Three-dimensional slope risk assessment method considering non-Gaussian cross-correlation of soil parameters

Abstract

The present invention discloses a three-dimensional slope risk assessment method that considers the non-Gaussian cross-correlation of soil parameters. The method comprises the following steps: first, determining the statistical information of soil parameters, and then determining the marginal distribution and Copula function of soil parameters based on engineering experience or measured data; then establishing a finite element numerical model and deriving unit information; employing K-L expansion to discretize a large three-dimensional autocorrelation random field and couple the non-Gaussian cross-correlation random field based on Copula; embedding the non-Gaussian cross-correlation random field into the finite element model, and performing stability analysis and calculation; employing a K clustering method based on the displacement data of each unit to identify sliding units and calculate the sliding volume; and performing Monte-Carlo simulation to obtain statistical results of risk assessment. The present invention is applicable to the risk analysis of geotechnical structures, and directly implements the three-dimensional slope risk assessment method that considers the non-Gaussian cross-correlation of soil parameters. The assessment results are more reasonable and closer to the actual situation, thereby improving the credibility of the risk assessment results.

Description

Technical Field

[0001] The present invention belongs to the technical field of geotechnical engineering risk assessment, and in particular relates to a three-dimensional slope risk assessment method considering non-Gaussian cross-correlation of soil parameters. Background Art

[0002] Slope stability is a critical issue in geotechnical engineering. Slope instability frequently occurs in practical engineering projects. Conducting slope risk assessment is a crucial means of ensuring the safe operation of projects. Geotechnical parameters exhibit spatially uneven distributions due to processes such as sedimentation and transport, often referred to as spatial variability. Extensive research has demonstrated significant correlations between parameters. Therefore, how to account for the impact of spatial variability and correlation in risk assessment remains an urgent challenge. Currently, spatial variability of parameters is generally characterized using random fields, which describe the values ​​of the parameters at different locations in space. Commonly used methods include the KL expansion method, the Cholesky method, and stepwise decomposition. However, given the significant correlations between geotechnical parameters, the random fields of each parameter should be transformed and coupled when discretizing them. A commonly used method is the Nataf transform. However, this method assumes that the parameters follow a Gaussian correlation structure, which does not always hold true in practical engineering. Therefore, the Nataf transform has certain limitations in geotechnical engineering problems. To solve this problem, the Copula theory was introduced. Since it can characterize a variety of different correlation structures and is more flexible in describing the correlation between parameters, the random fields of each parameter can be coupled into a non-Gaussian cross-correlation random field, thereby more accurately reflecting the complex situations in actual engineering. The application of this method provides a new tool for risk assessment in geotechnical engineering.

[0003] Furthermore, the impact of parameter cross-correlation on 2D slope reliability analysis has been extensively studied. However, 3D slopes are more representative of the real-world situation than 2D slopes, and 2D slope analysis results may be conservative due to oversimplification. However, limited research has been conducted on 3D slopes. These findings highlight the necessity of using 3D slope models in all analyses.

[0004] Therefore, this paper uses a parametric non-Gaussian cross-correlation random field to conduct a three-dimensional slope risk assessment, exploring the impact of parameter spatial variability and correlation on the results. Since the volume of the sliding body is directly related to the consequences of a slope failure, the risk assessment results are quantified using the sliding body volume. A K-clustering method is used to identify and calculate the sliding body volume. The proposed method is theoretically simple and highly practical, providing a more accurate and comprehensive solution for solving practical geotechnical engineering problems. Summary of the Invention

[0005] The purpose of this invention is to address the deficiencies of existing research and provide a three-dimensional slope risk assessment method that considers the non-Gaussian cross-correlation structure between rock and soil parameters. This method takes into account the non-Gaussian cross-correlation structure between parameters and the possible situations in actual engineering.

[0006] This method takes into account the spatial variability of parameters and the non-Gaussian cross-correlation between parameters, constructs a non-Gaussian cross-correlation random field of parameters, and conducts three-dimensional slope reliability analysis on this basis. It is more in line with actual engineering conditions and can provide more accurate reliability analysis results, providing support for the safe operation of geotechnical engineering.

[0007] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0008] In one aspect, the present invention provides a three-dimensional slope risk assessment method considering non-Gaussian cross-correlation of soil parameters, comprising the following steps:

[0009] Determine several soil parameters required according to the type of three-dimensional slope to be evaluated, and obtain statistical information of the corresponding soil parameters;

[0010] Determine the marginal distribution of soil parameters and the Copula function that characterizes the correlation between soil parameters;

[0011] Establish a finite element numerical model of a three-dimensional slope and derive the unit information of the finite element numerical model;

[0012] The KL expansion is used to discretize the large 3D autocorrelation random field of the 3D slope and obtain the autocorrelation random field of soil parameters.

[0013] Based on the non-Gaussian cross-correlation random field coupling of Copula, the non-Gaussian cross-correlation random field of soil parameters is obtained;

[0014] The non-Gaussian cross-correlation random field is embedded in the finite element model, and the displacement data of each unit is calculated through stability analysis;

[0015] Based on the displacement data of each unit, the clustering method is used to identify the sliding unit and calculate the sliding volume;

[0016] Repeat the above steps to obtain multiple results of sliding volume calculation, and use statistical methods to evaluate the three-dimensional slope risk.

[0017] Furthermore, the soil parameters include any number of density, soil particle specific gravity, water content, void ratio, porosity, saturation, dry density, saturated density, buoyancy, cohesion, internal friction angle, elastic modulus, Poisson's ratio, bulk density, and permeability coefficient; the statistical information of the soil parameters is the mean and variance of the corresponding soil parameters.

[0018] Furthermore, the AIC rule or BIC rule is used to determine the optimal fitting marginal distribution and optimal Copula function of soil parameters.

[0019] Furthermore, there are two soil parameters, which are respectively recorded as soil parameters c 、 The method of using KL expansion to discretize large 3D autocorrelation random fields of 3D slopes is as follows:

[0020] Representing a random field as a continuous function H ( x , i ), H ( x , i ) value represents the continuous domain A point in x ∈ Ω m The value of the variable, m is the dimension of the topological space Ω, i ∈ Θ is the coordinate of a point in the sample space Θ, (Θ, F , P ) is a complete probability space;

[0021] The Gaussian random field is expressed as:

[0022]

[0023] In the above formula, m ( x )and s ( x ) are the mean and variance functions of the Gaussian random field, x i ( i ) is a random vector that follows a standard normal distribution, l i and ϕ i ( x ) are the autocorrelation functions r ( x , x’ )'s eigenvalues ​​and eigenvectors satisfy the formula

[0024]

[0025] right H ( x , i )Use a finite number of expansion terms to convert the eigenvalue l i Arrange from largest to smallest, using the first M indivual l i and the corresponding ϕ i ( x ) is approximated by the sum of products of H ( x , i ),Right now

[0026]

[0027] Where, M is the number of expansion terms of KL expansion, and the autocorrelation error is controlled by e ρ, M ( x , x’ ) is less than a preset threshold value;

[0028] By finding the eigenvalue l i and eigenvectors ϕ i ( x ) completes the approximate solution of the continuous function H ( x , i )’s KL expansion;

[0029] Based on the above expansion, the autocorrelation random field of the variable is established Z IN = [ Z c IN , Z φ IN ], Z c IN , Z φ IN Represent soil parameters c 、 Random field of .

[0030] Furthermore, the method of the non-Gaussian cross-correlation random field between soil parameters is as follows:

[0031] Using Copula theory, the joint distribution of variables is expressed as

[0032]

[0033] Where, 、 Represent soil parameters c 、 The marginal cumulative distribution function of is the cumulative distribution function of the two-dimensional Copula; i is the Copula parameter;

[0034] Kendall rank correlation coefficient t Convert i , the calculation formula is

[0035]

[0036] based on c and f The joint distribution function of c and f The joint probability density function of

[0037]

[0038] Where, f 1( c )and f 2( f ) are respectively c and f The marginal probability density function of D ( u , v ; i )Depend on C ( u , v ; i ) The probability density function of the two-dimensional copula obtained by derivation;

[0039] Completing the autocorrelation random field based on Rosenblatt transform Z IN = [ Z c IN , Z φ IN ] coupling, generating a cross-correlated random field Z CNN = [ Z c CNN , Z φ CNN ], Z c CNN Considering the soil parameters c, After cross-correlation, the random field of soil parameter c is obtained. Z φ CNN Considering the soil parameters c, Soil parameters are obtained after cross-correlation Random field of .

[0040] Furthermore, the steps of Rosenblatt transformation are as follows:

[0041] Z c IN = Φ -1 ( F c ( Z c CNN ))

[0042] Z φ IN = Φ -1 ( F ( Z φ CNN | Z c CNN )) = h ( F φ ( Z φ CNN ), Φ( Z c IN ); i )

[0043] In the above formula, Φ -1 (·) represents the inverse function of the standard normal distribution CDF, F c (·)and F φ (·) respectively represent c and f The marginal CDF of F (·|·) represents the conditional CDF of the copula, h () indicates the Copula h function;

[0044] Transforming the above formula, we get c and f Cross-correlation random field Z CNN = [ Z c CNN , Z φ CNN ]

[0045] Z c CNN = F c-1 (Φ( Z c IN ))

[0046] Z φ CNN = F φ -1 ( h -1 (Φ( Z φ IN ), F c ( Z c CNN ); i ))

[0047] In the above formula, F c -1 (·)and F φ -1 (·) respectively c and f The inverse of the marginal cumulative distribution function, h -1 ( ) indicates the Copula h -1 function.

[0048] Furthermore, the Copula function includes but is not limited to Gaussian, Frank, and Clayton functions.

[0049] Furthermore, the strength reduction method is used to conduct stability analysis.

[0050] Furthermore, the K clustering method is used to identify the sliding unit and calculate the sliding volume. After the calculation is completed, the displacement corresponding to each node can be obtained, and the displacement mean of the node on each unit can be obtained. N The displacement of the unit ( d 1, d 2, ..., d N ). Using the K clustering method, we can N The displacement of each unit is minimized by E , which is divided into M cluster{ C 1, C 2, …, C M}( M ≤N ), clustering error E The expression is as follows

[0051]

[0052] Where, c k ( k = 1, 2, …, M ) is the cluster center of each cluster. By minimizing the above error, N Observations are divided into M In the present invention, each unit can be divided into a stable unit and a sliding unit. M= 2. The specific implementation steps of the K clustering method are as follows Figure 4 shown.

[0053] Furthermore, when assessing the three-dimensional slope risk, Monte-Carlo simulation is used to generate multiple N 1 standard normal random matrix ξ, and repeat all the above steps to complete N The non-Gaussian cross-correlation random field is embedded in the finite element model once, the displacement data of each unit is calculated through stability analysis, and the calculation results of N Monte-Carlo simulations are statistically analyzed to obtain the statistical results of the slope sliding volume as the result of three-dimensional slope risk assessment.

[0054] On the other hand, the present invention provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the three-dimensional slope risk assessment method as described in any one of the above items is implemented.

[0055] On the other hand, the present invention provides a non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements any of the above-mentioned three-dimensional slope risk assessment methods.

[0056] On the other hand, the present invention provides a computer program product, comprising a computer program, wherein when the computer program is executed by a processor, the computer program implements any one of the above three-dimensional slope risk assessment methods.

[0057] Compared with the prior art, the beneficial effects of the present invention are as follows: In the prior art, many methods assume that the parameters obey the Gaussian cross-correlation structure and use the Nataf transform to characterize the cross-correlation of parameters. This assumption is not applicable to all situations and may cause deviations in the analysis results. At the same time, most current studies are still limited to two-dimensional models, which are still inconsistent with the actual three-dimensional slopes, and also have a certain impact on the accuracy of the analysis results. In response to the shortcomings of the existing technology and research, the present invention proposes a three-dimensional slope risk assessment method with stronger applicability and accuracy. On the basis of considering the spatial variability and correlation of the parameters, the K clustering method is used to identify the sliding units of the three-dimensional slope and calculate the sliding body volume. Unlike the traditional method of using a fixed threshold to divide the sliding units and stable units, this method can more accurately identify the sliding units, which is more reasonable than the method using a fixed threshold, and the method has high computational efficiency and good accuracy. At the same time, the docking of ABAQUS and MATLAB and Python is realized, the random field is embedded in the ABAQUS finite element model, and the automatic submission of calculations and the export of calculation results are realized, which greatly reduces the computational time. The advantage of the present invention lies in its wide range of applications. It can be used for two-dimensional slope models and can also be easily extended to three-dimensional models. More importantly, by constructing a random field model that accounts for the non-Gaussian cross-correlations of soil parameters, we are able to more closely approximate the true spatial distribution of soil. Combined with a three-dimensional slope model, our results are closer to reality, providing a more reliable assessment. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 Flowchart of a three-dimensional slope risk assessment method considering non-Gaussian cross-correlation of soil parameters provided by an embodiment of the present invention.

[0059] Figure 2 A technical roadmap for a three-dimensional slope risk assessment method considering non-Gaussian cross-correlations of soil parameters provided by an embodiment of the present invention.

[0060] Figure 3 In the embodiment of the present invention e ρ, M ( x , x’ ) with the number of expanded items M Changes.

[0061] Figure 4 These are the specific implementation steps of the K clustering method in an embodiment of the present invention.

[0062] Figure 5 This is the result of clustering four randomly selected groups of samples using the K clustering method in the embodiment of the present invention, where: Figure 5 (a) is the clustering result of sample 1. Figure 5(b) is the clustering result of sample 2. Figure 5 (c) is the clustering result of sample 3. Figure 5 (d) in the middle is the clustering result of sample 4.

[0063] Figure 6 Frequency distribution histogram of sliding body volume.

[0064] Figure 7 Schematic diagram of a three-dimensional double-layer slope stability analysis model in an embodiment of the present invention. DETAILED DESCRIPTION

[0065] The following will provide a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0066] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0067] The present invention will be further described below with reference to specific examples, but they are not intended to limit the present invention.

[0068] The embodiment of the present invention discloses a three-dimensional slope risk assessment method considering the non-Gaussian cross-correlation of soil parameters, such as Figure 1 and Figure 2 As shown, the following steps are included:

[0069] S100, determining several required soil parameters according to the type of the three-dimensional slope to be evaluated, and obtaining statistical information of the corresponding soil parameters;

[0070] The soil parameters include any number of density, soil particle specific gravity, water content, void ratio, porosity, saturation, dry density, saturated density, buoyancy, cohesion, internal friction angle, elastic modulus, Poisson's ratio, bulk density, and permeability coefficient. At least two or more of these soil parameters can be selected. The specific type to be selected should be the soil parameter that has a greater impact on the three-dimensional slope stability.

[0071] The statistical information of the soil parameters is the mean value, variance, etc. of the corresponding soil parameters, and the specific type is not specific. In this embodiment, cohesion is used as the c and internal friction angle f Taking soil as an example, the mean and variance of the two soil parameters are statistically analyzed and calculated for subsequent analysis.

[0072] Soil parameters can be obtained through engineering experience or field survey data of three-dimensional slopes.

[0073] S200, determining the marginal distribution of soil parameters and the Copula function representing the correlation between soil parameters;

[0074] There are two methods for determining the marginal distribution of geotechnical parameters:

[0075] 1. Based on engineering experience, it is assumed that the marginal distribution and statistical information of soil parameters, such as shear strength parameters (i.e. cohesion c and internal friction angle f ) is generally considered to obey the log-normal distribution;

[0076] 2. Based on the measured data, the statistical information of soil parameters can be calculated and the AIC rule or BIC rule can be used to determine the optimal fitting marginal distribution of soil parameters. In this method, the AIC criterion is used, that is, the parameter marginal distribution with the smallest AIC value is the optimal fitting marginal distribution. The calculation formula of the AIC value is:

[0077]

[0078] Where, f (·) is the probability density function of the marginal distribution, p and q is the characteristic parameter of the marginal distribution function, k m is the number of characteristic parameters, N is the number of groups of measured data, x (d)k represents the k The soil parameters d Group measured values.

[0079] Under the premise of having measured data, the AIC criterion can also be used to select the optimal Copula, so that the Copula function with the smallest AIC value is the optimal fitting Copula of the soil parameters. At this time, the calculation formula of AIC is:

[0080]

[0081]

[0082]

[0083] Where rank(·) represents x (d) k is the measured data sorted in ascending order { x (1)k, x (2)k, ..., x rank in (N)k}, c(·, ·; i ) is the probability density function of the Copula function, subscript i andj Representative i Hedi j Soil parameters, i is the characteristic parameter of the Copula function, k c is the number of characteristic parameters of the Copula function.

[0084] In the embodiment of the present invention, the cohesion assumed by engineering experience is used c and internal friction angle f The marginal distribution and Copula function of the parameters are determined based on the statistical information of the assumed engineering experience. The mean and coefficient of variation of Soil1 and Soil2 are listed in Table 3. c and internal friction angle f The marginal distributions of all obey the lognormal distribution. c and f Kendall rank correlation coefficient between t =-0.5. Taking into account c and f There is an obvious negative correlation between c and f The cross-correlation of is described, but the method proposed in the present invention is not limited to FrankCopula. t and i Conversion relationship

[0085]

[0086] The parameters corresponding to the Frank Copula can be obtained i It is -5.7363.

[0087] Table 1 Probability information of shear strength parameters

[0088]

[0089] S300. Establish a finite element numerical model of the three-dimensional slope and derive unit information of the finite element numerical model; specifically, determine the geometric dimensions, boundary conditions, mesh type, etc. of the research object, use ABAQUS to establish the finite element model of the research object, and derive the center point coordinates of each unit in the finite element model.

[0090] In this step, the geometric dimensions and boundary conditions of the research object are first determined. The research slope is a soil slope with a length of 50m, a width of 30m, and a height of 15m, and a slope angle of 26.6. ° ABAQUS was used to establish the finite element model of the double-layer soil three-dimensional slope, as shown in Figure 7As shown in the figure, the slope is divided into two layers of soil, the upper layer of which is Soil1 and the lower layer of which is Soil2. The Drucker-Prager constitutive model is used. Normal constraints are set on the front, back, left, and right sides of the slope, and the bottom is fully constrained. The element type used is C3D8, with a total of 17,950 elements. The coordinates of each node in the model are derived, and the coordinates of each element center are calculated.

[0091] S400, using the Karhunen-Loève expansion (KL expansion) to discretize the large 3D autocorrelation random field of the 3D slope and obtain the autocorrelation random field of soil parameters;

[0092] The Karhunen-Loève expansion (KL expansion) is used to discretize large three-dimensional autocorrelated random fields and couple them with non-Gaussian cross-correlated random fields based on Copula.

[0093] S410, using the KL expansion method, the random field can be represented as a continuous function H ( x , i ), H ( x , i ) value represents the continuous domain A point in x ∈ Ω m The value of the variable, m is the dimension of the topological space Ω, i ∈ Θ is the coordinate of a point in the sample space Θ, (Θ, F , P ) is a complete probability space. The Gaussian random field can be expressed as

[0094]

[0095] In the above formula, m ( x )and s ( x ) are the mean and variance functions of the Gaussian random field, x i ( i ) is a random vector that follows a standard normal distribution, l i and ϕ i ( x ) are the autocorrelation functions r ( x , x’ )'s eigenvalues ​​and eigenvectors satisfy the formula

[0096]

[0097] Where, r ( x , x’ ) is the autocorrelation function, the above formula can be converted to

[0098]

[0099] S420, yes H ( x , i )Use a finite number of expansion terms to convert the eigenvalue l i Arrange from largest to smallest; theoretically, H ( x , i ) can be expressed as the sum of an infinite number of KL expansion terms, but in practice, it is impractical to calculate an infinite number of expansion terms. Therefore, in order to approximate H ( x , i ), we can use a finite number of expansion terms to convert the eigenvalue l i Arrange from largest to smallest, using the first M indivual l i and the corresponding ϕ i ( x ) is approximated by the sum of products of H ( x , i ),Right now

[0100]

[0101] Where, M is the number of expansion terms of KL expansion, which can be used to control the autocorrelation error e ρ, M ( x , x’ ) is less than a preset threshold to determine, e ρ, M ( x , x’ ) can be obtained using the following formula

[0102]

[0103] S430, by obtaining characteristic values l i and eigenvectors ϕ i ( x ) completes the approximate solution of the continuous function H ( x , i ) of the KL expansion.

[0104] Finding eigenvalues l i and eigenvectors ϕ i ( x ) include the Nyström method, the Galerkin method, etc., which will not be described here.

[0105] S440, based on the above expansion, establish the autocorrelation random field of the variable Z IN = [ Z c IN , Z φ IN ], Z c IN , Z φ IN Represent soil parameters c 、 Random field of .

[0106] In this step, the autocorrelation function type (ACF) and autocorrelation distance (ACD) are first determined. The square exponential autocorrelation function is better adapted to the KL expansion method. Therefore, in the embodiment of the present invention, the square exponential ACF is used, and the expression is:

[0107]

[0108] Where, t xij = | x i - x j |, t yij = | y i - y j |, t zij = | z i - z j |, respectively represent the first i Point and j Points in x 、 y 、 z Relative distances in three directions; d x , d y , d z Respectively x 、 y 、 z The autocorrelation distance in three directions. In the embodiment of the present invention, take [ d x , d y , d z ] = [40, 40, 4]m.

[0109] Then, according to the autocorrelation error formula of the KL expansion method

[0110]

[0111] by e ρ, M ( x , x’ )<0.5 as the number of expansion items M After analysis, when M = 14, there is e ρ, M ( x , x’ )<0.5; e ρ, M ( x , x’ ) with the number of expanded items M Changes such as Figure 3 shown.

[0112] Then, the KL expansion method can be used to perform cohesion c and internal friction angle f Discretization of the autocorrelation random field to obtain the autocorrelation random field of the slope model Z IN .

[0113] S500, based on the non-Gaussian cross-correlation random field coupling of Copula, obtains the non-Gaussian cross-correlation random field of soil parameters.

[0114] S510. In the present invention, only cohesion is considered. c and internal friction angle f Two variables, using Copula theory, the joint distribution of the variables is expressed as

[0115]

[0116] Where, 、 Represent soil parameters c 、 The marginal cumulative distribution function of is the cumulative distribution function of the two-dimensional Copula; Table 1 lists the probability density function (PDF) of several commonly used Copulas. h- function, h -1 - Function and corresponding i The value range of i is the Copula parameter.

[0117] Several commonly used binary Copula models are listed below:

[0118] Gaussian model:

[0119] The probability density function (PDF) is

[0120] h-function (h function) is

[0121] h-1-function

[0122] parameter i The value range is [-1, 1].

[0123] Frank model:

[0124] The probability density function (PDF) is

[0125] h-function (h function) is

[0126] h-1-function

[0127] parameter i The value range is (-∞, +∞)\{0}.

[0128] Clayton model:

[0129] The probability density function (PDF) is

[0130] h-function (h function) is

[0131] h-1-function

[0132] parameter i The value range is [0, +∞).

[0133] S520, using Kendall rank correlation coefficient t Convert i , the calculation formula is

[0134]

[0135] S530, based on c and f The joint distribution function of c and f The joint probability density function of

[0136]

[0137] Where, f 1( c )and f 2( f ) are respectively c and f The marginal probability density function of D ( u , v ; i )Depend on C ( u , v ; i ) The probability density function of the two-dimensional Copula obtained by derivation; the derivation process is as follows

[0138]

[0139] S540, complete autocorrelation random field based on Rosenblatt transform Z IN = [ Z c IN , Z φ IN ] coupling, generating a cross-correlated random field Z CNN = [ Z c CNN , Z φ CNN ], Z c CNN Considering the soil parameters c, After cross-correlation, the random field of soil parameter c is obtained. Z φ CNN Considering the soil parameters c, Soil parameters are obtained after cross-correlation Random field of .

[0140] The Rosenblatt transformation steps are as follows:

[0141] Z c IN = Φ -1 ( F c ( Z c CNN ))

[0142] Z φ IN = Φ -1 ( F ( Z φ CNN | Z c CNN )) = h ( F φ ( Z φ CNN ), Φ( Z c IN ); i )

[0143] Where, Φ -1 (·) represents the inverse function of the standard normal distribution CDF, F c (·)and F φ (·) respectively represent c and f The marginal CDF of F (·|·) represents the conditional CDF of the copula. By transforming the above formula, we can get c and f Cross-correlation random field Z CNN = [ Z c CNN , Z φ CNN ]

[0144] Z c CNN = F c -1 (Φ( Zc IN ))

[0145] Z φ CNN = F φ -1 ( h -1 (Φ( Z φ IN ), F c ( Z c CNN ); i ))

[0146] In the above formula, F c -1 (·)and F φ -1 (·) respectively c and f The inverse function of the marginal cumulative distribution function. After the above steps, we can convert c and f The autocorrelation random field Z IN = [ Z c IN , Z φ IN ]Use different Copula functions to couple into cross-correlated random fields Z CNN = [ F c -1 ( Z c CU ), F φ -1 ( Z φ CU ) ].

[0147] S600, embedding the non-Gaussian cross-correlation random field into the finite element model, and calculating the displacement data of each unit through stability analysis;

[0148] S610: The method for embedding a non-Gaussian cross-correlation random field into a finite element model is as follows:

[0149] MATLAB is used to embed the non-Gaussian cross-correlation random field into the finite element model, and Python is used to realize the automatic submission calculation and result export of inp file.

[0150] In this step, based on the cross-correlation random field obtained by the discretization of the previous steps, the results of the random field are assigned to the material properties of each unit of the finite element model. MATLAB is used to write the inp file statement for each finite element unit, and the random field value corresponding to each unit is written into the inp file of the original finite element model. This can realize the embedding of the non-Gaussian cross-correlation random field into the finite element model. After completing the rewriting of the inp file, in order to complete the batch calculation, it is necessary to call Python to realize the automatic submission of the inp file to ABAQUS. For reference, the following Python statement can be used to submit the inp file. For reference, the model inp file of this article is named 'SLOPE3D.inp', and the corresponding Python statement can be written as

[0151] FileName = 'SLOPE3D'

[0152] mdb.JobFromInputFile(name=FileName, inputFileName=FileName+'.inp')

[0153] mdb.jobs[FileName].submit()

[0154] mdb.jobs[FileName].waitForCompletion().

[0155] S620, Stability Analysis (ABAQUS built-in function module) calculates the displacement data of each unit as follows:

[0156] In this embodiment, after Python is used to complete the batch automatic export of calculation results, the strength reduction method is used in ABAQUS to carry out stability analysis, and the following Python statement is used to obtain the corresponding value of any set when the calculation reaches the last stack. FS , here we get set-10000 FS

[0157] o = openOdb(path=FileName + '.odb')

[0158] step = o.steps.values()[1]

[0159] lastframe = o.steps['reduce'].frames[-1]

[0160] sglele = o.rootAssembly.instances['SLOPE-1'].elementSets['SET-10000']F = lastframe.fieldOutputs['FV1'].getSubset(region=sglele).values.

[0161] The strength reduction method can be expressed as

[0162]

[0163]

[0164] Where, Fr is the reduction factor, c and f Respectively represent the cohesion and internal friction angle values ​​obtained after the last reduction, c m and f m In the present invention, the reduction factor at the end of the calculation is regarded as the safety factor of the slope. FS , that is, the reduction coefficient corresponding to the last stack of the last analysis step of any set in ABAQUS. As a reference, the following Python statement can be used to obtain the reduction coefficient corresponding to the last stack FS .

[0165] S700 , based on the acquired displacement data of each unit, a clustering method is used to identify the sliding unit and calculate the sliding volume; in this embodiment, a K clustering method is used to identify the sliding unit and calculate the sliding volume.

[0166] After the stability analysis is completed, the displacement of each node can be obtained, and the displacement of each node can be obtained by solving the mean displacement of each unit node. N The displacement of the unit ( d 1, d 2, ..., d N ). Using the K clustering method, we can N The displacement of each unit is minimized by E , which is divided into M cluster{ C 1, C 2, …, C M}( M ≤ N ), clustering error E The expression is as follows

[0167]

[0168] Where, c k ( k = 1, 2, …, M ) is the cluster center of each cluster. By minimizing the above error, N Observations are divided into M In the present invention, each unit can be divided into a stable unit and a sliding unit. M= 2. The specific implementation steps of the K clustering method are as follows Figure 4 shown.

[0169] In this step, the unit displacements calculated in the previous step are classified using the K clustering method, and the units are divided into two clusters according to their displacements { C 1, C 2}, respectively, sliding unit and stable unit. In the embodiment of the present invention, four calculation results are randomly selected to perform corresponding unit classification. Figure 5 Cluster centers in the four-fold K clustering implementation c 1. c 2 As the number of iterations changes, it can be seen from the figure that the K clustering method has a high computational efficiency. It only takes 20 iterations to iteratively cluster the displacement results of 17950 units. At the same time, it is not difficult to find from the results of the four calculations that when considering parameter uncertainty (that is, considering the spatial variability of the variables), the cluster centers obtained by different random fields to achieve the corresponding calculation results are c 1. c 2 are not the same, which indirectly proves that it is not reasonable to use a fixed threshold to divide the sliding and stable units, which may affect the analysis results and verify the rationality of this method.

[0170] Based on the sliding units and stable units obtained by the K clustering method, the sliding body volume of the slope can be obtained by calculating the sum of the volumes of the sliding units.

[0171] S800: Repeat the above steps to obtain multiple results of sliding volume calculation, and use statistical methods to evaluate the three-dimensional slope risk.

[0172] As a preferred approach, a statistical method is used to obtain a sliding volume frequency distribution histogram to assess the three-dimensional slope risk.

[0173] As a specific implementation method, when assessing the three-dimensional slope risk, Monte-Carlo simulation is used to generate multiple N 1 standard normal random matrix ξ, and repeat all the above steps to complete NThe non-Gaussian cross-correlation random field is embedded in the finite element model once, the displacement data of each unit is calculated through stability analysis, and the calculation results of N Monte-Carlo simulations are statistically analyzed to obtain the statistical results of the slope sliding volume as the result of three-dimensional slope risk assessment.

[0174] In this step, Monte-Carlo simulation is used to generate N 1 ( N 1=500) independent standard normal random matrices x , and repeat the above steps to achieve N In the embodiment of the present invention, a total of 500 Monte-Carlo simulations were performed, and Frank Copula was used to discretize the random field, and the corresponding sliding body volume distribution was calculated as follows: Figure 6 shown.

[0175] Therefore, the results of the embodiments of the present invention verify the beneficial effects of the present invention, showing that it is easy to be applied in practice and has innovation.

[0176] The above are only preferred embodiments of the present invention and do not limit the implementation mode and protection scope of the present invention. For those skilled in the art, it should be aware that all solutions obtained by equivalent substitutions and obvious changes made using the contents of the present invention specification should be included in the protection scope of the present invention.

Claims

1. A three-dimensional slope risk assessment method considering non-Gaussian cross-correlation of soil parameters, characterized by: The steps include: Determine several soil parameters required according to the type of three-dimensional slope to be evaluated, and obtain statistical information of the corresponding soil parameters; Determine the marginal distribution of soil parameters and the Copula function that characterizes the correlation between soil parameters; Establish a finite element numerical model of a three-dimensional slope and derive the unit information of the finite element numerical model; The KL expansion is used to discretize the large 3D autocorrelation random field of the 3D slope and obtain the autocorrelation random field of soil parameters. Based on the non-Gaussian cross-correlation random field coupling of Copula, the non-Gaussian cross-correlation random field of soil parameters is obtained; The non-Gaussian cross-correlation random field is embedded in the finite element model, and the displacement data of each unit is calculated through stability analysis; Based on the displacement data of each unit, the clustering method is used to identify the sliding unit and calculate the sliding volume; Repeat the above steps to obtain multiple results of sliding volume calculation, and use statistical methods to evaluate the three-dimensional slope risk.

2. The three-dimensional slope risk assessment method considering non-Gaussian cross-correlation of soil parameters according to claim 1 is characterized in that: The soil parameters include any number of density, soil particle specific gravity, water content, void ratio, porosity, saturation, dry density, saturated density, buoyancy, cohesion, internal friction angle, elastic modulus, Poisson's ratio, bulk density, and permeability coefficient; the statistical information of the soil parameters is the mean and variance of the corresponding soil parameters.

3. The three-dimensional slope risk assessment method considering non-Gaussian cross-correlation of soil parameters according to claim 1 is characterized in that: The AIC rule or BIC rule is used to determine the optimal fitting marginal distribution and optimal Copula function of soil parameters.

4. The three-dimensional slope risk assessment method considering non-Gaussian cross-correlation of soil parameters according to claim 2 is characterized in that: There are two soil parameters, which are respectively recorded as soil parameters c 、 The method of using KL expansion to discretize large 3D autocorrelation random fields of 3D slopes is as follows: Representing a random field as a continuous function H ( x , θ ), H ( x , θ ) value represents the continuous domain A point in x ∈ Ω m The value of the variable, m is the dimension of the topological space Ω, θ ∈ Θ is the coordinate of a point in the sample space Θ, (Θ, F , P ) is a complete probability space; The Gaussian random field is expressed as: In the above formula, μ ( x )and σ ( x ) are the mean and variance functions of the Gaussian random field, ξ i ( θ ) is a random vector that follows a standard normal distribution, λ i and ϕ i ( x ) are the autocorrelation functions ρ ( x , x’ )'s eigenvalues ​​and eigenvectors satisfy the formula right H ( x , θ )Use a finite number of expansion terms to convert the eigenvalue λ i Arrange from largest to smallest, using the first M indivual λ i and the corresponding ϕ i ( x ) is approximated by the sum of products of H ( x , θ ),Right now Where, M is the number of expansion terms of KL expansion, and the autocorrelation error is controlled by ε ρ, M ( x , x’ ) is less than a preset threshold value; By finding the eigenvalue λ i and eigenvectors ϕ i ( x ) completes the approximate solution of the continuous function H ( x , θ )’s KL expansion; Based on the above expansion, the autocorrelation random field of the variable is established Z IN = [ Z c IN , Z φ IN ], Z c IN , Z φ IN Represent soil parameters c 、 Random field of .

5. The three-dimensional slope risk assessment method considering non-Gaussian cross-correlation of soil parameters according to claim 4 is characterized in that: The method of the non-Gaussian cross-correlation random field between soil parameters is as follows: Using Copula theory, the joint distribution of variables is expressed as Where, 、 Represent soil parameters c 、 The marginal cumulative distribution function of is the cumulative distribution function of the two-dimensional Copula; θ is the Copula parameter; Kendall rank correlation coefficient τ Convert θ , the calculation formula is based on c and φ The joint distribution function of c and φ The joint probability density function of Where, f 1( c )and f 2( φ ) are respectively c and φ The marginal probability density function of D ( u , v ; θ )Depend on C ( u , v ; θ ) The probability density function of the two-dimensional copula obtained by derivation; Completing the autocorrelation random field based on Rosenblatt transform Z IN = [ Z c IN , Z φ IN ] coupling, generating a cross-correlated random field Z CNN = [ Z c CNN , Z φ CNN ], Z c CNN Considering the soil parameters c, After cross-correlation, the random field of soil parameter c is obtained. Z φ CNN Considering the soil parameters c, Soil parameters are obtained after cross-correlation Random field of .

6. The three-dimensional slope risk assessment method considering non-Gaussian cross-correlation of soil parameters according to claim 5, characterized in that: The steps of Rosenblatt transformation are as follows: Z c IN = F -1 ( F c ( Z c CNN )) Z φ IN = F -1 ( F ( Z φ CNN | Z c CNN )) = h ( F φ ( Z φ CNN ), Φ( Z c IN ); θ ) In the above formula, Φ -1 (·) represents the inverse function of the standard normal distribution CDF, F c (·)and F φ (·) respectively represent c and φ The marginal CDF of F (·|·) represents the conditional CDF of the copula, h () indicates the Copula h function; Transforming the above formula, we get c and φ Cross-correlation random field Z CNN = [ Z c CNN , Z φ CNN ] Z c CNN = F c -1 (Φ( Z c IN )) Z φ CNN = F φ -1 ( h -1 (Φ( Z φ IN ), F c ( Z c CNN ); θ )) In the above formula, F c -1 (·)and F φ -1 (·) respectively c and φ The inverse of the marginal cumulative distribution function, h -1 ( ) indicates the Copula h -1 function.

7. The three-dimensional slope risk assessment method considering non-Gaussian cross-correlation of soil parameters according to claim 4 is characterized in that: The Copula functions include Gaussian, Frank, and Clayton functions.

8. The three-dimensional slope risk assessment method considering non-Gaussian cross-correlation of soil parameters according to claim 4 is characterized in that: The strength reduction method is used for stability analysis.

9. The three-dimensional slope risk assessment method considering non-Gaussian cross-correlation of soil parameters according to claim 4 is characterized in that: When evaluating the three-dimensional slope risk, Monte-Carlo simulation is used to generate multiple standard normal random matrices ξ, and all steps of claim 1 are repeated to complete the embedding of the non-Gaussian cross-correlation random field into the finite element model. The displacement data of each unit is calculated through stability analysis, and the calculation results of the Monte-Carlo simulation are statistically analyzed to obtain the statistical results of the slope sliding volume as the result of the three-dimensional slope risk assessment.

10. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the three-dimensional slope risk assessment method according to any one of claims 1 to 9 is implemented.

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