Rockfill dam slope reliability calculation method considering parameter intrinsic correlation

Abstract

The invention discloses a rock-fill dam slope reliability calculation method considering parameter internal correlation, which comprises the following steps of: constructing a two-dimensional finite element model of a rock-fill dam to be analyzed, searching a slippage channel of the rock-fill dam slope, and then constructing a reliability performance function of a downstream dam slope of the rock-fill dam to be analyzed; constructing a parameter multi-dimensional joint regular vine Copula function model; randomly extracting a plurality of groups of Duncan E-B model parameters from the parameter multi-dimensional joint regular vine Copula function model; the dam slope stability reliability corresponding to each group of Duncan E-B model parameters is calculated by adopting the reliability performance function of the downstream dam slope of the rock-fill dam, and the number of the Duncan E-B model parameters with the reliability smaller than zero is counted to serve as the failure number; and calculating the failure probability of the rock-fill dam to be analyzed according to the total number of the extracted Duncan E-B model parameters and the failure number.

Description

Technical Field

[0001] The invention relates to a dam reliability analysis technology, and in particular to a rockfill dam slope reliability calculation method taking into account the intrinsic correlation of parameters. Background Art

[0002] Rockfill dams, with their advantages of low cost, strong adaptability and simple construction, have become one of the most promising types of dams. In particular, with the in-depth advancement of national hydropower development, a large number of high rockfill dams have been built and put into operation, such as Changhe Dam (dam height 240m), Nuozadu (dam height 261.5m), Lianghekou (dam height 293m), etc. However, due to the complex occurrence environment, super high dam height and deep overburden, these high rockfill dams face huge challenges in safety assessment and risk control. Among them, dam slope stability is a major cause of rockfill dam instability. Slope instability will greatly affect the safety of life and property of hydraulic structures and downstream people. Dam slope stability reliability has gradually become one of the common means of dam structure safety evaluation. In my country, the development of reliability analysis methods started late, and the current research on slope stability reliability analysis is still in the research and exploration stage. Many scholars have improved the dam slope stability reliability theory based on parameter randomness, algorithm optimization and other directions, making the dam slope stability reliability theory develop in a more scientific and reasonable direction. However, traditional reliability analysis generally focuses on the uncertainty caused by the inherent spatial variability of material parameters, while ignoring the intrinsic correlation between parameters. If the objective intrinsic correlation between random variables is not considered, the random variable combination obtained by sampling is very likely to deviate from the true nature of the rockfill material, resulting in the deviation of the reliability analysis results of the dam slope stability from the actual situation. Therefore, the intrinsic correlation between parameters is an inherent property of the parameters themselves, and it is necessary to take it into account when conducting reliability analysis. Summary of the invention

[0003] In view of the above-mentioned deficiencies in the prior art, the present invention provides a rockfill dam slope reliability calculation method taking into account the intrinsic correlation of parameters to solve the problem that the traditional reliability analysis results deviate from reality and affect the accurate selection of slope protection strategies.

[0004] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0005] A method for calculating the reliability of a rockfill dam slope taking into account the intrinsic correlation of parameters is provided, which comprises the following steps:

[0006] S1. Construct a two-dimensional finite element model of the rockfill dam to be analyzed, and search for the sliding channel of the rockfill dam slope by the strength reduction search method;

[0007] S2. According to the obtained sliding channel, a reliability function of the downstream slope of the rockfill dam to be analyzed is constructed;

[0008] S3, obtaining Duncan-Zhang EB model parameters of several rockfill dams and the marginal distribution function of each model parameter, and calculating the Pearson correlation coefficient between each model parameter and any model parameter of the remaining model parameters;

[0009] S4. Construct a parameter multi-dimensional joint regular vine Copula function model based on all model parameters and their corresponding marginal distribution functions and all Pearson correlation coefficients;

[0010] S5, randomly extracting several groups of Duncan Zhang EB model parameters from the parameter multidimensional joint regular vine Copula function model by Monte-Carlo method;

[0011] S6. The reliability function of the downstream slope of the rockfill dam is used to calculate the reliability of each group of Duncan Zhang EB model parameters, and the number of reliability values ​​less than zero is counted as the number of failures;

[0012] S7. Calculate the failure probability of the rockfill dam to be analyzed based on the total number of extracted Duncan-Zhang EB model parameters and the number of failures.

[0013] Furthermore, step S2 further comprises:

[0014] S21. By adjusting the friction coefficient, cohesion, normal stress and / or shear stress of different units in the sliding channel, several groups of dam slope stability safety factors F are calculated. s :

[0015]

[0016] Where M is the total number of units on the slip channel; f k 、c k are the friction coefficient and cohesion of the kth unit on the sliding channel, σ k , τ k are the normal stress and shear stress of the kth unit in the slip channel direction respectively; l k is the unit length of the kth unit along the slip channel direction;

[0017] S22. Based on several groups of dam slope stability safety factors and their corresponding Duncan-Zhang EB model parameters, the response surface equation is used to calculate the unknown coefficients a and b. i 、c i , the expression of the response surface equation is:

[0018]

[0019] Among them, x i is the i-th model parameter, 1≤i≤7; b i 、c iare the undetermined coefficients corresponding to the i-th model parameter; I is the total number of model parameters;

[0020] S23, using the calculated unknown coefficients a and b i 、c i Update the response surface equation as the fitting formula:

[0021]

[0022] Among them, K e is the tangent modulus coefficient; n is the tangent modulus index; K b is the bulk modulus coefficient; m is the bulk modulus index; R f is the destruction ratio; All are nonlinear strength indicators; K e ,n,K b ,m,R f , The 7 model parameters included in the Duncan Zhang EB model parameters;

[0023] S23. According to the fitting formula, the downstream dam slope reliability function Z=F is constructed. s -1.

[0024] Furthermore, the calculation formula of the Pearson correlation coefficient in step S3 is:

[0025]

[0026] Among them, x oi and x oj are the i-th and j-th model parameters of the o-th rockfill dam; and are the average values ​​of the i-th and j-th model parameters of N rockfill dams; N is the total number of rockfill dams; r ij is the Pearson correlation coefficient between the i-th and j-th model parameters; 1≤i≤7, 1≤j≤7, and i≠j.

[0027] Furthermore, step S4 further comprises:

[0028] S41, using the maximum spanning tree method, based on the principle that the sum of the absolute values ​​of the Pearson correlation coefficients of each layer in the tree structure is the largest, generating a tree structure of each layer;

[0029] S42, determine the Copula function set;

[0030] S43, selecting the optimal pair copula function of the variables connected by each edge in the tree structure from the copula function set by using the AIC criterion and the maximum likelihood estimation method, and obtaining the optimal parameter estimation of the optimal pair copula function;

[0031] S44, the optimal Pair Copula function of the combined tree structure and the edge line is constructed to obtain a parameter multi-dimensional joint regular vine Copula function model.

[0032] Furthermore, the Copula function set includes Gaussian Copula, t Copula, Clayton Copula, Frank Copula, Gumbel Copula, Joe Copula and Indep Copula;

[0033] The tree structure of the regular vine Copula function model consists of six layers. The first layer of the tree structure has 7 nodes and 6 edges. With each additional layer, the number of nodes decreases by one and the number of edges decreases by one.

[0034] Furthermore, the rockfill dam includes a main rockfill area and a secondary rockfill area, and the two rockfill areas are both subjected to corresponding dam slope failure probability calculation according to the method of steps S3 to S7;

[0035] The optimal pair copula function corresponding to the node edge and node edge of each layer of the tree structure in the main rockfill area is:

[0036] The node edges of the first layer tree structure Tree1 are m, n, K b , n, n, R f , R f , K e , K e , and The optimal Pair Copula functions corresponding to these node edges are Joe, Gumbel180°, Student, Joe, Gumbel, and Gumbel;

[0037] The node edges of the second-level tree structure Tree2 are m, K b |n, K b , R f |n, K e ,n|R f , R f , and K e , The optimal Paiir Copula functions corresponding to these node edges are Independence, Gaussian, Independence, Independence, and Joe180°;

[0038] The node edges of the third-level tree structure Tree3 are m, R f|K b , n, K b , K e |R f , n, n, R f and R f e , the optimal pair copula functions corresponding to these node edges are Independence, Clayton180°, Independence and Gaussian;

[0039] The node edges of the fourth-level tree structure Tree4 are m, K e |R f , K b , n, K R f , n and n, K e , R f , the optimal Pair Copula functions corresponding to these node edges are Gaussian, Independence and Independence respectively;

[0040] The node edge of the fifth-level tree structure Tree5 is m. R f , K b ,n and K b , K e , R f , n, the optimal pair copula functions of the two node edges are both Independence;

[0041] The node edge of the sixth-level tree structure Tree6 is m. K e , R f , K b , n, its optimal Pair Copula function is Independence;

[0042] The optimal pair copula function corresponding to the node edge and node edge of each layer of tree structure in the secondary rockfill area is:

[0043] The node edge of the first layer tree structure Tree1 is R f , n, m, n, n, K b , and The optimal pair copula functions corresponding to these node edges are Joe, Gumbel, Gumbel180°, Joe 180°, Joe, and Gumbel;

[0044] The node edges of the second-level tree structure Tree2 are R f , m|n, m, K b |n,n K e , and K b The optimal Pair Copula functions corresponding to these node edges are all Independence;

[0045] The node edge of the third-level tree structure Tree3 is R f , K b |m,n、m, 、n, b , and Ke, The optimal Pair Copula functions corresponding to these node edges are Independence;

[0046] The node edge of the fourth layer tree structure Tree4 is R f , m, n, m, K b , n and n, K b , the optimal Pair Copula functions corresponding to these node edges are Gaussian, Independence and Independence respectively;

[0047] The node edge of the fifth layer tree structure Tree5 is R f , K b , m, n and m, K b , n, the optimal pair copula functions of the two node edges are both Independence;

[0048] The node edge of the sixth layer tree structure Tree6 is R f , K b , m, n, its optimal Pair Copula function is Joe 180°.

[0049] Furthermore, the tree structure multiplies the marginal distribution functions of the seven model parameters with the optimal Pair Copula functions corresponding to all node edges as the correlation of the model parameters of the regular vine Copula function.

[0050] Furthermore, the method for selecting the marginal distribution function of the model parameters in step S3 includes:

[0051] S31, using KS test to determine the marginal distribution function that the model parameters meet;

[0052] S32, according to all marginal distribution functions that each model parameter conforms to, using the AIC criterion to calculate the AIC value corresponding to each marginal distribution function;

[0053] S33. Select the marginal distribution with the minimum AIC value as the optimal distribution of the model parameters.

[0054] Furthermore, for the main rockfill area, n1 and It follows the truncated normal distribution, and the remaining model parameters follow the Weibull distribution; for the secondary rockfill area, n2, R f2 and The remaining model parameters all obey the Weibull distribution.

[0055] The beneficial effects of the present invention are as follows: a large number of Duncan-Zhang EB model parameters of rockfill dams are statistically analyzed, marginal distribution optimization is performed on each parameter, and the correlation between each pair of parameters is analyzed. The intrinsic correlation between the parameters of the Duncan-Zhang EB model is intuitively revealed through the tree structure by using the regular vine Copula function. It can be found from the reliability calculation results of whether the intrinsic correlation of the model parameters is considered that the correlation between the model parameters has a certain influence on the reliability of the stability of the rockfill dam slope, and the reliability index considering the intrinsic correlation of the parameters is higher than the reliability index not considering the intrinsic correlation of the parameters. In this scheme, when the intrinsic correlation of the parameters is considered, the model parameter pairs with higher correlation will appear in a combination with a higher probability when extracted by the Monte-Carlo method. The failure probability calculated in this way is consistent with the actual situation of the parameters, and the probability of the appearance of parameter groups that do not conform to the actual correlation of the parameters is greatly reduced when selecting.

[0056] The reliability analysis method of rockfill dam slope stability considering the intrinsic correlation of parameters solves the problem that independent fluctuations of parameters may deviate from the intrinsic characteristics of the material and cause misjudgment of the risk of slope instability. The reliability index results are more reasonable and can reflect the true state of rockfill dam slope stability, so as to select relatively reasonable maintenance strategies during dam maintenance and improve the safe and stable operation of the dam. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1Flow chart of the slope reliability calculation method of rockfill dam considering the intrinsic correlation of parameters.

[0058] Figure 2 This is a schematic diagram of the finite element model of the 0+103.00 section of the DL concrete face rockfill dam.

[0059] Figure 3 Schematic diagram of the plastic zone of the downstream slope of DL Dam.

[0060] Figure 4 Schematic diagram of the edge distribution test results of parameter m1 in the main rockfill area.

[0061] Figure 5 Vine structure diagram of material parameters of primary and secondary rockfill areas, (a) is the primary rockfill area, (b) is the secondary rockfill area.

[0062] Figure 6 The comparison diagram of the sampling results of rockfill material parameters using the regular vine Copula function model and the Duncan Zhang EB model parameters of 36 rockfill dams; (a) is the sampling results and the parameters of the main rockfill area of ​​36 rockfill dams (b) is the comparison diagram of the sampling results and the main rockfill area of ​​36 rockfill dams with respect to parameter K e ~K b (c) is the comparison chart of the sampling results and the main rockfill area of ​​36 rockfill dams with respect to parameters m~K b (d) Comparison of sampling results with parameters m~n of the main rockfill area of ​​36 rockfill dams; (e) Comparison of sampling results with parameters m~n of the secondary rockfill area of ​​36 rockfill dams (f) is the comparison chart of the sampling results and the secondary rockfill area of ​​36 rockfill dams about the parameter K e ~K b (g) is the comparison chart of sampling results and the secondary rockfill area of ​​36 rockfill dams with respect to parameters m~K b (h) Comparison diagram of sampling results and secondary rockfill areas of 36 rockfill dams regarding parameters m~n.

[0063] Figure 7 The comparison chart of the joint sampling results of the model parameters of this scheme and the independent sampling results of the existing technical parameters; (a) is the main rockfill material parameters Comparison of sampling results; (b) Main rockfill material parameter K b1 ~K e1 Comparison of sampling results; (c) Main rockfill material parameter K b1 ~R f1 Comparison of sampling results; (d) is the secondary rockfill parameters Comparison of sampling results; (e) is the secondary rockfill parameter K b2 ~Ke2 Comparison of sampling results; (f) is the comparison of sampling results of secondary rockfill parameters m2~n2; in (a)~(f), the left side is the joint sampling result of the model parameters of this scheme, and the right side is the independent sampling result of the existing technology parameters. DETAILED DESCRIPTION

[0064] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0065] refer to Figure 1 , Figure 1 The flowchart of the slope reliability calculation method of rockfill dam considering the intrinsic correlation of parameters is shown in FIG. Figure 1 As shown, the method S includes steps S1 to S7.

[0066] In step S1, a two-dimensional finite element model of the rockfill dam to be analyzed is constructed, and a sliding channel of the rockfill dam slope is searched by a strength reduction search method;

[0067] In order to facilitate the understanding of the search for sliding channels, an example is used here to illustrate the problem. The maximum section (0+103.00) of the DL concrete face rockfill dam is selected for two-dimensional finite element modeling. The simulation range is extended by 2 times the dam height in both the upstream and downstream directions and in the depth direction. It is discretized into 1719 units and 3364 nodes, including 705 dam body units and 1014 dam foundation units. The constructed finite element model is referenced Figure 2 .

[0068] The rockfill materials in the downstream rockfill area, secondary rockfill area and main rockfill area are all mined from the block rock field at the lower dam site, with the same lithology. At the same time, in order to coordinate the uneven deformation of the dam body, the downstream rockfill area and secondary rockfill area adopt the same design control parameters as the main rockfill, and the main rockfill material has the same gradation as the downstream rockfill material. For the convenience of calculation, the upstream rockfill material and the downstream rockfill material are analyzed as the same material. Since the deformation of the face rockfill dam mainly occurs in the rockfill area, only the main rockfill material and the secondary rockfill material are analyzed this time. The Duncan-Zhang EB model parameters for the materials of each partition of the dam body are selected. The dam design parameters are shown in Table 1.

[0069] Table 1 Parameters of Duncan-Zhang EB model for DL ​​concrete face rockfill dam

[0070]

[0071] The failure path of the DL face rockfill dam slope is searched by the strength reduction method. In the numerical model, the material strength parameters (cohesion and internal friction angle) are gradually reduced until the calculation does not converge, that is, the dam slope is considered to have reached the limit state and the corresponding stability judgment criterion is used to determine the minimum stability safety factor F of the dam slope. s , and the sliding failure surface of the dam slope is obtained, that is, the strip that runs through the dam body composed of failure units.

[0072] The reduced shear strength parameter is calculated by the following formula:

[0073]

[0074] In the formula, c′, are the cohesion and internal friction angle reduction of the dam material respectively; F r is the reduction factor.

[0075] When the reduction factor increases to 2.26, the plastic zone of the dam slope is basically connected, and the calculation no longer converges. Figure 3 As shown in the SL274-2020 Code for Design of Rolled Earth-Rock Dams, under normal operating conditions of a Class 1 earth-rock dam, the minimum safety factor of the dam slope's anti-sliding stability [K] = 1.5, so the dam slope's anti-sliding stability safety meets the design standards.

[0076] In step S2, according to the obtained slip channel, a reliability function of the downstream slope of the rockfill dam to be analyzed is constructed; when implemented, the preferred step S2 of this scheme further includes:

[0077] S21. By adjusting the friction coefficient, cohesion, normal stress and / or shear stress of different units in the sliding channel, several groups of dam slope stability safety factors F are calculated. s :

[0078]

[0079] Where M is the total number of units on the slip channel; f k 、c k are the friction coefficient and cohesion of the kth unit on the sliding channel, σ k , τ k are the normal stress and shear stress of the kth unit in the slip channel direction respectively; l k is the unit length of the kth unit along the slip channel direction;

[0080] S22. Based on several groups of dam slope stability safety factors and their corresponding Duncan-Zhang EB model parameters, the response surface equation is used to calculate the unknown coefficients a and b. i 、c i , the expression of the response surface equation is:

[0081]

[0082] Among them, x i is the i-th model parameter, 1≤i≤7; b i 、c i are the undetermined coefficients corresponding to the i-th model parameter; I is the total number of model parameters;

[0083] S23, using the calculated unknown coefficients a and b i 、c i Update the response surface equation as the fitting formula:

[0084]

[0085] Among them, K e is the tangent modulus coefficient; n is the tangent modulus index; K b is the bulk modulus coefficient; m is the bulk modulus index; R f is the destruction ratio; All are nonlinear strength indicators; K e ,n,K b ,m,R f , The 7 model parameters included in the Duncan Zhang EB model parameters;

[0086] S23. According to the fitting formula, the downstream dam slope reliability function Z=F is constructed. s -1.

[0087] In step S3, the Duncan-Zhang EB model parameters of several rockfill dams and the marginal distribution function of each model parameter are obtained, and the Pearson correlation coefficient between each model parameter and any model parameter of the remaining model parameters is calculated.

[0088] In this scheme, the Duncan-Zhang EB model parameters of 36 rockfill dams in China were statistically analyzed, and their mean values, standard deviations, and coefficients of variation were calculated. Table 2 shows the statistical characteristics of these model parameters.

[0089] Table 2 Statistical characteristics of Duncan-Zhang EB model parameters for 36 rockfill dams

[0090]

[0091] During implementation, the method for selecting the marginal distribution function of the model parameters in step S3 of this solution preferably includes:

[0092] S31, using KS test to determine the marginal distribution function that the model parameters meet;

[0093] Most of the parameters of geotechnical materials obey the Weibull distribution, truncated normal distribution, lognormal distribution, extreme value distribution, t distribution, etc. These distributions are usually used to accurately describe the uncertainty of soil. This scheme uses the above five marginal distributions to analyze the parameter distribution type. First, the KS test is used to determine the marginal distribution type that the parameter conforms to.

[0094] The Kolmogorov-Smirnov test is a test method that compares a frequency distribution F(x) with a preset distribution G(x) through a cumulative distribution function. Since the distribution of the data does not need to be known in advance, the KS test is a non-parametric test method. The empirical distribution function of the sample is calculated as follows:

[0095]

[0096] Where n is the sample size to be tested; I(x i ≤x) is the indicator function, when x i When ≤x, the value is 1, otherwise the value is 0.

[0097] The five distributions mentioned above are used as the preset distribution G(x). Table 3 shows the cumulative distribution and probability density function of these five distributions.

[0098] Table 3 Cumulative probability functions and marginal distribution functions of five marginal distributions

[0099]

[0100]

[0101] The KS statistic is used to evaluate the difference between the empirical distribution function of the sample data and the theoretical distribution function. The calculation method is:

[0102] D n =max|F(x)-G(x)|

[0103] According to the sample size n = 36 and the significance level α = 0.05, the KS critical value D is calculated by looking up the table. a =0.226. If D n <D a , accept the original hypothesis, the sample follows the preset distribution. Otherwise, the sample does not conform to the preset distribution.

[0104] The marginal distribution test results of each parameter in the primary and secondary rockfill areas are shown in Tables 4 and 5. It can be seen from Tables 4 and 5 that most parameters conform to the five preset distributions. Taking m1 as an example, the statistical value D of the five preset distributions n 0.090, 0.116, 0.077, 0.080 and 0.067 respectively, Figure 4Results from fitting five distributions are shown.

[0105] Table 4 Test results of marginal distribution of Duncan-Zhang EB parameters in the main rockfill area

[0106]

[0107]

[0108] Table 5 Test results of marginal distribution of Duncan-Zhang EB parameters in secondary rockfill area

[0109]

[0110]

[0111] S32, according to all marginal distribution functions that each model parameter conforms to, using the AIC criterion to calculate the AIC value corresponding to each marginal distribution function;

[0112] The AIC criterion, or Akaike Information Criterion, evaluates the degree of model fit to data based on the concept of entropy and is a criterion for measuring the goodness of statistical model fit. Therefore, this paper uses the AIC criterion to select the optimal marginal distribution function. Traversing all marginal distribution types, the marginal distribution with the smallest AIC calculated value is the optimal marginal distribution. The calculation formula for the AIC value is:

[0113] AIC=2K-2ln(L)

[0114] Where K is the number of parameters of the marginal distribution type; L is the likelihood function, where the probability density function of the marginal distribution type is taken.

[0115] S33, select the marginal distribution with the minimum AIC value as the optimal distribution of model parameters, specifically: for the main rockfill area, n1 and It follows the truncated normal distribution, and the remaining model parameters follow the Weibull distribution; for the secondary rockfill area, n2, R f2 and The remaining model parameters all obey the Weibull distribution.

[0116] During implementation, the calculation formula of the Pearson correlation coefficient in step S3 of this solution is preferably:

[0117]

[0118] Among them, x oi and x oj are the i-th and j-th model parameters of the o-th rockfill dam; and are the average values ​​of the i-th and j-th model parameters of N rockfill dams; N is the total number of rockfill dams; r ij is the Pearson correlation coefficient between the i-th and j-th model parameters; 1≤i≤7, 1≤j≤7, and i≠j.

[0119] The correlation coefficient r ranges from [-1, 1], where 1 and -1 indicate that the variables are completely linearly correlated, and 0 indicates that there is no correlation between the variables. The specific correlation level classification is shown in Table 6.

[0120] Table 6 Correlation levels

[0121]

[0122] The Pearson coefficients for each pair of parameters are shown in Tables 7 and 8. Among them, the nonlinear strength index in the primary and secondary rockfill areas is and The Pearson coefficients are 0.857 and 0.870, respectively, indicating a significant linear correlation. e1 and R f1 ,K e1 and K e1 and and n1 and K b1 Through correlation analysis, the correlation between parameters is revealed, which lays a solid foundation for the subsequent establishment of multi-vine copula functions.

[0123] Table 7 Duncan-Zhang EB model parameters versus Pearson coefficient in the main rockfill area

[0124]

[0125] Table 8 Duncan-Zhang EB model parameters versus Pearson coefficient in secondary rockfill area

[0126]

[0127]

[0128] In step S4, a parameter multi-dimensional joint regular vine Copula function model is constructed according to all model parameters and their corresponding marginal distribution functions and all Pearson correlation coefficients;

[0129] In one embodiment of the present invention, step S4 further comprises:

[0130] S41, generating a tree structure of each layer by using the maximum spanning tree method, based on the principle that the sum of the absolute values ​​of the correlation coefficients of each layer in the tree structure is the largest;

[0131] S42, determine the Copula function set; the preferred Copula function set of this scheme includes Gaussian Copula, tCopula, Clayton Copula, Frank Copula, Gumbel Copula, Joe Copula and Indep Copula.

[0132] S43. In the Copula function set, the optimal Pair Copula function of the variables connected by each edge in the tree structure is selected by the AIC criterion and the maximum likelihood estimation method, and the optimal parameter estimation of the optimal Pair Copula function is obtained; taking Gaussian_copula as an example, the code for fitting the pair copula function between variables is shown in Table 9.

[0133] Table 9

[0134]

[0135]

[0136] S44. Combining the tree structure and the optimal Pair Copula function of the edge line, a parameter multi-dimensional joint regular vine Copula function model is constructed, wherein the tree structure multiplies the marginal distribution function of the 7 model parameters and the optimal Pair Copula function corresponding to all node edges as the correlation of the regular vine Copula function model parameters.

[0137] The tree structure of the regular vine Copula function model consists of six layers. The first layer of the tree structure has 7 nodes and 6 edges. With each additional layer, the number of nodes decreases by one and the number of edges decreases by one.

[0138] In this scheme, the rockfill dam includes a main rockfill area and a secondary rockfill area. The failure probability of the corresponding dam slope is calculated in the two rockfill areas according to the method of steps S3 to S7. The schematic diagram of the canonical Copula function model of the main rockfill area and the secondary rockfill area in this scheme can be referred to Figure 5 The optimal Copula function type and parameter estimation results of the Duncan-Zhang EB model parameters in the main rockfill area and the optimal Copula function type and parameter estimation results of the Duncan-Zhang EB model parameters in the secondary rockfill area can be referred to Table 10 and Table 11 respectively.

[0139] Table 10 Optimal Copula function type and parameter estimation results of Duncan-Zhang EB model parameters in the main rockfill area

[0140]

[0141]

[0142] Table 11 Optimal Copula function type and parameter estimation results of Duncan-Zhang EB model parameters in secondary rockfill area

[0143]

[0144] The established multi-dimensional joint probability distribution Vine Copula function model was simulated and sampled 1000 times, and the Pearson correlation coefficients between the parameters were calculated, as shown in Tables 12 and 13. The parameter joint sampling shows that the correlation of the sampled data set is similar to that of the sample ( Figure 6 The samples in the above table refer to the Duncan-Zhang EB model parameters of the 36 selected dams. The correlation is close. The parameters with large correlation, such as the main rockfill area The Pearson correlation coefficient and Kendall rank correlation coefficient between the sample set and the sampling set were 0.857 and 0.899, 0.682 and 0.712, respectively, and the correlations were good. f The Pearson correlation coefficient and Kendall rank correlation coefficient between the sample set and the sampling set are 0.019 and 0.081, 0.060 and 0.114, respectively, which are not significantly correlated.

[0145] The sampling results of some parameter pairs are plotted as shown in Figure 6 The joint sampling distribution results of the parameters can well cover the original sample distribution, and the VineCopula function model of the multidimensional joint probability distribution of the parameters of the Duncan-Zhang EB model of the panel rockfill dam can reasonably describe the inherent correlation between the parameters and the joint probability distribution of the parameters.

[0146] Table 12 Correlation coefficients of the joint sampling results of Duncan-Zhang EB model parameters in the main rockfill area

[0147]

[0148] Table 13 Correlation coefficients of the joint sampling results of Duncan-Zhang EB model parameters in the rockfill area

[0149]

[0150] In step S5, a number of groups of Duncan Zhang EB model parameters are randomly extracted from the parameter multidimensional joint regular vine Copula function model by Monte-Carlo method;

[0151] In step S6, the reliability function of the downstream slope of the rockfill dam is used to calculate the reliability of each group of Duncan Zhang EB model parameters, and the number of reliability values ​​less than zero is counted as the number of failures;

[0152] In step S7, the failure probability of the rockfill dam to be analyzed is calculated according to the total number of extracted Duncan-Zhang EB model parameters and the number of failures.

[0153] The random variable was truncated with μ-3σ and μ+3σ as the upper and lower limits, and the Monte-Carlo method was used to perform 1×10 9 Sampling times, calculate the failure probability p of dam slope stability f And the reliability index β. When sampling, we consider two situations: the existence of internal correlation between parameters and the absence of internal correlation between parameters.

[0154] When the intrinsic correlation of parameters is not considered, each parameter obeys its original marginal distribution. The marginal distribution model of each parameter is established and sample simulation is performed. The failure probability p is calculated through the proxy model of the dam slope stability function. f 2.51×10 -6 , the reliability index β is 4.56. When considering the intrinsic correlation of parameters, the sampling simulation is carried out through the multidimensional joint distribution model of the Duncan-Zhang EB model parameters of rockfill materials, and the failure probability p is calculated through the proxy model of the dam slope stability function function. f 5.42×10 -7 , the reliability index β is 4.87. Both cases meet the minimum target reliability index β of the ultimate limit state of the Class I structural component bearing capacity permanent design condition specified in GB50199-2013 "Uniform Standard for Reliability Design of Water Conservancy and Hydropower Engineering Structures" t The standard is 4.2, the dam slope safety risk level is low and the operation is reliable.

[0155] The reliability calculation results of whether to consider the intrinsic correlation of parameters show that the correlation between parameters has a certain influence on the reliability of the slope stability of the face rockfill dam. The reliability index considering the intrinsic correlation of parameters is higher than the reliability index not considering the intrinsic correlation of parameters. When the intrinsic correlation of parameters is considered, the parameter pairs with higher correlation will appear in the combination with higher probability when sampling their joint distribution. Figure 7 Main rockfill area parameters For example, the joint distribution of parameters is mainly concentrated in the middle shaded part, while the probability of parameters appearing in the blank part in the upper left corner and the lower right corner is low, which reflects the joint distribution characteristics of parameters; while in independent sampling, the parameters obey their own marginal distribution, with the highest probability appearing in the center, and the probability decreasing from the center to the outside, ignoring the coupling characteristics of the parameters, and the results of parameter sampling are distorted. The sampling results of the joint distribution take into account the relationship between the parameters, which conforms to the actual situation of the parameters. When sampling, the probability of parameter groups that do not conform to the actual correlation of the parameters is greatly reduced.

[0156] The reliability analysis method of slope stability of panel rockfill dam considering the intrinsic correlation of parameters solves the problem that independent fluctuation of parameters may deviate from the intrinsic characteristics of materials and cause misjudgment of slope instability risk. The reliability index result is more reasonable and can reflect the real state of slope stability of DL panel rockfill dam. The reliability analysis method of slope stability of panel rockfill dam considering the intrinsic correlation of parameters has theoretical and practical application value for the risk assessment of slope stability of high panel rockfill dam.

Claims

1. A method for calculating the reliability of rockfill dam slope considering the intrinsic correlation of parameters, characterized in that: Includes steps: S1. Construct a two-dimensional finite element model of the rockfill dam to be analyzed, and search for the sliding channel of the rockfill dam slope by the strength reduction search method; S2. According to the obtained sliding channel, a reliability function of the downstream slope of the rockfill dam to be analyzed is constructed; S3, obtaining Duncan-Zhang EB model parameters of several rockfill dams and the marginal distribution function of each model parameter, and calculating the Pearson correlation coefficient between each model parameter and any model parameter of the remaining model parameters; S4. Construct a parameter multi-dimensional joint regular vine Copula function model based on all model parameters and their corresponding marginal distribution functions and all Pearson correlation coefficients; S5, randomly extracting several groups of Duncan Zhang EB model parameters from the parameter multidimensional joint regular vine Copula function model by Monte-Carlo method; S6. The reliability function of the downstream slope of the rockfill dam is used to calculate the reliability of each group of Duncan Zhang EB model parameters, and the number of reliability values ​​less than zero is counted as the number of failures; S7. Calculate the failure probability of the rockfill dam to be analyzed based on the total number of extracted Duncan-Zhang EB model parameters and the number of failures.

2. The method for calculating the reliability of rockfill dam slope considering the intrinsic correlation of parameters according to claim 1 is characterized in that: Step S2 further comprises: S21. By adjusting the friction coefficient, cohesion, normal stress and / or shear stress of different units in the sliding channel, several groups of dam slope stability safety factors F are calculated. s : Where M is the total number of units on the slip channel; f k 、c k are the friction coefficient and cohesion of the kth unit on the sliding channel, σ k , τ k are the normal stress and shear stress of the kth unit in the slip channel direction respectively; l k is the unit length of the kth unit along the slip channel direction; S22. Based on several groups of dam slope stability safety factors and their corresponding Duncan-Zhang EB model parameters, the response surface equation is used to calculate the unknown coefficients a and b. i 、c i , the expression of the response surface equation is: Among them, x i is the i-th model parameter, 1≤i≤7; b i 、c i are the undetermined coefficients corresponding to the i-th model parameter; I is the total number of model parameters; S23, using the calculated unknown coefficients a and b i 、c i Update the response surface equation as the fitting formula: Among them, K e is the tangent modulus coefficient; n is the tangent modulus index; K b is the bulk modulus coefficient; m is the bulk modulus index; R f is the destruction ratio; All are nonlinear strength indicators; K e ,n,K b ,m,R f , The 7 model parameters included in the Duncan Zhang EB model parameters; S23. According to the fitting formula, the downstream dam slope reliability function Z=F is constructed. s -1.

3. The method for calculating the reliability of rockfill dam slope considering the intrinsic correlation of parameters according to claim 1 is characterized in that: The calculation formula of the Pearson correlation coefficient in step S3 is: Among them, x oi and x oj are the i-th and j-th model parameters of the o-th rockfill dam; and are the average values ​​of the i-th and j-th model parameters of N rockfill dams; N is the total number of rockfill dams; r ij is the Pearson correlation coefficient between the i-th and j-th model parameters; 1≤i≤7, 1≤j≤7, and i≠j.

4. The method for calculating the reliability of rockfill dam slope considering the intrinsic correlation of parameters according to claim 1 is characterized in that: Step S4 further comprises: S41, using the maximum spanning tree method, based on the principle that the sum of the absolute values ​​of the Pearson correlation coefficients of each layer in the tree structure is the largest, generating a tree structure of each layer; S42, determine the Copula function set; S43, selecting the optimal pair copula function of the variables connected by each edge in the tree structure from the copula function set by using the AIC criterion and the maximum likelihood estimation method, and obtaining the optimal parameter estimation of the optimal pair copula function; S44, the optimal Pair Copula function of the combined tree structure and the edge line is constructed to obtain a parameter multi-dimensional joint regular vine Copula function model.

5. The method for calculating the reliability of rockfill dam slope considering the intrinsic correlation of parameters according to claim 4 is characterized in that: The Copula function set includes Gaussian Copula, t Copula, Clayton Copula, Frank Copula, Gumbel Copula, Joe Copula and Indep Copula; The tree structure of the regular vine Copula function model consists of six layers. The first layer of the tree structure has 7 nodes and 6 edges. With each additional layer, the number of nodes decreases by one and the number of edges decreases by one.

6. The method for calculating the reliability of rockfill dam slope considering the intrinsic correlation of parameters according to claim 5 is characterized in that: The rockfill dam comprises a main rockfill area and a secondary rockfill area, and the two rockfill areas are both subjected to corresponding dam slope failure probability calculation according to steps S3 to S7; The optimal pair copula function corresponding to the node edge and node edge of each layer of the tree structure in the main rockfill area is: The node edges of the first layer tree structure Tree1 are m, n, K b , n, n, R f , R f , K e , K e , and The optimal Pair Copula functions corresponding to these node edges are Joe, Gumbel180°, Student, Joe, Gumbel, and Gumbel; The node edges of the second-level tree structure Tree2 are m, K b |n, K b , R f |n, K e ,n|R f , R f , and K e , The optimal Pair Copula functions corresponding to these node edges are Independence, Gaussian, Independence, Independence, and Joe180°; The node edges of the third-level tree structure Tree3 are m, R f |K b , n, K b , K e |R f , n, n, R f and R f , K e , the optimal Pair Copula functions corresponding to these node edges are Independence, Clayton180°, Independence and Gaussian; The node edges of the fourth-level tree structure Tree4 are m, K e |R f , K b , n, K b , R f , n and n, K e , R f , the optimal Pair Copula functions corresponding to these node edges are Gaussian, Independence and Independence respectively; The node edge of the fifth-level tree structure Tree5 is m. R f , K b , n and K b , K e , R f , n, the optimal pair copula functions of the two node edges are both Independence; The node edge of the sixth-level tree structure Tree6 is m. K e , R f , K b , n, its optimal Pair Copula function is Independence; The optimal pair copula function corresponding to the node edge and node edge of each layer of tree structure in the secondary rockfill area is: The node edge of the first layer tree structure Tree1 is R f , n, m, n, n, K b , K e , K b , and The optimal pair copula functions corresponding to these node edges are Joe, Gumbel, Gumbel180°, Joe 180°, Joe, and Gumbel; The node edges of the second-level tree structure Tree2 are R f , m|n, m, K b |n, n, K e , and K b , The optimal Pair Copula functions corresponding to these node edges are all Independence; The node edge of the third-level tree structure Tree3 is R f , K b |m,n、m, n, n, K b , and K e The optimal Pair Copula functions corresponding to these node edges are Independence; The node edge of the fourth layer tree structure Tree4 is R f , m, n, m K b , n and n, K b , the optimal Pair Copula functions corresponding to these node edges are Gaussian, Independence and Independence respectively; The node edge of the fifth layer tree structure Tree5 is R f , K b , m, n and m, K b , n, the optimal pair copula functions of the two node edges are both Independence; The node edge of the sixth layer tree structure Tree6 is R f , K b , m, n, its optimal Pair Copula function is Joe 180°.

7. The method for calculating the reliability of rockfill dam slope considering the intrinsic correlation of parameters according to claim 6 is characterized in that: The tree structure multiplies the marginal distribution functions of the seven model parameters and the optimal Pair Copula functions corresponding to all node edges as the correlation of the regular vine Copula function model parameters.

8. The method for calculating the reliability of rockfill dam slope considering the intrinsic correlation of parameters according to claim 6 is characterized in that: The method for selecting the marginal distribution function of the model parameters in step S3 includes: S31, using KS test to determine the marginal distribution function that the model parameters meet; S32, according to all marginal distribution functions that each model parameter conforms to, using the AIC criterion to calculate the AIC value corresponding to each marginal distribution function; S33. Select the marginal distribution with the minimum AIC value as the optimal distribution of the model parameters.

9. The method for calculating the reliability of rockfill dam slope considering the intrinsic correlation of parameters according to claim 8, characterized in that: For the main rockfill area, n1 and It follows the truncated normal distribution, and the remaining model parameters follow the Weibull distribution; for the secondary rockfill area, n2, R f2 and The remaining model parameters all obey the Weibull distribution.

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