Geotechnical reliability analysis method, device, electronic equipment, medium and program product

Abstract

The application relates to the technical field of geotechnical analysis, in particular to a geotechnological reliability analysis method and device, an electronic device, a medium and a program product, wherein the method comprises the following steps: establishing a function function of a retaining wall to determine geotechnological parameter and probability distribution information in an uncertain physical space; converting the geotechnological parameter to an independent standard normal space based on the probability distribution information to iteratively calculate a geotechnological parameter design point in the independent standard normal space; converting the geotechnological parameter design point to the uncertain physical space to calculate a reliability index and a failure probability of the retaining wall and generate a geotechnological reliability analysis result. The application can be applied to the calculation of the reliability index and the failure probability of the retaining wall in various scenes, has high flexibility and calculation efficiency, effectively meets the actual needs of geotechnological reliability analysis in different scenes, and provides stronger guarantee for the safe and stable operation of geotechnological structures.

Description

Technical Field

[0001] This application relates to the field of geotechnical analysis technology, and in particular to a geotechnical reliability analysis method, apparatus, electronic equipment, medium, and program product. Background Technology

[0002] In geotechnical engineering, soil and rock parameters generally exhibit complex correlations. For example, there is a common negative correlation between the shear strength index cohesion and the internal friction angle of soil. For reliability analysis and risk assessment in geotechnical engineering, constructing a model that accurately reflects the probabilistic characteristics of soil and rock parameters is crucial. However, the practical challenge lies in the fact that test data or experimental data obtained from geotechnical engineering sites are often very limited. This directly leads to the difficulty in comprehensively establishing a multivariate probability distribution model for soil and rock parameters, i.e., facing the problem of incomplete probabilistic information. Therefore, when conducting engineering reliability analysis, geotechnical engineers must confront the reality of incomplete probabilistic information and instead rely on unilateral probabilistic descriptions of soil and rock parameters and limited knowledge of the correlation coefficients between these parameters to conduct risk assessments.

[0003] In related technologies, many researchers combine Copula theory with Monte Carlo simulation to solve complex geotechnical engineering reliability analysis problems. Research results show that the differences in how different Copula functions characterize the correlation structure between geotechnical parameters directly lead to different distribution patterns of sample points generated under the same failure domain conditions, thus affecting the final reliability assessment results of geotechnical structures. The root cause of this difference lies in the sensitivity of Copula functions to the number of samples within the failure domain and their unique sample generation mechanism. Specifically, some Copula functions may tend to generate samples in the edge regions of the failure domain, while others may more evenly cover the entire failure domain. This uneven distribution of samples directly affects the reliability analysis results. Furthermore, this method gradually reveals its efficiency bottleneck when performing numerical simulations of implicit function (EV) commonly found in practical engineering. Implicit function often involves complex physical processes and computational models, requiring significant computational resources for each simulation. Therefore, with limited computational resources, this method may struggle to efficiently complete geotechnical structure reliability analysis under low failure probability conditions, limiting its widespread application in engineering practice.

[0004] A first-order reliability method based on the first-order Taylor series expansion of the function has attracted considerable attention. This method approximates the complex nonlinear function as a linear function by performing a first-order Taylor series expansion of the function at the design point, thus greatly simplifying the reliability assessment calculation process. This method not only effectively reduces computational costs, making it possible to perform rapid and repeated reliability analyses even with limited resources, but also, through reasonable approximations, often meets the accuracy requirements of engineering practice for reliability assessment while maintaining high precision. Specifically, the first-order reliability method iteratively approximates the true failure probability of the soil structure by iterating through the design points of the soil and rock parameters. In each iteration, the position of the next design point is estimated based on the current computational conditions, the first-order Taylor series expansion of the function is recalculated, and the estimated value of the design point is updated accordingly until the convergence condition is met.

[0005] However, when Copula theory and first-order reliability methods are combined in related technologies, the design point iteration process may converge slowly or even diverge, resulting in low computational efficiency. Furthermore, it can cause the design point to fall into periodic and chaotic solutions, leading to low stability. This severely limits the application of the first-order reliability method based on Copula theory in geotechnical engineering reliability analysis, and urgently needs to be addressed. Summary of the Invention

[0006] This application provides a geotechnical reliability analysis method, apparatus, electronic device, medium, and program product to address the problems in related technologies where the design point iteration process may converge slowly or even diverge when Copula theory and first-order reliability methods are combined, resulting in low computational efficiency and causing the design point to fall into periodic and chaotic solutions with low stability, which seriously limits the application of the first-order reliability method based on Copula theory in geotechnical engineering reliability analysis.

[0007] The first aspect of this application provides a method for geotechnical reliability analysis, comprising the following steps: establishing a function function for a retaining wall to determine the geotechnical parameters and probability distribution information in an uncertain physical space; based on the probability distribution information, transforming the geotechnical parameters into an independent standard normal space to iteratively calculate the design points of the geotechnical parameters in the independent standard normal space; transforming the design points of the geotechnical parameters into the uncertain physical space to calculate the reliability index and failure probability of the retaining wall, and generating the geotechnical reliability analysis results.

[0008] Optionally, in one embodiment of this application, the iterative calculation of the soil and rock mass parameter design points in the independent standard normal space includes: setting the allowable error of the design points and the initial soil and rock mass parameter design points; calculating the function value and gradient of the current iteration based on the initial soil and rock mass parameter design points to calculate the soil and rock mass parameter design points and the quasi-Newton method BFGS matrix for the next iteration; determining whether the iteration converges, wherein if the iteration converges, the soil and rock mass parameter design points within the allowable error range of the design points are obtained based on the soil and rock mass parameter design points and the BFGS matrix for the next iteration.

[0009] Optionally, in one embodiment of this application, the expression of the function may be, but is not limited to, the following:

[0010]

[0011] in, The weight of the triangular region of the retaining wall. The weight of the rectangular region of the retaining wall. Let $\mathbf{ ... Let $\mathbf{ ... For active earth pressure, This is the distance between the active earth pressure and the bottom of the wall.

[0012] Optionally, in one embodiment of this application, the conversion formula for the soil and rock parameters may be, but is not limited to, the following:

[0013]

[0014] in, These are the parameters of the soil and rock mass in an independent standard normal space. , For cohesion in independent standard normal space, Let be the angle of internal friction in an independent standard normal space, with the superscript "T" indicating the transpose of the vector. The inverse function of the standard normal distribution function and This is a conditional Copula function.

[0015] Optionally, in one embodiment of this application, the expression for transforming the design point of the soil and rock mass parameters to the uncertain physical space may be, but is not limited to, the following:

[0016]

[0017] in, For the design points of soil and rock parameters in an uncertain physical space, , Design point for cohesion in physical space. Design point for internal friction angle in physical space. It is the inverse function of the cumulative distribution function of cohesion. It is the inverse function of the cumulative distribution function of the internal friction angle. It is the inverse function of the conditional Copula function. It is the standard normal distribution function.

[0018] A second aspect of this application provides a geotechnical reliability analysis device, comprising: a determination module for establishing a function function of a retaining wall to determine the geotechnical parameters and probability distribution information in an uncertain physical space; a calculation module for converting the geotechnical parameters to an independent standard normal space based on the probability distribution information, and iteratively calculating the design points of the geotechnical parameters in the independent standard normal space; and an analysis module for converting the design points of the geotechnical parameters to the uncertain physical space to calculate the reliability index and failure probability of the retaining wall, and generating the geotechnical reliability analysis results.

[0019] Optionally, in one embodiment of this application, the calculation module includes: a setting unit for setting the allowable error of the design point and the initial design point of the soil and rock mass parameters; a calculation unit for calculating the function value and gradient of the current iteration based on the initial design point of the soil and rock mass parameters, so as to calculate the design point of the soil and rock mass parameters and the quasi-Newton method BFGS matrix for the next iteration; and a judgment unit for judging whether the iteration has converged, wherein if the iteration has converged, the design point of the soil and rock mass parameters within the allowable error range of the design point is obtained based on the design point of the soil and rock mass parameters and the BFGS matrix for the next iteration.

[0020] Optionally, in one embodiment of this application, the expression of the function may be, but is not limited to, the following:

[0021]

[0022] in, The weight of the triangular region of the retaining wall. The weight of the rectangular region of the retaining wall. Let $\mathbf{ ... Let $\mathbf{ ... For active earth pressure, This is the distance between the active earth pressure and the bottom of the wall.

[0023] Optionally, in one embodiment of this application, the conversion formula for the soil and rock parameters may be, but is not limited to, the following:

[0024]

[0025] in, These are the parameters of the soil and rock mass in an independent standard normal space. , For cohesion in independent standard normal space, Let be the angle of internal friction in an independent standard normal space, with the superscript "T" indicating the transpose of the vector. The inverse function of the standard normal distribution function and This is a conditional Copula function.

[0026] Optionally, in one embodiment of this application, the expression for transforming the design point of the soil and rock mass parameters to the uncertain physical space may be, but is not limited to, the following:

[0027]

[0028] in, For the design points of soil and rock parameters in an uncertain physical space, , Design point for cohesion in physical space. Design point for internal friction angle in physical space. It is the inverse function of the cumulative distribution function of cohesion. It is the inverse function of the cumulative distribution function of the internal friction angle. It is the inverse function of the conditional Copula function. It is the standard normal distribution function.

[0029] A third aspect of this application provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the geotechnical reliability analysis method as described in the above embodiments.

[0030] A fourth aspect of this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described geotechnical reliability analysis method.

[0031] A fifth aspect of this application provides a computer program product, including a computer program that, when executed, is used to implement the above-described geotechnical reliability analysis method.

[0032] This application's embodiments can determine the parameters and probability information of soil and rock masses in an uncertain physical space, calculate the design points of soil and rock mass parameters in an independent standard normal space, and transform them back into an uncertain physical space. This yields the reliability index and failure probability of the retaining wall, and ultimately, the reliability analysis results of the soil and rock mass. Therefore, it realizes the analysis of soil and rock reliability based on the iHLRF-BFGS efficient iterative technique, accurately locking the design points of soil and rock mass parameters with only a few iterations. Even when facing highly complex nonlinear functional functions, its iterative process exhibits extremely high stability, effectively improving the stability and computational efficiency of this application. Furthermore, it demonstrates high adaptability to different Copula function selections, exhibiting high practicality and applicability, effectively meeting the needs of soil and rock mass reliability analysis in various scenarios. This solves the problems in related technologies where the combination of Copula theory and first-order reliability methods can result in slow convergence or even divergence in the design point iteration process, low computational efficiency, and the possibility of design points falling into periodic and chaotic solutions, leading to low stability and severely limiting the application of first-order reliability methods based on Copula theory in geotechnical engineering reliability analysis.

[0033] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0034] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0035] Figure 1 This is a flowchart of a geotechnical reliability analysis method provided according to an embodiment of this application;

[0036] Figure 2 This is a schematic diagram of a retaining wall according to one embodiment of this application;

[0037] Figure 3 This is a schematic diagram of the design point iteration cloud of a Gaussian Copula function according to an embodiment of this application;

[0038] Figure 4 This is a schematic diagram of the design point iteration cloud of the Plackett Copula function according to an embodiment of this application;

[0039] Figure 5 This is a schematic diagram of the design point iteration cloud of the Frank Copula function according to an embodiment of this application;

[0040] Figure 6 This is a schematic diagram of the design point iteration cloud of the No.16 Copula function according to an embodiment of this application;

[0041] Figure 7 This is a flowchart of a geotechnical reliability analysis method based on iHLRF-BFGS according to an embodiment of this application;

[0042] Figure 8 This is a schematic diagram of the geotechnical reliability analysis device provided according to an embodiment of this application;

[0043] Figure 9 This is a schematic diagram of the structure of an electronic device provided according to an embodiment of this application.

[0044] Figure label:

[0045] 10-Geotechnical Reliability Analysis Device: 100-Determination Module, 200-Calculation Module and 300-Analysis Module; 901-Memory, 902-Processor and 903-Communication Interface. Detailed Implementation

[0046] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0047] The following description, with reference to the accompanying drawings, outlines a method, apparatus, electronic device, medium, and program product for geotechnical reliability analysis according to embodiments of this application. Addressing the issues mentioned in the background section regarding the slow convergence or even divergence of the design point iteration process when combining Copula theory and first-order reliability methods, resulting in low computational efficiency and the potential for design points to become trapped in periodic and chaotic solutions with low stability, this application severely limits the application of Copula-based first-order reliability methods in geotechnical engineering reliability analysis. This application provides a geotechnical reliability analysis method. In this method, the parameters and probability information of the geotechnical mass in an uncertain physical space can be determined, the design points of the geotechnical mass parameters in an independent standard normal space can be calculated, and the results can be transformed back into the uncertain physical space. This yields the reliability index and failure probability of the retaining wall, ultimately providing the geotechnical reliability analysis results. Therefore, this invention achieves efficient iterative analysis of soil and rock reliability based on iHLRF-BFGS, accurately pinpointing the design points of soil and rock parameters with only a few iterations. Even when facing highly complex nonlinear functional functions, the iterative process exhibits extremely high stability, effectively improving the stability and computational efficiency of this application. Furthermore, it demonstrates high adaptability to different Copula function choices, exhibiting high practicality and applicability, effectively meeting the needs of soil and rock reliability analysis in various scenarios. This solves the problems in related technologies where combining Copula theory and first-order reliability methods can result in slow convergence or even divergence in the design point iteration process, low computational efficiency, and the potential for design points to fall into periodic and chaotic solutions, leading to low stability and severely limiting the application of Copula-based first-order reliability methods in geotechnical engineering reliability analysis.

[0048] Specifically, Figure 1 This is a flowchart of a geotechnical reliability analysis method provided in an embodiment of this application.

[0049] like Figure 1 As shown, the geotechnical reliability analysis method includes the following steps:

[0050] In step S101, a function for the retaining wall is established to determine the soil and rock parameters and probability distribution information in the uncertain physical space. The expression for the function can be, but is not limited to, as follows:

[0051] ,

[0052] in, For the gravity of the triangular region of the retaining wall, The weight of the rectangular area of ​​the retaining wall. Let the moment arm of gravity at the toe of the retaining wall be the moment arm of gravity in the triangular region of the retaining wall. Let the moment arm of gravity at the toe of the retaining wall be the moment arm of gravity in the rectangular region of the retaining wall. For active earth pressure, This is the distance between the active earth pressure and the bottom of the wall.

[0053] It is understandable that the function of a retaining wall can describe its stability state, and retaining walls can be used to support rock and improve its stability. Based on this, in analyzing the reliability of soil and rock in this embodiment, the function of the retaining wall can be established first, and its formula can be, but is not limited to, expressed as:

[0054] ,

[0055] in, This indicates the functional stability of the retaining wall. For the gravity of the triangular region of the retaining wall, The weight of the rectangular area of ​​the retaining wall. Let the moment arm of gravity at the toe of the retaining wall be the moment arm of gravity in the triangular region of the retaining wall. Let the moment arm of gravity at the toe of the retaining wall be the moment arm of gravity in the rectangular region of the retaining wall. For active earth pressure, This is the distance between the active earth pressure and the bottom of the wall.

[0056] Gravity of the triangular region of the retaining wall The formula can be, but is not limited to, expressed as:

[0057] ;

[0058] in, For the heavy-duty retaining wall, Let be the length of the base of the triangular region of the retaining wall. The height of the retaining wall;

[0059] Gravity of the rectangular area of ​​the retaining wall The formula can be, but is not limited to, expressed as:

[0060] ;

[0061] in, This is the length of the bottom side of the rectangular area of ​​the retaining wall;

[0062] The lever arm of the gravity in the triangular region of the retaining wall at the toe of the wall. The formula can be, but is not limited to, expressed as:

[0063] ;

[0064] The lever arm of the gravity of the rectangular area of ​​the retaining wall at the toe of the wall The formula can be, but is not limited to, expressed as:

[0065] ;

[0066] Active earth pressure The formula can be, but is not limited to, expressed as:

[0067] ;

[0068] in, The unit weight of the backfill soil behind the retaining wall. This refers to the cohesion of the backfill soil behind the retaining wall. The internal friction angle of the backfill soil behind the retaining wall;

[0069] Distance between active earth pressure and the bottom of the wall The formula can be, but is not limited to, expressed as:

[0070] .

[0071] Figure 2 This is a schematic diagram of a retaining wall according to one embodiment of this application. Figure 2 As shown, the retaining wall is situated on hard clay, with a smooth, vertical backing. The height of the retaining wall is... =5.5m, the length of the base of the rectangular area of ​​the retaining wall =0.4m, the length of the base of the triangular region of the retaining wall =1.4m, unit weight of retaining wall =24 kN / The unit weight of the backfill soil behind the retaining wall =18kN / .

[0072] After establishing the functional functions of the retaining wall, the embodiments of this application can determine the parameters of the soil and rock mass and their probability distribution information in a physical space with uncertainty.

[0073] Among them, the parameters of the soil and rock mass include, but are not limited to, cohesion. and internal friction angle Probability distribution information includes, but is not limited to, the cumulative distribution function with cohesion. Cumulative distribution function of internal friction angle And the Copula function between cohesion and internal friction angle ,in, The Copula parameter can be obtained through the Kendall rank correlation coefficient between cohesion and internal friction angle. The inverse solution yields a formula that can, but is not limited to, be expressed as:

[0074] .

[0075] Table 1 shows the cohesive strength in one embodiment of this application. and internal friction angle Statistical information table, cumulative distribution function of cohesion The cumulative distribution function of the internal friction angle It can be uniquely determined by statistical information. Table 1 can be represented as follows:

[0076] Table 1

[0077]

[0078] In this application embodiment, four calculation conditions can be considered, namely the Copula function between cohesion and internal friction angle. Four calculation scenarios can be considered: Gaussian Copula function, Plackett Copula function, Frank Copula function, and No. 16 Copula function. The Kendall rank correlation coefficient between cohesion and internal friction angle can be, but is not limited to, taking [variable name missing]. .

[0079] After Kendall's rank correlation coefficient The inverse solution, the formula for the Gaussian Copula function, can be expressed, but is not limited to, as:

[0080] ,

[0081] in, Used to simplify representation , Used to simplify representation The Copula parameter can be taken as follows: ;

[0082] The formula for the Plackett Copula function can be, but is not limited to, expressed as:

[0083] ,

[0084] in, Used to simplify representation , Used to simplify representation The Copula parameter can be taken as follows: θ =0.0877;

[0085] The formula for the Frank Copula function can be, but is not limited to, expressed as:

[0086] ,

[0087] in, Used to simplify representation , Used to simplify representation The Copula parameter can be taken as follows: θ = -5.7363;

[0088] The formula for Copula function No. 16 can be, but is not limited to, expressed as:

[0089] ,

[0090] in, Used to simplify representation , Used to simplify representation The Copula parameter can be taken as follows: θ =0.0145.

[0091] The embodiments of this application are highly adaptable to different Copula functions, can be applied to different structures, are extremely flexible, and can meet the analysis needs of geotechnical reliability in various scenarios.

[0092] Step S102: Based on the probability distribution information, the soil and rock mass parameters are transformed into an independent standard normal space to iteratively calculate the design points of the soil and rock mass parameters in the independent standard normal space. The transformation formula for the soil and rock mass parameters can be, but is not limited to, expressed as:

[0093] ,

[0094] in, These are the parameters of the soil and rock mass in an independent standard normal space. , For cohesion in independent standard normal space, Let be the angle of internal friction in an independent standard normal space, with the superscript "T" indicating the transpose of the vector. The inverse function of the standard normal distribution function and This is a conditional Copula function.

[0095] After obtaining the soil and rock mass parameters and their probability distribution information in a physical space with uncertainty, the embodiments of this application can then transform the soil and rock mass parameters into an independent standard normal space in order to iteratively calculate the design points of the soil and rock mass parameters in the independent standard normal space.

[0096] First, to transform the parameters of soil and rock masses in a physical space with uncertainty to an independent standard normal space, the transformation formula can be expressed, but is not limited to, as follows:

[0097] ,

[0098] in, u These are the parameters of the soil and rock mass in an independent standard normal space. , For cohesion in independent standard normal space, Let be the angle of internal friction in an independent standard normal space, with the superscript "T" indicating the transpose of the vector. The inverse function of the standard normal distribution function and For a conditional Copula function, its formula can be, but is not limited to, expressed as:

[0099] .

[0100] The process of iteratively calculating the design points of soil and rock parameters in the independent standard normal space will be explained next.

[0101] Optionally, in one embodiment of this application, calculating the design points of soil and rock mass parameters in the independent standard normal space includes: setting the allowable error of the design points and the initial design points of soil and rock mass parameters; calculating the function value and gradient of the current iteration based on the initial design points of soil and rock mass parameters to calculate the design points of soil and rock mass parameters and the quasi-Newton BFGS matrix for the next iteration; determining whether the iteration has converged, wherein if the iteration has converged, the design points of soil and rock mass parameters within the allowable error range of the design points are obtained based on the design points of soil and rock mass parameters and the quasi-Newton BFGS matrix for the next iteration.

[0102] In other embodiments, after transforming the soil and rock parameters in the uncertain physical space to an independent standard normal space, this application can iteratively calculate the design points of the soil and rock parameters in the independent standard normal space. The specific steps can be expressed as follows:

[0103] (1) First, set the allowable error of the design point. ε ;

[0104] (2) Next, set the number of iterations. k The value is 1, which represents the initial soil and rock parameter design point for the first iteration. , ,in The cohesion design point for the first iteration. The design point for the internal friction angle in the first iteration and the BFGS matrix in the first iteration. = [1 0; 0 1];

[0105] (3) Calculate the first The function value of the next iteration and the k gradient of the next iteration ,in For the first Design points for soil and rock parameters in the next iteration , For the first The cohesion design point of the next iteration and For the first The design point for the internal friction angle in the next iteration;

[0106] (4) Calculate the first Design points for soil and rock parameters in the next iteration Its formula can be, but is not limited to, expressed as:

[0107] ;

[0108] in, This refers to the iteration step size used in calculations based on the Armijo criterion. For the direction of iteration, its formula can be, but is not limited to, expressed as:

[0109] ;

[0110] (5) Calculation BFGS matrix of the next iteration Its formula can be, but is not limited to, expressed as:

[0111] ;

[0112] in, For the iterative increment of the design point, , The iterative increment of the Lagrange function gradient can be expressed, but is not limited to, as follows:

[0113] ;

[0114] in, The iterative increment of the uncorrected Lagrange function gradient can be expressed, but is not limited to, as:

[0115] ;

[0116] in, As a correction factor, its formula can be, but is not limited to, expressed as:

[0117] ;

[0118] (6) The convergence criterion can be expressed as, but is not limited to, the following formula:

[0119] ;

[0120] If the convergence criterion is satisfied and the error is within the allowable error of the design point, then let the first... Design points for soil and rock parameters in the next iteration Design points for soil and rock parameters in independent standard normal space , ,in, The cohesion design point in the independent standard normal space. Let be the design point of the internal friction angle in the independent standard normal space; conversely, if the convergence criterion is not satisfied, then let the number of iterations be... Then return to step (3).

[0121] For example, in the embodiments of this application, an allowable design point error can be established. ; Figure 3 This is a schematic diagram of the design point iteration contour plot of a Gaussian Copula function according to an embodiment of this application, as shown below. Figure 3 As shown, the design points for soil and rock parameters in the independent standard normal space can be... ; Figure 4 This is a schematic diagram of the design point iteration cloud of the Plackett Copula function according to an embodiment of this application, as shown below. Figure 4 As shown, the design points for soil and rock parameters in the independent standard normal space can be... ; Figure 5 This is a schematic diagram of the design point iteration cloud of the FrankCopula function according to an embodiment of this application, as shown below. Figure 5 As shown, this represents the design point of the soil and rock mass parameters in the independent standard normal space. ; Figure 6 This is a schematic diagram of the design point iteration cloud of the No.16 Copula function according to an embodiment of this application, as shown below. Figure 6 As shown, this represents the design point of the soil and rock mass parameters in the independent standard normal space. .

[0122] Step S103: Transform the design points of the soil and rock mass parameters into an uncertain physical space to calculate the reliability index and failure probability of the retaining wall, generating the soil and rock reliability analysis results. The expression for transforming the design points of the soil and rock mass parameters into the uncertain physical space can be, but is not limited to, the following:

[0123]

[0124] in, For the design points of soil and rock parameters in an uncertain physical space, , Design point for cohesion in physical space. Design point for internal friction angle in physical space. It is the inverse function of the cumulative distribution function of cohesion. It is the inverse function of the cumulative distribution function of the internal friction angle. It is the inverse function of the conditional Copula function. It is the standard normal distribution function.

[0125] As one possible approach, after calculating the design points of soil and rock parameters in the independent standard normal space, this embodiment of the application also needs to transform the design points of soil and rock parameters in the independent standard normal space to a physical space with uncertainty. The transformation formula can be, but is not limited to, expressed as:

[0126] ,

[0127] in, x* Design points for soil and rock parameters in physical space. ,in Design points for cohesion in physical space and Design point for internal friction angle in physical space. It is the inverse function of the cumulative distribution function of cohesion. It is the inverse function of the cumulative distribution function of the internal friction angle. It is the inverse function of the conditional Copula function. It is the standard normal distribution function.

[0128] In this embodiment of the application, the design points for soil and rock parameters in the physical space corresponding to the Gaussian Copula function can be... The design points for soil and rock parameters in the physical space corresponding to the Plackett Copula function can be... The design points for soil and rock parameters in the physical space corresponding to the Frank Copula function can be... And the design points for soil and rock mass parameters in the physical space corresponding to the No.16 Copula function can be... .

[0129] After obtaining the design points of the soil and rock parameters in the corresponding target physical space, the embodiments of this application can calculate the reliability index and failure probability of the retaining wall.

[0130] Among them, the failure probability of the retaining wall The formula can be, but is not limited to, expressed as:

[0131] .

[0132] Ultimately, we can obtain the reliability index corresponding to the Gaussian Copula function. = 3.5063 and failure probability The reliability index corresponding to the Plackett Copula function = 2.7048 and failure probability The reliability index corresponding to the Frank Copula function = 2.9790 and failure probability Reliability metrics corresponding to the No. 16 Copula function = 2.1506 and failure probability .

[0133] The reliability analysis results of the soil and rock can be generated based on the reliability index and failure probability of the retaining wall. For example, when the reliability index of the retaining wall is high and the failure probability is low, the soil and rock reliability is high; conversely, when the reliability index of the retaining wall is low and the failure probability is high, the soil and rock reliability is low. It should be noted that the specific reliability analysis results generated from the reliability index and failure probability of the retaining wall can be set or adjusted by those skilled in the art according to the actual situation. This is only an illustrative example and does not impose any specific limitations.

[0134] This application's embodiments, when faced with the significant impact of Copula functions on the reliability indicators and failure probability of retaining walls, seamlessly adapt to various complex and ever-changing related structures through its high flexibility, providing an effective tool for related research and development. This deepens engineers' understanding of how the uncertainty and correlation of geotechnical parameters subtly affect the reliability of geotechnical structures, and greatly enhances the ability to predict risks in the early stages of geotechnical structure design. It helps engineers formulate more precise and effective construction strategies to flexibly address various challenges caused by uncertainties during construction, thereby ensuring the overall safety and stability of geotechnical engineering.

[0135] The present application will be described in detail below with reference to a specific embodiment.

[0136] Figure 7 This is a flowchart of a geotechnical reliability analysis method based on iHLRF-BFGS according to an embodiment of this application, as shown below. Figure 7 As shown:

[0137] Step S701: Establish the function for the retaining wall;

[0138] Step S702: Determine the parameters and probability distribution information of the soil and rock mass in the physical space with uncertainty;

[0139] Step S703: Transform the soil and rock mass parameters in the physical space with uncertainty to an independent standard normal space;

[0140] Step S704: Iteratively calculate the design points of soil and rock parameters in the independent standard normal space;

[0141] Step S705: Transform the design points of soil and rock parameters in the independent standard normal space to a physical space with uncertainty;

[0142] Step S706: Calculate the reliability index and failure probability of the retaining wall.

[0143] According to the geotechnical reliability analysis method proposed in this application, the parameters and probability information of geotechnical mass in an uncertain physical space can be determined, the design points of geotechnical mass parameters in an independent standard normal space can be calculated, and the result can be transformed back to the uncertain physical space. This yields the reliability index and failure probability of the retaining wall, and ultimately the reliability analysis results of the geotechnical mass. Thus, the geotechnical reliability analysis based on the iHLRF-BFGS efficient iterative technique is realized. Only a few iterations are needed to accurately pinpoint the design points of geotechnical mass parameters. Even when facing highly complex nonlinear functional functions, the iterative process exhibits extremely high stability, effectively improving the stability and computational efficiency of this application. Furthermore, it demonstrates high adaptability to different Copula function selections, exhibiting high practicality and applicability, effectively meeting the needs of geotechnical mass reliability analysis in various scenarios. This solves the problems in related technologies, such as the slow convergence or even divergence of the design point iteration process when combining Copula theory and the first-order reliability method, resulting in low computational efficiency and the design point getting trapped in periodic and chaotic solutions with low stability, which seriously limits the application of the first-order reliability method based on Copula theory in geotechnical engineering reliability analysis.

[0144] Next, the geotechnical reliability analysis apparatus proposed according to the embodiments of this application is described with reference to the accompanying drawings.

[0145] Figure 8 This is a schematic diagram of the structure of the geotechnical reliability analysis device according to an embodiment of this application.

[0146] like Figure 8 As shown, the geotechnical reliability analysis device 10 includes: a determination module 100, a calculation module 200, and an analysis module 300.

[0147] Among them, the determination module 100 is used to establish the function of the retaining wall in order to determine the parameters and probability distribution information of the soil and rock mass in the uncertain physical space;

[0148] The calculation module 200 is used to transform the soil and rock mass parameters into an independent standard normal space based on probability distribution information, so as to iteratively calculate the design points of soil and rock mass parameters in the independent standard normal space;

[0149] Analysis module 300 is used to convert the design points of soil and rock parameters into an uncertain physical space to calculate the reliability index and failure probability of the soil and rock of the retaining wall and generate soil and rock reliability analysis results.

[0150] Optionally, in one embodiment of this application, the calculation module 200 includes: a setting unit, a calculation unit, and a judgment unit.

[0151] The setting unit is used to set the allowable error of the design point and the design point of the initial soil and rock parameters.

[0152] The calculation unit is used to calculate the function value and gradient of the current iteration based on the initial soil and rock mass parameter design point, so as to calculate the soil and rock mass parameter design point and the quasi-Newton method BFGS matrix for the next iteration.

[0153] The judgment unit is used to determine whether the iteration has converged. If the iteration has converged, the design point of the soil and rock mass parameters within the allowable error range of the design point is obtained based on the design point of the soil and rock mass parameters in the next iteration and the BFGS matrix.

[0154] Optionally, in one embodiment of this application, the expression of the function may be, but is not limited to, the following:

[0155] ,

[0156] in, For the gravity of the triangular region of the retaining wall, The weight of the rectangular area of ​​the retaining wall. Let the moment arm of gravity at the toe of the retaining wall be the moment arm of gravity in the triangular region of the retaining wall. Let the moment arm of gravity at the toe of the retaining wall be the moment arm of gravity in the rectangular region of the retaining wall. For active earth pressure, This is the distance between the active earth pressure and the bottom of the wall.

[0157] Optionally, in one embodiment of this application, the conversion formula for soil and rock parameters may be, but is not limited to, the following:

[0158] ,

[0159] in, These are the parameters of the soil and rock mass in an independent standard normal space. , For cohesion in independent standard normal space, Let be the angle of internal friction in an independent standard normal space, with the superscript "T" indicating the transpose of the vector. The inverse function of the standard normal distribution function and This is a conditional Copula function.

[0160] Optionally, in one embodiment of this application, the expression for transforming the design points of soil and rock parameters to the target physical space can be, but is not limited to, the following:

[0161]

[0162] in, For the design points of soil and rock parameters in an uncertain physical space, , Design point for cohesion in physical space. Design point for internal friction angle in physical space. It is the inverse function of the cumulative distribution function of cohesion. It is the inverse function of the cumulative distribution function of the internal friction angle. It is the inverse function of the conditional Copula function. It is the standard normal distribution function.

[0163] It should be noted that the foregoing explanation of the embodiment of the geotechnical reliability analysis method also applies to the geotechnical reliability analysis device of this embodiment, and will not be repeated here.

[0164] According to the geotechnical reliability analysis device proposed in this application, the parameters and probability information of geotechnical mass in an uncertain physical space can be determined, the design points of geotechnical mass parameters in an independent standard normal space can be calculated, and the results can be transformed back to the uncertain physical space. This yields the reliability index and failure probability of the retaining wall, and ultimately, the reliability analysis results of the geotechnical mass. Thus, geotechnical reliability analysis based on the iHLRF-BFGS efficient iterative technique is achieved. Only a few iterations are needed to accurately pinpoint the design points of geotechnical mass parameters. Even when facing highly complex nonlinear functional functions, the iterative process exhibits extremely high stability, effectively improving the stability and computational efficiency of this application. Furthermore, it demonstrates high adaptability to different Copula function selections, exhibiting high practicality and applicability, effectively meeting the needs of geotechnical mass reliability analysis in various scenarios. This solves the problems in related technologies, such as the slow convergence or even divergence of the design point iteration process when combining Copula theory and the first-order reliability method, resulting in low computational efficiency and the design point getting trapped in periodic and chaotic solutions with low stability, which seriously limits the application of the first-order reliability method based on Copula theory in geotechnical engineering reliability analysis.

[0165] Figure 9 A schematic diagram of the structure of an electronic device provided in an embodiment of this application. The electronic device may include:

[0166] The memory 901, the processor 902, and the computer program stored on the memory 901 and capable of running on the processor 902.

[0167] When processor 902 executes the program, it implements the geotechnical reliability analysis method provided in the above embodiments.

[0168] Furthermore, electronic devices also include:

[0169] Communication interface 903 is used for communication between memory 901 and processor 902.

[0170] The memory 901 is used to store computer programs that can run on the processor 902.

[0171] The memory 901 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage device.

[0172] If the memory 901, processor 902, and communication interface 903 are implemented independently, then the communication interface 903, memory 901, and processor 902 can be interconnected via a bus to complete communication between them. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of representation, Figure 9 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0173] Optionally, in a specific implementation, if the memory 901, processor 902, and communication interface 903 are integrated on a single chip, then the memory 901, processor 902, and communication interface 903 can communicate with each other through an internal interface.

[0174] The processor 902 may be a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of this application.

[0175] This application also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the above-described geotechnical reliability analysis method.

[0176] This application also provides a computer program product, including a computer program that can run computer instructions. When the computer instructions are executed by a processor, they implement the geotechnical reliability analysis method provided in this application.

[0177] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0178] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0179] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0180] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0181] It should be understood that the various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. If implemented in hardware, as in another embodiment, it can be implemented using any one or more of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0182] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0183] Furthermore, the functional units in the various embodiments of this application can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0184] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of this application.

Claims

1. A method for geotechnical reliability analysis, characterized in that, Includes the following steps: Establish the function of the retaining wall to determine the parameters and probability distribution of the soil and rock mass in the uncertain physical space; Based on the probability distribution information, the soil and rock parameters are transformed into an independent standard normal space to iteratively calculate the design points of the soil and rock parameters in the independent standard normal space. The design points of the soil and rock parameters are transformed into the uncertain physical space to calculate the reliability index and failure probability of the retaining wall, and generate the soil and rock reliability analysis results. The probability distribution information includes the cumulative distribution function of cohesion, the cumulative distribution function of internal friction angle, and the Copula function between cohesion and internal friction angle. The Copula function includes Gaussian Copula, Plackett Copula, Frank Copula, and No. 16 Copula functions. The iterative calculation of the soil and rock mass parameter design points in the independent standard normal space includes: setting the allowable error of the design points, the number of iterations k, the initial soil and rock mass parameter design points, and the BFGS matrix of the first iteration using the quasi-Newton method; calculating the function value of the k-th iteration and the gradient of the k-th iteration to calculate the soil and rock mass parameter design points of the (k+1)-th iteration; and calculating the Lagrange function of the k-th iteration based on the iteration increment of the uncorrected Lagrange function gradient, the correction factor, the BFGS matrix of the k-th iteration, and the iteration increment of the soil and rock mass parameter design points of the k-th iteration. The iterative increment of the gradient is used to calculate the BFGS matrix for the (k+1)th iteration, combining the BFGS matrix of the k-th iteration, the iterative increment of the soil and rock parameter design point of the k-th iteration, and the iterative increment of the Lagrange function gradient. Based on the soil and rock parameter design point of the (k+1)th iteration, the soil and rock parameter design point of the k-th iteration, and the allowable error of the design point, it is determined whether the soil and rock parameter design point of the (k+1)th iteration belongs to the soil and rock parameter design point in the independent standard normal space. The expression for the correction factor is: ， in, As a correction factor, The iterative increment of the uncorrected Lagrange function gradient. For the iterative increment of the design point, for The BFGS matrix of the next iteration.

2. The method according to claim 1, characterized in that, The expression for the function is: in, The weight of the triangular region of the retaining wall. The weight of the rectangular region of the retaining wall. Let $\mathbf{ ... Let $\mathbf{ ... For active earth pressure, This is the distance between the active earth pressure and the bottom of the wall.

3. The method according to claim 1, characterized in that, The conversion formula for the soil and rock parameters is as follows: in, These are the parameters of the soil and rock mass in an independent standard normal space. , For cohesion in independent standard normal space, The internal friction angle in an independent standard normal space, indicated by the superscript "". " is the transpose of the vector. The inverse function of the standard normal distribution function and For conditional Copula functions; This is the cumulative distribution function of cohesion. Let be the cumulative distribution function of the internal friction angle. Indicates cohesion. Indicates the angle of internal friction. For Copula parameters.

4. The method according to claim 1, characterized in that, The expression for transforming the design points of the soil and rock parameters into the uncertain physical space is: in, For the design points of soil and rock parameters in an uncertain physical space, , Design point for cohesion in physical space. Design point for internal friction angle in physical space. It is the inverse function of the cumulative distribution function of cohesion. It is the inverse function of the cumulative distribution function of the internal friction angle. It is the inverse function of the conditional Copula function. It is the standard normal distribution function; The cohesion design point in the independent standard normal space. The design point for the internal friction angle in an independent standard normal space. For Copula parameters, Indicates cohesion. This represents the angle of internal friction.

5. A geotechnical reliability analysis device, characterized in that, include: The determination module is used to establish the functional functions of the retaining wall in order to determine the parameters and probability distribution information of the soil and rock mass in the uncertain physical space. The calculation module is used to transform the soil and rock mass parameters into an independent standard normal space based on the probability distribution information, so as to iteratively calculate the design points of the soil and rock mass parameters in the independent standard normal space; The analysis module is used to convert the design points of the soil and rock parameters to the uncertain physical space, so as to calculate the reliability index and failure probability of the retaining wall and generate the soil and rock reliability analysis results. The probability distribution information includes the cumulative distribution function of cohesion, the cumulative distribution function of internal friction angle, and the Copula function between cohesion and internal friction angle. The Copula function includes Gaussian Copula, Plackett Copula, Frank Copula, and No. 16 Copula functions. The iterative calculation of the soil and rock mass parameter design points in the independent standard normal space includes: setting the allowable error of the design points, the number of iterations k, the initial soil and rock mass parameter design points, and the BFGS matrix of the first iteration using the quasi-Newton method; calculating the function value of the k-th iteration and the gradient of the k-th iteration to calculate the soil and rock mass parameter design points of the (k+1)-th iteration; and calculating the Lagrange function of the k-th iteration based on the iteration increment of the uncorrected Lagrange function gradient, the correction factor, the BFGS matrix of the k-th iteration, and the iteration increment of the soil and rock mass parameter design points of the k-th iteration. The iterative increment of the gradient is used to calculate the BFGS matrix for the (k+1)th iteration, combining the BFGS matrix of the k-th iteration, the iterative increment of the soil and rock parameter design point of the k-th iteration, and the iterative increment of the Lagrange function gradient. Based on the soil and rock parameter design point of the (k+1)th iteration, the soil and rock parameter design point of the k-th iteration, and the allowable error of the design point, it is determined whether the soil and rock parameter design point of the (k+1)th iteration belongs to the soil and rock parameter design point in the independent standard normal space. The expression for the correction factor is: ， in, As a correction factor, The iterative increment of the uncorrected Lagrange function gradient. For the iterative increment of the design point, for The BFGS matrix of the next iteration.

6. An electronic device, characterized in that, include: A memory, a processor, and a computer program stored in the memory and executable on the processor, the processor executing the program to implement the geotechnical reliability analysis method as described in any one of claims 1-4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, The program is executed by the processor to implement the geotechnical reliability analysis method as described in any one of claims 1-4.

8. A computer program product, comprising a computer program, characterized in that, When the computer program is executed, it is used to implement the geotechnical reliability analysis method as described in any one of claims 1-4.

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