Method, device and equipment for efficiently analyzing reliability of soil rock slope

Abstract

The invention provides a soil rock slope reliability efficient analysis method, device and equipment, belongs to the technical field of data processing, and aims to solve the problems of parameter representation distortion and low calculation efficiency in current soil rock mixed stratum slope analysis, the Kendall coefficient can be adopted to describe the nonlinear cross-correlation relationship of non-Gaussian parameters, and layered random field modeling is combined, so that the reliability of the soil rock slope can be effectively analyzed. Parameter space distribution characteristics of the soil-rock mixed stratum are accurately reflected, a polynomial response surface agent model is used for replacing a large amount of repeated finite element calculation, and the slope stability analysis efficiency and the precision 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: respectively determining a first soil layer state parameter of a soil layer unit in a sample slope region, a first unit center coordinate, and a first rock layer state parameter of a rock layer unit in the sample slope region and a second unit center coordinate; respectively calculating a Kendall correlation coefficient matrix between the first soil layer state parameter and the first rock layer state parameter; 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, a cross-correlation arbitrary distribution random field is generated by using a Latin hypercube sampling method combined with an equal probability non-Gaussian conversion method; Based on the first soil layer state parameter, the first rock layer state parameter and the Kendall correlation coefficient matrix, a first slope safety factor of a target slope region is determined by using a Monte Carlo reliability analysis method combined with a polynomial response surface function. 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.

[0006] 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.

[0007] 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 respectively determined based on the first soil layer state parameter and the first rock layer state parameter by using a K-S test method.

[0008] Optionally, the Kendall correlation coefficient matrix between the first soil layer state parameter and the first rock layer state parameter is calculated, comprising: respectively determining 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 parameter and the first rock layer state parameter; 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. This represents the Kendall correlation coefficient for the knotted condition.

[0009] Secondly, embodiments of this application provide a high-efficiency reliability analysis device for soil and rock slopes, the device comprising: 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 calculation module is used to 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. 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 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.

[0010] 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.

[0011] 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.

[0012] Optionally, the computing module includes: 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. 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. 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. This represents the Kendall correlation coefficient for the knotted condition.

[0013] Thirdly, embodiments of this application provide an electronic device, including 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 any of the above claims.

[0014] Fourthly, embodiments of this application provide a readable storage medium storing a program or instructions, which, when executed by a processor, implements the efficient reliability analysis method for soil and rock slopes as described above.

[0015] The specific beneficial effects are as follows: This application embodiment determines the first soil state parameter and the center coordinates of the first unit of the soil layer in the sample slope area, and the first rock state parameter and the center coordinates of the second unit of the rock layer in the sample slope area. Based on the first soil state parameter, the center coordinates of the first unit, the first rock state parameter, and the center coordinates of the second unit, a Latin hypercube sampling method combined with an equal-probability non-Gaussian transformation method is used to generate a cross-correlated arbitrary distribution random field. Based on the parameter space mapping corresponding to the cross-correlated arbitrary distribution random field, the sample slope safety factor of the sample slope area is calculated. The sample slope safety factor is then integrated with the first soil state parameter and the first rock state parameter to obtain a sample set. The first soil state parameter and the first rock state parameter are then calculated respectively with respect to the sample slope area. The Kendall correlation coefficient matrix between slope safety factors is used in Monte Carlo reliability analysis. 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 first slope safety factor of the target slope area is determined. The first number of slope safety factors less than 1 is determined, and the structural failure probability of the target slope area is calculated based on the first number. The Kendall coefficient can be used to characterize the nonlinear cross-correlation relationship of non-Gaussian parameters. Combined with layered random field modeling, it can accurately reflect the spatial distribution characteristics of parameters in soil-rock mixed strata. Furthermore, the polynomial response surface surrogate model replaces a large number of repetitive finite element calculations, improving the efficiency of slope stability analysis and the accuracy and reliability of complex strata engineering simulation. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments of this application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a flowchart illustrating an efficient reliability analysis method for soil and rock slopes provided in an embodiment of this application. Figure 2 This is a flowchart illustrating the generation process of a cross-correlated random field provided in an embodiment of this application; Figure 3 This is a flowchart illustrating the generation process of a parameter space mapping provided in an embodiment of this application; Figure 4 This is a schematic diagram illustrating a parameter filtering method provided in an embodiment of this application; Figure 5 This is a logic block diagram of a high-efficiency reliability analysis device for soil and rock slopes provided in an embodiment of this application; Figure 6 This is a schematic diagram of an electronic device provided in an embodiment of this application. Detailed Implementation

[0018] Exemplary embodiments of this application will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of this application are shown in the drawings, it should be understood that this application may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of this application and to fully convey the scope of this application to those skilled in the art.

[0019] Reference Figure 1 , Figure 1 This application provides a flowchart illustrating an efficient reliability analysis method for soil and rock slopes. The method may include: Step 101: Determine the first soil layer state parameters and the center coordinates of the first unit of the soil layer unit in the sample slope area, and the first rock layer state parameters and the center coordinates of the second unit of the rock layer unit in the sample slope area.

[0020] In the embodiments of this application, the first soil layer state parameters and the first rock layer state parameters of the soil layer in the slope engineering can be obtained through engineering geological surveys, wherein the state parameters may include the mean value. (elastic modulus E, cohesion C, angle of internal friction) The coefficient of variation (COV) can be used to determine the optimal distribution type and cumulative distribution function of each parameter, serving as a data source for Latin hypercube sampling. Slope areas can be modeled using FLAC3D, extracting the center coordinates of the first unit of the soil layer and the center coordinates of the second unit of the rock layer.

[0021] Step 102: Calculate the Kendall correlation coefficient matrix between the state parameters of the first soil layer and the state parameters of the first rock layer.

[0022] In the embodiments of this application, the Kendall correlation coefficient matrix is ​​a nonparametric statistic used to measure the degree of monotonic association between two ordinal variables. Its core idea is to reflect the correlation between variables by calculating the difference in the number of "consistent pairs" and "inconsistent pairs" in two sets of data. Suppose there are two sets of data... , For any two observation points (i,j), if and ,or and If, then this pair of data is called a consistent pair, if and ,or and If, then this pair of data is called an inconsistent pair, if or This pair of data is called a knotted pair (the above is a specific explanation of the Kendall correlation coefficient; the parameter symbols have no practical meaning). Based on the number of consistent pairs, inconsistent pairs, and knotted pairs between the first soil layer state parameters and the first rock layer state parameters, the Kendall correlation coefficient matrix between them can be calculated.

[0023] Optionally, step 102 may include the following sub-steps: Step 1021: Determine the number of first consistent pairs, the number of first inconsistent pairs, and the number of first knotted pairs between the first soil state parameters and the first rock state parameters.

[0024] Step 1022: 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.

[0025] In the embodiments of this application, firstly, based on the definitions of consistent pairs, inconsistent pairs, and knotted pairs in the Kendall correlation coefficient matrix, the number of first consistent pairs, first inconsistent pairs, and first knotted pairs between the first soil layer state parameters and the first rock layer state parameters are counted. Then, the Kendall correlation coefficient matrix is ​​calculated using the correlation coefficient calculation formulas for the case without knots and the case with knots.

[0026] The Kendall correlation coefficient matrix is ​​calculated using the following formula: The calculation formula for the case without knots is: (Equation 1); In equation 1 above, 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: (Equation 2); In equation 2 above, 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 coefficients for the knotted case. Kendall correlation coefficient matrix. Represented as: (Equation 3); In Equation 3, The number of parameters for the state of the first soil layer. This is the Kendall correlation coefficient matrix for soil and rock slopes.

[0027] In the embodiments of this application, by determining the number of first consistent pairs, the number of first inconsistent pairs, and the number of first knotted pairs between the first soil state parameters and the first rock state parameters, and based on the number of first consistent pairs, the number of first inconsistent pairs, and the number of first knotted pairs, the Kendall correlation coefficient matrix under the first soil state parameters can be calculated. This can improve the accuracy and reliability of the Kendall correlation coefficient matrix to a certain extent.

[0028] 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-correlated arbitrary distribution random field is generated using the Latin hypercube sampling method combined with the equal probability non-Gaussian transformation method.

[0029] In the embodiments of this application, reference is made to Figure 2 , Figure 2This document provides a flowchart for generating a cross-correlated random field according to an embodiment of the present application. Independent standard normal fields are generated using Latin hypercube sampling based on the state parameters of the first soil layer, the state parameters of the first rock layer, and "tczb.dat" (center coordinates of the first unit) and "yczb.dat" (center coordinates of the second unit). Then, the nonlinear cross-correlation between the parameters is controlled using the Kendall correlation coefficient matrix. A cross-correlated standard normal field is constructed through Cholesky decomposition of the covariance matrix. Finally, an equal-probability non-Gaussian transformation is performed by combining the optimal marginal distributions of the soil and rock layers to ultimately generate a cross-correlated arbitrary distribution random field. The specific process is as follows: (1) Based on the statistical characteristics of soil and rock mass parameters (i.e., the state parameters of the first rock stratum and the state parameters of the first rock stratum), Latin hypercube sampling is used to generate independent standard normal vectors. : (Equation 4); In Equation 4, This indicates that the dimensions of the random variable are determined according to the requirements.

[0030] The autocorrelation matrix is ​​obtained by using a stochastic exponential function. Autocorrelation matrix The lower triangular matrix L is obtained by Cholesky decomposition.

[0031] (Equation 5); (Formula 6); In Equations 5 and 6, This represents the total number of random field elements, consistent with the number of grid cells in a finite difference partitioning. It is a lower triangular matrix. It is an upper triangular matrix. for The transpose of .

[0032] Generate an independent standard normal field X: .

[0033] (2) Regarding the Kendall correlation coefficient matrix Performing Cholesky decomposition yields its lower triangular matrix: (Equation 7); In Equation 7, It is a lower triangular matrix. It is an upper triangular matrix, that is The transpose of .

[0034] (3) Generate a cross-correlation standard normal field N: Let ,in , Assuming k=3, we can obtain the elastic modulus E, cohesion c, and internal friction angle. The cross-correlation standard normal distribution random field.

[0035] (Equation 8); In equation 8 above, The cross-correlation of the elastic modulus represents a standard normal distribution. The cross-correlation of cohesion is represented by the standard normal distribution. The cross-correlation standard normal distribution of the internal friction angle is represented.

[0036] (4) Let ,in Given the cumulative distribution function of the standard normal distribution, we can obtain E, c, ... Cross-correlation standard uniform distribution random field: (Equation 9); In equation 9 above, These represent the elastic modulus E, cohesion c, and internal friction angle, respectively. The cross-correlation standard is uniformly distributed.

[0037] (5) According to E, c, The cumulative distribution function determines its inverse function. By transforming the cross-correlation standard uniform distribution random field using the equal probability transformation method, a multivariate cross-correlation random field of surrounding rock parameters of the target distribution can be constructed. (Equation 10); In equation 10 above, , , These represent the elastic modulus E, cohesion c, and internal friction angle, respectively. The cross-correlation distribution of multivariate surrounding rock parameters.

[0038] The final output is the non-Gaussian random field parameter files "Ei.txt", "ci.txt", and " -i.txt.

[0039] 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.

[0040] In the embodiments of this application, the optimal distribution of the state parameters of the first soil layer and the state parameters of the first rock layer can be determined by the KS test. The KS test is more practical in engineering because it has clear physical meaning, requires no data grouping, and exhibits strong stability with small samples. Therefore, this patent uses the KS test to determine the optimal distribution of soil parameters and adopts a commonly used significance level. A KS test is performed with a value of 0.5 to determine the optimal probability density distribution of soil and rock mass parameters. Finally, the distribution functions of each parameter are accumulated as the source of Latin hypercube sampling data. This improves the accuracy and reliability of Latin hypercube sampling.

[0041] Step 104: Using 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, the first slope safety factor of the target slope area is determined by combining the polynomial response surface function.

[0042] In the embodiments of this application, 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 can be used as a basis. Multiple sets of random samples were generated using Gaussian Copula coupled with Latin hypercube sampling, and then PRSM was called to predict the safety factor F of the first slope. S PRSM is a multinomial response surface, which can be obtained by fitting the first soil layer state parameters and the first rock layer state parameters with the Kendall correlation coefficient matrix. The specific steps for generating multiple sets of random samples using Gaussian Copula coupled with Latin hypercube sampling are as follows: (1) First Kendall The Pearson correlation coefficient matrix required to convert the matrix to a Gaussian Copula The conversion can be performed using the following formula: (Equation 11); In Equation 11, Kendall correlation coefficient matrix of soil and rock layers .

[0043] (2) For the matrix Performing Cholesky decomposition yields a lower triangular matrix L.

[0044] (Equation 12); In Equation 12, It is a lower triangular matrix. for The transpose of .

[0045] (3) Perform Latin hypercube sampling 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.

[0046] (Equation 13); In Equation 13, The number of parameters for the state parameters of the first soil layer.

[0047] (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.

[0048] (Equation 14); (5) For each independent sample in V Calculate its cumulative probability in the standard normal distribution. .

[0049] (Equation 15); In Equation 15, This is the cumulative distribution function of the standard normal distribution.

[0050] (6) Using the inverse cumulative distribution function of the target parameter, the probability is... Convert to parameter value .

[0051] (Equation 16); In Equation 16, It is the inverse cumulative distribution function of the optimal marginal distribution of parameters.

[0052] (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.

[0053] 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.

[0054] In the embodiments of this application, the polynomial response surface function can be obtained through the following process: Reference Figure 3 , Figure 3A flowchart for generating a parameter space mapping provided in this application includes the following steps (1) to (4): (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).

[0055] (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.

[0056] (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.

[0057] (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.

[0058] 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 .

[0059] Then, the parameters can be calculated. Kendall coefficient, according to Sort by value in descending order, such asFigure 4 As shown, Figure 4 This is a schematic diagram illustrating parameter filtering as provided in an embodiment of this application. Assume a filtering threshold. and , , , , , Remove low-sensitivity parameters and retain a subset of key parameters. , , .

[0060] Kendall The calculation uses: (Equation 17); In Equation 17, and Samples and samples The first slope safety factor, where X is the state parameter of the first soil layer or the state parameter of the first rock layer. This represents the number of samples.

[0061] Based on the above sample set Based on the key parameters selected through Kendall's global sensitivity analysis, a polynomial function is used to approximate the slope safety factor. The relationship between key geotechnical state parameters is used to replace numerical models.

[0062] The polynomial form uses a second-order polynomial, and the polynomial coefficients are fitted using the least squares method. (include , , as well as ): (Equation 18); (Equation 19); In Equations 18 and 19, matrix X contains the parameter values ​​and polynomial terms for all samples. and The labels representing two distinct samples, and the response vector. for value.

[0063] Through the above process, the degree of matching between the fitted model and the actual scenario can be improved, and the accuracy and reliability of the polynomial response surface function can be enhanced.

[0064] Step 105: Determine a first number of times that the safety factor of the first slope is less than 1, and calculate the structural failure probability of the target slope area based on the first number.

[0065] In the embodiments of this application, statistics can be calculated. The first number of failure samples less than 1 is used to calculate the failure probability. : (Equation 20); In Equation 20, for The first number of failure samples less than 1, This represents the total number of samples.

[0066] In the embodiments of this application, by determining the first soil state parameter and the center coordinates of the first unit of the soil layer unit in the sample slope area, and the first rock state parameter and the center coordinates of the second unit of the rock layer unit in the sample slope area, a cross-correlated arbitrary distribution random field is generated based on the first soil state parameter, the center coordinates of the first unit, the first rock state parameter, and the center coordinates of the second unit. The Latin hypercube sampling method, combined with the equal probability non-Gaussian transformation method, is used. Based on the parameter space mapping corresponding to the cross-correlated arbitrary distribution random field, the sample slope safety factor of the sample slope area is calculated. The sample slope safety factor is then integrated with the first soil state parameter and the first rock state parameter to obtain a sample set. The first soil state parameter and the first rock state parameter are then calculated with the sample slope area. The Kendall correlation coefficient matrix between the safety factors of this slope is used in Monte Carlo reliability analysis. Based on the state parameters of the first soil layer, the state parameters of the first rock layer, and the Kendall correlation coefficient matrix, the first slope safety factor of the target slope area is determined by combining the polynomial response surface function. The first number of the first slope safety factors less than 1 is determined, and the structural failure probability of the target slope area is calculated based on the first number. The Kendall coefficient can be used to characterize the nonlinear cross-correlation relationship of non-Gaussian parameters. Combined with layered random field modeling, it can accurately reflect the spatial distribution characteristics of parameters in soil-rock mixed strata. Furthermore, the polynomial response surface surrogate model replaces a large number of repetitive finite element calculations, improving the efficiency of slope stability analysis and the accuracy and reliability of complex strata engineering simulation.

[0067] In the embodiments of this application, code corresponding to the efficient reliability analysis method for soil and rock slopes is provided as follows: import numpy as np from scipy.stats import norm, kendalltau from scipy.linalg import cholesky # Set a random seed for repeatability np.random.seed(42) # Parameter distribution definition mu_c, sigma_c = 25, 12 # Cohesion mu_phi, sigma_phi = 20, 6 # Angle of internal friction mu_E, sigma_E = 200, 100 # Elastic modulus # Kendall Correlation Matrix tau_matrix = np.array([ [1.0, 0.3, 0.2], [0.3, 1.0, 0.4], [0.2, 0.4, 1.0] ]) # Convert Kendall's tau to Pearson correlation coefficient def kendall_to_pearson(tau): return np.sin(np.pi * tau / 2) rho_matrix = kendall_to_pearson(tau_matrix) # Check and ensure the matrix is ​​positive definite if np.all(np.linalg.eigvals(rho_matrix) > 0): L = cholesky(rho_matrix, lower=True) else rho_matrix += np.eye(3) * 0.01 L = cholesky(rho_matrix, lower=True) # Generate samples def generate_samples(n, L): U = np.random.normal(0, 1, (n, 3)) V = U @ LT P = norm.cdf(V) c = norm.ppf(P[:, 0], loc=mu_c, scale=sigma_c) phi = norm.ppf(P[:, 1], loc=mu_phi, scale=sigma_phi) E = norm.ppf(P[:, 2], loc=mu_E, scale=sigma_E) return c, phi, E n_train = 100 c_train, phi_train, E_train = generate_samples(n_train, L) # Calculate the safety factor FS def compute_fs(c, phi, E): return (0.012 * c + 0.025 * phi - 0.0005 * E + 0.0001 * c * phi - 0.000001 * E**2 + 0.6 + np.random.normal(0, 0.2, len(c))) fs_train = compute_fs(c_train, phi_train, E_train) # Kendall Global Sensitivity Analysis tau_c = kendalltau(c_train, fs_train).correlation tau_phi = kendalltau(phi_train, fs_train).correlation tau_E = kendalltau(E_train, fs_train).correlation # Output Kendall's τ sensitivity coefficients for each parameter print("Kendall's τ sensitivity coefficient:") print(f"c: {tau_c:.3f}") print(f"phi: {tau_phi:.3f}") print(f"E: {tau_E:.3f}") # Filter key parameters (threshold |τ|>0.1) key_params = [] if abs(tau_c) > 0.1: key_params.append('c') if abs(tau_phi) > 0.1: key_params.append('phi') if abs(tau_E) > 0.1: key_params.append('E') # Output key parameters print(f"\nKey parameters: {key_params}") # Build polynomial response surface (second order) def create_polynomial_features(X, degree=2): n_samples, n_features = X.shape features = [] features.append(np.ones(n_samples)) for i in range(n_features): features.append(X[:, i]) if degree >= 2: for i in range(n_features): features.append(X[:, i]**2) for i in range(n_features): for j in range(i+1, n_features): features.append(X[:, i] * X[:, j]) return np.column_stack(features) X_train = np.column_stack([c_train, phi_train, E_train]) X_poly = create_polynomial_features(X_train, degree=2) beta = np.linalg.lstsq(X_poly, fs_train, rcond=None)[0] def predict_fs(X, beta): X_poly = create_polynomial_features(X, degree=2) return X_poly @ beta # Monte Carlo Reliability Analysis n_mc = 20000 # Calculate the average failure probability by running the program multiple times num_runs = 5 # Number of runs pfs = [] for i in range(num_runs): # Use a different random seed for each run np.random.seed(42 + i) c_mc, phi_mc, E_mc = generate_samples(n_mc, L) X_mc = np.column_stack([c_mc, phi_mc, E_mc]) fs_mc = predict_fs(X_mc, beta) pf = np.sum(fs_mc < 1) / n_mc pfs.append(pf) # The result of the first run (to maintain consistency with the original output) np.random.seed(42) c_mc, phi_mc, E_mc = generate_samples(n_mc, L) X_mc = np.column_stack([c_mc, phi_mc, E_mc]) fs_mc = predict_fs(X_mc, beta) failure_count = np.sum(fs_mc < 1) pf = failure_count / n_mc # Output failure probability print(f"\nProbability of failure P_f: {pf:.4f}") # Calculate and output the average failure probability avg_pf = np.mean(pfs) print(f"Average failure probability over multiple runs: {avg_pf:.4f}") # Verify response surface accuracy fs_true_mc = compute_fs(c_mc, phi_mc, E_mc) mse = np.mean((fs_mc - fs_true_mc)**2) # Output the prediction accuracy of the response surface model print(f"Prediction accuracy (MSE) of response surface model: {mse:.4f}") The code is explained as follows: 1. Distribution parameters (statistical properties of random variables): Cohesion (c): c=25 (mean), standard deviation=12; Angle of internal friction ( ): =20° (mean), standard deviation = 6); elastic modulus (E): E = 200 (mean), standard deviation = 100.

[0068] 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).

[0069] 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).

[0070] 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).

[0071] 5. Response surface model parameters: Polynomial order: degree=2 (second-order polynomial) 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.

[0072] 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.

[0073] 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: 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. Calculation module 502 is used to 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. The generation module 503 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 second determining module 504 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, and combining the polynomial response surface function. The third determining module 505 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.

[0074] 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.

[0075] 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.

[0076] Optionally, the 502 calculation module includes: 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. 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. 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. This represents the Kendall correlation coefficient for the knotted condition.

[0077] The efficient analysis device for soil and rock slope reliability in this application embodiment can be an electronic device or a component of an electronic device, such as an integrated circuit or a chip. The electronic device can be a terminal or other devices besides a terminal. For example, the electronic device can be a mobile phone, tablet computer, laptop computer, PDA, in-vehicle electronic device, mobile internet device (M-identifier), augmented reality (AR) / virtual reality (VR) device, robot, wearable device, ultra-mobile personal computer (UMPC), netbook, or personal digital assistant (PDA), etc., and can also be a server, network attached storage (NAS), personal computer (PC), etc. This application embodiment does not specifically limit the specific devices.

[0078] 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.

[0079] The efficient soil and rock slope reliability analysis device 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.

[0080] 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.

[0081] 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.

[0082] 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.

[0083] 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.

[0084] 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.

[0085] 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.

[0086] 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.

[0087] 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.

[0088] 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.

[0089] 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 slope safety factors less than 1 is determined, and the structural failure probability of the target slope area is calculated based on the first number.

2. The method according to claim 1, characterized in that, 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.

3. 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.

4. The method according to claim 1, characterized in that, 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. This represents the Kendall correlation coefficient for the knotted condition.

5. A high-efficiency analysis device for the reliability of soil and rock slopes, characterized in that, The device includes: 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.

6. 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 any one of claims 1 to 4.

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