A soil-rock slope reliability efficient analysis method, device and equipment

Abstract

The application provides a soil-rock slope reliability efficient analysis method, device and equipment, belongs to the technical field of data processing, and aims at the problems of parameter representation distortion and low calculation efficiency in current soil-rock mixed stratum slope analysis. The Kendall coefficient can be used to describe the nonlinear cross-correlation relationship of non-Gaussian parameters, combined with layered random field modeling, the parameter space distribution characteristics of the soil-rock mixed stratum can be accurately reflected, and a polynomial response surface proxy model is used to replace a large number of repeated finite element calculations, so that the slope stability analysis efficiency and the accuracy and reliability of complex stratum engineering simulation are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of data processing, and in particular to a soil-rock slope reliability efficient analysis method, device and equipment. BACKGROUND

[0002] Slope stability analysis is the core link of geotechnical engineering safety evaluation. In particular, in the soil-rock mixed stratum, due to the geological characteristics of "soft on top and hard on bottom", the geotechnical parameters show significant spatial variability and cross-medium difference, which brings great challenges to accurate analysis. The traditional random field model has obvious limitations in describing the parameter correlation: on the one hand, it relies on the Pearson correlation coefficient to describe the parameter mutual correlation, which is only suitable for linear relationship and Gaussian distribution scenario, and it is difficult to capture the nonlinear dependence characteristics and non-Gaussian distribution properties (such as the skewness distribution of cohesion and internal friction angle) commonly existing in soil-rock parameters, resulting in misjudgment of the correlation structure; on the other hand, when simulating the soil-rock mixed stratum with a unified model, it is difficult to distinguish the mechanical parameter difference between soil layer and rock layer (such as the elastic modulus which can differ by hundreds of times), and it is easy to appear the phenomenon of "excessive smoothing of soil layer parameters and weakening of rock layer parameters", which makes the parameter probability density distribution deviate from the actual site conditions, and further leads to the distortion of the slope safety factor calculation results. In addition, the existing random field discretization method (such as K-L series expansion method) has high computational complexity and is difficult to program when dealing with irregular grids and multi-parameter mutual correlation scenarios, which cannot meet the needs of fine modeling in engineering.

[0003] In engineering practice, slope stability analysis needs to consider both accuracy and efficiency, and traditional numerical simulation methods are difficult to balance the relationship between the two. Although the strength reduction method based on finite element or finite difference can accurately calculate the safety factor, when combined with the random field model to consider the spatial variability of parameters, it needs to perform repeated calculations on a large number of samples, resulting in a long analysis period (a single three-dimensional simulation can take several hours, and batch calculation can take several weeks), which seriously restricts the efficiency of engineering decision-making. Although the proxy model (such as response surface method) can replace complex numerical simulation by constructing a simplified function, the existing framework has obvious defects: most response surface models do not fully couple the spatial correlation of parameters and are only based on independent random variables, which cannot reflect the spatial distribution characteristics of the random field; at the same time, the polynomial response surface is prone to insufficient fitting accuracy when dealing with high-dimensional parameters and strong nonlinear relationships due to the neglect of parameter mutual correlation, which makes it difficult to support reliable stability evaluation. These problems make the existing methods always face the dual bottlenecks of "parameter distortion" and "low computational efficiency" in the analysis of soil-rock mixed stratum slopes, and it is urgent to build an integrated analysis framework that considers the correlation description accuracy and computational efficiency. SUMMARY

[0004] In view of the above problems, the embodiments of the present application provide a soil-rock slope reliability efficient analysis method, device, electronic equipment and readable storage medium, so as to overcome the above problems or at least partially solve the above problems.

[0005] In a first aspect, the embodiments of the present application provide a soil-rock slope reliability efficient analysis method, which comprises:

[0006] determining a first soil layer state parameter of a soil layer unit in a sample slope region, a first unit center coordinate, a first rock layer state parameter of a rock layer unit in the sample slope region, and a second unit center coordinate, respectively;

[0007] calculating a Kendall correlation coefficient matrix between the first soil layer state parameter and the first rock layer state parameter, respectively;

[0008] based on the first soil layer state parameter, the first unit center coordinate, the first rock layer state parameter, and the second unit center coordinate, generating a cross-correlation arbitrary distribution random field by using a Latin hypercube sampling method combined with an equal-probability non-Gaussian conversion method;

[0009] determining a first slope safety factor of a target slope region by using a Monte Carlo reliability analysis method based on the first soil layer state parameter, the first rock layer state parameter, and the Kendall correlation coefficient matrix, combined with a polynomial response surface function;

[0010] determining a first number of the first slope safety factor less than 1, and calculating a structural failure probability of the target slope region based on the first number.

[0011] Optionally, the polynomial response surface function is fitted in a second-order polynomial form by using a least square method based on a parameter space sample set and the Kendall correlation coefficient matrix; the parameter space sample set is obtained by integrating a sample slope safety factor with the first soil layer state parameter and the first rock layer state parameter; the sample slope safety factor is calculated based on a parameter space mapping corresponding to the cross-correlation arbitrary distribution random field.

[0012] Optionally, the sampling data source of the Latin hypercube sampling method is a first optimal distribution of the first soil layer state parameter and a second optimal distribution of the first rock layer state parameter; the first optimal distribution and the second optimal distribution are determined by using a K-S test method based on the first soil layer state parameter and the first rock layer state parameter, respectively.

[0013] Optionally, the Kendall correlation coefficient matrix between the first soil layer state parameter and the first rock layer state parameter is calculated, comprising:

[0014] determine a first number of consistent pairs, a first number of inconsistent pairs and a first number of tied pairs between the first soil layer state parameters and the first rock layer state parameters, respectively;

[0015] calculate a Kendall correlation coefficient matrix under the first soil layer state parameters based on the first number of consistent pairs, the first number of inconsistent pairs and the first number of tied pairs;

[0016] The Kendall correlation coefficient matrix is calculated according to the following formula:

[0017] The calculation formula under the untied condition is as follows:

[0018] ;

[0019] In the above formula, is the total number of first soil layer state parameters, is the first number of consistent pairs between the first soil layer state parameters and the first rock layer state parameters, is the first number of inconsistent pairs between the first soil layer state parameters and the first rock layer state parameters, is the Kendall correlation coefficient under the untied condition;

[0020] The calculation formula under the tied condition is as follows:

[0021] ;

[0022] In the above formula, is the total number of first soil layer state parameters, and are the first number of tied pairs in the first soil layer state parameters and the first rock layer state parameters, respectively, is the Kendall correlation coefficient under the tied condition.

[0023] In a second aspect, the embodiments of the present application provide a device for efficiently analyzing the reliability of a soil-rock slope, and the device comprises:

[0024] a first determining module configured to determine a first soil layer state parameter of a soil layer unit, a first unit center coordinate in a sample slope region, and a first rock layer state parameter of a rock layer unit and a second unit center coordinate in the sample slope region, respectively;

[0025] a calculating module configured to calculate a Kendall correlation coefficient matrix between the first soil layer state parameter and the first rock layer state parameter, respectively;

[0026] The generation module is used to generate a cross-correlated arbitrary distribution random field based on the first soil layer state parameters, the first unit center coordinates, the first rock layer state parameters and the second unit center coordinates, using the Latin hypercube sampling method combined with the equal probability non-Gaussian transformation method.

[0027] The second determination module is used to determine the first slope safety factor of the target slope area by adopting the Monte Carlo reliability analysis method, based on the first soil layer state parameters, the first rock layer state parameters and the Kendall correlation coefficient matrix, combined with the polynomial response surface function.

[0028] The third determining module is used to determine a first number of times that the safety factor of the first slope is less than 1, and to calculate the structural failure probability of the target slope area based on the first number.

[0029] Optionally, the polynomial response surface function is obtained by fitting a second-order polynomial form using the least squares method based on the parameter space sample set and the Kendall correlation coefficient matrix; the parameter space sample set is obtained by integrating the sample slope safety factor with the first soil layer state parameters and the first rock layer state parameters; the sample slope safety factor is calculated based on the parameter space mapping corresponding to the cross-correlated arbitrary distribution random field.

[0030] Optionally, the sampling data source of the Latin hypercube sampling method is the first optimal distribution of the first soil layer state parameters and the second optimal distribution of the first rock layer state parameters; the first optimal distribution and the second optimal distribution are determined by the KS test method based on the first soil layer state parameters and the first rock layer state parameters, respectively.

[0031] Optionally, the computing module includes:

[0032] The determination submodule is used to determine the number of first consistent pairs, the number of first inconsistent pairs, and the number of first knot pairs between the first soil layer state parameters and the first rock layer state parameters, respectively.

[0033] The calculation submodule is used to calculate the Kendall correlation coefficient matrix under the first soil state parameters based on the number of the first consistent pairs, the number of the first inconsistent pairs, and the number of the first knotted pairs.

[0034] The Kendall correlation coefficient matrix is ​​calculated using the following formula:

[0035] The calculation formula for the case without knots is:

[0036] ;

[0037] In the above formula, the total number of the first soil layer state parameters, the first number of consistent pairs between the first soil layer state parameters and the first rock layer state parameters, the first number of inconsistent pairs between the first soil layer state parameters and the first rock layer state parameters, the Kendall correlation coefficient without the knot condition;

[0038] the calculation formula with the knot condition is:

[0039]

[0040] in the above formula, the total number of the first soil layer state parameters, and respectively the first number of knots in the first soil layer state parameters and the first rock layer state parameters, the Kendall correlation coefficient with the knot condition.

[0041] In a third aspect, an embodiment of the present application provides an electronic device, including a memory, a processor, and a computer program stored in the memory, and the processor executes the computer program to implement the soil-rock slope reliability efficient analysis method according to any one of the above.

[0042] In a fourth aspect, an embodiment of the present application provides a readable storage medium, and the readable storage medium stores a program or instructions, and the program or instructions are executed by a processor to implement the soil-rock slope reliability efficient analysis method according to any one of the above.

[0043] Specific beneficial effects are:

[0044] ​The embodiment of the application determines the first soil layer state parameter of the soil layer unit, the first unit center coordinate in the sample slope region, and the first rock layer state parameter and the second unit center coordinate of the rock layer unit in the sample slope region respectively, generates a cross-correlation arbitrary distribution random field based on the first soil layer state parameter, the first unit center coordinate, the first rock layer state parameter and the second unit center coordinate, and calculates the sample slope safety factor of the sample slope region based on the parameter space mapping corresponding to the cross-correlation arbitrary distribution random field, integrates the sample slope safety factor with the first soil layer state parameter and the first rock layer state parameter, obtains a sample set, calculates the Kendall correlation coefficient matrix between the first soil layer state parameter and the first rock layer state parameter and the sample slope safety factor respectively, determines the first slope safety factor of the target slope region based on the first soil layer state parameter, the first rock layer state parameter and the Kendall correlation coefficient matrix by using the Monte Carlo reliability analysis method and combining a polynomial response surface function, determines the first quantity of the first slope safety factor less than 1, and calculates the structure failure probability of the target slope region based on the first quantity. The Kendall coefficient can be used to describe the nonlinear cross-correlation relationship of the non-Gaussian parameters, the layered random field modeling is combined, the parameter space distribution characteristics of the soil-rock mixed stratum are accurately reflected, and the polynomial response surface proxy model is used to replace a large number of repeated finite element calculations, so that the slope stability analysis efficiency and the accuracy and reliability of the complex stratum engineering simulation are improved. BRIEF DESCRIPTION OF DRAWINGS

[0045] In order to more clearly illustrate the technical solutions of the embodiments of the application, the drawings needed to be used in the description of the embodiments of the application will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the application, and other drawings can be obtained by those skilled in the art without creative labor.

[0046] Figure 1 is a flowchart of a soil-rock slope reliability efficient analysis method provided by the embodiments of the application;

[0047] Figure 2 is a generation flowchart of a cross-correlation random field provided by the embodiments of the application;

[0048] Figure 3 is a generation flowchart of a parameter space mapping provided by the embodiments of the application;

[0049] Figure 4 is a schematic diagram of parameter screening provided by the embodiments of the application;

[0050] Figure 5A logic block diagram of a soil-rock slope reliability efficient analysis device provided in an embodiment of the present application;

[0051] Figure 6 A schematic diagram of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0052] Exemplary embodiments of the present application will be described in greater detail below with reference to the accompanying drawings. Although exemplary embodiments of the present application are shown in the drawings, it is understood that the present application can be implemented in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided so that the present application can be more thoroughly understood, and so that the scope of the present application can be completely conveyed to those skilled in the art.

[0053] Reference Signs List Figure 1 , Figure 1 A flowchart of a soil-rock slope reliability efficient analysis method provided in an embodiment of the present application, which can include:

[0054] Step 101, respectively determining a first soil layer state parameter of a soil layer unit in a sample slope region, a first unit center coordinate of the soil layer unit, and a first rock layer state parameter of a rock layer unit in the sample slope region and a second unit center coordinate of the rock layer unit.

[0055] In an embodiment of the present application, the first soil layer state parameter of the soil layer and the first rock layer state parameter of the rock layer in the slope engineering can be obtained through engineering geological investigation, wherein the state parameters can include mean value (elastic modulus E, cohesion C, internal friction angle ), coefficient of variation COV, and the optimal distribution type and cumulative distribution function of each parameter can be determined as the data source of Latin hypercube sampling. The first unit center coordinate of the soil layer and the second unit center coordinate of the rock layer can be extracted by modeling the slope region through FLAC3D.

[0056] Step 102, respectively calculating a Kendall correlation coefficient matrix between the first soil layer state parameter and the first rock layer state parameter.

[0057] In an embodiment of the present application, the Kendall correlation coefficient matrix is a non-parametric statistical quantity for measuring the degree of monotone association between two ordered variables, and its core idea is to reflect the correlation between variables by calculating the number difference of “consistent pairs” and “inconsistent pairs” in two groups of data. Assuming that there are two groups of data , For any two observation points (i, j), if and , or and then the pair of data is called a concordant pair, if and or and then the pair of data is called a discordant pair, if or then the pair of data is called a tied pair (the above is a specific explanation of Kendall correlation coefficient, and the parameter symbols have no actual meaning). According to the number of concordant pairs, discordant pairs and tied pairs between the first soil layer state parameters and the first rock layer state parameters, the Kendall correlation coefficient matrix between the first soil layer state parameters and the first rock layer state parameters can be calculated.

[0058] Optionally, in step 102, the following sub-steps can be included:

[0059] Step 1021, respectively determining a first concordant pair number, a first discordant pair number and a first tied pair number between the first soil layer state parameters and the first rock layer state parameters.

[0060] Step 1022, calculating the Kendall correlation coefficient matrix under the first soil layer state parameters based on the first concordant pair number, the first discordant pair number and the first tied pair number.

[0061] In the embodiment of the present application, first, the first concordant pair number, the first discordant pair number and the first tied pair number between the first soil layer state parameters and the first rock layer state parameters can be counted according to the definition of the Kendall correlation coefficient matrix about concordant pairs, discordant pairs and tied pairs. Then, the Kendall correlation coefficient matrix can be calculated according to the correlation coefficient calculation formula without tied pairs and the correlation coefficient calculation formula with tied pairs in the Kendall correlation coefficient matrix.

[0062] Wherein, the calculation formula of the Kendall correlation coefficient matrix is as follows:

[0063] The calculation formula without tied pairs is as follows:

[0064] (Formula 1);

[0065] In the above formula 1, is the total number of the first soil layer state parameters, is the first concordant pair number between the first soil layer state parameters and the first rock layer state parameters, is the first discordant pair number between the first soil layer state parameters and the first rock layer state parameters, is the Kendall correlation coefficient without tied pairs;

[0066] The calculation formula in the tied case is:

[0067] (Formula 2);

[0068] In the above formula 2, is the total number of first soil layer state parameters, and are the first tied pair numbers in the first soil layer state parameters and the first rock layer state parameters, respectively, is the Kendall correlation coefficient in the tied case. The Kendall correlation coefficient matrix is represented as:

[0069] (Formula 3);

[0070] In formula 3, is the number of parameters of the first soil layer state parameters, is the Kendall correlation coefficient matrix of the soil-rock slope.

[0071] In the embodiments of the present application, by respectively determining the first consistent pair number, the first inconsistent pair number and the first tied pair number between the first soil layer state parameters and the first rock layer state parameters, and based on the first consistent pair number, the first inconsistent pair number and the first tied pair number, the Kendall correlation coefficient matrix under the first soil layer state parameters is calculated, the Kendall correlation coefficient matrix between the first soil layer state parameters and the first rock layer state parameters can be calculated, and the accuracy and reliability of the Kendall correlation coefficient matrix can be improved to a certain extent.

[0072] In step 103, based on the first soil layer state parameters, the first unit center coordinates, the first rock layer state parameters and the second unit center coordinates, a cross-correlation arbitrary distribution random field is generated by using the Latin hypercube sampling method combined with the equal-probability non-Gaussian conversion method.

[0073] In the embodiments of the present application, with reference to Figure 2 , Figure 2 is a flowchart of a cross-correlation random field generation provided in the embodiments of the present application. According to the first soil layer state parameters, the first rock layer state parameters, and “tczb.dat” (first unit center coordinates) and “yczb.dat” (second unit center coordinates), independent standard normal fields can be respectively generated by using the Latin hypercube sampling. Then, the Kendall correlation coefficient matrix can be used to control the nonlinear cross-correlation between parameters, the cross-correlation standard normal field can be constructed by Cholesky decomposition of the covariance matrix, and finally the equal-probability non-Gaussian conversion can be performed in combination with the optimal marginal distribution of the soil layer and the rock layer, so as to finally generate the cross-correlation arbitrary distribution random field. The specific process is as follows:

[0074] (1) Based on the statistical characteristics of the rock mass parameters (i.e., the first rock mass state parameters and the first rock mass state parameters), independent standard normal vectors are generated by Latin hypercube sampling :

[0075] (Formula 4);

[0076] In Formula 4, represents the determination of the dimension of the random variable according to the demand.

[0077] The autocorrelation matrix is calculated by selecting a random exponential function , and the autocorrelation matrix is decomposed by Cholesky to obtain the lower triangular matrix L.

[0078] (Formula 5);

[0079] (Formula 6);

[0080] In Formulas 5 and 6, is the total number of random field units, which is consistent with the number of finite difference division grids; is the lower triangular matrix, is the upper triangular matrix, is the transpose of.

[0081] Generate independent standard normal field X: .

[0082] (2) Cholesky decomposition is performed on the Kendall correlation coefficient matrix to obtain its lower triangular matrix:

[0083] (Formula 7);

[0084] In Formula 7, is the lower triangular matrix, is the upper triangular matrix, i.e. the transpose of.

[0085] (3) Generate the cross-correlation standard normal field N: let , , , assuming k=3, the cross-correlation standard normal distribution random field of the elastic modulus E, the cohesion c, and the internal friction angle can be obtained.

[0086] (Formula 8);

[0087] In the above Formula 8, a cross-correlation standard normal distribution representing elastic modulus, a cross-correlation standard normal distribution representing cohesion, a cross-correlation standard normal distribution representing internal friction angle.

[0088] (4) Let wherein is the cumulative distribution function of the standard normal distribution, the cross-correlation standard uniform distribution random field of E, c,

[0089] (Formula 9);

[0090] In the above formula 9, respectively represent the cross-correlation standard uniform distribution of elastic modulus E, cohesion c, and internal friction angle .

[0091] (5) According to the cumulative distribution function of E, c, , the inverse function of the cumulative distribution function is determined , and the cross-correlation standard uniform distribution random field is converted by the equal probability transformation method, so as to construct the cross-correlation random field of the multi-element surrounding rock parameter of the target distribution:

[0092] (Formula 10);

[0093] In the above formula 10, , , respectively represent the cross-correlation distribution of the multi-element surrounding rock parameter of elastic modulus E, cohesion c, and internal friction angle .

[0094] Finally, the non-Gaussian random field parameter file "E-i.txt", "c-i.txt", and -i.txt" is output.

[0095] Optionally, the sampling data of the Latin hypercube sampling method is from the first optimal distribution of the first soil layer state parameter and the second optimal distribution of the first rock layer state parameter; the first optimal distribution and the second optimal distribution are respectively based on the first soil layer state parameter and the first rock layer state parameter, and are determined by using the K-S test method.

[0096] In the embodiments of the present application, the optimal distribution of the first soil layer state parameter and the first rock layer state parameter can be determined by the K-S test method. The K-S test method has clear physical meaning, does not need data grouping, and has strong stability in small samples, and is more practical in actual engineering. Therefore, the K-S test method is selected in the patent to determine the optimal distribution to which the soil parameters are subjected, and the commonly used significance level ​The K-S test is performed on =0.5, and then the optimal probability density distribution of the soil and rock mass parameters is determined. Finally, the distribution functions of the parameters are accumulated to serve as the data source for the Latin hypercube sampling. In this way, the accuracy and reliability of the Latin hypercube sampling can be improved.

[0097] In step 104, the Monte Carlo reliability analysis method is used to determine the first slope safety factor of the target slope region based on the first soil layer state parameters, the first rock layer state parameters and the Kendall correlation coefficient matrix, in combination with the polynomial response surface function.

[0098] In the embodiments of the present application, first, the first soil layer state parameters and the first rock layer state parameters (mean μ, coefficient of variation COV, distribution type) and the Kendall correlation coefficient matrix are used to generate a plurality of groups of random samples by using Gaussian Copula coupling Latin hypercube sampling, and then the PRSM is called to predict the first slope safety factor F S . The PRSM is a polynomial response surface, which can be fitted by the first soil layer state parameters and the first rock layer state parameters in combination with the Kendall correlation coefficient matrix. The specific steps of generating a plurality of groups of random samples by using Gaussian Copula coupling Latin hypercube sampling are as follows:

[0099] (1) First, the Kendall matrix is converted into a Pearson correlation coefficient matrix required by the Gaussian Copula, which is converted by the following formula:

[0100] (Formula 11);

[0101] In Formula 11, is the Kendall correlation coefficient matrix of the soil layer and the rock layer.

[0102] (2) The matrix is subjected to Cholesky decomposition to obtain a lower triangular matrix L.

[0103] (Formula 12);

[0104] In Formula 12, is the lower triangular matrix, is the transpose of .

[0105] (3) Latin hypercube sampling is performed to generate M groups (M is the total sample size) of independent random samples from the standard normal distribution N(0, 1), denoted as matrix U.

[0106] (Equation 13);

[0107] In Equation 13, The number of parameters for the state parameters of the first soil layer.

[0108] (4) Combine the generated independent standard normal samples U with the obtained lower triangular matrix Multiplying these results yields a standard normal sample V that conforms to Pearson correlation.

[0109] (Equation 14);

[0110] (5) For each independent sample in V Calculate its cumulative probability in the standard normal distribution. .

[0111] (Equation 15);

[0112] In Equation 15, This is the cumulative distribution function of the standard normal distribution.

[0113] (6) Using the inverse cumulative distribution function of the target parameter, the probability is... Convert to parameter value .

[0114] (Equation 16);

[0115] In Equation 16, It is the inverse cumulative distribution function of the optimal marginal distribution of parameters.

[0116] (7) Finally, a random sample X that conforms to the optimal marginal distribution in step 101 is generated, which conforms to the marginal distribution of each parameter (mean, COV, distribution type) and also satisfies the nonlinear cross-correlation characterized by the Kendall correlation coefficient matrix.

[0117] Optionally, the polynomial response surface function is obtained by fitting a second-order polynomial form using the least squares method based on the parameter space sample set and the Kendall correlation coefficient matrix; the parameter space sample set is obtained by integrating the sample slope safety factor with the first soil layer state parameters and the first rock layer state parameters; the sample slope safety factor is calculated based on the parameter space mapping corresponding to the cross-correlated arbitrary distribution random field.

[0118] In the embodiments of this application, the polynomial response surface function can be obtained through the following process:

[0119] Reference Figure 3 , Figure 3A flowchart for generating a parameter space mapping provided in this application includes the following steps (1) to (4):

[0120] (1) Clarify the core information of the input file: Based on the relevant arbitrary distribution random field files, including "Ei.txt" (elastic modulus random field), "ci.txt" (cohesion random field), " -i.txt (random field of internal friction angle), etc. Each record in these files contains the center coordinates (x, y, z) of the element and the parameter values ​​at the corresponding coordinates; step 101 can also generate the full model coordinate "ztzb.dat" file, which can record the identifier of all elements in the slope model and their corresponding center coordinates (x, y, z).

[0121] (2) Establish a mapping dictionary between coordinates and cell identifiers. First, read the "ztzb.dat" file and extract the data pairs of "cell identifier" and "(x,y,z) coordinates". Then, establish a dictionary data structure identifier_map={(x,y,z):cell identifier}, where the key is the coordinate tuple and the value is the corresponding cell identifier.

[0122] (3) Generate the "final.txt" assignment file. First, iterate through all the cross-correlation random field files generated in step 103, read the records in the random field files line by line, and find the corresponding element identifier in the identifier_map according to the coordinates (x,y,z). Then, convert the record format to "element identifier parameter value". Finally, summarize all the converted records and generate a unified parameter assignment file "final.txt". This file contains the identifiers of all elements in the whole model and their corresponding elastic modulus, cohesion, internal friction angle and other parameter values.

[0123] (4) Call FLAC3D to complete the parameter space mapping. First, start the FLAC3D software, load the slope model, and then read the "final.txt" file through the script function of FLAC3D. According to the "element identifier" in the file, locate the target element in the model and assign the corresponding parameter values ​​(E, c, φ, etc.) to the mechanical parameter properties of the element. Finally, after completing the parameter assignment of all elements, the model contains the spatial variability and cross-correlation characteristics of random field simulation.

[0124] After completing the parameter space mapping, the safety factor of the first slope can be calculated using the strength reduction method built into FLAC3D. Store sample sets .

[0125] Then, the parameters can be calculated. Kendall coefficient, according to Values are sorted in descending order, as shown in Figure 4 , Figure 4 An example of parameter screening is provided for the embodiments of the present application. Assume that the screening threshold and , , , , , , the low sensitivity parameters are removed, and the key parameter subset is retained , , .

[0126] Kendall The calculation uses:

[0127] (Equation 17);

[0128] In Equation 17, and are the first slope safety factors of samples and samples , X is the first soil state parameter or the first rock state parameter, is the sample number.

[0129] Based on the above sample set and the key parameters screened by Kendall global sensitivity analysis, a polynomial function is used to approximate and simulate the relationship between the slope safety factor and the key geotechnical state parameters, to replace the numerical model.

[0130] The polynomial form uses a second-order polynomial, and the least squares method is used to fit the polynomial coefficients (including , , and ):

[0131] (Equation 18);

[0132] (Equation 19);

[0133] In Equation 18 and Equation 19, the matrix X contains the parameter values and polynomial terms of all samples, and represent the labels of two different samples, the response vector is the value.

[0134] Through the above process, the matching degree of the fitting model and the actual scene can be improved, and the accuracy and reliability of the polynomial response surface function are improved.

[0135] In step 105, a first number of the first slope safety factors less than 1 is determined, and a structural failure probability of the target slope region is calculated based on the first number.

[0136] In the embodiments of the present application, the first number of failure samples less than 1 can be counted, and the failure probability can be calculated according to the first number <1 of the failure samples, and the failure probability is calculated according to the first number :

[0137] (Formula 20);

[0138] In formula 20, is the first number of failure samples less than 1, <1 of the failure samples, and the failure probability is calculated according to the first number is the total number of samples.

[0139] In the embodiments of the present application, by respectively determining the first soil state parameter of the soil unit, the first unit center coordinate of the sample slope region, and the first rock state parameter of the rock unit and the second unit center coordinate of the sample slope region, based on the first soil state parameter, the first unit center coordinate, the first rock state parameter and the second unit center coordinate, using the Latin hypercube sampling method, combined with the equal probability non-Gaussian conversion method, a cross-correlation arbitrary distribution random field is generated, based on the parameter space mapping corresponding to the cross-correlation arbitrary distribution random field, the sample slope safety factor of the sample slope region is calculated and the sample slope safety factor is integrated with the first soil state parameter and the first rock state parameter to obtain a sample set, the Kendall correlation coefficient matrix between the first soil state parameter and the first rock state parameter and the sample slope safety factor is calculated respectively, the first slope safety factor of the target slope region is determined based on the first soil state parameter, the first rock state parameter and the Kendall correlation coefficient matrix, combined with the polynomial response surface function, the first number of the first slope safety factor less than 1 is determined, and the structural failure probability of the target slope region is calculated based on the first number, the Kendall coefficient can be used to describe the nonlinear cross-correlation relationship of non-Gaussian parameters, combined with hierarchical random field modeling, the parameter space distribution characteristics of soil-rock mixed stratum can be accurately reflected, and the efficiency of slope stability analysis and the accuracy and reliability of complex stratum engineering simulation are improved by replacing a large number of repeated finite element calculations through the polynomial response surface proxy model.

[0140] In the embodiments of the present application, the code corresponding to the soil-rock slope reliability efficient analysis method is provided as follows:

[0141] import numpy as np

[0142] from scipy.stats import norm, kendalltau

[0143] from scipy.linalg import cholesky

[0144] # Set random seed for reproducibility

[0145] np.random.seed(42)

[0146] # Parameter distribution definitions

[0147] mu_c, sigma_c = 25, 12 # Cohesion

[0148] mu_phi, sigma_phi = 20, 6 # Internal friction angle

[0149] mu_E, sigma_E = 200, 100 # Elastic modulus

[0150] # Kendall correlation coefficient matrix

[0151] tau_matrix = np.array([

[0152] [1.0, 0.3, 0.2],

[0153] [0.3, 1.0, 0.4],

[0154] [0.2, 0.4, 1.0] ])

[0156] # Convert Kendall tau to Pearson correlation coefficient

[0157] def kendall_to_pearson(tau):

[0158] return np.sin(np.pi * tau / 2)

[0159] rho_matrix = kendall_to_pearson(tau_matrix)

[0160] # Check and ensure matrix positive definiteness

[0161] if np.all(np.linalg.eigvals(rho_matrix) > 0):

[0162] L = cholesky(rho_matrix, lower=True)

[0163] else

[0164] rho_matrix += np.eye(3) * 0.01

[0165] L = cholesky(rho_matrix, lower=True)

[0166] # Generate samples

[0167] def generate_samples(n, L):

[0168] U = np.random.normal(0, 1, (n, 3))

[0169] V = U @ L.T

[0170] P = norm.cdf(V)

[0171] c = norm.ppf(P[:, 0], loc=mu_c, scale=sigma_c)

[0172] phi = norm.ppf(P[:, 1], loc=mu_phi, scale=sigma_phi)

[0173] E = norm.ppf(P[:, 2], loc=mu_E, scale=sigma_E)

[0174] return c, phi, E

[0175] n_train = 100

[0176] c_train, phi_train, E_train = generate_samples(n_train, L)

[0177] # Calculate safety factor FS

[0178] def compute_fs(c, phi, E):

[0179] return (0.012 * c + 0.025 * phi - 0.0005 * E +

[0180] 0.0001 * c * phi - 0.000001 * E**2 +

[0181] 0.6 + np.random.normal(0, 0.2, len(c)))

[0182] fs_train = compute_fs(c_train, phi_train, E_train)

[0183] # Kendall Global Sensitivity Analysis

[0184] tau_c = kendalltau(c_train, fs_train).correlation

[0185] tau_phi = kendalltau(phi_train, fs_train).correlation

[0186] tau_E = kendalltau(E_train, fs_train).correlation

[0187] # Output Kendall's τ sensitivity coefficients for each parameter

[0188] print("Kendall's τ sensitivity coefficient:")

[0189] print(f"c: {tau_c:.3f}")

[0190] print(f"phi: {tau_phi:.3f}")

[0191] print(f"E: {tau_E:.3f}")

[0192] # Filter key parameters (threshold |τ|>0.1)

[0193] key_params = []

[0194] if abs(tau_c) > 0.1:

[0195] key_params.append('c')

[0196] if abs(tau_phi) > 0.1:

[0197] key_params.append('phi')

[0198] if abs(tau_E) > 0.1:

[0199] key_params.append('E')

[0200] # Output key parameters

[0201] print(f"\nKey parameters: {key_params}")

[0202] # Build polynomial response surface (second order)

[0203] def create_polynomial_features(X, degree=2):

[0204] n_samples, n_features = X.shape

[0205] features = []

[0206] features.append(np.ones(n_samples))

[0207] for i in range(n_features):

[0208] features.append(X[:, i])

[0209] if degree >= 2:

[0210] for i in range(n_features):

[0211] features.append(X[:, i]**2)

[0212] for i in range(n_features):

[0213] for j in range(i+1, n_features):

[0214] features.append(X[:, i] * X[:, j])

[0215] return np.column_stack(features)

[0216] X_train = np.column_stack([c_train, phi_train, E_train])

[0217] X_poly = create_polynomial_features(X_train, degree=2)

[0218] beta = np.linalg.lstsq(X_poly, fs_train, rcond=None)[0]

[0219] def predict_fs(X, beta):

[0220] X_poly = create_polynomial_features(X, degree=2)

[0221] return X_poly @ beta

[0222] # Monte Carlo reliability analysis

[0223] n_mc = 20000

[0224] # Run the calculation multiple times to average the failure probability

[0225] num_runs = 5 # number of runs

[0226] pfs = []

[0227] for i in range(num_runs):

[0228] # Use a different random seed for each run

[0229] np.random.seed(42 + i)

[0230] c_mc, phi_mc, E_mc = generate_samples(n_mc, L)

[0231] X_mc = np.column_stack([c_mc, phi_mc, E_mc])

[0232] fs_mc = predict_fs(X_mc, beta)

[0233] pf = np.sum(fs_mc < 1) / n_mc

[0234] pfs.append(pf)

[0235] # Results of the first run (to align with the original output)

[0236] np.random.seed(42)

[0237] c_mc, phi_mc, E_mc = generate_samples(n_mc, L)

[0238] X_mc = np.column_stack([c_mc, phi_mc, E_mc])

[0239] fs_mc = predict_fs(X_mc, beta)

[0240] failure_count = np.sum(fs_mc < 1)

[0241] pf = failure_count / n_mc

[0242] # Output the failure probability

[0243] print(f"\nFailure probability P_f: {pf:.4f}")

[0244] # Calculate and output the average failure probability

[0245] avg_pf = np.mean(pfs)

[0246] print(f"Average failure probability over multiple runs: {avg_pf:.4f}")

[0247] # Verify the response surface accuracy

[0248] fs_true_mc = compute_fs(c_mc, phi_mc, E_mc)

[0249] mse = np.mean((fs_mc - fs_true_mc)**2)

[0250] # Output the prediction accuracy of the response surface model

[0251] print(f"Prediction accuracy of the response surface model (MSE): {mse:.4f}")

[0252] Code explanation:

[0253] 1. Distribution parameters (statistical properties of random variables): Cohesive force (c): c=25 (mean), standard deviation=12; Internal friction angle (phi): phi=30 (mean), standard deviation=5 ): =20° (mean), standard deviation = 6); elastic modulus (E): E = 200 (mean), standard deviation = 100.

[0254] 2. Correlation parameters (correlation between variables): Kendall correlation coefficient matrix Calculated (From left to right, from top to bottom, the numbers are c, ...) (Correlation between E).

[0255] 3. Sample size parameters: Training sample size: n=100 (used to build the response surface model); Monte Carlo simulation sample size: n=20000 (used to calculate the failure probability); Number of runs: n=5 (used to calculate the average failure probability).

[0256] 4. Safety factor function parameters (composition of the performance function): Coefficients defined in the function: Linear term coefficients: 0.012 (coefficient of c), 0.025 (… The coefficient of the nonlinear term: -0.0005 (coefficient of E) 0.0001 (c*) The coefficients of E² are 0.000001. The constant term is 0.6. The random perturbation is np.random.normal(0,0.2,len(c)) (mean 0, standard deviation 0.2).

[0257] 5. Response surface model parameters: Polynomial order: degree=2 (second-order polynomial)

[0258] These parameters can be adjusted according to the needs of actual engineering problems. In particular, the composition of the distributed parameters, correlation coefficient matrix, and safety factor function directly affects the results of reliability analysis.

[0259] The failure probability obtained by the method in this application The mean squared error (MSE) was 0.0772, the average failure probability after multiple runs was 0.0753, and the prediction accuracy of the response surface model (measured by mean squared error, MSE) was 0.0429.

[0260] Reference Figure 5 , Figure 5 This application provides a logic block diagram of a high-efficiency soil and rock slope reliability analysis device 500, which may include:

[0261] The first determining module 501 is used to determine the first soil state parameters and the center coordinates of the first unit of the soil layer unit in the sample slope area, and the first rock state parameters and the center coordinates of the second unit of the rock layer unit in the sample slope area.

[0262] The computing module 502 is configured to calculate a Kendall correlation coefficient matrix between the first soil layer state parameters and the first rock layer state parameters, respectively.

[0263] The generating module 503 is configured to generate a cross-correlation arbitrary distribution random field based on the first soil layer state parameters, the first unit center coordinates, the first rock layer state parameters and the second unit center coordinates, by using a Latin hypercube sampling method in combination with an equal-probability non-Gaussian conversion method.

[0264] The second determining module 504 is configured to determine a first slope safety factor of a target slope region by using a Monte Carlo reliability analysis method based on the first soil layer state parameters, the first rock layer state parameters and the Kendall correlation coefficient matrix in combination with a polynomial response surface function.

[0265] The third determining module 505 is configured to determine a first quantity of the first slope safety factors less than 1, and calculate a structural failure probability of the target slope region based on the first quantity.

[0266] Optionally, the polynomial response surface function is fitted in a second-order polynomial form by using a least square method based on a parameter space sample set and the Kendall correlation coefficient matrix; the parameter space sample set is obtained by integrating sample slope safety factors with the first soil layer state parameters and the first rock layer state parameters; and the sample slope safety factors are calculated based on parameter space mapping corresponding to the cross-correlation arbitrary distribution random field.

[0267] Optionally, sampling data of the Latin hypercube sampling method is from a first optimal distribution of the first soil layer state parameters and a second optimal distribution of the first rock layer state parameters; the first optimal distribution and the second optimal distribution are determined by using a K-S test method based on the first soil layer state parameters and the first rock layer state parameters, respectively.

[0268] Optionally, the computing module 502 comprises:

[0269] The determining sub-module is configured to determine a first number of consistent pairs, a first number of inconsistent pairs and a first number of tied pairs between the first soil layer state parameters and the first rock layer state parameters, respectively.

[0270] The computing sub-module is configured to calculate the Kendall correlation coefficient matrix under the first soil layer state parameters based on the first number of consistent pairs, the first number of inconsistent pairs and the first number of tied pairs.

[0271] The Kendall correlation coefficient matrix is calculated according to the following formula:

[0272] The calculation formula in the case of no knot is:

[0273] ;

[0274] In the above formula, is the total number of first soil layer state parameters, is the first consistent pair number between the first soil layer state parameters and the first rock layer state parameters, is the first inconsistent pair number between the first soil layer state parameters and the first rock layer state parameters, is the Kendall correlation coefficient in the case of no knot;

[0275] The calculation formula in the case of knot is:

[0276] ;

[0277] In the above formula, is the total number of first soil layer state parameters, and are respectively the first knot pair number in the first soil layer state parameters and the first rock layer state parameters, is the Kendall correlation coefficient in the case of knot.

[0278] The soil-rock slope reliability efficient analysis device in the embodiments of the present application can be an electronic device, or a component in an electronic device, such as an integrated circuit or a chip. The electronic device can be a terminal, or other devices other than the terminal. Illustratively, the electronic device can be a mobile phone, a tablet computer, a notebook computer, a palm computer, a vehicle-mounted electronic device, a mobile Internet device (MID), an augmented reality (AR) / virtual reality (VR) device, a robot, a wearable device, an ultra-mobile personal computer (UMPC), a netbook, or a personal digital assistant (PDA), etc., and can also be a server, a network attached storage (NAS), a personal computer (PC), etc., and the embodiments of the present application are not limited in this regard.

[0279] The efficient reliability analysis device for soil and rock slopes in this application embodiment can be a device with an operating system. This operating system can be Android, Linux, Windows, or other possible operating systems; this application embodiment does not specifically limit it.

[0280] The efficient reliability analysis device for soil and rock slopes provided in this application embodiment can achieve... Figures 1 to 3 The various processes implemented in the method implementation examples will not be described again here to avoid repetition.

[0281] This application provides an electronic device, see [link to relevant documentation] Figure 6 The electronic device 60 includes a processor 601, a memory 602, and a computer program 6021 stored in the memory 602 and executable on the processor 601. When the processor 601 executes the program, it implements the efficient reliability analysis method for soil and rock slopes described in the foregoing embodiments.

[0282] This application also provides a computer-readable storage medium storing a computer program / instruction thereon, which, when executed by a processor, implements the steps in the efficient reliability analysis method for soil and rock slopes disclosed in this application.

[0283] This application also provides a computer program product that, when run on an electronic device, enables the processor to execute the steps in the efficient reliability analysis method for soil and rock slopes disclosed in this application.

[0284] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0285] This application describes embodiments with reference to flowchart illustrations and / or block diagrams of methods, apparatuses, electronic devices, and computer program products according to embodiments of this application. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0286] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0287] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal equipment, causing a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0288] Although preferred embodiments of the present application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of this application.

[0289] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0290] The above provides a detailed description of the efficient method, apparatus, and equipment for analyzing the reliability of soil and rock slopes provided in this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the method and its core ideas. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application areas based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A highly efficient method for reliability analysis of soil and rock slopes, characterized in that, The method includes: The first soil state parameters and the center coordinates of the first unit of the soil layer unit in the sample slope area are determined respectively, as are the first rock layer state parameters and the center coordinates of the second unit of the rock layer unit in the sample slope area. Calculate the Kendall correlation coefficient matrix between the state parameters of the first soil layer and the state parameters of the first rock layer, respectively; Based on the first soil layer state parameters, the first unit center coordinates, the first rock layer state parameters, and the second unit center coordinates, a cross-correlated arbitrary distribution random field is generated by using the Latin hypercube sampling method combined with the equal probability non-Gaussian transformation method. The Monte Carlo reliability analysis method is used to determine the first slope safety factor of the target slope area based on the first soil layer state parameters, the first rock layer state parameters and the Kendall correlation coefficient matrix, combined with the polynomial response surface function. A first number of times the safety factor of the first slope is less than 1 is determined, and the structural failure probability of the target slope area is calculated based on the first number. The calculation of the Kendall correlation coefficient matrix between the state parameters of the first soil layer and the state parameters of the first rock layer includes: Determine the number of first consistent pairs, the number of first inconsistent pairs, and the number of first knotted pairs between the first soil layer state parameters and the first rock layer state parameters, respectively. Based on the number of the first consistent pairs, the number of the first inconsistent pairs, and the number of the first knotted pairs, calculate the Kendall correlation coefficient matrix under the first soil layer state parameters; The Kendall correlation coefficient matrix is ​​calculated using the following formula: The calculation formula for the case without knots is: ； In the above formula, This represents the total number of state parameters for the first soil layer. This represents the number of first consistent pairs between the state parameters of the first soil layer and the state parameters of the first rock layer. This represents the number of the first inconsistencies between the state parameters of the first soil layer and the state parameters of the first rock layer. Kendall correlation coefficient for the case without knots; The calculation formula for the knotted case is: ； In the above formula, This represents the total number of state parameters for the first soil layer. and These are the number of the first knot pairs in the state parameters of the first soil layer and the first rock layer, respectively. Kendall correlation coefficient for the knotted case; The polynomial response surface function is obtained by fitting a second-order polynomial form using the least squares method based on the parameter space sample set and the Kendall correlation coefficient matrix; the parameter space sample set is obtained by integrating the sample slope safety factor with the first soil layer state parameters and the first rock layer state parameters; the sample slope safety factor is calculated based on the parameter space mapping corresponding to the cross-correlated arbitrary distribution random field.

2. The method according to claim 1, characterized in that, The sampling data for the Latin hypercube sampling method comes from the first optimal distribution of the first soil layer state parameters and the second optimal distribution of the first rock layer state parameters; the first optimal distribution and the second optimal distribution are determined by the KS test method based on the first soil layer state parameters and the first rock layer state parameters, respectively.

3. A high-efficiency analysis device for the reliability of soil and rock slopes, characterized in that, The method is implemented using claim 1 or 2, wherein the apparatus comprises: The first determining module is used to determine the first soil state parameters and the center coordinates of the first unit of the soil layer unit in the sample slope area, and the first rock state parameters and the center coordinates of the second unit of the rock layer unit in the sample slope area. The generation module is used to generate a cross-correlated arbitrary distribution random field based on the first soil layer state parameters, the first unit center coordinates, the first rock layer state parameters and the second unit center coordinates, using the Latin hypercube sampling method combined with the equal probability non-Gaussian transformation method. The first calculation module is used to calculate the sample slope safety factor of the sample slope area based on the parameter space mapping corresponding to the cross-correlated arbitrary distribution random field, and integrate the sample slope safety factor with the first soil layer state parameter and the first rock layer state parameter to obtain a sample set. The calculation module is used to calculate the Kendall correlation coefficient matrix between the first soil layer state parameters and the first rock layer state parameters and the safety factor of the sample slope, respectively. The second determination module is used to determine the first slope safety factor of the target slope area by adopting the Monte Carlo reliability analysis method, based on the first soil layer state parameters, the first rock layer state parameters and the Kendall correlation coefficient matrix, combined with the polynomial response surface function. The third determining module is used to determine a first number of times that the safety factor of the first slope is less than 1, and to calculate the structural failure probability of the target slope area based on the first number.

4. An electronic device, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the efficient reliability analysis method for soil and rock slopes as described in claim 1 or 2.

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