Estimation Method and System for the Reliability of Levees with Hanging Rivers under Single Failure Modes

Abstract

The present invention belongs to the technical field of reliability estimation of levees of suspended rivers, and specifically relates to a method and system for estimating the reliability of levees of suspended rivers under a single failure mode, including: determining the random variables causing the failure mode and the corresponding performance function according to the failure mode of the levees of suspended rivers; using the Latin hypercube sampling method to extract samples of the parameter values of the random variables; substituting the extracted parameter values of the random variables into the performance function under the corresponding failure mode, calculating the failure states of the levees of suspended rivers under different combinations of the parameter values of the random variables, and judging whether the levees of suspended rivers are in a failure state according to the positive or negative of the performance function value; counting the number of times in the failure state in all sampling results, and calculating the failure probability of the levees of suspended rivers and the reliability of the levees. The present invention establishes a reliability estimation model of levees of suspended rivers under different single failure modes, and combines the Latin hypercube sampling and the particle flow discrete element analysis method to propose a method for estimating the reliability of levees of suspended rivers under a single failure mode.

Description

Technical Field

[0001] The present invention belongs to the technical field of reliability estimation of levees of hanging rivers, and particularly relates to a method and system for estimating the reliability of levees of hanging rivers under a single failure mode. Background Art

[0002] The soil body of the levee of a hanging river is mainly composed of granular materials with contact bonding, and has complex non-linear characteristics. The research on the reliability estimation of the levee is based on the analysis of its failure modes. Due to the many uncertainties in the construction and operation management of the levee, its failure modes show complex and changeable characteristics.

[0003] Traditional methods for estimating the reliability of levees of hanging rivers include the first-order second-moment method, Monte Carlo sampling method, etc. Among them: the first-order second-moment method can effectively solve the problem of structural reliability analysis with an explicit functional expression, but will produce large errors when the functional expression is implicit or highly non-linear; the Monte Carlo method has strong universality, but its sampling workload is large and the calculation efficiency is low. At the same time, in the process of reliability analysis, the analysis content of the mechanical response of the soil body of the levee of a hanging river is involved. The traditional finite element analysis method can only reflect the macroscopic performance change effect of the levee soil body, and it is difficult to simulate the mesoscopic mechanical response of the soil particles.

[0004] It is common for a single failure mode to occur in the failure of the levee of a hanging river. When estimating the reliability of the levee of a hanging river, the traditional analysis method based on simple structural reliability theory is difficult to accurately estimate the reliability of non-linear structures; the Monte Carlo method has low efficiency when estimating the reliability of complex structures, and the calculation accuracy and efficiency of the surrogate model method for estimating the structural reliability are restricted by the performance of the surrogate model. Therefore, it is necessary to further study the method for estimating the reliability of the levee of a hanging river under each single failure mode. Summary of the Invention

[0005] Object of the Invention: The object of the present invention is to provide a method and system for estimating the reliability of levees of hanging rivers under a single failure mode in view of the deficiencies of the prior art, and to propose a method for estimating the reliability of levees of hanging rivers under different failure modes by combining the Latin hypercube sampling technique and the particle discrete element method.

[0006] Technical Solution: The method for estimating the reliability of levees of hanging rivers under a single failure mode according to the present invention includes the following steps:

[0007] S1. Determine the random variables causing the failure mode and the corresponding functional function according to the failure mode of the levee of a hanging river;

[0008] S2. Use the Latin hypercube sampling method to extract samples of the parameter values of the random variables to ensure that the samples can fully reflect the probability distributions of the random variables;

[0009] S3. Substitute the extracted random variable parameter values into the performance function under the corresponding failure mode, calculate the failure state of the levee of the suspended river under different combinations of random variable parameter values, and determine whether the levee of the suspended river is in a failure state based on the positive or negative value of the performance function value;

[0010] S4. Count the number of times in the failure state among all sampling results, and calculate the failure probability of the levee of the suspended river based on the number of failure state samples and the total number of samples;

[0011] S5. Calculate the reliability of the levee according to the failure probability.

[0012] To further improve the above technical solution, the failure mode of the levee of the suspended river is any one of the following: overtopping failure mode, seepage failure mode or instability failure mode.

[0013] Furthermore, the Latin hypercube sampling method includes: equally dividing the cumulative distribution function of the random variables affecting the service of the levee of the suspended river into several non-overlapping sub-intervals; conducting an independent and equiprobable sampling once in each sub-interval. For the n random variables affecting the service of the levee of the suspended river, when conducting m sampling times, the maximum number of combinations is i ; the random number in the

[0014] th sub-interval should comply with the following regulations:

[0015] In the formula: , N is the number of sub-intervals, X is the random number uniformly distributed in the interval, is the random number of the

[0016] th sub-interval; only one random number will be generated in each sub-interval. Randomly combine the sampling values of multiple random variables into a multi-dimensional sample to simulate the joint distribution of multi-dimensional random variables, and obtain n groups of random numbers, with each group containing m variables. Furthermore, the calculation of the failure probability is carried out through the following formula: ; in the formula: L is the number of samples in the failure state, N is the total number of samples, is the failure probability; the calculation formula for the reliability is: ; in the formula:

[0017] Furthermore, the random variables in the overtopping failure mode include the levee top elevation , the wind setup height , and the wave run-up ; the performance function in the overtopping failure mode is: ; Wherein: is the embankment top elevation, is the flood level on the water-facing side of the levee for the hanging river, is the wave run-up, is the wind set-up height.

[0018] Furthermore, the failure probability calculation formula for the levee of the hanging river under the overtopping failure mode is:

[0019] ;

[0020] Wherein: represents the performance function of the flood overtopping failure mode; h is the flood level on the water-facing side of the levee for the hanging river; is the embankment top elevation; is the starting water level for calculation; is the probability density function of the flood overtopping failure mode, which is a function of the flood level h .

[0021] Furthermore, the random variables under the seepage failure mode include the soil permeability coefficient , the flood level , the cohesion and the internal friction angle ; The performance function under the seepage failure mode is: , wherein: is the maximum hydraulic gradient on the water-back side of the levee, is the critical hydraulic gradient for seepage resistance of the levee.

[0022] Furthermore, the random variables under the instability failure mode include the cohesion , the internal friction angle , the soil unit weight and the friction coefficient of the soil of the levee for the hanging river; The performance function under the instability failure mode is: , wherein: K is the safety factor of the levee slope, is the allowable value of the anti-sliding stability safety factor.

[0023] Furthermore, the steps of calculating the maximum hydraulic gradient on the water-back side of the levee or the safety factor of the levee slope are calculated through a particle flow discrete element analysis model, and the process includes: (1) constructing a discrete element calculation model grid for the levee of the hanging river; (2) inputting the soil parameters obtained by random sampling; (3) simulating the transmission of the hydraulic gradient during the seepage process; (4) calculating the inter-particle contact force and pore water pressure; (5) determining the maximum hydraulic gradient or the safety factor.

[0024] A system for implementing the reliability estimation method of levees on the suspended river under the above single failure mode, comprising:

[0025] A random variable parameter acquisition module, configured to obtain random variables affecting the reliability of the levees on the suspended river according to the failure modes of the levees on the suspended river;

[0026] A Latin hypercube sampling module, configured to perform sampling according to the input random variables;

[0027] A failure mode function judgment module, configured to substitute the sampling results into the function for calculation and judge whether the levee is in a failure state;

[0028] A failure probability and reliability calculation module, configured to count the number of samples in the failure state and calculate the failure probability and reliability according to the number of failure samples;

[0029] An output module, configured to output the reliability result of the levees on the suspended river.

[0030] Beneficial effects: Compared with the prior art, the advantages of the present invention are as follows: Based on the basic principle of the reliability estimation of the levees on the suspended river, the particle flow discrete element analysis method for the mechanical response of the soil body of the levees on the suspended river is explored. On the basis of analyzing the characteristics of different failure modes of the levees on the suspended river, a reliability estimation method for the levees on the suspended river under a single failure mode is proposed. Through the analysis of the overtopping, seepage failure and instability failure modes of the levees on the suspended river, a function for estimating the reliability of the levees on the suspended river under the overtopping, seepage failure and instability failure modes is established, and a reliability estimation model for the levees on the suspended river under different single failure modes is constructed. Combining the Latin hypercube sampling and the particle flow discrete element analysis method, a reliability estimation method for the levees on the suspended river under a single failure mode is proposed, and based on a certain levee section of the suspended river, the effectiveness of this method is verified. Description of the Drawings

[0031] Figure 1 is the flowchart for estimating the reliability of the levees on the suspended river under the overtopping failure mode;

[0032] Figure 2 is the flowchart for estimating the reliability of the levees on the suspended river under the seepage failure mode;

[0033] Figure 3 is the flowchart for estimating the reliability of the levees on the suspended river under the instability failure mode;

[0034] Figure 4 is the calculated cross-section of a certain levee section of the levees on the suspended river in Example 5;

[0035] Figure 5 is the specimen diagram of the biaxial numerical test in Example 5;

[0036] Figure 6 is the particle flow discrete element analysis model of the levee section of the suspended river in Example 5. Specific Embodiments

[0037] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings, but the protection scope of the present invention is not limited to the described embodiments.

[0038] Embodiment 1: When analyzing the reliability of the levee structure of a suspended river, two types of parameters are mainly considered: one is the direct action applied to the levee or the indirect action that causes additional deformation or constrained deformation of the levee, collectively referred to as action; the other is the ability of the levee structure and its materials to withstand the action effect, called resistance. Both types of parameters in the reliability analysis of the levee structure of a suspended river can be considered as random variables. For the reliability analysis of the levee structure of a suspended river, it is based on whether the levee structure reaches the limit state. According to the functional requirements of the levee structure and the corresponding limit state, a limit state function corresponding to the random variable is established, and its expression is:

[0039] (1);

[0040] When , the levee structure of the suspended river is in a reliable state; when , the levee structure of the suspended river is in a failure state; when , the structure is in the limit state, and the corresponding limit state equation is:

[0041] (2);

[0042] The random variables are divided into two categories: resistance R and action S, and the corresponding function is:

[0043] (3);

[0044] When the resistance effect of the levee structure of the suspended river is greater than the action effect, it is considered that the levee structure of the suspended river is reliable, that is, the levee structure can complete its predetermined function under certain conditions, and its reliability can be represented by the reliability probability . On the contrary, when the action effect of the levee structure of the suspended river is greater than the resistance effect, it is considered that the levee structure is unreliable, and this situation can be represented by the failure probability . The expressions of the reliability probability and the failure probability are respectively:

[0045] (4);

[0046] (5);

[0047] Where: z is a continuous random variable; is the probability density function of Z.

[0048] To determine the failure probability , it is necessary to first determine the joint probability density function of each basic random variable and perform multiple integration on the probability density function of the performance function. The failure probability result obtained by the direct integration method is accurate, but it is only applicable to reliability analysis problems with explicit performance functions. In actual situations, since the probability density function of the performance function may be in the form of an implicit function and is mostly nonlinear, the direct integration method is difficult to apply. Therefore, the reliable index is introduced As a quantitative basis for measuring the level of structural reliability. Failure probability of structural reliability The calculation formula is related to the distribution of Z. Assuming that Z follows a normal distribution, its standard deviation is , whose mean is , then its probability density function can be expressed as:

[0049] (6);

[0050] right In the case of normal distribution, its reliability index The calculation expression is:

[0051] (7);

[0052] According to the concepts of reliability index and failure probability, the relationship between failure probability and reliability index is:

[0053] (8);

[0054] Where: is the standard normal distribution function; is the inverse function of the standard normal distribution function. When the normal distribution is followed, the relationship between failure probability and reliability index can be transformed into each other according to formula (8).

[0055] Sampling the random parameters of the functional function, counting the number of functional function samples in the failure state, and then estimating the probability of structural failure risk is a widely used calculation method in the reliability analysis of suspended river embankments. Among them, selecting an appropriate sampling method is the key link in the reliability analysis of suspended river embankments. The Monte Carlo method is a commonly used reliability analysis sampling method, but it has the problems of large sampling samples and low estimation efficiency. In view of the above problems, the present invention adopts Latin hypercube sampling technology for reliability estimation of suspended river embankments.

[0056] Latin Hypercube Sampling (LHS) is a multidimensional stratified sampling method. Compared with traditional sampling methods, the LHS method can significantly reduce the number of samples and has high sampling efficiency.

[0057] The basic idea of the LHS method is stratified sampling. Taking the sampling process of the one-dimensional random variable x as an example, assuming the total number of samplings is N, the random variable x is first divided into several regions with equal probability. , then it satisfies:

[0058] (9);

[0059] Taking the case of a normal variable as an example. Assume the sample size N = 5, and the stratified sampling method is used to divide the cumulative curve into 5 equal-probability intervals, and the probability of each interval being sampled is 0.2. Stratified sampling follows the principle of "sampling without replacement", that is, one sample is drawn from each stratum. Once a sample is drawn from a stratum, this stratum will no longer be sampled, so there will be no repeated sampling. Using the stratified sampling method, the sampled samples can more accurately reflect the probability distribution of the input values, thus improving the accuracy of reliability analysis.

[0060] Based on the above one-dimensional random variable stratified sampling method, multiple variables are introduced to achieve stratified sampling of multi-dimensional random variables. In the research process, the Latin hypercube sampling method treats all coordinate axes equally. By only stratifying the one-dimensional boundaries of the multi-dimensional joint distribution, it avoids the problem of exponential growth of the sampling quantity when stratifying the multi-dimensional joint distribution.

[0061] This method first fixes the dimension d and the sample size K, and for each coordinate , conducts independent stratified samples generated from the unit interval , and each stratified sample conducts independent equal-probability sampling on . If the d stratified samples are arranged by column, then each row gives the coordinates of a point. The first row corresponds to a point in , the second row corresponds to a point in , and so on. Then it corresponds to

[0062] (10);

[0063] On this basis, randomly transform the values of each column in the sequence, and let be the permutation of , which is equivalent to independent sampling from all K! such permutations with an equal-probability distribution. Assume is the value after the i-th permutation obtained by the -th permutation, and the rows of the sequence still correspond For the points in , they are no longer restricted to the diagonal line, but each row is still a set of points uniformly distributed on the unit hypercube. The following formula is the result of K random samplings with d variables;

[0064] (11);

[0065] In summary, the specific steps of the random number generation process based on the Latin hypercube sampling method are as follows:

[0066] (1) First, determine the number of simulations, and then equally divide the cumulative distribution function of the random variables affecting the service of the levee on the suspended river into multiple non-overlapping subintervals.

[0067] (2) Then, conduct an independent and equally probable sampling within each subinterval. For the LHS simulation method involving n random variables affecting the service of the levee on the suspended river, when conducting m samplings, the maximum number of combinations is .

[0068] (3) To ensure that random numbers are sampled in each subinterval, the random number i in the subinterval should comply with the following regulations:

[0069] (12);

[0070] In the formula: , X is a random number uniformly distributed within the interval, and is the random number in the i-th subinterval.

[0071] (4) Only one random number is generated in each subinterval. Through relevant transformations, the sampling values of variables obeying a certain probability density function can be obtained. By randomly combining these sampling values, all the required random numbers can be obtained. The final number of groups obtained is n , and each group contains m random numbers of variables.

[0072] The particle flow discrete element method is based on the meso-mechanics principle to simulate the interaction between particles and the overall behavior of the soil mass. In the analysis of the levee on the suspended river, the particle flow discrete element method is used to describe the behavior of particles in the levee soil and the contact forces between particles, as well as the deformation and failure process of the soil mass under external forces. The basic unit in the particle flow discrete element model uses Newton's second law as the calculation rule, and the contact model between soil particles follows the force-displacement law. In the cyclic calculation of soil particles in the particle discrete element model, the velocity and acceleration of particles are constant values within each time step, and the shorter the time step, the more accurate the calculation.

[0073] In the particle flow simulation of soil mechanical response, the constitutive relationship of macroscopic continuous mechanics of materials can be reflected by setting the contact model between soil particles. Typical soil contact models mainly include contact stiffness model, sliding model, bonding model, etc.

[0074] Calibration method of mesoscopic parameters for particle flow discrete element model of soil: Obtaining its mesoscopic mechanical parameters from known macroscopic parameters is the key to particle flow analysis of soil mechanical response of levees along the suspended river. At present, the calibration of mesoscopic parameters of the numerical model of soil particle flow is often completed by the method of soil biaxial compression numerical test.

[0075] For the specimen generated by the radius expansion method, the overlapping amount between soil particles is different, forming uneven interlocking stress, which has a great influence on the subsequent establishment of the contact model. Therefore, it is necessary to fine-tune the radius of soil particles to reduce the overlapping amount so that the interlocking stress of the specimen reaches the set stress value, generally less than 1% of the peak strength. During the research process, it is necessary to eliminate the suspended particles in the specimen, that is, soil particles with less than three contacts. Since the soil particles in the specimen are randomly generated, many of them are suspended particles. The existence of suspended soil particles will cause characteristic responses of non-uniformity and increase the uncertainty of numerical model calculation. Therefore, it is necessary to remove the suspended soil particles. The method to eliminate suspended soil particles is to first set the velocity of non-suspended soil particles within a certain range in the specimen to zero, and then expand the radius of the suspended soil particles in it by 30%. This method can effectively increase the contact between suspended soil particles and surrounding soil particles to achieve the purpose of eliminating suspended soil particles. After eliminating the suspended soil particles, select a suitable contact model and assign the mesoscopic parameters to the numerical model of soil mechanical response particle flow.

[0076] Under the influence of uncertain factors such as action and resistance, the levees along the suspended river have multiple failure modes. Typical failure modes include overtopping, seepage failure, and instability, etc. Based on the theory of reliability and particle flow discrete element analysis, explore the reliability estimation method of levees along the suspended river under a single failure mode, including the following steps:

[0077] S1. Determine the random variables causing the failure mode and the corresponding performance function according to the failure mode of the levees along the suspended river;

[0078] S2. Use the Latin hypercube sampling method to extract samples of random variable parameter values to ensure that the samples can fully reflect the probability distribution of each random variable;

[0079] S3. Substitute the extracted random variable parameter values into the performance function under the corresponding failure mode, calculate the failure state of the levees along the suspended river under different combinations of random variable parameter values, and judge whether the levees along the suspended river are in a failure state according to the positive or negative value of the performance function value;

[0080] S4. Count the number of times in the failure state among all sampling results, and calculate the failure probability of the levee of the suspended river according to the number of failure state samples and the total number of samples;

[0081] S5. Calculate the reliability of the levee according to the failure probability.

[0082] Embodiment 2: Estimation method for the reliability of the levee of the suspended river under the overtopping failure mode

[0083] (1) Construction of the overtopping failure performance function

[0084] The overtopping failure mode of the levee of the suspended river refers to the failure of the levee of the suspended river caused by the wave run-up exceeding the levee top. From the above analysis, it can be seen that the overtopping failure of the levee of the suspended river is related to variables such as the levee top elevation, the wind set-up water surface height, and the wave run-up. Therefore, the performance function of the overtopping failure mode of the levee of the suspended river can be expressed as:

[0085] (13);

[0086] In the formula: is the levee top elevation; is the wave run-up; is the wind set-up height; is the flood water level on the water-facing side of the levee of the suspended river.

[0087] The failure probability calculation formula of the levee of the suspended river under this failure mode is:

[0088] (14);

[0089] In the formula: represents the performance function of the flood overtopping failure mode; is the flood water level on the water-facing side of the levee of the suspended river; is the levee top elevation; is the starting water level for calculation; is the probability density function of the flood overtopping failure mode, which is a function of the flood water level of.

[0090] In the process of estimating the reliability of the levee of the suspended river under the overtopping failure mode, due to the complexity of the levee system of the suspended river and the limitations of relevant statistical data, the probability density function of the overtopping failure mode is difficult to obtain directly, and the calculation of the integral has a certain degree of difficulty. In this case, the simulation method for solving the overtopping failure probability has been widely used. Latin hypercube sampling is one of the commonly used simulation methods at present. Its principle is to randomly extract a large number of variables simulating the overtopping failure mode of the levee of the suspended river to achieve the purpose of calculating the failure probability , and the following specifically studies the realization of the reliability estimation of the levee of the suspended river under the overtopping failure mode based on the Latin hypercube sampling method.

[0091] (2)Reliability Estimation of Levee in Meandering River under Overtopping Failure Mode Based on Latin Hypercube Sampling

[0092] Based on the Latin hypercube sampling method, explore the principle of reliability estimation of levee in meandering river under overtopping failure mode. This method can be summarized as follows: By sampling the variables sufficiently many times (set as N times), for each set of variable values obtained from random sampling, solve the load effect and the resistance , and count the number of times among them , then the failure probability can be obtained by the following formula:

[0093] (15);

[0094] Figure 1 is the reliability estimation process of overtopping failure based on Latin hypercube sampling. The specific implementation steps are as follows:

[0095] S101. Determine the random variables and statistical characteristics of the overtopping failure function of the levee in meandering river;

[0096] S102. Use the Latin hypercube sampling method to extract a set of random variable parameter values;

[0097] S103. Substitute the parameters extracted in S102 into the function of the overtopping failure mode, and judge the positive and negative of the function;

[0098] S104. If , then add 1 to L (L is the number of times the levee in meandering river has not failed, with an initial value of 0), otherwise remain unchanged;

[0099] S105. Repeat steps S101 - S104 N times (N is determined by the requirements of the sampling method), and count the final value of L;

[0100] S106. Estimate the failure probability of the levee in meandering river under the overtopping failure mode by the formula ;

[0101] S107. On the basis of obtaining the failure probability, obtain the reliability of the levee in meandering river under the overtopping failure mode from .

[0102] Through the above analysis, the reliability of the levee in meandering river under the overtopping failure mode is obtained.

[0103] Example 3: Reliability Estimation Method of Levee in Meandering River under Seepage Failure Mode

[0104] (1)Establishment of Seepage Failure Function

[0105] The seepage failure of the levee of a suspended river is affected by various factors, and its manifestations are mainly piping and soil flow on the levee foundation. Under the given structure of the levee of a suspended river, as the flood level outside the levee rises, the hydraulic gradient inside the levee also continuously increases. Based on this analysis, when the hydraulic gradient inside the levee exceeds the anti-seepage critical gradient of the levee body and the levee foundation soil, the seepage failure phenomenon will occur. Based on the basic principle of seepage failure, taking the soil permeability coefficient, flood level, cohesion and internal friction angle as random variables, the function of the failure mode of the seepage failure of the levee of a suspended river is established as follows:

[0106] (16);

[0107] In the formula: is the maximum hydraulic gradient on the backwater side of the levee; is the anti-seepage critical hydraulic gradient of the levee.

[0108] Under this failure mode, the failure probability of the levee of a suspended river can be calculated according to the following formula:

[0109] (17);

[0110] The above content constructs the function of the seepage failure of the levee of a suspended river and clarifies the calculation method of the failure probability. On this basis, the following studies the calculation process of the failure probability of the levee of a suspended river under the seepage failure mode.

[0111] (2) Reliability estimation of the levee of a suspended river under the seepage failure mode based on Latin hypercube sampling and particle flow analysis

[0112] According to the Latin hypercube sampling method, samples of random variables are extracted, and the mesoscopic parameters of the particle flow discrete element analysis model of the mechanical response of the soil body of the levee of a suspended river are calibrated. Through the particle flow discrete element analysis and calculation, the reliability of the levee of a suspended river under the seepage failure mode is estimated. Figure 2 is the reliability estimation process of the levee of a suspended river under the seepage failure mode, and the specific implementation steps are as follows:

[0113] S201. Determine the random variables and their statistical characteristics of the function under the seepage failure mode;

[0114] S202. Use the Latin hypercube sampling method to extract a set of random variable parameter values;

[0115] S203. Assign the parameter values extracted in S202 to the particle flow discrete element model and calculate the maximum hydraulic gradient on the backwater side of the levee ;

[0116] S204. Compare the calculated maximum hydraulic gradient with the anti-seepage critical hydraulic gradient and judge the function The positive or negative value of, if , then add 1 ( is the number of failure times, and the initial value is 0), otherwise remain unchanged;

[0117] S205. Repeat steps S201 - S204 N times and count the value;

[0118] S206. Calculate the failure probability from the formula ;

[0119] S207. Obtain the reliability of the levee under the seepage failure mode from ;

[0120] The seepage failure mode is usually caused by the instability of soil and water due to the flow of water through the levee, mainly manifested as the destruction of the soil structure or the loss of strength caused by the seepage force of the water flow. In this mode, the hydraulic gradient on the back surface of the levee is one of the key factors to measure the stability of the levee. Through the particle flow discrete element analysis method, the hydraulic gradient can be calculated and the failure mode can be evaluated.

[0121] Specifically, in S203, the parameter values extracted by LHS are assigned to the particle flow discrete element model to calculate the maximum hydraulic gradient on the back surface of the levee including:

[0122] Determine the definition of the hydraulic gradient: The hydraulic gradient J represents the rate of change of water pressure per unit distance. Usually on the back surface of the levee, the hydraulic gradient is closely related to factors such as the permeability properties of soil particles and the contact strength between particles;

[0123] Set up the particle flow discrete element model: In the particle flow discrete element model, it is necessary to combine the hydraulic properties of the levee soil (such as the permeability coefficient) with the microscopic parameters of soil particles (such as particle size, contact stiffness, bond strength, etc.), and simulate the action of water flow on the back surface of the levee by applying water pressure;

[0124] Simulate the seepage of water flow and the contact force between particles: Use the particle flow discrete element model to calculate the seepage process of water flow in the soil, which is realized by simulating the interaction between water flow among particles. Especially in the particle contact area, the seepage of water flow will change the contact force between particles and the structural strength of the soil;

[0125] Calculate the hydraulic gradient: At each time step, calculate the influence of water flow on soil particles through the particle flow discrete element model and obtain the pressure change of the water flow. Calculate the hydraulic gradient J through the following formula:

[0126] (18);

[0127] where is the water head change, is the distance in the flow direction.

[0128] The maximum hydraulic gradient refers to the maximum value of the hydraulic gradient when the water flow passes through the backwater side of the levee during the simulation process. This value can reflect the critical point of seepage failure. If the maximum hydraulic gradient reaches or exceeds the critical value of the anti-seepage capacity of the levee, it may lead to seepage failure.

[0129] Example 4: Estimation method for the reliability of a levee on a suspended river under the failure mode of instability

[0130] During the operation of a levee on a suspended river, instability failures mainly include landslides and bank collapses, etc. For a long time, the slopes of levees on suspended rivers have been affected by water level changes, and the shear strength of the soil in the levee body and foundation gradually decreases. Under the action of seepage force, the possibility of landslides on the backwater side slope of the levee is relatively high. When the water level drops suddenly, the pore water pressure in the levee body cannot dissipate, resulting in a reverse pressure, and it is easy to occur landslides on the water-facing side slope of the levee.

[0131] (1) Establishment of the instability failure function

[0132] To establish a complete calculation model for the failure mode of levee instability failure, it is necessary to consider the sliding instability modes of the water-facing side and the backwater side slopes separately. According to past engineering practices of levees on suspended rivers, the probability of simultaneous sliding instability of the water-facing side and the backwater side slopes in the same unit levee section is extremely low. Therefore, the instability mode of the unit levee section slope can be divided into the water-facing side slope instability mode and the backwater side slope instability mode.

[0133] Based on the above analysis, the probability estimation models for the instability failures of the backwater side and the water-facing side slopes of the levee on a suspended river are respectively:

[0134] (19);

[0135] (20);

[0136] Where: represents the sliding instability function of the backwater side slope; represents the sliding instability function of the water-facing side slope; is the conditional probability density function of the backwater side slope instability, which is a function of the water level outside the levee; is the conditional probability density function of the water-facing side slope instability, which is a function of the flood water level inside the levee; f ( h ) is the probability density function of the flood water level.

[0137] The function of the instability of the levee slope of the suspended river can be obtained from the limit state equation in the reliability analysis of the slope. The sliding instability of the levee slope occurs when the sliding force (sliding moment) along a certain sliding arc of the levee slope is greater than its anti-sliding force (anti-sliding moment) under various external forces. According to the theory of the Swedish circle method, the expression of the limit state equation for the instability of the levee slope of the suspended river is established as follows:

[0138] (21);

[0139] In the formula: is the cohesion at the bottom of the i soil slice; the i circular arc length at the bottom of the soil slice; i is the self-weight of the soil slice, where , , are the unit weight, width and average height of the soil slice respectively; is the internal friction angle of the i soil slice; is the horizontal dip angle at the bottom of the i soil slice.

[0140] It can be seen that the anti-sliding force and the sliding force can be simply expressed as functions of random variables, which are the cohesion, internal friction angle, soil unit weight and friction coefficient of the soil body of the suspended river levee respectively. Then the function of the failure mode of the levee instability can be expressed as:

[0141] (22);

[0142] In the formula: K is the safety factor of the levee slope; is the allowable value of the anti-sliding stability safety factor.

[0143] Common calculation methods for the safety factor of the levee slope of the suspended river include the simplified Bishop method, the Swedish circle method, the finite element method, etc. Taking the Swedish circle method as an example, its safety factor calculation formula is:

[0144] (23);

[0145] Then the failure probability of the suspended river levee in the failure mode of instability can be calculated according to the following formula:

[0146] (24);

[0147] The above content constructs the function of the instability failure of the suspended river levee and proposes the calculation method of the failure probability. Next, the implementation process of the reliability estimation of the suspended river levee in the failure mode of instability will be studied.

[0148] (2)The method for estimating the reliability of the levee of the suspended river under the instability failure mode based on Latin hypercube sampling and particle flow discrete element analysis is similar to the method for estimating the reliability of the levee of the suspended river under the seepage failure mode. The process for estimating the reliability of the levee of the suspended river under the instability failure mode is shown in Figure 3 , and the specific implementation steps are as follows:

[0149] S301. Determine the random variables and statistical characteristics of the performance function under the instability failure mode;

[0150] S302. Use the Latin hypercube sampling method to extract a set of random variable parameter values;

[0151] S303. Assign the parameter values extracted in S302 to the particle flow discrete element model and calculate the safety factor of the levee slope;

[0152] S304. Judge the positive and negative of the performance function . If , then L is incremented by 1 ( L is the number of failures, and the initial value is 0), otherwise it remains unchanged.

[0153] S305. Repeat steps S301 to S304 N times and count the L value;

[0154] S306. Calculate the failure probability from Equation ;

[0155] S307. Obtain the reliability of the levee of the suspended river under the instability failure mode from Equation .

[0156] In the estimation of the reliability of the levee of the suspended river under the instability failure mode, the safety factor is an important indicator to measure the stability of the levee slope and reflects whether the levee will become unstable or landslide under external actions. Calculating the safety factor of the levee slope usually requires combining the mechanical properties and mechanical behaviors of the soil mass, and the particle flow discrete element (DEM) method can provide accurate modeling of these mechanical properties.

[0157] In step S301, the random variables and their statistical characteristics under the instability failure mode have been determined, including the following parameters: cohesion c: which affects the bonding force between particles and directly affects the shear strength of the levee; internal friction angle :The frictional force that controls the sliding between particles affects the stability of the levee; the unit weight of soil γ: the mass density of the soil, which affects the self-weight and total stress of the levee; the friction coefficient μ: controls the magnitude of the frictional force during particle sliding. These random variables are sampled using the Latin Hypercube Sampling method (LHS). Each set of sampled random variable values represents a set of soil mechanical parameters, which are used as inputs to the Discrete Element Method (DEM) of particle flow.

[0158] In step S302, the sampled random variable parameters will be assigned to the particle flow discrete element model for calculation. The specific process is as follows: Using the random variables obtained by Latin Hypercube Sampling as input parameters, define the characteristics of soil particles in the particle flow discrete element model; calculate the safety factor of the levee slope by simulating the dynamic response of soil particles under external loads; determine whether the safety factor is lower than the critical value. If it is lower than the critical value, it is determined that the levee is unstable and the failure event is recorded; through multiple simulations and statistics, estimate the reliability of the levee under the unstable failure mode.

[0159] Example 5: Engineering Example

[0160] The elevation of the levee crest of the suspended river section is taken as 37m, the top width is 8m, the slope ratio on the river side is 1:2.5, the slope ratio on the back river side is 1:3, the elevation of the river-side slope toe is 27m, and the elevation of the back-river slope toe is 24m. There is a pond with an average depth of 1m and a width of 35m, 20m away from the slope toe outside the levee, and the boundary is taken 20m further out; inside the levee, the boundary is taken 70m away from the slope toe; the soil quality of the levee is generalized into four layers, and the soil layers are all horizontal. Starting from the levee crest, from top to bottom, they are sandy loam 1, loam 2, clay 3, and sandy loam 4, with soil layer thicknesses of 5.6m, 10m, 2m, and 15m respectively, and the bottom surface of the lowest layer of soil is taken as the fixed boundary. Figure 4 It is a schematic diagram of the calculation section of the suspended river section.

[0161] This paper conducts statistical analysis on the permeability coefficient , cohesion c and the value of the internal friction angle of various soils in this suspended river section. The results show that conforms to the logarithmic normal distribution with base e, and other random variables approximately conform to the normal distribution. The specific statistical parameter results are shown in Table 1:

[0162] Table 1 Statistical Table of Soil Property Parameters of a Certain Suspended River Levee

[0163]

[0164] By selecting the biaxial compression numerical test for mesoscopic parameter calibration, Table 2 lists the geometric dimensions of the biaxial numerical test samples and the mesoscopic physical and mechanical property parameters of the soil particle elements.

[0165] Table 2 Control Parameters of the Test Model

[0166]

[0167] Figure 5 It is a specimen for biaxial numerical tests. During the tests, the upper and lower boundary walls act as loading platens, moving from both ends towards the middle at a specified speed, and the left and right boundary walls apply a constant confining pressure to the granular elements.

[0168] According to the initially established geometric model of the levee section of the suspended river (as Figure 4 shown), boundary walls are generated in the PFC program. Then, a granular assembly with a specified radius size is generated within the boundary, and the model is stress-balanced. The granular materials filled in the generated granular flow levee model are grouped according to soil types, which are sandy loam, loam, clay, and sandy loam from top to bottom, and the stress field is initialized. When the maximum unbalanced force of the granular assembly reaches of the maximum contact force, it is considered that the granular assembly is in an equilibrium state, and at this time, the suspended particles are eliminated. The top surface of the levee model is set as a free surface, and the bottom surface and the left and right sides are fixed as rigid walls using the "fix" command, thereby constructing a discrete element analysis model of granular flow for this levee section of the suspended river, as Figure 6 .

[0169] According to the statistical parameters of the soil mass of this levee section of the suspended river obtained, using the Latin hypercube sampling method and the established discrete element analysis model of granular flow for this levee section of the suspended river, the reliability of this levee section of the suspended river under three single failure modes of overtopping, seepage failure, and instability is estimated respectively.

[0170] (1) Estimation of the reliability of this levee section of the suspended river under the overtopping failure mode

[0171] According to the established reliability estimation model of the overtopping failure mode of this levee section of the suspended river, using the Latin hypercube sampling method, taking the upstream flood water level, wind set-up height, and wave run-up of the levee section as random variables, whose statistical characteristic values are shown in Table 3, the levee top elevation is 37m, and other parameters are fixed values, the number of calculations N=105 , and the calculation results are shown in Table 6. Thus, the reliability probability of this levee section under the overtopping failure mode is 99.996%.

[0172] Table 3 Statistical table of characteristic values of random variables in the overtopping failure mode

[0173]

[0174] (2) Estimation of the reliability of this levee section of the suspended river under the seepage failure mode

[0175] According to the established reliability estimation model for the seepage failure mode of a certain levee section of the suspended river, using the Latin hypercube sampling method, taking the flood level, cohesion, internal friction angle, and soil permeability coefficient as random variables, whose characteristic values are shown in Table 4, and other parameters as fixed values. Input the sample parameters obtained by random sampling into the particle flow model to calculate the permeability coefficient, and the calculation results are shown in Table 6. Thus, the reliability of this levee section of the suspended river under the seepage failure mode is determined to be 99.992%.

[0176] Table 4 Statistical Table of Characteristic Values of Random Variables for the Seepage Failure Mode

[0177]

[0178] (3)Reliability Estimation of the Levee of the Suspended River under the Instability Failure Mode

[0179] Based on the established reliability estimation model for the instability failure mode of a certain levee section of the suspended river, using the Latin hypercube sampling method, taking cohesion, friction coefficient, internal friction angle, etc. as random variables. At the same time, considering that when the particle flow analysis model is established, the particles are randomly generated within a certain range, so the minimum radius of the particles is also taken as a random variable, and other parameters as fixed values. The corresponding characteristic values of the random variables are shown in Table 5. Input the sample parameters obtained by random sampling into the particle flow model to calculate the permeability coefficient, and finally the reliable probability of this levee section under the instability failure mode is obtained as 99.993%.

[0180] Table 5 Statistical Table of Characteristic Values of Random Variables for the Instability Failure Mode

[0181]

[0182] As shown in Table 6, using the reliability calculation method for a single failure mode of the levee of the suspended river proposed by the present invention, which is based on the Latin hypercube sampling and the particle discrete element method, the random variables of each failure mode are sampled 105 times. On this basis, the reliabilities of this levee section of the suspended river under the overtopping, seepage failure, and instability failure modes are 99.996%, 99.992%, and 99.993% respectively, reflecting that the reliability of this levee section of the suspended river is relatively high, and verifying the effectiveness of the method proposed by the present invention.

[0183] Table 6 Reliability Estimation Table of a Certain Levee Section of the Suspended River under a Single Failure Mode

[0184]

[0185] Through the analysis of the overtopping, seepage failure and instability failure modes of the levees of the suspended river, a performance function for estimating the reliability of the levees of the suspended river under the overtopping, seepage failure and instability failure modes is established, and a reliability estimation model for the levees of the suspended river under different single failure modes is constructed. Combining the Latin hypercube sampling and the particle flow discrete element analysis method, a method for estimating the reliability of the levees of the suspended river under a single failure mode is proposed, and based on a certain levee section of the suspended river, the effectiveness of the method is verified.

[0186] As described above, although the present invention has been shown and described with reference to specific preferred embodiments, it should not be construed as a limitation of the present invention itself. Various changes in form and detail may be made without departing from the spirit and scope of the present invention as defined by the appended claims.

Claims

1. A reliability estimation method for suspended river embankments under a single failure mode, characterized in that: The steps include: S1. Determine the random variable causing the failure mode and the corresponding function according to the failure mode of the suspended river embankment, wherein the failure mode of the suspended river embankment is a seepage failure mode or an instability failure mode; S2. Use Latin hypercube sampling method to extract samples of random variable parameter values ​​to ensure that the samples can fully reflect the probability distribution of each random variable; S3, substituting the extracted random variable parameter value into the functional function under the corresponding failure mode, calculating the failure state of the suspended river embankment under different combinations of random variable parameter values, and judging whether the suspended river embankment is in a failure state according to the positive or negative value of the functional function; The random variables in the seepage failure mode include the soil permeability coefficient , Flood level , cohesion and internal friction angle ; 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 of embankment anti-seepage; The random variables in the instability failure mode include the cohesion of the soil in the suspended river embankment , internal friction angle , soil bulk density and friction coefficient ; The functional function in the instability failure mode is: , where: K is the safety factor of the embankment slope, is the allowable value of the anti-sliding stability safety factor; The maximum hydraulic gradient of the backwater surface of the dike or safety factor of embankment slope K The calculation is performed using a particle flow discrete element analysis model, which is based on simulating the interaction and contact mechanical behavior between the discrete particles that make up the embankment soil, including: (a) Based on the soil parameters obtained by random sampling, a discrete element model of the suspended river embankment is constructed, and the contact model and parameters between particles are set; (b) When performing penetration damage analysis calculations When the water flow infiltration process and its influence on the contact force between particles and the soil structure strength are simulated in the model, the maximum hydraulic gradient is determined accordingly. (c) When calculating K for instability failure analysis, the mechanical response and displacement of the discrete particle system under external loads and seepage are simulated in the model, and the safety factor is determined accordingly; S4. Count the number of failure states in all sampling results, and calculate the failure probability of the hanging river embankment according to the number of failure state samples and the total number of samples; S5. Calculate the reliability of the embankment based on the failure probability.

2. The reliability estimation method of suspended river embankment under single failure mode according to claim 1 is characterized in that: The Latin hypercube sampling method includes: The cumulative distribution function of the random variable affecting the service life of the suspended river embankment is divided into several non-overlapping sub-intervals; An independent equal probability sampling is carried out in each sub-interval, and the n random variables, in m When sampling, the maximum number of combinations is , No. i Random numbers in the subinterval The following provisions shall be met: Where: , N is the number of subintervals, X is A random number uniformly distributed in the interval, is the random number of the i-th subinterval; Only one random number will be generated in each subinterval, and the sampled values ​​of multiple random variables will be randomly combined into a multidimensional sample to simulate the joint distribution of multidimensional random variables, thus obtaining n groups of random numbers, each containing m variables.

3. The reliability estimation method of suspended river embankment under single failure mode according to claim 1 is characterized in that: The failure probability is calculated using the following formula: ; Where: L is the number of samples under failure state, N is the total number of samples, is the failure probability; The calculation formula of the reliability is: ; Where: For reliability.

4. A system for implementing the method for estimating the reliability of a suspended river embankment under a single failure mode as claimed in claim 1, characterized in that: include: A random variable parameter acquisition module is used to obtain random variables that affect the reliability of the suspended river embankment according to the failure mode of the suspended river embankment; Latin hypercube sampling module, used to sample based on input random variables; The failure mode function judgment module is used to substitute the sampling results into the function function for calculation and judge whether the dike is in a failure state; The failure probability and reliability calculation module is used to count the number of samples in the failure state and calculate the failure probability and reliability based on the number of failure samples; The output module is used to output the reliability results of the suspended river embankment.

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