Method and system for estimating reliability of suspension river dike in single 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 single failure mode, and the method comprises the steps: determining a random variable causing the failure mode and a corresponding performance function according to the failure mode of the suspension river dike; using a Latin hypercube sampling method to extract samples of random variable parameter values; substituting the extracted random variable parameter values into the performance function in the corresponding failure mode, calculating the failure state of the suspension river dike under the combination of different random variable parameter values, and judging whether the suspension river dike is in the failure state or not according to the positive or negative of the function value; and counting the number of times of failure states in all sampling results, and calculating the failure probability of the suspension river embankment and the reliability of the embankment. According to the method, a reliability estimation model for the suspension river dike in different single failure modes is established, and the reliability estimation method for the suspension river dike in the single failure mode is provided by combining Latin hypercube sampling and a particle flow discrete element analysis method.

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 single failure mode. Background Art

[0002] The soil of suspended river embankment is mainly composed of contact-bonded loose granular materials, which have complex nonlinear characteristics. The research on embankment reliability estimation is based on the analysis of its failure mode. Due to the many uncertainties in the construction and operation management of embankments, its failure mode shows complex and changeable characteristics.

[0003] Traditional methods for estimating the reliability of suspended river embankments include the first-order second moment method and the Monte Carlo sampling method. Among them: the first-order second moment method can effectively solve the structural reliability analysis problem when the function function is expressed explicitly, but it will produce large errors when the function function is expressed implicitly or is highly nonlinear; 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 reliability analysis process, the analysis content of the mechanical response of the suspended river embankment soil is involved. The traditional finite element analysis method can only reflect the macroscopic performance change effect of the embankment soil, but it is difficult to simulate the mechanical response of the soil particles at the microscopic level.

[0004] It is common for a suspended river embankment to fail in a single failure mode. When estimating the reliability of a suspended river embankment, the traditional analysis method based on simple structural reliability theory is difficult to accurately estimate the reliability of a nonlinear structure; the Monte Carlo method is less efficient when estimating the reliability of a complex structure, and the accuracy and efficiency of the proxy model method in estimating structural reliability are limited by the performance of the surrogate model. Therefore, it is necessary to further study the reliability estimation method of the suspended river embankment under each single failure mode. Summary of the invention

[0005] 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 and system for a suspended river embankment under a single failure mode. By combining Latin hypercube sampling technology with particle discrete element method, a reliability estimation method for a suspended river embankment under different failure modes is proposed.

[0006] Technical solution: The reliability estimation method of the suspended river embankment under a single failure mode of the present invention comprises the following steps: S1. Determine the random variables causing the failure mode and the corresponding functional functions according to the failure mode of the suspended river embankment; 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; 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.

[0007] To further improve the above technical solution, the failure mode of the suspended river embankment is any one of the following: overtopping failure mode, seepage damage failure mode or instability failure mode.

[0008] Furthermore, the Latin hypercube sampling method includes: dividing the cumulative distribution function of the random variable affecting the service of the suspended river embankment into a number of non-overlapping sub-intervals; performing an independent equal-probability sampling in each sub-interval, and sampling the random variable affecting the service of the suspended river embankment once for each sub-interval; 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 ith subinterval; each subinterval will only generate one random number, and the sampling values ​​of multiple random variables are randomly combined into a multidimensional sample to simulate the joint distribution of multidimensional random variables, and obtain n groups of random numbers, each containing m variables.

[0009] Furthermore, the failure probability is calculated by 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.

[0010] Furthermore, the random variables in the overtopping failure mode include the dike top elevation , Windblock height , wave climbing ; 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, The height of the wind chimney.

[0011] Furthermore, the failure probability calculation formula of the suspended river embankment in the overtopping failure mode is: ; 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.

[0012] Furthermore, 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 for embankment anti-seepage.

[0013] Furthermore, the random variables in the instability failure mode include the cohesion of the soil of 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, It is the allowable value of anti-sliding stability safety factor.

[0014] Furthermore, the step of calculating the maximum hydraulic gradient on the back surface of the levee or the safety factor of the levee slope is performed by a particle flow discrete element analysis model, and the process includes: (1) constructing a discrete element calculation model grid for a suspended river levee; (2) inputting soil parameters obtained by random sampling; (3) simulating the transmission of hydraulic gradient during seepage; (4) calculating the contact force between particles and the pore water pressure; and (5) determining the maximum hydraulic gradient or the safety factor.

[0015] The system for implementing the reliability estimation method of the suspended river embankment under the above single failure mode comprises: 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.

[0016] Beneficial effects: Compared with the prior art, the advantages of the present invention are as follows: Based on the basic principle of reliability estimation of suspended river embankments, the present invention explores the particle flow discrete element analysis method of the mechanical response of the soil of suspended river embankments, and proposes a method for estimating the reliability of suspended river embankments under a single failure mode based on the analysis of the characteristics of different failure modes of suspended river embankments. After analyzing the failure modes of overtopping, seepage damage and instability of suspended river embankments, a function for estimating the reliability of suspended river embankments under overtopping, seepage damage and instability failure modes is established, and a reliability estimation model for suspended river embankments under different single failure modes is constructed. Combining Latin hypercube sampling and particle flow discrete element analysis methods, a method for estimating the reliability of suspended river embankments under a single failure mode is proposed, and the effectiveness of the method is verified based on a certain suspended river embankment section. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flow chart for reliability estimation of hanging river embankment under overtopping failure mode; Figure 2 It is a flow chart for estimating the reliability of hanging river embankments under the seepage damage failure mode; Figure 3 It is a flow chart for estimating the reliability of suspended river embankments under the instability failure mode; Figure 4 The cross section of a certain embankment section of the hanging river embankment in Example 5 is calculated; Figure 5 This is a diagram of the biaxial numerical test specimen in Example 5; Figure 6 This is the discrete element analysis model of particle flow in the hanging river embankment section in Example 5. DETAILED DESCRIPTION

[0018] 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.

[0019] Example 1: When analyzing the reliability of a suspended river embankment structure, two types of parameters are mainly considered: one is the direct action imposed on the embankment or the indirect action that causes the embankment to deform externally or constrains deformation, collectively referred to as action; the other is the ability of the embankment structure and its materials to withstand the effects of the action, referred to as resistance. Both types of parameters in the reliability analysis of a suspended river embankment can be considered as random variables. The reliability analysis of a suspended river embankment structure is based on whether the suspended river embankment structure has reached the limit state. According to the functional requirements of the embankment structure and the corresponding limit state, a random variable is established. The corresponding limit state performance function is expressed as: (1); when When When , the levee structure is in failure state; when When , the structure is in the limit state, and the corresponding limit state equation is: (2); The random variables are divided into two categories: resistance R and action S. The corresponding performance function is: (3); When the resistance effect of the suspended river embankment structure is greater than the action effect, the suspended river embankment structure is considered to be reliable, that is, the embankment structure can complete its predetermined function under certain conditions, and its reliability can be determined by the reliability probability On the contrary, when the action effect of the suspended river embankment structure is greater than the resistance effect, the embankment structure is considered to be unreliable. This situation can be expressed by the failure probability To express the reliable probability and failure probability The expressions are: (4); (5); Where: z is a continuous random variable; is the probability density function of Z.

[0020] 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: (6); right In the case of normal distribution, its reliability index The calculation expression is: (7); According to the concepts of reliability index and failure probability, the relationship between failure probability and reliability index is: (8); 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).

[0021] 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.

[0022] 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.

[0023] The basic idea of ​​the LHS method is stratified sampling. Taking the sampling process of a one-dimensional random variable x as an example, assuming that the total number of samplings is N, the random variable x is first divided into several regions with equal probability. , then it satisfies: (9); Take the case of normal variables as an example. Assuming that the sample size N=5, the stratified sampling method is used to divide the cumulative curve into 5 equal probability intervals, and the probability of each interval being drawn is 0.2. Stratified sampling follows the principle of "sampling without replacement", that is, a sample is drawn from each stratum. Once a sample is drawn from a stratum, this stratum will no longer be drawn, so there will be no repeated sampling. Using the stratified sampling method, the sample drawn can more accurately reflect the probability distribution of the input value, thereby improving the accuracy of reliability analysis.

[0024] On the basis of the above one-dimensional random variable stratified sampling method, multiple variables are introduced to realize stratified sampling of multidimensional random variables. In the research process, the Latin hypercube sampling method treats all coordinate axes equally and only stratifies the one-dimensional boundary of the multidimensional joint distribution, thus avoiding the problem of exponential growth of the number of samples when stratifying the multidimensional joint distribution.

[0025] This method first fixes the dimension d and sample size K, and for each coordinate ,conduct Generate stratified samples from the unit interval independently , each stratified sample exist If d stratified samples are arranged in columns, each row gives the coordinates of a point. The second row corresponds to In the point, and so on, it corresponds to points that enter the unit hypercube to form sub-cubes along the diagonal, namely: (10); On this basis, randomly transform the value of each column in the sequence, for The permutation of is equivalent to independent sampling from all K! such equally possible distributions. Assume For the The values ​​of i after the permutation are mapped, and the rows of the sequence still correspond to If we take the points in , they are no longer restricted to the diagonal, but each row is still a uniformly distributed point on the unit hypercube. The following is the result of K random samplings with d variables; (11); In summary, the specific steps of the random number generation process based on the Latin hypercube sampling method are as follows: (1) First, the number of simulations is determined, and then the cumulative distribution function of the random variable affecting the service life of the suspended river levee is divided into multiple non-overlapping sub-intervals.

[0026] (2) Then, an independent equal probability sampling is performed in each sub-interval, and the n The LHS simulation method of random variables is used in m When sampling, the maximum number of combinations is .

[0027] (3) To ensure that random numbers are sampled in each subinterval, i Random numbers in the subinterval The following provisions shall be met: (12); Where: , X is A random number uniformly distributed in the interval, is a random number in the ith subinterval.

[0028] (4) Each subinterval will only generate one random number. Through the relevant transformation, we can obtain the sampled values ​​of the variable that obeys a certain probability density function. These sampled values ​​are randomly combined to obtain all the required random numbers. The final number of groups is n , each group contains m A variable of random numbers.

[0029] The particle flow discrete element method is based on the principle of micromechanics and simulates the interaction between particles and the overall behavior of the soil. In the analysis of suspended river embankments, the particle flow discrete element method is used to describe the behavior of particles in the embankment soil and the contact force between particles, as well as the deformation and failure process of the soil under the action of 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 soil particle circulation calculation in the particle discrete element model, the velocity and acceleration of the particles in each time step are constant values, and the shorter the time step, the more accurate the calculation.

[0030] In the particle flow simulation of soil mechanical response, the constitutive relationship of the macroscopic continuum mechanics of the material can be reflected by setting the contact model between soil particles. Typical soil contact models include contact stiffness model, sliding model and bonding model.

[0031] Mesoscopic parameter calibration method of particle flow discrete element model: Using known macroscopic parameters to obtain its mesoscopic mechanical parameters is the key to particle flow analysis of the mechanical response of suspended river embankment soil. At present, the calibration of mesoscopic parameters of soil particle flow numerical model is often completed by the method of soil biaxial compression numerical test.

[0032] The samples generated by the radius expansion method have different overlaps between soil particles, forming unbalanced internal locking stress, which has a great impact on the subsequent establishment of the contact model. Therefore, it is necessary to fine-tune the radius of the soil particles to reduce the overlap so that the internal locking stress of the sample reaches the set stress value, which should generally be less than 1% of the peak strength. In the research process, it is necessary to eliminate the suspended particles in the sample, that is, the soil particles that contact less than three. Since the soil particles in the sample are randomly generated, many of them are suspended particles. The presence of suspended soil particles will cause inhomogeneous characteristic responses and increase the uncertainty of numerical model calculations. 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 sample to zero, and then expand the radius of the suspended soil particles by 30%. This method can effectively increase the contact between the suspended soil particles and the surrounding soil particles, thereby achieving the purpose of eliminating suspended soil particles. After eliminating the suspended soil particles, a suitable contact model is selected, and the microscopic parameters are assigned to the particle flow numerical model of soil mechanical response.

[0033] Under the influence of uncertain factors such as action and resistance, the suspended river embankment has multiple failure modes, typical of which are overtopping, seepage damage and instability. Based on the reliability and particle flow discrete element analysis theory, the reliability estimation method of the suspended river embankment under a single failure mode is explored, including the following steps: S1. Determine the random variables causing the failure mode and the corresponding functional functions according to the failure mode of the suspended river embankment; 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; 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.

[0034] Example 2: Reliability estimation method for suspended river embankment under overtopping failure mode (1) Construction of the flood failure function The overtopping failure mode of the suspended river embankment refers to the failure of the suspended river embankment caused by the wave climbing over the embankment top. From the above analysis, it can be seen that the overtopping failure of the suspended river embankment is related to variables such as the embankment top elevation, the height of the wind-dammed water surface, and the wave climbing height. Therefore, the functional function of the overtopping failure mode of the suspended river embankment can be expressed as: (13); Where: is the dike top elevation; Climb high for the waves; is the windblock height; It is the flood level on the water surface of the hanging river embankment.

[0035] The failure probability calculation formula of the suspended river embankment under this failure mode is: (14); Where: Function representing the flood overtopping failure mode; 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 function.

[0036] In the process of estimating the reliability of suspended river embankments under the overtopping failure mode, due to the complexity of the suspended river embankment system and the limitations of relevant statistical data, the probability density function of the overtopping failure mode is It is difficult to obtain directly, and the integral calculation is somewhat difficult. 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. Its principle is to extract a large number of random variables of the simulated overtopping failure mode of the suspended river embankment to calculate the failure probability. For the purpose of this study, the reliability estimation of hanging river embankments under overtopping failure mode is realized based on the Latin hypercube sampling method.

[0037] (2) Reliability estimation of suspended river embankments under overtopping failure mode based on Latin hypercube sampling The principle of reliability estimation of suspended river embankments under overtopping failure mode is explored based on the Latin hypercube sampling method. The method can be summarized as follows: Sampling is performed enough times (set as N times), and the load effect is solved for each set of variable values ​​obtained by random sampling. and resistance , statistics show that The number of , then the failure probability can be calculated by the following formula: (15); Figure 1 The reliability estimation process of flooding failure based on Latin hypercube sampling is as follows: S101, determine the random variables and statistical characteristics of the overtopping failure function of the suspended river embankment; S102, extracting a set of random variable parameter values ​​using a Latin hypercube sampling method; S103, substitute the parameters extracted from S102 into the function of the flooding failure mode , determine whether the function is positive or negative; S104, if , then L increases by 1 (L is the number of times the suspension river embankment fails, and the initial value is 0), otherwise it remains unchanged; S105, repeat steps S101 to S104 N times (N is determined by the sampling method requirements), and calculate the final L value; S106, by formula Estimate the failure probability of hanging river levees under overtopping failure mode; S107. Based on the failure probability, The reliability of the hanging river embankment under the overtopping failure mode is obtained.

[0038] Through the above analysis, the reliability of the hanging river embankment under the overtopping failure mode is obtained.

[0039] Example 3: Reliability estimation method for suspended river embankment under seepage failure mode (1) Establishment of the failure function of penetration damage The seepage failure of suspended river embankments is affected by many factors, and its manifestations are mainly pipe bursts and soil flow at the embankment foundation. Under a given suspended river embankment structure, as the flood level outside the embankment rises, the hydraulic gradient inside the embankment also increases. According to this analysis, when the hydraulic gradient inside the embankment exceeds the critical gradient of the seepage resistance of the embankment body and embankment foundation soil, the seepage failure phenomenon will occur. Based on the basic principle of seepage failure, the soil permeability coefficient, flood level, cohesion and internal friction angle are taken as random variables, and the function function of the failure mode of seepage failure of suspended river embankments is established as follows: (16); Where: It is the maximum hydraulic gradient on the back side of the dike; It is the critical hydraulic gradient for embankment anti-seepage.

[0040] Under this failure mode, the failure probability of the hanging river embankment can be calculated as follows: (17); The above content constructs the functional function of the seepage damage failure of the suspended river embankment and clarifies the calculation method of the failure probability. On this basis, the calculation process of the failure probability of the suspended river embankment under the seepage damage failure mode is studied below.

[0041] (2) Reliability estimation of suspended river embankments under seepage failure mode based on Latin hypercube sampling and particle flow analysis The random variable samples were extracted by Latin hypercube sampling method, and the microscopic parameters of the particle flow discrete element analysis model of the mechanical response of the suspended river embankment soil were calibrated. The reliability of the suspended river embankment under the seepage failure mode was estimated through particle flow discrete element analysis. Figure 2 This is the reliability estimation process of the suspended river embankment under the seepage failure mode. The specific implementation steps are as follows: S201. Determine the random variables and statistical characteristics of the functional function under the penetration damage failure mode; S202, extracting a set of random variable parameter values ​​using a Latin hypercube sampling method; S203, assign the parameter values ​​extracted in S202 to the particle flow discrete element model to calculate the maximum hydraulic gradient on the back surface of the levee ; S204, the calculated maximum hydraulic gradient Critical hydraulic gradient Comparison and judgment function If ,but Add 1 ( is the number of failures, the initial value is 0), otherwise it remains unchanged; S205, repeat steps s201~s204 N Times, Statistics value; S206, by Calculate the probability of failure; S207, by The reliability of hanging river embankment under the seepage damage failure mode was obtained.

[0042] The seepage failure mode is usually caused by water and soil instability caused by water flowing through the embankment, which is mainly manifested as soil structure damage or strength loss caused by water seepage. In this mode, the hydraulic gradient on the back of the embankment is one of the key factors to measure the stability of the embankment. The particle flow discrete element analysis method can be used to calculate the hydraulic gradient and perform failure mode evaluation.

[0043] Specifically, S203 assigns the parameter values ​​extracted from LHS to the particle flow discrete element model to calculate the maximum hydraulic gradient on the back surface of the dike. include: Determine the definition of hydraulic gradient: Hydraulic gradient J represents the rate of change of water pressure per unit distance. Usually on the back surface of the embankment, the hydraulic gradient is closely related to factors such as the permeability properties of soil particles and the contact strength between particles; Setting of particle flow discrete element model: In the particle flow discrete element model, it is necessary to combine the hydraulic properties of the embankment soil (such as permeability coefficient) with the microscopic parameters of the soil particles (such as particle size, contact stiffness, bonding strength, etc.), and simulate the effect of water flow on the back surface of the embankment by applying water flow pressure; Simulating water penetration and contact force between particles: The particle flow discrete element model is used to calculate the penetration process of water flow in soil. This is achieved by simulating the interaction between water flow and particles, especially in the particle contact area. Water penetration will change the contact force of particles and the structural strength of the soil. Calculate hydraulic gradient: In each time step, the particle flow discrete element model is used to calculate the effect of water flow on soil particles and obtain the pressure change of water flow. The hydraulic gradient J is calculated by the following formula: (18); in, It is the change of water head. is the distance in the direction of flow.

[0044] Maximum hydraulic gradient It refers to the maximum value of hydraulic gradient when water flows through the back surface of the dike during the simulation process. This value can reflect the critical point of seepage damage. If the maximum hydraulic gradient reaches or exceeds the critical value of the dike's anti-seepage capacity, it may cause seepage damage.

[0045] Example 4: Reliability estimation method for suspended river embankment under unstable failure mode During the operation of suspended river embankments, instability damage mainly includes landslides and bank collapse. For a long time, the slopes of suspended river embankments have been affected by water level changes, and the shear strength of the embankment body and foundation soil has gradually decreased. Under the action of seepage force, the backwater side of the embankment is more likely to slide. When the water level drops suddenly, the pore water pressure of the embankment body cannot dissipate, thus generating reverse pressure, which is prone to landslides on the waterside of the embankment.

[0046] (1) Establishment of instability failure function In order to establish a complete calculation model for the failure mode of levee instability, it is necessary to consider the sliding instability mode of the bank slope facing the water surface and the back surface of the water surface separately. According to the previous engineering practice of suspended river levees, the probability of sliding instability of the bank slope facing the water surface and the back surface of the same unit levee section at the same time is extremely low. Therefore, the unit levee section bank slope instability mode can be divided into the bank slope instability mode facing the water surface and the bank slope instability mode facing the back surface.

[0047] Based on the above analysis, the probability estimation models for the instability failure of the back and front sides of the suspended river embankment are: (19); (20); Where: It represents the sliding instability function of the back-water slope; It represents the instability function of the slope sliding on the water surface; is the probability density function of the instability condition of the back-water slope, which is a function of the water level outside the dike; is the probability density function of the instability condition of the waterside slope, which is a function of the flood level inside the dike; f ( h ) is the probability density function of flood level.

[0048] The instability function of the suspended river embankment slope can be obtained from the limit state equation in the slope reliability analysis. The embankment slope sliding instability occurs when the sliding force (sliding moment) of the embankment slope along a certain sliding arc is greater than its anti-sliding force (anti-sliding moment) under the action of various external forces. According to the Swedish arc method theory, the limit state equation expression of the instability of the suspended river embankment slope is established as follows: (twenty one); Where: For the i cohesion at the bottom of the soil strip; No. i The length of the arc at the bottom of the soil strip; For the i Weight of soil strip ,in , , are the weight, width and average height of the soil strip respectively; For the i The internal friction angle of the soil strip; For the i The horizontal inclination of the bottom of the soil strip.

[0049] It can be seen that the anti-sliding force and sliding force can be simply expressed as functions of the cohesion, internal friction angle, soil bulk density and friction coefficient of the suspended river embankment soil, respectively. The functional function under the embankment instability failure mode can be expressed as: (twenty two); Where: K is the safety factor of the embankment slope; It is the allowable value of anti-sliding stability safety factor.

[0050] Commonly used methods for calculating the safety factor of the slope of suspended river embankments include the simplified Bishop method, the Swedish arc method, the finite element method, etc. Taking the Swedish arc method as an example, the safety factor calculation formula is: (twenty three); The failure probability of the suspended river embankment in the instability failure mode can be calculated as follows: (twenty four); The above content constructs the functional function of the instability failure of the suspended river embankment and proposes a calculation method for the failure probability. The following is a study on the implementation process of the reliability estimation of the suspended river embankment under the instability failure mode.

[0051] (2) The reliability estimation method of the suspended river embankment under the instability failure mode based on Latin hypercube sampling and particle flow discrete element analysis is similar to the estimation method of the reliability of the suspended river embankment under the seepage failure mode. The process of estimating the reliability of the suspended river embankment under the instability failure mode is shown in Figure 3 , the specific implementation steps are: S301, determining random variables and statistical characteristics of a functional function under an unstable failure mode; S302, extracting a set of random variable parameter values ​​using a Latin hypercube sampling method; S303, assigning the parameter values ​​extracted in S302 to the particle flow discrete element model to calculate the safety factor of the embankment slope; S304, judging function If ,but L Add 1 ( L is the number of failures, the initial value is 0), otherwise it remains unchanged.

[0052] S305, repeat steps S301 to S304 N Times, Statistics L value; S306, by Calculate the probability of failure; S307, by The reliability of the suspended river embankment under the unstable failure mode is obtained.

[0053] In the reliability estimation of suspended river embankments under unstable failure modes, the safety factor is an important indicator to measure the stability of the embankment slope, reflecting whether the embankment will become unstable or slide under external forces. The calculation of the safety factor of the embankment slope usually requires the combination of the mechanical properties and mechanical behavior of the soil, and the particle flow discrete element (DEM) method can provide accurate modeling of these mechanical properties.

[0054] In step S301, the random variables and their statistical characteristics under the instability failure mode have been determined, including the following parameters: cohesion c: affects the bonding force between particles and directly affects the shear strength of the embankment; internal friction angle : controls the friction between particles and affects the stability of the embankment; soil bulk density γ: the mass density of the soil, which affects the deadweight and total stress of the embankment; friction coefficient μ: controls the friction between particles when sliding. These random variables are sampled by the Latin hypercube sampling method (LHS). Each set of random variable values ​​extracted represents a set of soil mechanics parameters, which are used to input the particle flow discrete element (DEM) model.

[0055] In step S302, the extracted 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 soil particle characteristics in the particle flow discrete element model; calculate the safety factor of the embankment 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, the embankment is determined to be unstable and the failure event is recorded; through multiple simulations and statistics, the reliability of the embankment in the unstable failure mode is estimated.

[0056] Example 5: Engineering Example The top elevation of the hanging river embankment section is 37m, the top width is 8m, the slope ratio near the river is 1:2.5, the slope ratio away from the river is 1:3, the slope foot elevation near the river is 27m, and the slope foot elevation away from the river is 24m. There is a pond with an average depth of 1m and a width of 35m 20m away from the slope foot outside the embankment, and it is extended 20m outward as the boundary; the boundary inside the embankment is 70m away from the slope foot; the soil of the embankment is generalized into four layers, and the soil layers are all horizontal. Starting from the top of the embankment, from top to bottom, they are sandy loam 1, loam 2, clay 3, and sandy loam 4, and the soil layer thicknesses are 5.6m, 10m, 2m, and 15m respectively, and the bottom surface of the lowest soil layer is the fixed boundary. Figure 4 This is a schematic diagram of the calculated section of the hanging river embankment section.

[0057] In this paper, the permeability coefficient of various soils in the suspended river embankment section is , Cohesion c and internal friction angle The statistical analysis showed that It conforms to the log-normal distribution with e as the base, and other random variables are approximately in line with the normal distribution. The specific statistical parameter results are shown in Table 1: Table 1 Statistics of soil parameters of a suspended river embankment

[0058] The mesoscopic parameters are calibrated by selecting biaxial compression numerical tests. Table 2 lists the geometric dimensions of the biaxial numerical test samples and the mesoscopic physical and mechanical properties of the soil particle units.

[0059] Table 2 Control parameters of the test model

[0060] Figure 5 It is a biaxial numerical test specimen. During the test, the upper and lower boundary walls act as loaded pressure plates, moving from both ends toward the middle at a specified speed, and the left and right boundary walls apply a constant confining pressure to the particle unit.

[0061] According to the initial geometric model of the suspended river embankment section (such as Figure 4 As shown in Figure 1, a boundary wall is generated in the PFC program, and then a particle set of a specified radius is generated within the boundary range, and the model is subjected to stress balance. The particles filled in the generated particle flow embankment model are grouped according to the soil type, from top to bottom, sandy loam, loam, clay and sandy loam, and the stress field is initialized. When the maximum unbalanced force of the particle set reaches the maximum contact force When , the particle collection is considered to be in equilibrium, and 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. This constructs the particle flow discrete element analysis model of the suspended river levee section, as shown in Figure 6 .

[0062] According to the obtained statistical parameters of the soil of the suspension river embankment section, the Latin hypercube sampling method and the established particle flow discrete element analysis model of the suspension river embankment section are used to estimate the reliability of the suspension river embankment section under three single failure modes: overtopping, seepage damage and instability.

[0063] (1) Reliability estimation of the suspended river embankment section under the overtopping failure mode According to the established reliability estimation model of the overtopping failure mode of the hanging river embankment section, the Latin hypercube sampling method is used to take the upstream flood water level, windblock height and wave run-up of the embankment section as random variables. The statistical characteristic values ​​are shown in Table 3. The embankment top elevation is 37m, and the other parameters are fixed values. The calculation times are N=105 The calculation results are shown in Table 6, from which the reliability probability of this embankment section under the overtopping failure mode is 99.996%.

[0064] Table 3 Statistics of random variable characteristic values ​​of random variable mode of flooding failure mode

[0065] (2) Reliability estimation of the suspended river embankment section under the seepage failure mode According to the established reliability estimation model of the seepage failure mode of a hanging river embankment section, the Latin hypercube sampling method is used, and the flood level, cohesion, internal friction angle and soil permeability coefficient are taken as random variables. Their characteristic values ​​are shown in Table 4. Other parameters are taken as constants. The randomly sampled sample parameters are input into the particle flow model to calculate the permeability coefficient. The calculation results are shown in Table 6. It is determined that the reliability of the hanging river embankment section under the seepage failure mode is 99.992%.

[0066] Table 4 Statistics of random variable characteristic values ​​of penetration failure mode

[0067] (3) Reliability estimation of suspended river embankments under unstable failure mode Based on the established reliability estimation model of the instability failure mode of a suspended river embankment section, the Latin hypercube sampling method is used, and the cohesion, friction coefficient, internal friction angle, etc. are taken as random variables. At the same time, considering that the particles are randomly generated within a certain range when the particle flow analysis model is established, the minimum radius of the particles is also taken as a random variable, and other parameters are taken as fixed values. The corresponding random variable eigenvalues ​​are shown in Table 5. The randomly sampled sample parameters are input into the particle flow model to calculate the permeability coefficient, and finally the reliability probability of the instability failure mode of the embankment section is 99.993%.

[0068] Table 5 Statistics of random variable characteristic values ​​of instability failure mode

[0069] As shown in Table 6, the reliability calculation method for a single failure mode of a suspended river embankment based on Latin hypercube sampling and particle discrete element method proposed in the present invention was used, and the random variables of each failure mode were sampled 105 times. On this basis, the reliability of the suspended river embankment section in the overtopping, seepage damage and instability failure modes were obtained to be 99.996%, 99.992% and 99.993%, respectively, reflecting that the reliability of the suspended river embankment section is relatively high, and the effectiveness of the method proposed in the present invention is verified.

[0070] Table 6 Reliability estimation table of a hanging river embankment section under single failure mode

[0071] Through the analysis of the overtopping, seepage damage and instability failure modes of the suspended river embankment, the present invention establishes the function of estimating the reliability of the suspended river embankment under the overtopping, seepage damage and instability failure modes, and constructs the reliability estimation model of the suspended river embankment under different single failure modes. Combining Latin hypercube sampling and particle flow discrete element analysis methods, a method for estimating the reliability of the suspended river embankment under a single failure mode is proposed, and the effectiveness of the method is verified based on a suspended river embankment section.

[0072] 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 a single failure mode, characterized in that: The steps include: S1. Determine the random variables causing the failure mode and the corresponding functional functions according to the failure mode of the suspended river embankment; 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; 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 failure mode of the suspended river embankment is any one of the following: overtopping failure mode, seepage damage failure mode or instability failure mode.

3. The reliability estimation method of suspended river embankment under single failure mode according to claim 2 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 The random number uniformly distributed in the interval is the random number of the i-th subinterval; Each subinterval will only generate one random number, and the sampled values ​​of multiple random variables are randomly combined into a multidimensional sample to simulate the joint distribution of multidimensional random variables, and obtain n groups of random numbers, each containing m variables.

4. 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.

5. The reliability estimation method of suspended river embankment under single failure mode according to claim 3 is characterized in that: The random variables in the overtopping failure mode include the top elevation , Windblock height , wave climbing ; 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, The height of the wind chimney.

6. The reliability estimation method of suspended river embankment under single failure mode according to claim 5 is characterized in that: The failure probability calculation formula of the suspended river embankment under the overtopping failure mode is: ； 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.

7. The reliability estimation method of suspended river embankment under single failure mode according to claim 3 is characterized in that: The random variables in the seepage failure mode include the soil permeability coefficient , Flood level , cohesion and internal friction angle ; 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.

8. The reliability estimation method of suspended river embankment under single failure mode according to claim 3 is characterized in that: 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, It is the allowable value of anti-sliding stability safety factor.

9. The reliability estimation method of suspended river embankment under single failure mode according to claim 7 or 8, characterized in that: The step of calculating the maximum hydraulic gradient on the back water surface of the levee or the safety factor of the levee slope is performed by a particle flow discrete element analysis model, and the process includes: (1) constructing a discrete element calculation model grid for a suspended river levee; (2) inputting soil parameters obtained by random sampling; (3) simulating the transmission of hydraulic gradient during seepage; (4) calculating the contact force between particles and the pore water pressure; and (5) determining the maximum hydraulic gradient or the safety factor.

10. 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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