Method for calculating annual failure probability of slope under rainfall condition based on vulnerability analysis

Abstract

The present application relates to a kind of slope annual failure probability calculation method under rainfall condition based on vulnerability analysis, comprising the following steps: S1, obtaining sample data, and data sample is classified into two categories;S2, establish the slope stability classification prediction proxy model based on support vector machine;S3, through binary joint distribution calibration rainfall condition uncertainty, using random variable method calibration soil parameter uncertainty;S4, extract several groups of soil parameters, based on total probability theory and slope stability classification prediction proxy model, calculate the failure probability of slope under different rainfall conditions, and establish vulnerability surface;S5, extract annual average rainfall condition, based on vulnerability surface analysis slope maximum failure probability;S6, repeat step S5 multiple times, calculate the average value of all slope maximum failure probability, obtain the slope annual failure probability.Compared with prior art, the present application improves the theoretical basis of slope annual failure probability calculation under rainfall condition, and improves the calculation efficiency.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of landslide disaster prevention, and particularly relates to a calculation method of annual failure probability of a slope under rainfall conditions based on vulnerability analysis. BACKGROUND

[0002] Quantitative risk assessment is an important means of landslide disaster management. This method evaluates the landslide risk by establishing a relationship curve between the annual occurrence probability and the consequences of landslides. For example, the F-N curve is widely used internationally, where F represents the annual occurrence probability of exceeding a certain number of deaths, and N represents the number of deaths caused by landslides. Therefore, calculating the annual failure probability of a slope is a necessary step for landslide risk assessment and management.

[0003] Rainfall is a common factor that induces slope failure. Currently, the methods for calculating the annual failure probability of a slope under rainfall conditions can be divided into two categories: empirical methods and mechanical methods. Empirical methods estimate the annual failure probability of a slope based on historical landslide data. This method is simple in principle and easy to use, but the annual failure probability obtained is usually the average failure probability of slopes in a region, and cannot consider the influence of individual slope soil parameters. Mechanical methods can overcome the limitations of empirical methods. By establishing a mechanical model, the stability of a slope under rainfall infiltration conditions is analyzed to calculate the annual failure probability. Calculating the annual failure probability of a slope under rainfall conditions based on a mechanical model requires considering the uncertainty of both rainfall and soil parameters. The paper "Rainfall Infiltration Slope Failure Mechanism and Reliability Analysis Considering Multi-Parameter Spatial Variability" (Jiang Shuihua, Liu Xian, Huang Faming, et al., Rock and Soil Mechanics, 2020, 42(05): 900-907) uses the random variable method and random field theory to better calibrate the uncertainty of slope soil parameters under rainfall conditions. However, the current methods for calibrating rainfall uncertainty are still lacking. In theory, calibrating rainfall uncertainty requires calibrating the uncertainty of both rainfall intensity and duration. Only a few documents have proposed related methods. The rainfall uncertainty model used in the paper "Method for Identifying Suitable Rainfall Intensity-Duration-Frequency Model" (Lu Baohong, Tang Youguang, Lu Xiaoming, et al., Journal of Yangzhou University (Natural Science Edition), 2001(04): 109-115) is the intensity-duration-frequency curve, which gives the return period of different rainfall intensity and duration. However, according to the basic establishment process of the intensity-duration-frequency curve, the rainfall duration given in the curve is predetermined, so the curve cannot consider the uncertainty of rainfall duration. In summary, the existing methods for calculating the annual failure probability of a slope under rainfall conditions based on mechanical models still have problems such as incomplete theoretical framework and low calculation efficiency, and a method for calculating the annual failure probability of a slope under rainfall conditions needs to be designed to support the risk assessment and management of rainfall-induced landslides. SUMMARY

[0004] The present application aims at providing a slope annual failure probability calculation method under rainfall condition based on vulnerability analysis to overcome the defects of the prior art, perfecting the theoretical basis of slope annual failure probability calculation under rainfall condition, and improving the calculation efficiency.

[0005] The object of the present application can be achieved by the following technical solutions.

[0006] A slope annual failure probability calculation method under rainfall condition based on vulnerability analysis comprises the following steps:

[0007] S1, sample data is obtained, the sample data includes soil parameters and rainfall conditions, the safety factor of the slope corresponding to each sample data is calculated, whether the sample is stable is determined according to the safety factor of the slope, and the data sample is classified into two categories;

[0008] S2, a slope stability classification prediction proxy model based on support vector machine is established, and the sample data after classification is used for training;

[0009] S3, the uncertainty of the rainfall condition is calibrated through a binary joint distribution, and the uncertainty of the soil parameters is calibrated by using a random variable method;

[0010] S4, based on the uncertainty of the soil parameters, a plurality of groups of soil parameters are randomly extracted, the slope failure probability under different rainfall conditions is calculated based on the total probability theory and the slope stability classification prediction proxy model, and a vulnerability surface is established;

[0011] S5, based on the uncertainty of the rainfall condition, a same number of rainfall conditions as the annual average rainfall times are randomly extracted, and the maximum failure probability of the slope is analyzed based on the vulnerability surface;

[0012] S6, step S5 is repeated multiple times, the average value of all the maximum failure probabilities of the slope is calculated, and the slope annual failure probability is obtained.

[0013] Further, in step S1, the safety factor of the slope is calculated by a slope stability mechanical analysis model, and the slope stability mechanical analysis model is a finite element numerical analysis model.

[0014] Further, the process of calculating the safety factor of the slope by the slope stability mechanical analysis model is as follows:

[0015] S101, a slope stability mechanical analysis model is established in software GEO-STUDIO, and the rainfall condition, the soil parameters and the boundary condition are given;

[0016] S102, the change of the pore water pressure of the slope under the given rainfall condition is analyzed based on the unsaturated soil theory by the SEEP / W module;

[0017] S103, import the analysis result of step S102 into the SLOPE / W module, and calculate the slope safety factor by the limit equilibrium method.

[0018] Further, in step S2, after the slope stability classification prediction agent model is trained, the classification accuracy of the model is evaluated by using a confusion matrix.

[0019] Further, the specific process of calibrating the rainfall condition uncertainty by the binary joint distribution is as follows:

[0020] S301, the single-variable marginal distribution of each variable in the rainfall condition is fitted by using a generalized Pareto distribution.

[0021] S302, the Frank Copula function is used to connect each single-variable marginal distribution to obtain a binary joint distribution.

[0022] Further, the marginal distribution related parameters are fitted by using a maximum likelihood method.

[0023] Further, in steps S4 and S5, the soil parameters and the rainfall condition are randomly extracted by using a Monte Carlo simulation.

[0024] Further, in step S4, the calculation formula of the slope failure probability is as follows:

[0025] p f (r)=∫…∫∫S[F s (θ,r)]f(θ)dθ

[0026] Wherein, p f (r) is the slope failure probability under a given rainfall condition r, F s (θ,r) is the slope safety factor when the soil parameter is θ under a given rainfall condition r, S[F s (θ,r)] is an indicator function for judging whether the slope is unstable, and f(θ) is a soil parameter uncertainty function.

[0027] Further, the indicator function S[F s (θ,r) for judging whether the slope is unstable is obtained by the slope stability classification prediction agent model, and is defined as follows:

[0028]

[0029] Further, in step S5, the annual average rainfall frequency is obtained according to the historical rainfall frequency.

[0030] Compared with the prior art, the present application has the following beneficial effects:

[0031] 1. The application converts the slope stability analysis problem under rainfall conditions based on the safety factor into a binary classification problem, establishes a slope stability classification prediction proxy model based on support vector machines, and avoids a large amount of mechanical calculation that may be involved in the slope annual failure probability reliability analysis; the application is based on the total probability theory and the slope stability classification prediction proxy model, calculates the slope failure probability under different rainfall, establishes a vulnerability surface, analyzes the maximum failure probability of the slope based on the vulnerability surface, avoids the complexity of considering all rainfall condition uncertainties, and further improves the solution efficiency of the slope annual failure probability calculation under rainfall conditions.

[0032] 2. The application calibrates the rainfall condition uncertainty by a binary joint distribution, calibrates the soil parameter uncertainty by a random variable method, considers the rainfall condition uncertainty and the soil parameter uncertainty to solve the slope annual failure probability, and further perfects the theoretical framework of the slope annual failure probability calculation under rainfall conditions. BRIEF DESCRIPTION OF DRAWINGS

[0033] Figure 1 The flowchart of the method of the application is shown in the figure;

[0034] Figure 2 The slope geometry is shown in the figure;

[0035] Figure 3 The rainfall intensity-duration joint distribution is shown in the figure;

[0036] Figure 4 The slope vulnerability surface is shown in the figure. DETAILED DESCRIPTION

[0037] The application will be described in detail below in combination with the drawings and specific embodiments. The embodiments are implemented on the premise of the technical solution of the application, detailed implementation modes and specific operation processes are given, but the protection scope of the application is not limited to the following embodiments.

[0038] Embodiment:

[0039] This embodiment introduces the specific implementation mode of the method of the application based on a slope example in Edmonton City, Canada. The slope geometry is shown in the figure, the slope height is 20 m, the slope is 35°, and the slope soil is sandy loam. Based on literature research, the rainfall event intensity-duration joint distribution in Edmonton City, Canada is shown in the figure. This embodiment provides a slope annual failure probability calculation method under rainfall conditions based on vulnerability analysis, as shown in the figure, including the following steps: Figure 2 Figure 3 Figure 1

[0040] ​​​S1. Obtain sample data, including soil parameters and rainfall conditions. Calculate the slope safety factor corresponding to each sample data. Determine whether the sample is stable based on the slope safety factor and classify the data samples into two categories.

[0041] Specifically, the slope safety factor is calculated using a slope stability mechanical analysis model. One-dimensional, two-dimensional, and three-dimensional models are all acceptable, with finite element numerical analysis models being the most common. These models can be built using common commercial software such as GEO-STUDIO and FLAC 2D / 3D. Taking GEO-STUDIO as an example, the specific steps are as follows:

[0042] S101. Establish a slope stability mechanical analysis model. The model uses a hybrid quadrilateral and triangular grid with a grid size of 0.5m, comprising a total of 5286 grids. Rainfall conditions, soil parameters, and boundary conditions are assigned. The boundary condition is that the slope sides and bottom are undrained, and a flow boundary is assigned to the slope surface to simulate rainfall infiltration. The slope surface water accumulation effect is not considered. The initial analysis condition uses a constant pore water pressure distribution of -50kPa.

[0043] S102. Using the SEEP / W module, based on the unsaturated soil theory, the changes in pore water pressure on the slope under rainfall conditions are analyzed. The distribution of pore water pressure and volumetric water content on the slope under rainfall infiltration conditions is solved. The soil-water characteristic curve adopts the VanGenuchten model.

[0044] S103. Import the analysis results from the SEEP / W module into the SLOPE / W module and perform limit equilibrium analysis using the Morgenstern-Price limit equilibrium method. The total number of potential sliding surfaces analyzed is 2200, and the minimum safety factor value corresponding to the critical sliding surface is the slope safety factor.

[0045] The uncertain soil parameters considered include: effective cohesion c′ and effective internal friction angle. Van Genuchten model parameters α, n, and saturated permeability coefficient k s Referring to typical sandy loam soil values, the mean and coefficient of variation of various uncertain soil parameters are shown in Table 1. Rainfall uncertainty parameters include intensity I and duration D. To ensure the applicability of the surrogate prediction model, the sample values ​​of the random variables for soil parameters range from [x...]. u -3x σ ,x u +3x σ ], where x u and x σ The values ​​represent the mean and standard deviation of a random variable within a standard normal space, respectively; the ranges for rainfall intensity and duration are [1, 15 mm / h] and [0, 40 h], respectively. A uniform sample of 1000 samples is generated within these ranges, producing 1000 seven-dimensional input vectors containing soil parameters and rainfall conditions. The slope safety factor under 1000 parameter vector conditions was calculated using a finite element model, and the samples were divided into two categories based on whether the safety factor was greater than 1.

[0046] Table 1. Mean, coefficient of variation, and distribution of random variables for soil parameters.

[0047]

[0048] S2. Establish a slope stability classification and prediction proxy model based on support vector machine, and train it using the binary-classified sample data.

[0049] The classified training samples were divided into a test sample set and a training sample set at a 1:9 ratio to construct a slope stability prediction surrogate model based on support vector machines. The trained support vector machine surrogate model can be evaluated for its classification accuracy based on the confusion matrix. Common evaluation metrics include accuracy, Kappa coefficient, and AUC value. In this embodiment, the AUC value calculated based on the confusion matrix of the test sample set is 0.99, indicating that the surrogate model has high prediction accuracy.

[0050] S3. The uncertainty of rainfall conditions is calibrated by a binary joint distribution, and the uncertainty of soil parameters is calibrated by a random variable method.

[0051] For convenience, we assume that the uncertain soil parameters all follow a log-normal distribution and are independent of each other. First, we need to construct a univariate marginal distribution. In this embodiment, we use a generalized Pareto distribution to fit the marginal distribution of rainfall intensity I and duration D. Based on the generalized Pareto distribution formula, it can be written in the following form:

[0052]

[0053] In the formula, k, μ and σ represent shape, position and scale parameters, respectively, and r = I or D.

[0054] After constructing the univariate marginal distributions, the Frank Copula function is used to connect the univariate marginal distributions to obtain the bivariate joint distribution, as shown in the following expression:

[0055]

[0056] In the formula, δ is the Frank Copula parameter, F(I) and F(D) are the cumulative marginal distributions of rainfall intensity I and duration D, respectively, and r = {I, D}.

[0057] By collecting historical rainfall events in the region or conducting literature surveys, the frequency distributions of rainfall intensity and duration can be statistically analyzed, and relevant parameters can be fitted using the maximum likelihood method. Common distributions of soil parameter random variables include normal and log-normal distributions. The rainfall distribution parameters obtained by calibration using the maximum likelihood method are shown in Table 2.

[0058] Table 2 Binary Joint Distribution Parameters of Rainfall Events

[0059]

[0060] S4. Based on the uncertainty of soil parameters, several sets of soil parameters are randomly selected. Based on the full probability theory and the slope stability classification prediction surrogate model, the slope failure probability under different rainfall conditions is calculated, and a vulnerable surface is established.

[0061] First, rainfall events are sampled uniformly according to the probability distribution of rainfall, with the sampling range consistent with step S2, namely, the rainfall intensity range is 1 to 15 mm / h and the rainfall duration range is 0 to 40 h; then, 10,000 sets of soil parameters are randomly sampled through Monte Carlo simulation.

[0062] Secondly, based on the slope stability classification prediction surrogate model and formula (3), the slope failure probability under different rainfall conditions is calculated. The formula for calculating the slope failure probability is as follows:

[0063] p f (r)=∫…∫∫S[F s (θ,r)]f(θ)dθ (3)

[0064] Where, p f (r) represents the slope failure probability under given rainfall condition r, F s (θ,r) is the slope safety factor when the soil parameter is θ under constant rainfall condition r, f(θ) is the uncertainty function of the soil parameter, and S[F s [θ,r] is an indicator function for determining whether a slope is unstable based on its safety factor. It is obtained through a slope stability classification prediction surrogate model and is defined as follows:

[0065]

[0066] The surface representing the variation of slope failure probability under different rainfall intensities and durations is known as the vulnerability surface, such as... Figure 4 As shown.

[0067] S5. Based on the uncertainty of rainfall conditions, randomly select the same number of rainfall conditions as the annual average number of rainfalls, and analyze the maximum failure probability of the slope based on the vulnerable surface.

[0068] The average annual rainfall frequency was predicted based on historical rainfall frequency for the region. Based on a literature review, the average annual number of rainfall events in Edmonton, Canada, is 15. First, 15 rainfall events were randomly selected using a rainfall uncertainty model. Then, based on the slope vulnerability surface under rainfall conditions, the maximum failure probability of the slope under these 15 rainfall events was analyzed, and the corresponding rainfall events are identified as the most dangerous rainfall events of the year.

[0069] Extracting each rainfall event based on the binary distribution essentially involves extracting the intensity and duration of each rainfall event, with each rainfall event being independent of the others. By performing vulnerability analysis using vulnerable surfaces, the most dangerous rainfall event with the highest probability of slope failure within a year can be quickly determined, eliminating the need to repeatedly calculate the slope failure probability under different rainfall events within a year based on formula (3), thus significantly improving the solution efficiency.

[0070] S6. Repeat step S5 multiple times to calculate the average of the maximum failure probability of all slopes, and obtain the annual failure probability of the slope.

[0071] By obtaining a sufficient number of the most dangerous annual rainfall events to simulate their uncertainty, the annual slope failure probability p can be calculated. fa The estimation formula is:

[0072]

[0073] Where M is the number of simulations, r max,i Let p be the rainfall condition corresponding to the maximum failure probability of the slope obtained in the i-th simulation. f (r max,i ) represents the maximum failure probability of the slope obtained in the i-th simulation.

[0074] In this embodiment, M is set to 10000, which yields 10000 samples of slope failure probability under the most dangerous annual rainfall. Based on formula (5), the annual failure probability of the slope under rainfall conditions is calculated to be 0.034, with a standard deviation of 0.002.

[0075] If the above methods are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0076] The above description of the embodiments is provided to enable those skilled in the art to understand and use the invention. It will be apparent to those skilled in the art that various modifications can be made to these embodiments, and the general principles described herein can be applied to other embodiments without inventive effort. Therefore, the present invention is not limited to the above embodiments, and any improvements and modifications made by those skilled in the art based on the disclosure of the present invention without departing from the scope of the invention should be within the protection scope of the present invention.

Claims

1. A method for calculating the annual failure probability of slope under rainfall conditions based on vulnerability analysis, characterized in that, Includes the following steps: S1. Obtain sample data, which includes soil parameters and rainfall conditions. Calculate the slope safety factor corresponding to each sample data. Determine whether the sample is stable based on the slope safety factor. Divide the data samples into two categories. S2. Establish a slope stability classification and prediction proxy model based on support vector machine, and train it using the binary-classified sample data; S3. The uncertainty of rainfall conditions is calibrated using a binary joint distribution, and the uncertainty of soil parameters is calibrated using the random variable method. The specific process of calibrating the uncertainty of rainfall conditions using a binary joint distribution is as follows: S301. Use the generalized Pareto distribution to fit the univariate marginal distribution of each variable in the rainfall conditions; S302. Use the Frank Copula function to connect the marginal distributions of each univariate to obtain a binary joint distribution; S4. Based on the uncertainty of soil parameters, several sets of soil parameters are randomly selected. Based on the total probability theory and the slope stability classification prediction surrogate model, the slope failure probability under different rainfall conditions is calculated, and a vulnerability surface is established. The formula for calculating the slope failure probability is as follows: in, Given rainfall conditions Downslope failure probability Given rainfall conditions The parameters of the underlying soil are The slope safety factor at that time An indicator function for determining whether a slope is unstable. The soil parameter uncertainty function is the indicator function for determining whether the slope is unstable. The slope stability is predicted by the aforementioned surrogate model, and is defined as follows: ； S5. Based on the uncertainty of rainfall conditions, randomly select the same number of rainfall conditions as the annual average number of rainfalls, and analyze the maximum failure probability of the slope under the rainfall conditions based on the vulnerable surface. S6. Repeat step S5 multiple times to calculate the average of the maximum failure probability of all slopes, and obtain the annual failure probability of the slope.

2. The method for calculating the annual failure probability of slope under rainfall conditions based on vulnerability analysis according to claim 1, characterized in that, In step S1, the slope safety factor is calculated using a slope stability mechanical analysis model, which is a finite element numerical analysis model.

3. The method for calculating the annual failure probability of slope under rainfall conditions based on vulnerability analysis according to claim 2, characterized in that, The process of calculating the slope safety factor using the aforementioned slope stability mechanical analysis model is as follows: S101. Establish a slope stability mechanical analysis model in the software GEO-STUDIO, and assign rainfall conditions, soil parameters and boundary conditions; S102. Using the SEEP / W module, analyze the changes in pore water pressure on slopes under given rainfall conditions based on unsaturated soil theory. S103. Import the analysis results from step S102 into the SLOPE / W module and calculate the slope safety factor using the limit equilibrium method.

4. The method for calculating the annual failure probability of slope under rainfall conditions based on vulnerability analysis according to claim 1, characterized in that, In step S2, after the slope stability classification prediction surrogate model is trained, the classification accuracy of the model is evaluated using a confusion matrix.

5. The method for calculating the annual failure probability of slope under rainfall conditions based on vulnerability analysis according to claim 1, characterized in that, The marginal distribution parameters were fitted using the maximum likelihood method.

6. The method for calculating the annual failure probability of slope under rainfall conditions based on vulnerability analysis according to claim 1, characterized in that, In steps S4 and S5, Monte Carlo simulation is used to randomly sample soil parameters and rainfall conditions.

7. The method for calculating the annual failure probability of slope under rainfall conditions based on vulnerability analysis according to claim 1, characterized in that, In step S5, the annual average number of rainfall events is obtained based on the historical rainfall events prediction.

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