Method and system for estimating reliability of suspension river embankment in mixed failure mode

Abstract

The invention belongs to the technical field of reliability estimation of a suspension river dike, and particularly relates to a reliability estimation method and system for the suspension river dike in a mixed failure mode, and the method comprises the steps: recognizing the failure mode of the suspension river dike, and determining the performance functions of different failure modes of the suspension river dike; taking the performance function of each failure mode in the suspension river dike as a random variable, and quantifying the correlation between different failure modes by adopting a Copula function; an optimal Copula function is determined; unknown parameters in the selected optimal Copula function are estimated; constructing a reliability estimation model of the suspension river dike in the mixed failure mode, and substituting the Copula function into the reliability estimation model of the suspension river dike project in the mixed failure mode; and calculating the reliability probability of the river embankment in the mixed failure mode by using a reliability estimation formula. According to the method, the description of the correlation among different failure modes is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of reliability estimation of suspended river embankments, and in particular relates to a method and system for estimating the reliability of suspended river embankments under a mixed failure mode. Background Art

[0002] The soil of the suspended river embankment is mainly composed of contact-bonded loose granular materials, which have complex nonlinear characteristics. The suspended river embankment has a long embankment line and a wide range. The soil materials of the embankment body and the embankment foundation are very different. It is subjected to various random loads such as water pressure and waves, which makes the suspended river embankment have multiple failure modes. At the same time, there are complex correlations between different failure modes. The occurrence of one failure mode may trigger other failure modes, which reduces the redundancy performance of the suspended river embankment project and increases the probability of failure and damage of the suspended river embankment. The traditional reliability estimation method of the suspended river embankment under mixed failure mode usually assumes that the failure modes are independent of each other, or uses the reliability of a certain main failure mode to represent the reliability of the entire embankment structure, or uses a simple correlation coefficient to represent the correlation between failure modes. However, the simple correlation coefficient cannot fully and accurately reflect the relevant information between the failure modes of the suspended river embankment, resulting in deviations between the analysis results and the actual conditions of the embankment, and a decrease in credibility. Summary of the invention

[0003] Purpose of the invention: The purpose of the present invention is to address the deficiencies of the prior art and provide a reliability estimation method for a suspended river embankment under a mixed failure mode. The method for measuring the correlation between different failure modes of a suspended river embankment is studied, thereby achieving the characterization of the correlation between different failure modes.

[0004] Technical solution: The reliability estimation method of the suspended river embankment under the mixed failure mode of the present invention comprises the following steps: (1) By comprehensively analyzing the geometric structure, geological characteristics and external loads of the suspended river embankment, the failure modes of the suspended river embankment are identified, and reliability analysis is performed on each failure mode to determine the functional functions of different failure modes of the suspended river embankment; (2) The functional functions of each failure mode in the suspended river embankment are taken as random variables, and the Copula function is used to quantify the correlation between different failure modes; (3) Determine the optimal Copula function; (4) Estimate the unknown parameters in the selected optimal Copula function; (5) Based on the occurrence conditions and interrelationships of various failure modes, a reliability estimation model for suspended river embankments under mixed failure modes is constructed, and the Copula function is substituted into the reliability estimation model for suspended river embankments under mixed failure modes; (6) The reliability estimation formula is used to calculate the reliability probability of the suspended river embankment under the mixed failure mode.

[0005] Further improving the above technical solution, the failure modes include overtopping, penetration damage and instability failure modes; The functional function in the flooding failure mode is: ; Where: is the embankment top elevation, The flood level of the suspended river embankment facing the water surface, Climbing high for the waves, is the windblock height; The failure probability calculation formula of the suspended river embankment under the overtopping failure mode is:

[0006] Where: Function representing the flood overtopping failure mode; h It is the flood level of the hanging river embankment facing the water surface; is the dike top elevation; To calculate the starting water level; is the probability density function of the flood overtopping failure mode, and is the flood level h Function of The functional function of the penetration failure mode is: , where: is the maximum hydraulic gradient on the back side of the dike, It is the critical hydraulic gradient for embankment anti-seepage.

[0007] Furthermore, in step (2), at least one of the Pearson linear correlation coefficient, the Kendall rank correlation coefficient, the Spearman rank correlation coefficient or the tail correlation coefficient is used to quantify the correlation between different failure modes.

[0008] Furthermore, the method for determining the optimal Copula function in step (3) includes: a selection method based on a correlation measurement index; a selection method based on a distribution test; and a selection method based on an AIC criterion.

[0009] Furthermore, the estimation method of the unknown parameters of the Copula function in step (4) includes: moment estimation method; maximum likelihood estimation method; semi-parametric estimation method.

[0010] Furthermore, the reliability estimation model of the suspended river embankment under the mixed failure mode is:

[0011] Where: For the Failure probability of a failure mode; is the Copula function; Furthermore, the reliability probability of the suspended river embankment under the mixed failure mode is Estimate.

[0012] Furthermore, if the mixed failure mode of the suspended river embankment is composed of n different failure modes, the Copula function of the mixed failure mode is It is the joint distribution function of n-dimensional random variables whose variables all satisfy the standard uniform distribution, and has the following properties: Domain: ; range: ; Monotonicity: The Copula function of the mixed failure mode of the suspended river embankment is a joint distribution function, which is monotonically non-decreasing in each dimension of the variable of different failure modes; Boundedness: The Copula function of the mixed failure mode of the suspended river embankment satisfies the Fréchet-Hoeffding boundary: , Where: , , ; When the random variables of the mixed failure modes of the suspended river embankment are independent of each other, ; For any different failure mode variables , there is the following relationship: hour, ; hour, ; Used to indicate: if one dimension variable with different failure modes is 0, then the value of the Copula function for the mixed failure mode of the suspended river embankment is 0; if If all dimensions are 1, the mixed failure mode Copula function is equal to the variable values ​​of the remaining dimensions.

[0013] A system for implementing the above method comprises: Data acquisition module for collecting embankment geometry, soil parameters and external loads; Model building module, used to build failure mode combination model and correlation analysis model; Calculation module, used for failure probability calculation and system reliability estimation; Analysis module, used for sensitivity analysis and outputting reliability optimization suggestions.

[0014] Beneficial effects: Compared with the prior art, the advantages of the present invention are: the present invention considers the correlation between different failure modes of suspended river embankments, introduces the Copula function to characterize the correlation between different failure modes, and proposes a reliability estimation method for suspended river embankments under mixed failure modes based on the Copula function after studying the optimal Copula function selection and parameter determination method, which has the following advantages: (1) To solve the correlation problem between different failure modes under mixed failure modes of suspended river embankments, the Copula function was introduced. Based on the definition and basic properties of the Copula function, the correlation measurement method between different failure modes of suspended river embankments was further studied, thereby achieving the characterization of the correlation between different failure modes.

[0015] (2) The reliability estimation method of suspended river embankments under mixed failure modes was studied, and the optimal Copula function selection and parameter determination technology were explored. On this basis, a reliability estimation implementation method for suspended river embankments under mixed failure modes was proposed. The feasibility and effectiveness of the proposed reliability estimation method were verified by taking a suspended river embankment section as an example. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a mixed failure mode diagram of the series structure suspended river embankment of the present invention; Figure 2 It is a flow chart of reliability estimation of suspended river embankment under mixed failure mode of the present invention. DETAILED DESCRIPTION

[0017] The technical solution of the present invention is described in detail below with reference to the accompanying drawings, but the protection scope of the present invention is not limited to the embodiments.

[0018] Example 1: The Copula function has the advantage of describing the degree of correlation between random variables and can characterize the correlation between various failure modes of suspended river embankments. By studying the definition and properties of the Copula function of the mixed failure mode of the suspended river embankment, the method for determining the correlation measurement index between different failure modes is explored, aiming to characterize the characteristics of the mixed failure mode of the suspended river embankment.

[0019] Any multivariate joint distribution function can be decomposed into the corresponding marginal distribution function and a Copula function. The Copula function expresses the dependency structure between random variables, also known as correlation. Copula function is essentially a function that connects the joint distribution function with the marginal distribution function of its random variables. The joint distribution function is obtained by using multiple marginal distribution functions to describe the correlation between random variables. Sklar's theorem lays the foundation for the application of Copula function. The following takes the mixed failure mode of suspended river embankment as an example to characterize Sklar's theorem.

[0020] make To have n A mixed failure mode of suspended river embankment with a single failure mode. The marginal cumulative distribution functions of different failure modes in this mode are , then there exists a Copula function , the joint cumulative distribution function of different failure modes of the suspended river embankment , and the marginal cumulative distribution function Connect them, then: (1) If the marginal cumulative distribution functions of different failure modes of suspended river embankments are continuous functions, then is unique; otherwise, is the marginal cumulative distribution function, is a Copula function, then the mixed failure mode determined by formula (1) , is a marginal cumulative distribution function The n-variable joint cumulative distribution function of .

[0021] According to the derivation rule, the random variables in the mixed failure mode of the suspended river embankment can be obtained from formula (1): Joint probability density function for

[0022] Will and Substituting into formula (2), we can get:

[0023] Where: is the probability density function of the Copula function; is the random variable of different failure modes of suspended river embankment The marginal probability density function of .

[0024] According to the above analysis, if the marginal distribution function of the random variable and the selected Copula function type are known, the random variable represented by different failure modes of the suspended river embankment can be established by equations (2) and (3): Taking the common two-dimensional case as an example, according to Sklar's theorem, the variables representing two different failure modes of the suspended river embankment can be obtained: and The joint cumulative distribution function of , and the joint probability density function They are: (4) (5) Where: and There are two different failure mode variables and The marginal cumulative distribution function of ; is a two-dimensional Copula function; is the probability density function of the two-dimensional Copula function; It is the parameter of the Copula function.

[0025] If the marginal distribution functions of two different failure mode variables 1X and 2X of the suspended river embankment are known and the Copula function type is determined, the variables can be established using equations (4) and (5). and Two-dimensional distribution model.

[0026] If the mixed failure mode of the suspended river embankment is composed of n different failure modes, then the Copula function of the mixed failure mode is the joint distribution function of n-dimensional random variables whose variables all satisfy the standard uniform distribution, and has the following properties: Domain: ; range: ; Monotonicity: The Copula function of the mixed failure mode of the suspended river embankment is a joint distribution function, which is monotonically non-decreasing in each dimension of the variable of different failure modes; Boundedness: The Copula function of the mixed failure mode of the suspended river embankment satisfies the Fréchet-Hoeffding boundary, that is: , , , ; When the random variables of the mixed failure modes of the suspended river embankment are independent of each other, ; For any different failure mode variables , there is the following relationship: hour, ; hour, ; That is, if one dimension variable with different failure modes is 0, the value of the Copula function of the mixed failure mode of the suspended river embankment is 0; if If all dimensions are 1, the mixed failure mode Copula function is equal to the variable values ​​of the remaining dimensions.

[0027] According to the characteristics of the failure mode of the suspended river embankment, the typical Copula function can be mainly divided into two categories: the elliptic family Copula function and the Archimedean family Copula function. The correlation of different failure modes of the suspended river embankment can be measured by a variety of indicators. Commonly used measurement indicators include Pearson linear correlation coefficient, Kendall rank correlation coefficient, Spearman rank correlation coefficient, tail correlation coefficient, etc. Different indicators measure the correlation of different failure modes of the suspended river embankment from different perspectives. The Kendall rank correlation coefficient and the Spearman rank correlation coefficient have similar properties.

[0028] On the above basis, a reliability estimation method for suspended river embankments under mixed failure modes based on Copula function is proposed using Copula function.

[0029] 1. Implementation method of reliability estimation of suspended river embankment under mixed failure mode When conducting reliability analysis of suspended river embankments, the complex suspended river embankment system is simplified into a combination of simple structural systems to construct a reliability estimation method for suspended river embankments. Assuming the limit state function of different failure mode systems, the mixed failure mode of suspended river embankments is a structural system composed of different failure modes in series.

[0030] Figure 1 Schematic diagram of mixed failure mode system of series structure suspended river embankment. Failure probability of mixed failure mode system The general expression for the calculation is: (6) Where: is the functional function of the ith failure mode.

[0031] According to the independence hypothesis theory, if the correlation is not considered, that is, each failure mode is independent of each other, then: (7) In the formula, is the failure probability of the ith failure mode.

[0032] According to the weakest link theory, which assumes that each failure mode is a completely correlated pairwise linear relationship, then: (8) For actual suspended river embankments, the single failure modes in the mixed failure mode are neither completely independent nor safety related. Therefore, the failure probability of the suspended river embankment system under the mixed failure mode is satisfy: (9) Based on the formula, the reliability probability of the suspended river embankment under the mixed failure mode is obtained as follows: (10) Taking the functional functions of different failure modes of the suspended river embankment as random variables, the reliability estimation method of the suspended river embankment related to each single failure mode is studied below.

[0033] (1) Reliability of suspended river embankments under a mixed failure mode consisting of two different failure modes Estimates make , are the failure probabilities of the two failure modes respectively. Based on the Copula function reflecting the correlation of different failure modes, the failure probability of the suspended river embankment mixed failure mode system is for: (11) Where: They are functional functions of the two failure modes respectively; is the Copula function of the two failure modes.

[0034] Based on formula (11), the reliability under the above failure mode is It can be obtained by formula (10).

[0035] (2) By Reliability of suspended river embankment under mixed failure mode composed of different failure modes Estimates When the mixed failure mode system of suspended river embankment has When there are failure modes, the Copula function reflects the correlation between different failure modes, then the failure probability of the system is : (12) Where: For the Failure probability of a failure mode; It is a Copula function.

[0036] In this invention, the three typical failure modes of suspended river embankments are mainly considered: the correlation between overtopping, seepage damage and instability failure modes, that is, Take 3, then the corresponding estimation formula for the failure probability of the suspended river embankment under the mixed failure mode is: (13) The corresponding reliability probability of the suspended river embankment It can be calculated by formula (10).

[0037] It can be seen from formula (13) that the key to estimating the reliability of suspended river embankments under mixed failure modes is to obtain the Copula function values ​​between different failure modes. According to the previous research content, there are many types of commonly used Copula functions. How to choose the most suitable Copula function is an important problem that needs to be solved.

[0038] 2. Method for determining the optimal Copula function Based on the above-mentioned reliability estimation model of suspended river embankments under mixed failure modes, the correlation structure between multiple failure modes of embankments is described by selecting the best Copula function. There are three main methods for determining the best Copula function in the reliability estimation model of suspended river embankments: (1) selection method based on correlation measurement index; (2) selection method based on distribution test; (3) selection method based on AIC criterion.

[0039] (1) Selection method based on correlation measurement indicators Typical failure modes of suspended river embankments include overtopping, seepage damage and instability failure modes. The present invention analyzes the correlation between two different failure modes as an example.

[0040] Assume two 2D random vectors with different failure modes, for If there are n samples of , then the Kendall nonparametric estimate based on the sample is: (14) When the sample is large enough, the nonparametric estimate It will be infinitely close to the true value, and then calculated according to the given Copula function , and Compare and choose and The closest Copula function type.

[0041] Can make and Close Enough That is the optimal Copula function.

[0042] (2) Selection method based on distribution test Assume two random vectors with different failure modes The marginal distributions of are uniform distributions on (0,1), and the Copula function is , the generator is , for a given The empirical distribution function after is: (15) (16) The selection steps are as follows: 1) Establish an empirical function, whose expression is: (17) Where: is an indicative function.

[0043] 2) Simulate , , then create The empirical distribution function of is: (18) Where: is an example function.

[0044]

[0045] Can make and Close Enough That is the optimal Copula function.

[0046] (3) Selection method using the AIC criterion When estimating parameters using the maximum likelihood estimation method, the AIC criterion can be used to select the Copula function. The expression of the AIC criterion is: (20), where A is the maximum likelihood function corresponding to the model; m is the number of parameters to be estimated in the model.

[0047] when When it is the maximum likelihood estimate, that is: (twenty one) but: (twenty two) Where: m is the parameter in the model The smaller the AIC value, the better the fitting effect.

[0048] In the reliability estimation of suspended river embankment under mixed failure mode, the corresponding optimal Copula function is selected according to the structural characteristics of the mixed failure mode.

[0049] 3. Estimation of Copula Function Parameters There are many methods for estimating unknown parameters in Copula functions. Currently, the most widely used methods include moment estimation, maximum likelihood estimation, and semi-parametric estimation.

[0050] (1) Moment estimation method Moment estimation method requires first determining the different failure mode variables X and YThe Kendall rank correlation coefficient of the given sample data is used to estimate the Copula function parameters by the relationship between the rank correlation coefficient of the given sample data and the Copula function parameters. This method does not require assumptions about the marginal distribution of different failure modes or calculations of marginal empirical distributions, and is more concise and efficient, but is not suitable for estimating the parameters of multidimensional (three-dimensional and above) Copula distribution models. For a certain type of Copula function, the Kendall rank correlation coefficient has a corresponding relationship with the parameters of the Copula function.

[0051] (2) Maximum Likelihood Estimation Considering the marginal distribution of random variables of different failure modes of suspended river embankments and the unknown parameters in the Copula function, let The random variables representing different failure modes are , then the joint probability density function and log-likelihood function of the mixed failure mode of the suspended river embankment are:

[0052] Where: is the random variable of different failure modes of suspended river embankment The marginal distribution function of The parameters to be estimated for the Copula function.

[0053] Substituting formula (23) into formula (24), we can obtain:

[0054] Where: The log-likelihood function of the Copula function is Describe, the maximum likelihood function of each marginal distribution is used It means that its expression is .

[0055] but Estimated value of It is obtained from the following formula: (26) To obtain the marginal estimation function, we need to use the log-likelihood function of the Copula function and then estimate the parameters of each marginal distribution: ; The parameter estimate is calculated by formula (27) , and substitute it into the log-likelihood function of the Copula function , then the unknown parameters of the Copula function are estimated by formula (28), that is: ; (3) Semiparametric estimation method Build a hanging river embankment The joint distribution function of the random variables with different failure modes is , and the marginal distributions are ,but:

[0056] Where: is the Copula function; is the parameter to be estimated of the Copula function; are the parameters in the marginal distribution function.

[0057] Assume that the marginal density function of each random variable of the suspended river embankment is , the Copula function probability density function is , then the mixed failure mode variable The joint density function of It can be expressed as:

[0058] Use empirical distribution function instead of marginal distribution function ,but: ; Where: is the indicative function.

[0059] make , so that Reach the maximum Estimates is the maximum likelihood estimator.

[0060] 4. Implementation method of reliability estimation of suspended river embankment under mixed failure mode A reliability estimation method for suspended river embankments under mixed failure modes based on Copula functions is proposed. After optimizing the best Copula function and estimating the parameters of the Copula function, the reliability estimation of suspended river embankments under mixed failure modes is realized. Figure 2 This is the process of estimating the reliability of suspended river embankments under mixed failure modes. The specific implementation steps are as follows: Step 1: Take the functional functions of each failure mode in the suspended river embankment as random variables.

[0061] Step 2 measures the correlation between different failure modes.

[0062] Step 3: Determine the optimal Copula function.

[0063] Step 4 estimates the unknown parameters in the selected optimal Copula function.

[0064] Step 5: Substitute the Copula function into the reliability estimation model of suspended river embankment engineering under mixed failure mode, that is, where:

[0065] Step 6 uses the formula to estimate the reliability probability of the hanging river embankment under the mixed failure mode.

[0066] Embodiment 2: By comprehensively analyzing the geometric structure, geological characteristics and external loads of the hanging river embankment, the main failure modes of the hanging river embankment are identified. The process is as follows: the landslide failure mode is analyzed through the embankment profile, the stability coefficient of the embankment slope is calculated, and the limit state equation of the embankment landslide failure is established; the instability failure mode is based on the groundwater seepage path and the soil particle characteristics, and the permeability and anti-permeability are compared and analyzed to identify the critical conditions of instability failure; the seepage damage mode is based on the seepage pressure distribution of the embankment and the effective stress criterion, combined with soil mechanics analysis to determine the failure mechanism of seepage damage.

[0067] This example only considers the correlation between overtopping, seepage damage and instability failure modes, and studies the reliability estimation method of the suspended river embankment under a mixed failure mode consisting of any two typical failure modes. Under typical failure modes, the functional functions for estimating the reliability of the suspended river embankment are: The function in the flooding failure mode is: ; Where: is the embankment top elevation, The flood level of the suspended river embankment facing the water surface, Climbing high for the waves, is the windblock height; The failure probability calculation formula of the suspended river embankment in the overtopping failure mode is:

[0068] Where: Function representing the flood overtopping failure mode; h It is the flood level of the hanging river embankment facing the water surface; is the dike top elevation; To calculate the starting water level; is the probability density function of the flood overtopping failure mode, and is the flood level h Function of The function function of the penetration failure mode is: , where: is the maximum hydraulic gradient on the back side of the dike, It is the critical hydraulic gradient for embankment anti-seepage.

[0069] Taking into account the random variables and their statistical characteristics of the reliability estimation of the hanging river embankment under each single failure mode, it is determined that the random variables of the hanging river embankment section under the mixed failure mode mainly include flood level, wind dam height, cohesion, etc. The statistical characteristics of each random variable are shown in Table 1.

[0070] Table 1 Statistics of random variable characteristic values ​​of mixed failure modes

[0071] The three typical single failure modes of this hanging river embankment section exist in series in the system, and there is correlation between the failure modes. According to the functional functions of different failure modes and the characteristic values ​​of each random variable, the statistical characteristics of the sample values ​​of the limit state functional functions of the three typical failure modes are obtained, as shown in Table 2.

[0072] Table 2 Statistical table of sample values ​​of functional functions of different failure modes in a suspended river embankment section

[0073] Considering that the Kendall rank calculation method is simple and the result is highly accurate, the Kendall rank values ​​between the failure modes of the suspended river embankments are calculated and the correlation measurement of the Copula function is performed. The calculation results are shown in Tables 3 and 4.

[0074] Table 3. Statistical table of sample values ​​of different failure mode function functions of a suspended river embankment section

[0075] Table 4 Correlation measures of Copula functions for mixed failure modes of suspended river embankments

[0076] By comparing the value of Kendall rank and the correlation measure of Copula, the closest Copula function is selected as the Copula function for reliability estimation of the hanging river embankment section under the mixed failure mode. As can be seen from Table 4, the correlation measure of the normal Copula is the closest, while the Clayton Copula function is poor, so the Clayton Copula function can be excluded, while t-Copula and Gumbel Copula are retained for comparative analysis.

[0077] Using the semi-parametric estimation method, the parameter values ​​of the normal copula function, t-copula function and Gumbel copula function are given respectively. The results are shown in Table 5.

[0078] Table 5 Estimated values ​​of Copula function parameters for mixed failure mode of a suspended river embankment section

[0079] It can be seen that the calculated values ​​of the AIC indicators of the three Copula functions are not much different, and the AIC indicator of the normal Copula function is the smallest, which verifies the rationality of the determination of the Copula function.

[0080] Combining the Copula function type for estimating the reliability of the suspended river embankment and its parameter estimation results, the estimated results of the reliability of the suspended river embankment section under the mixed failure mode are obtained. After estimation, the normal Copula, t-Copula and GumbelCopula functions are used to obtain the reliability of the suspended river embankment under the mixed failure mode of 99.991%, 99.988% and 99.990% respectively. It can be seen that the results of estimating the reliability of the suspended river embankment under the mixed failure mode using different Copula functions are not completely consistent, but the difference is not large, which indirectly proves the rationality of the calculation results.

[0081] As described above, although the present invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the present invention itself. Various changes in form and details may be made without departing from the spirit and scope of the present invention as defined in the appended claims.

Claims

1. A reliability estimation method for suspended river embankments under mixed failure modes, characterized in that: The following steps are involved: (1) By comprehensively analyzing the geometric structure, geological characteristics and external loads of the suspended river embankment, the failure modes of the suspended river embankment are identified, and reliability analysis is performed on each failure mode to determine the functional functions of different failure modes of the suspended river embankment; (2) The functional functions of each failure mode in the suspended river embankment are taken as random variables, and the Copula function is used to quantify the correlation between different failure modes; (3) Determine the optimal Copula function; (4) Estimate the unknown parameters in the selected optimal Copula function; (5) Based on the occurrence conditions and interrelationships of various failure modes, a reliability estimation model for suspended river embankments under mixed failure modes is constructed, and the Copula function is substituted into the reliability estimation model for suspended river embankments under mixed failure modes. (6) The reliability estimation formula is used to calculate the reliability probability of the suspended river embankment under the mixed failure mode.

2. The reliability estimation method of suspended river embankment under mixed failure mode according to claim 1 is characterized by: The failure modes include overtopping, penetration damage and instability failure modes; The functional function in the flooding failure mode is: ; Where: is the embankment top elevation, The flood level of the suspended river embankment facing the water surface, Climbing high for the waves, is the windblock height; The failure probability calculation formula of the suspended river embankment under the overtopping failure mode is: ； Where: The functional function representing the flood overtopping failure mode; h is the flood level on the water surface of the suspended river embankment; is the dike top elevation; To calculate the starting water level; is the probability density function of the flood overtopping failure mode, which is a function of the flood level h; The functional function of the penetration failure mode is: , where: is the maximum hydraulic gradient on the back side of the dike, It is the critical hydraulic gradient for embankment anti-seepage.

3. The reliability estimation method of suspended river embankment under mixed failure mode according to claim 2 is characterized in that: In the step (2), the correlation between different failure modes is quantified by using at least one of the Pearson linear correlation coefficient, the Kendall rank correlation coefficient, the Spearman rank correlation coefficient or the tail correlation coefficient.

4. The reliability estimation method of suspended river embankment under mixed failure mode according to claim 3 is characterized in that: The method for determining the optimal Copula function in step (3) includes: a selection method based on a correlation measurement index; a selection method based on a distribution test; and a selection method based on an AIC criterion.

5. The reliability estimation method of suspended river embankment under mixed failure mode according to claim 4 is characterized in that: The estimation method of the unknown parameters of the Copula function in step (4) includes: moment estimation method; maximum likelihood estimation method; semi-parametric estimation method.

6. The reliability estimation method of suspended river embankment under mixed failure mode according to claim 5 is characterized in that: The reliability estimation model of the suspended river embankment under the mixed failure mode is: ； Where: For the Failure probability of a failure mode; It is a Copula function.

7. The reliability estimation method of suspended river embankment under mixed failure mode according to claim 6 is characterized in that: The reliable probability utilization formula of the suspended river embankment under the mixed failure mode Estimate.

8. The reliability estimation method of suspended river embankment under mixed failure mode according to claim 1 is characterized in that: If the mixed failure mode of the suspended river embankment is composed of n different failure modes, then the Copula function of the mixed failure mode is It is the joint distribution function of n-dimensional random variables whose variables all satisfy the standard uniform distribution, and has the following properties: Domain: ; range: ; Monotonicity: The Copula function of the mixed failure mode of the suspended river embankment is a joint distribution function, which is monotonically non-decreasing in each dimension of the variable of different failure modes; Boundedness: The Copula function of the mixed failure mode of the suspended river embankment satisfies the Fréchet-Hoeffding boundary: ， Where: , , ； When the random variables of the mixed failure modes of the suspended river embankment are independent of each other, ; For any different failure mode variables , there is the following relationship: hour, ; hour, ; Used to indicate: if one dimension variable with different failure modes is 0, then the value of the Copula function for the mixed failure mode of the suspended river embankment is 0; if If all dimensions are 1, the mixed failure mode Copula function is equal to the variable values ​​of the remaining dimensions.

9. A system for implementing the method for estimating the reliability of a suspended river embankment under a mixed failure mode as claimed in claim 1, characterized in that: include: Data acquisition module for collecting embankment geometry, soil parameters and external loads; Model building module, used to build failure mode combination model and correlation analysis model; Calculation module, used for failure probability calculation and system reliability estimation; Analysis module, used for sensitivity analysis and outputting reliability optimization suggestions.

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