the design points of independent standard normal random variables Design point for shear strength parameters , ,in The design point for cohesion on sliding surface 1. Design point for the friction coefficient on sliding surface 1, The design point for cohesion on sliding surface 2. The design point for the friction coefficient on sliding surface 2.

[0040] Furthermore, the iteration step size The calculation method is as follows:

[0041] Set the maximum number of iteration step size reductions. M ;

[0042] Calculate the target descent amount D goal Its expression is:

[0043] ;

[0044] In the formula, a For the first non-exact search parameter, b For the second non-exact search parameter, m To reduce the number of times, It is a symbolic function;

[0045] Calculate the actual decrease D real Its expression is:

[0046] ;

[0047] Determination of the amount of decline: If the actual amount of decline D real Greater than or equal to the target descent amount D goal Then let the iteration step size Conversely, if the actual decrease is... D real Less than the target descent amount D goal If so, proceed to the step of determining the number of reductions;

[0048] Reduction Count Determination: If the number of reductions is... m Greater than or equal to the maximum number of iterations to reduce the step size M Then let the iteration step size Conversely, if the number of times is reduced... m The maximum number of iterations smaller than the iteration step size reduction M Then reduce the number of times. m = m +1, and return to the step of calculating the target descent.

[0049] Furthermore, the failure probability of the aforementioned double-slip surface rock slope P f The expression is:

[0050] .

[0051] This application 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, it implements an iterative method for designing shear strength parameters based on inaccurate search.

[0052] This application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements an iterative method for designing shear strength parameters based on inaccurate search.

[0053] In summary, this application includes the following beneficial technical effects:

[0054] This application addresses the problem of insufficient iterative stability of shear strength parameter design points in slope reliability analysis in geotechnical engineering. It proposes an iterative method for shear strength parameter design points based on inexact search. Specifically, it first constructs expressions for the safety factor and function of a double-slip surface rock slope, then determines the probability distribution information of the shear strength parameters, converts the shear strength parameters into independent standard normal random variables, and iteratively solves for the design points of the shear strength parameters. Finally, it calculates the failure probability of the double-slip surface rock slope. During the iterative solution of the shear strength parameter design points, a low-computational-cost inexact search theory is used to calculate the iteration step size. This ensures that the actual decrease in the performance function created based on the function is greater than or equal to the target decrease, thus allowing the design points to gradually approach the true solution. This effectively overcomes the convergence problem existing in current iterative processes, ensuring stable and rapid convergence of the design points in multidimensional nonlinear space, thereby significantly improving the accuracy and efficiency of reliability assessment. Therefore, this application provides solid technical support for slope reliability analysis and risk assessment, contributing to slope disaster prevention and mitigation. Attached Figure Description

[0055] Figure 1 This is a flowchart of an iterative method for designing shear strength parameters based on inaccurate search, provided in an embodiment of this application.

[0056] Figure 2 This is a schematic diagram of a double-slip surface rock slope in an embodiment of this application;

[0057] Figure 3 This is the design point iteration diagram in the embodiments of this application;

[0058] Figure 4 It is the first independent standard normal random variable in the embodiments of this application. u 1 and the second independent standard normal random variable u Design point iteration cloud diagram 2;

[0059] Figure 5 It is the first independent standard normal random variable in the embodiments of this application. u 1 and the third independent standard normal random variable u Design point iteration cloud diagram 3;

[0060] Figure 6 It is the first independent standard normal random variable in the embodiments of this application. u 1 and the fourth independent standard normal random variable u 4. Iterative cloud diagram of design points;

[0061] Figure 7 It is the second independent standard normal random variable in the embodiments of this application. u 2 and the third independent standard normal random variable uDesign point iteration cloud diagram 3;

[0062] Figure 8 It is the second independent standard normal random variable in the embodiments of this application. u 2 and the fourth independent standard normal random variable u 4. Iterative cloud diagram of design points;

[0063] Figure 9 It is the third independent standard normal random variable in the embodiments of this application. u 3 and the fourth independent standard normal random variable u Design point iteration cloud map 4. Detailed Implementation

[0064] The following is combined with Figure 1-9 This application is described in further detail.

[0065] This application discloses an iterative method for designing shear strength parameters based on inaccurate search. (Refer to...) Figure 1 The iterative method for designing shear strength parameters based on inaccurate search includes the following steps:

[0066] S100. Based on the parameters of the double-slip surface rock slope, the expression for the safety factor of the double-slip surface rock slope is established as follows:

[0067] ;

[0068] In the formula, FS The safety factor for a double-slip surface rock slope. c 1 represents the cohesive force on sliding surface 1. f 1 represents the coefficient of friction on sliding surface 1. c 2 represents the cohesion on sliding surface 2. f 2 represents the coefficient of friction on sliding surface 2. α 1 represents the inclination angle of sliding surface 1. α 2 is the inclination angle of sliding surface 2. l 1 represents the length of sliding surface 1. l 2 is the length of sliding surface 2. G 1 represents the weight of slider 1. G 2 represents the weight of slider 2.

[0069] In the embodiments of this application, Figure 2This is a schematic diagram of a double-slip surface rock slope. The rock mass of the slope mainly consists of Sinian siliceous dolomite (SLS), red clay layer (SC), and purplish-red siliceous rock (SQ). The rock mass of this slope exhibits a downslope layered structure and has developed a set of gently dipping joints occurring downslope, with an average dip of N70°E / SE∠30. It can be seen that the bedding planes are not very interconnected. The clay rock bedding plane and this set of joints may together constitute a double-slip surface shear failure mode, in which the clay rock bedding plane acts as the active slip surface, while the joint plane acts as the passive slip surface. The dip angle of slip surface 1 is... α 1 = 30°, the inclination angle of sliding surface 2 α 2 = 59.133°, the length of sliding surface 1 l 1 = 67.2 m, the length of sliding surface 2 l 2 = 96.8 m, weight of slider 1 G =1 = 46669 kN, the weight of slider 2 G 2 = 34274 kN.

[0070] S200. Based on the safety factor of the double-slip surface rock slope, the expression for the function of the double-slip surface rock slope is constructed as follows:

[0071] ;

[0072] In the formula, G This is a function for a double-slip surface rock slope.

[0073] S300. Determine the probability distribution information of shear strength parameters. The specific steps are as follows:

[0074] S310, shear strength parameters Including the cohesion on sliding surface 1 c 1. Coefficient of friction on sliding surface 1 f 1. Cohesion on sliding surface 2 c 2. Coefficient of friction on sliding surface 2 f 2, , where the superscript T is the transpose of the vector.

[0075] S320, the probability distribution information of shear strength parameters includes the cohesion on sliding surface 1. c Cumulative distribution function of 1 F 11 ( c 1) Coefficient of friction 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) Coefficient of friction on sliding surface 2 f Cumulative distribution function of 2 F 22 ( f 2) Cohesion on sliding surface 1 c 1 and coefficient of friction f Copula functions between 1 C 1( F 11 ( c 1), F 12 ( f 1); i 1) Cohesion on sliding surface 2 c 2 and coefficient of friction f Copula functions between 2 C 2( F 21 ( c 2), F 22 ( f 2); i 2), of which i 1 represents the first Copula parameter. i 2 is the second Copula parameter.

[0076] First Copula parameter i 1. Through the cohesive force on sliding surface 1 c 1 and coefficient of friction f Kendall rank correlation coefficient between 1 and 1 t 1. Obtained by inverse solution, the calculation expression is:

[0077] ;

[0078] The second Copula parameter i 2. Through the cohesion on the sliding surface 2 c 2 and coefficient of friction f Kendall rank correlation coefficient between 2 t 2. Obtained by inverse solution, the calculation expression is:

[0079] .

[0080] In this embodiment, the statistical information of shear strength parameters is shown in Table 1, and the cohesion on the sliding surface 1 is... c Cumulative distribution function of 1 F 11 ( c 1) Coefficient of friction on sliding surface 1 f Cumulative distribution function of 1 F12 ( f 1) Cohesion on sliding surface 2 c Cumulative distribution function of 1 F 21 ( c 2) Coefficient of friction on sliding surface 2 f Cumulative distribution function of 2 F 22 ( f 2) It can be uniquely determined by statistical information.

[0081] Table 1 Statistical information on shear strength parameters

[0082]

[0083] Cohesion on sliding surface 1 c 1 and coefficient of friction f Copula functions 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 coefficient of friction f Kendall rank correlation coefficient between 1 and 1 t 1 = -0.3, therefore, the first Copula parameter i 1 = 0.0413.

[0084] Cohesion on sliding surface 2 c 2 and coefficient of friction f Copula functions between 2 C 2( F 21 ( c 2), F 22 ( f 2); i 2) Consider the Frank Copula function, the cohesion on sliding surface 2 c 2 and coefficient of friction f Kendall rank correlation coefficient between 2 t 2 = -0.5, therefore, the second Copula parameter i 2 = -7.9296.

[0085] S400, the shear strength parameters are converted into independent standard normal random variables. The specific steps are as follows:

[0086] First, the cohesion on sliding surface 1 is converted. c 1 is the first independent standard normal random variable u 1. Its calculation expression is:

[0087] ;

[0088] In the formula, It is the inverse function of the standard normal distribution function;

[0089] Then, the coefficient of friction on sliding surface 1 is converted. f 1 is the second independent standard normal random variable u 2, its calculation expression is:

[0090] ;

[0091] In the formula, h 1( F 11 ( c 1), F 12 ( f 1); i 1) is the first conditional Copula function, whose expression is:

[0092] ;

[0093] Next, the cohesion on sliding surface 2 is converted. c 2 is the third independent standard normal random variable u 3, its calculation expression is:

[0094] ;

[0095] Finally, the coefficient of friction on sliding surface 2 is converted. f 2 is the fourth independent standard normal random variable u 4. Its calculation expression is:

[0096] ;

[0097] In the formula, h 2( F 21 ( c 2), F 22 ( f 2); i 2) The second conditional Copula function has the following expression:

[0098] .

[0099] S500, iteratively solve for the design points of independent standard normal random variables and obtain the design points of shear strength parameters. The specific steps are as follows:

[0100] S510, Set the maximum number of iterations N and allowable design point error Yes.

[0101] S520, First Iteration: Set the number of iterations k The design point of the independent standard normal random variable in the first iteration is 1. , ,in u 1 1 Design point for the first independent standard normal random variable in the first iteration. u 2 1 The design point is the second independent standard normal random variable in the first iteration. u 3 1 The design point is the third independent standard normal random variable in the first iteration. u 4 1 The design point is the fourth independent standard normal random variable in the first iteration.

[0102] S530, No. k The iteration: calculate the... k The function of the next iteration and the k gradient of the next iteration ,in For the first k Design points for independent standard normal random variables in the next iteration. ,in u 1 k For the first k The first independent standard normal random variable design point in the next iteration. u 2 k For the first k The design point of the second independent standard normal random variable in the next iteration. u 3 k For the first k The third independent standard normal random variable design point in the next iteration. u 4 k For the first k The fourth independent standard normal random variable design point in the next iteration.

[0103] S540, No. k +1 iteration: Calculate the... k +1 iterations of independent standard normal random variable design points , ,inu 1 k+1 For the first k The design point of the first independent standard normal random variable in +1 iterations u 2 k+1 For the first k The design point of the second independent standard normal random variable in the +1 iteration. u 3 k+1 For the first k The design point of the third independent standard normal random variable in +1 iterations. u 4 k+1 For the first k The design point of the fourth independent standard normal random variable in the +1 iteration. The expression is:

[0104] ;

[0105] In the formula, The iteration step size, For the iteration direction, its expression is:

[0106] .

[0107] Iteration step size The calculation method is as follows:

[0108] S541. Set the maximum number of iteration step size reductions. M ;

[0109] S542. Calculate the target descent amount D goal Its expression is:

[0110] ;

[0111] In the formula, a For the first non-exact search parameter, b For the second non-exact search parameter, m To reduce the number of times, Let L be the L2 norm of the vector. It is a symbolic function;

[0112] S543, Calculate the actual decrease D real Its expression is:

[0113] ;

[0114] In the formula, It is the absolute value symbol;

[0115] S544. Determination of Decline Amount: If the actual decline amount... Dreal Greater than or equal to the target descent amount D goal Then let the iteration step size Conversely, if the actual decrease is... D real Less than the target descent amount D goal Then proceed to step S545;

[0116] S545, Reduction Count Determination: If the reduction count... m Greater than or equal to the maximum number of iterations to reduce the step size M Then let the iteration step size Conversely, if the number of times is reduced... m The maximum number of iterations smaller than the iteration step size reduction M Then reduce the number of times. m = m +1, and return to step S542.

[0117] S550, Design Point Error Judgment: If the following conditions are met... Then let the first k +1 iterations of independent standard normal random variable design points Design points for independent standard normal random variables , ,in Design points for the first independent standard normal random variable. Design points for the second independent standard normal random variable. Design points for the third independent standard normal random variable. Design points for the fourth independent standard normal random variable and proceed to step S570; otherwise, if the following conditions are met... Then proceed to step S560.

[0118] S560. Iteration Count Determination: If the iteration count... k Greater than or equal to the highest number of iterations N Then let the first k +1 iterations 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 highest number of iterations N Then let the number of iterations be... k = k +1, and return to step S530.

[0119] S570, Result Transformation: Transforming the Design Point of Independent Standard Normal Random Variables Design point for shear strength parameters , ;

[0120] in The cohesion design point on sliding surface 1 is expressed as follows:

[0121] ;

[0122] In the formula, Cohesion on sliding surface 1 c The inverse function of the cumulative distribution function of 1, It is the standard normal distribution function;

[0123] The design point for the friction coefficient on sliding surface 1 is expressed as follows:

[0124] ;

[0125] In the formula, It is the inverse function of the first conditional Copula function. The coefficient of friction on sliding surface 1 f The inverse function of the cumulative distribution function of 1;

[0126] The cohesion design point on sliding surface 2 is expressed as follows:

[0127] ;

[0128] In the formula, Cohesion on sliding surface 2 c The inverse function of the cumulative distribution function of 2;

[0129] The design point for the friction coefficient on sliding surface 2 is expressed as follows:

[0130] ;

[0131] In the formula, It is the inverse function of the second conditional Copula function. The coefficient of friction on sliding surface 2 f The inverse function of the cumulative distribution function of 2.

[0132] In this embodiment of the application, the highest 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 non-exact search parameter a = 0.25, the second non-exact search parameter b= 0.5, see the design point iteration diagram. Figure 3 The first independent standard normal random variable u 1 and the second independent standard normal random variable u See the design point iteration cloud diagram for point 2. Figure 4 The first independent standard normal random variable u 1 and the third independent standard normal random variable u See the design point iteration cloud diagram for point 3. Figure 5 The first independent standard normal random variable u 1 and the fourth independent standard normal random variable u See the design point iteration cloud diagram for step 4. Figure 6 The second independent standard normal random variable u 2 and the third independent standard normal random variable u See the design point iteration cloud diagram for point 3. Figure 7 The second independent standard normal random variable u 2 and the fourth independent standard normal random variable u The design point iteration cloud diagram for step 4 is shown below. Figure 8 The third independent standard normal random variable u 3 and the fourth independent standard normal random variable u The design point iteration cloud diagram for step 4 is shown below. Figure 9 Design points for independent standard normal random variables = [-2.4235 -0.7752 -0.0509 -0.0147] T Design points for shear strength parameters = [106.18 0.680 38.67 0.277] T .

[0133] S600. Based on the design points of independent standard normal random variables, calculate the failure probability of a double-slip surface rock slope.

[0134] Failure probability of double-slip surface rock slope P f The expression is:

[0135] .

[0136] In the embodiments of this application, the failure probability of a double-slip surface rock slope P f = 5.464×10 -3 .

[0137] As can be seen, the iterative method for designing shear strength parameters based on inexact search in this invention converges to the correct design point on the limit state curve after 8 iterations. This process demonstrates good stability and efficiency when facing extremely complex and highly nonlinear functional challenges, reflecting the superior advantages and strong adaptability of inexact search theory in iterative algorithms. This invention closely aligns with the core needs of slope engineering design, providing a more robust and reliable technical solution. It not only significantly improves design accuracy and efficiency but also further enhances the scientific rigor and credibility of design decisions. Simultaneously, in a wide range of geotechnical engineering fields, particularly in safety assessment and long-term stable operation and maintenance, this invention provides dual protection for the safety and economy of engineering projects, effectively reducing potential risks and costs, and improving the overall sustainability and environmental friendliness of the project. For disaster prevention and mitigation in slope engineering, this invention provides strong technical support for preventing geological disasters and mitigating disaster losses through precise design and assessment.

[0138] 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, it implements the above-described iterative method for designing shear strength parameters based on inaccurate search.

[0139] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described iterative method for designing shear strength parameters based on inaccurate search.

[0140] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An iterative method for designing shear strength parameters based on inaccurate search, characterized in that: Includes the following steps: Based on the parameters of the double-slip surface rock slope, an expression for the safety factor of the double-slip surface rock slope is established; The double-slip surface rock slope includes sliding surface 1 and sliding surface 2; Based on the safety factor of the double-slip surface rock slope, construct the functional expression of the double-slip surface rock slope; Determine the probability distribution information of shear strength parameters, including the marginal cumulative distribution function of each parameter and the Copula function between parameters within the slip surface; Based on the probability distribution information, the shear strength parameter is transformed into an independent standard normal random variable; The process iteratively solves for the design points of independent standard normal random variables and obtains the design points for shear strength parameters. Specifically, this includes: setting the maximum number of iterations and the allowable design point error; calculating the iteration step size through an inexact search to ensure the actual decrease is greater than or equal to the target decrease; updating the design points of the independent standard normal random variables until convergence; and transforming the converged design points of the independent standard normal random variables. Design point for shear strength parameters ,in Obtained through inverse probability transformation; The failure probability of a double-slip surface rock slope is calculated based on the design points of independent standard normal random variables.

2. The iterative method for designing shear strength parameters based on inaccurate search according to claim 1, characterized in that: The functional function of the double-slip surface rock slope G The expression is: In the formula, FS The safety factor is the factor for a double-slip surface rock slope.

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

4. The iterative method for designing shear strength parameters based on inaccurate search according to claim 3, characterized in that: The probability distribution information of the shear strength parameters includes: Cohesion on sliding surface 1 c Cumulative distribution function of 1 F 11 ( c 1); coefficient of friction 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); coefficient of friction on sliding surface 2 f Cumulative distribution function of 2 F 22 ( f 2); Cohesion on sliding surface 1 c 1 and coefficient of friction f Copula functions between 1 C 1( F 11 ( c 1), F 12 ( f 1); θ 1); Cohesion on sliding surface 2 c 2 and coefficient of friction f Copula functions between 2 C 2( F 21 ( c 2), F 22 ( f 2); θ 2); in θ 1 is the first Copula parameter, determined by the cohesion on sliding surface 1. c 1 and coefficient of friction f Kendall rank correlation coefficient between 1 and 1 τ 1. Obtained by inverse solution; θ 2 is the second Copula parameter, determined by the cohesion on sliding surface 2. c 2 and coefficient of friction f Kendall rank correlation coefficient between 2 τ 2. Obtained by inverse solution.

5. The iterative method for designing shear strength parameters based on inaccurate search according to claim 4, characterized in that: Methods for converting shear strength parameters into independent standard normal random variables include: Conversion of cohesion 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; Conversion of cohesion on sliding surface 2 c 2 is the third independent standard normal random variable u 3; Convert the coefficient of friction on sliding surface 2 f 2 is the fourth independent standard normal random variable u 4.

6. The iterative method for designing shear strength parameters based on inaccurate search according to claim 1, characterized in that: Methods for iteratively solving for the design points of independent standard normal random variables and obtaining the design points of shear strength parameters include: Set the maximum number of iterations. N and allowable design point error ε; First iteration: Set the number of iterations. k The design point for the independent standard normal random variable in the first iteration is 1. ; No. k The iteration: calculate the... k The function of the next iteration Hedi k gradient of the next iteration ,in For the first k Design points for independent standard normal random variables in each iteration; No. k +1 iteration: Calculate the... k +1 iterations of independent standard normal random variable design points ; The expression is: ； Where, The iteration step size, For the iteration direction, its expression is: ； Design point error judgment: If the following conditions are met... Then let the first k +1 iterations of independent standard normal random variable design points Design points for independent standard normal random variables And proceed to the result transformation step; if the conditions are met... Then proceed to the iteration count determination step; where, Let L be the L2 norm of the vector. It is the absolute value symbol; Iteration count determination: If the iteration count k Greater than or equal to the highest number of iterations N Then let the first k +1 iterations of independent standard normal random variable design points Design points for independent standard normal random variables Then proceed to the result transformation step; if the number of iterations... k Less than the highest number of iterations N Then let the number of iterations be... k = k +1, and return the first k The next iteration step; Result Transformation: Transform the design points of independent standard normal random variables Design point for shear strength parameters , ,in The design point for cohesion on sliding surface 1. Design point for the friction coefficient on sliding surface 1, The design point for cohesion on sliding surface 2. The design point for the friction coefficient on sliding surface 2.

7. The iterative method for designing shear strength parameters based on inaccurate search according to claim 6, characterized in that: The iteration step size The calculation method is as follows: Set the maximum number of iteration step size reductions. M ; Calculate the target descent amount D goal , whose expression is: ； Where, a For the first imprecise search parameter, b For the second non-exact search parameter, m To reduce the number of times, It is a symbolic function; Calculate the actual decrease 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 descent amount D goal Then let the iteration step size ,in, b m for b of m The power, where b For the second non-exact search parameter, m To reduce the number of occurrences; conversely, if the actual decrease is... D real Less than the target descent amount D goal If so, proceed to the step of determining the number of reductions; Reduction Count Determination: If the number of reductions is... m Greater than or equal to the maximum number of iterations to reduce the step size M Then let the iteration step size Conversely, if the number of times is reduced... m The maximum number of iterations smaller than the iteration step size reduction M Then reduce the number of times. m = m +1, and return to the step of calculating the target descent.

8. The iterative method for designing shear strength parameters based on inaccurate search according to claim 7, characterized in that: The failure probability of the double-slip surface rock slope P f The expression is: ； in, It is the standard normal distribution function.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, it implements an iterative method for designing shear strength parameters based on inaccurate search as described in any one of claims 1-8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by the processor, it implements the iterative method for designing shear strength parameters based on inaccurate search as described in any one of claims 1-8.

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