A method for evaluating slope toughness probability under rainfall conditions

Abstract

The present application relates to a kind of slope toughness probability evaluation method under rainfall condition, comprising the following steps: S1, collect historical rainfall data, construct random rainfall model;S2, statistics rock-soil parameter mean and variation coefficient, calibrate rock-soil parameter probability density distribution function;S3, uniformly sample multiple groups of independent rainfall events and rock-soil parameter and calculate corresponding slope safety factor, extract sample binary classification, build landslide classification agent prediction model;S4, randomly sample rock-soil parameter and independent rainfall event in the service period of slope, predict landslide event based on the landslide classification agent model;S5, randomly extract the recovery time corresponding to landslide event occurrence, calculate slope toughness index;S6, repeat step S4 and S5 multiple times, solve the mean and standard deviation of all slope toughness index, evaluate slope toughness level.Compared with prior art, the present application further improves the theoretical basis of slope toughness evaluation under rainfall condition, and can efficiently and accurately evaluate slope toughness.

Description

Technical Field

[0001] This invention belongs to the field of landslide disaster prevention and control technology, and in particular relates to a method for probabilistic assessment of slope resilience under rainfall conditions. Background Technology

[0002] Resilience theory addresses the shortcomings of traditional risk theory. The literature "Research on the Resilience Evaluation Index System of Transportation Infrastructure" (Yang Chao, Li Xinghua, Long Zhigang, et al., Highway, 2023, Vol. 68(6):303-308) points out that by establishing resilience assessment methods and index systems, the ability of engineering projects to resist, adapt to, and quickly recover to normal service status in the face of disasters can be improved. Therefore, analyzing the probability and consequences of slope resilience risk under rainfall conditions and calculating slope resilience indices can provide a basis for assessing rainfall-induced landslide risks and restoring slope performance.

[0003] Extensive research has been conducted on evaluating engineering projects using resilience theory. The literature "Evaluation and Control of Toughness in Geotechnical and Underground Engineering Structures" (Zheng Gang, Cheng Xuesong, Zhou Haizuo, et al., Journal of Civil Engineering, 2022, 55(7):1-38) summarizes the research progress of resilience concepts and evaluation methods in the field of geotechnical and underground engineering. The calculation of resilience indices is usually based on deterministic methods, neglecting the impact of uncertainties on resilience assessment. Slope resilience assessment under rainfall conditions needs to consider the uncertainties of actual rainfall events, geotechnical parameters, and recovery time after landslide events. Combining resilience theory with probabilistic analysis can provide a more comprehensive assessment of slope resilience. After obtaining slope resilience indices through resilience model calculations, the Monte Carlo simulation-based probabilistic resilience assessment method can calculate the uncertainty range of slope resilience indices, providing richer information for engineering decision-making. The literature "A Method for Evaluating the Structural Toughness of Shield Tunnels Considering Multiple Disturbances and Its Application" (Lin Xingtao, Chen Xiangsheng, Su Dong, et al., Journal of Civil Engineering, 2022, 55(7):1-38) proposes that engineering projects may encounter various disasters throughout their life cycle, and their structural performance changes dynamically over time, exhibiting different capabilities at each stage. Slopes may experience multiple rainfall events during their service life, and these events are often random, leading to dynamic changes in slope performance over time. While existing toughness models can well describe the recovery process of engineering performance after a single disaster, they are usually insufficient to describe the cumulative performance changes of slopes under the influence of multiple rainfall events. In summary, due to complex uncertainties and the possibility of multiple disaster events during the service life of slopes, existing probabilistic assessment methods for slope toughness under rainfall conditions still suffer from problems such as an imperfect theoretical framework and low computational efficiency. A new assessment method needs to be designed to improve the theoretical foundation of slope toughness assessment under rainfall conditions, efficiently and accurately assess slope toughness, and enable engineering managers to better understand and plan the maintenance and recovery actions of the project. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a method for probabilistic assessment of slope toughness under rainfall conditions, improve the theoretical basis of slope toughness assessment under rainfall conditions, and conduct slope toughness assessment efficiently and accurately.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] A method for probabilistic assessment of slope resilience under rainfall conditions includes the following steps:

[0007] S1. Collect historical rainfall data of the area where the slope is located, identify independent rainfall events, and construct a stochastic rainfall model;

[0008] S2. Statistically calculate the mean and coefficient of variation of soil and rock parameters of the slope, and calibrate the probability density distribution function of soil and rock parameters;

[0009] S3. Based on the random rainfall model and the probability density distribution function of the soil and rock parameters, uniformly sample multiple independent rainfall events and soil and rock parameters and calculate the corresponding slope safety factor. Classify the sampled samples into two categories and construct a landslide classification proxy prediction model.

[0010] S4. Randomly sampled soil and rock parameters and independent rainfall events during the slope's service life, and predict landslide events based on the landslide classification proxy model;

[0011] S5. Randomly select the recovery time corresponding to the landslide event and calculate the slope resilience index.

[0012] S6. Repeat steps S4 and S5 multiple times to calculate the mean and standard deviation of all slope resilience indices and assess the slope resilience level.

[0013] Furthermore, in step S1, the construction process of the random rainfall model is as follows:

[0014] S101. Collect historical rainfall data for the area where the slope is located, define rainfall event interval thresholds and rainfall intensity thresholds, and identify independent rainfall events;

[0015] S102. Statistically analyze the intensity and duration frequency distribution characteristics of independent rainfall events, and fit the joint probability density distribution function of rainfall intensity and duration based on Copula theory;

[0016] S103. Statistically analyze the frequency distribution characteristics of the interval time of independent rainfall events, describe the interval time distribution function of rainfall events based on a Poisson process, combine the joint probability density distribution function of rainfall intensity and duration, calibrate the interval time distribution of rainfall events, and construct the random rainfall model.

[0017] Further, in step S102, univariate marginal distributions of rainfall intensity and duration are constructed based on the generalized Pareto distribution, and then connected using the Frank Copula function to obtain the joint probability density distribution function of rainfall intensity and duration.

[0018] Further, in step S103, the expression for the rainfall event interval distribution function is as follows:

[0019] f(Δt)=λexp(-λΔt)

[0020] Where Δt represents the interval between rainfall events, f(Δt) represents the probability of the occurrence of the interval between rainfall events, and λ represents the average occurrence rate of rainfall events.

[0021] Furthermore, in step S2, the probability density distribution function of the soil and rock parameters is calibrated using a log-normal distribution.

[0022] Furthermore, in step S3, uniform sampling is performed within a 95% confidence interval, and the slope safety factor is calculated using numerical analysis to construct a landslide classification proxy prediction model based on random forest.

[0023] Furthermore, in step S4, random sampling is simulated using Monte Carlo simulation.

[0024] Furthermore, in step S5, the recovery time following a landslide event is based on a triangular distribution, as described below:

[0025]

[0026] Where, δ r Indicates recovery time, δ r,min δ r,m and δ r,max These represent the lower limit, mode, and upper limit of the recovery time triangle distribution, respectively.

[0027] Furthermore, in step S5, the slope toughness index is calculated based on the ratio of total instability time to service life, as shown in the following formula:

[0028]

[0029] Among them, R e δ represents the slope resilience index. ri Let T represent the recovery time after the i-th landslide event, T represent the service life, and n represent the number of landslide events.

[0030] Furthermore, if a new landslide event occurs within the recovery period following a landslide event, the new landslide event will not be used to calculate the slope resilience index.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] 1. This invention constructs a random rainfall model and a probability density distribution function for soil and rock parameters, uniformly samples multiple sets of rainfall events and soil and rock parameters, calculates the corresponding slope safety factor, classifies the sampled data into two categories, constructs a landslide classification proxy prediction model, and then randomly samples soil and rock parameters and rainfall events during the slope's service life. Based on the landslide classification proxy prediction model, it predicts landslide events, avoiding a large number of mechanical calculations that may be involved in predicting landslide events, improving the solution efficiency of landslide event prediction under rainfall conditions, and fully considering the complexity of the uncertainty in slope toughness assessment under rainfall conditions.

[0033] 2. This invention considers the actual situation that slopes may be subjected to multiple rainfalls during their service life. It randomly selects the recovery time corresponding to multiple landslide events and calculates the total instability time caused by multiple landslide events during the service life of the slope. Based on the ratio of the total instability time to the service life of the slope, it calculates the slope toughness index, solves the mean and standard deviation of all slope toughness indices, and evaluates the slope toughness level. Therefore, this invention can evaluate the cumulative performance recovery of slopes, thereby providing a more intuitive and practical toughness evaluation index, efficiently and accurately assessing slope toughness, providing more effective assistance for engineering decision-making, and further improving the theoretical framework for slope toughness assessment under rainfall conditions. Attached Figure Description

[0034] Figure 1 This is a flowchart of the method of the present invention;

[0035] Figure 2 This is a schematic diagram showing the distribution of multiple rainfall events during the slope's service life.

[0036] Figure 3 This is a schematic diagram illustrating the principle of random forest.

[0037] Figure 4 This is a diagram showing the evolution of slope performance under multiple landslide events during the slope's service life.

[0038] The ordinate represents an indicator function for slope instability; a value of 1 indicates slope stability, while a value of 0 indicates slope instability and a landslide event. t 1n and t 2n Let δ represent the start and end times of the nth landslide event, respectively. rn This represents the recovery time after the nth landslide event occurs;

[0039] Figure 5 This is a histogram showing the distribution of slope toughness indices under multiple landslide events during the slope's service life. Detailed Implementation

[0040] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0041] Example:

[0042] This embodiment illustrates the specific implementation of the method of the present invention based on a slope example in Edmonton, Canada. The slope is 20m high with a slope angle of 35°, and the soil is sandy loam. This embodiment provides a method for probabilistic assessment of slope resilience under rainfall conditions, such as... Figure 1 As shown, it includes the following steps:

[0043] S1. Collect historical rainfall data for the area where the slope is located, identify independent rainfall events, and construct a stochastic rainfall model.

[0044] The construction of a random rainfall model needs to consider the uncertainties in rainfall event intensity, duration, and interval time. The specific construction process is as follows:

[0045] S101. Collect historical rainfall data for the area where the slope is located, define rainfall event interval thresholds and rainfall intensity thresholds, and identify independent rainfall events. If the rainfall intensity is greater than the rainfall intensity threshold, it is judged as a rainfall event. If the interval between two rainfall events is greater than the rainfall event interval threshold, they are judged as independent rainfall events; otherwise, they are judged as the same rainfall event. This processing method can further improve the accuracy of subsequent assessment results. Referring to hourly rainfall data and research results from Edmonton, Canada from 1984 to 2010, a rainfall event interval threshold of 4 hours and a rainfall intensity threshold of 1 mm / h were used, and a total of 417 independent rainfall events were separated.

[0046] S102. The intensity and duration frequency distribution characteristics of independent rainfall events were statistically analyzed. The obtained rainfall intensity was mainly distributed between 1-10 mm / h, and the rainfall duration was mainly distributed between 0.65-40 h. Based on the data distribution characteristics, this embodiment uses a generalized Pareto distribution to fit the marginal distributions of rainfall intensity I and duration D, respectively. The formula based on the generalized Pareto distribution can be written in the following form:

[0047]

[0048] Where k, μ, and σ represent shape, position, and scale parameters, respectively, and r = I or D.

[0049] 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:

[0050]

[0051] Where 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}. The rainfall distribution parameters obtained by the maximum likelihood method are shown in Table 1.

[0052] Table 1. Binary Joint Distribution Parameters of Rainfall Events

[0053]

[0054] S103. Statistically analyze the frequency distribution characteristics of the interval time of independent rainfall events, describe the interval time distribution function of rainfall events based on the Poisson process, combine the joint probability density distribution function of rainfall intensity and duration, calibrate the interval time distribution of rainfall events, and construct a stochastic rainfall model.

[0055] The expression for the interval distribution function of rainfall events is as follows:

[0056] f(Δt)=λexp(-λΔt)

[0057] Where Δt represents the interval between rainfall events in hours, f(Δt) represents the probability of the rainfall event interval occurring, and λ represents the average occurrence rate of rainfall events.

[0058] Dividing the total number of rainfall events in the region by the data time span yields the average annual occurrence rate of rainfall events, which is approximately 417 / 27 ≈ 15. Using a Poisson process to describe the random occurrence of rainfall, the number of rainfall events occurring in year t is n. r The probability of =k can be expressed by the following formula:

[0059]

[0060] When the occurrence of rainfall events follows a Poisson process, the interval Δt between rainfall events should follow an exponential distribution. The average occurrence rate of the interval is 15 / 365 / 24 = 0.0017. According to the exponential formula, the interval distribution function f(Δt) can be written in the following form:

[0061] f(Δt)=0.0017exp(-0.0017Δt)

[0062] By combining the joint probability distribution of rainfall intensity and duration with the Poisson distribution, the uncertainty of rainfall events in Edmonton, Canada, can be calibrated. To simulate random rainfall, the number of rainfall events within a certain period can be randomly selected using the Poisson formula, and then the intensity and duration of each rainfall event can be randomly selected based on the joint distribution.

[0063] S2. Consider the soil and rock parameters of the slope as random variables, calculate the mean and coefficient of variation of the soil and rock parameters, and use the log-normal distribution to calibrate the probability density distribution function of the soil and rock parameters.

[0064] 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 Based on typical sandy loam soil values, the mean and coefficient of variation of various uncertain soil parameters are shown in Table 2.

[0065] Table 2. Mean, coefficient of variation, and distribution of random variables for soil parameters.

[0066]

[0067] S3. Based on the random rainfall model and the probability density distribution function of soil and rock parameters, multiple independent rainfall events and soil and rock parameters are uniformly sampled and the corresponding slope safety factors are calculated. The sampled samples are then classified into two categories to construct a landslide classification proxy prediction model.

[0068] To ensure the applicability of the surrogate prediction model, uniform sampling is performed within a 95% confidence interval, and the sample values ​​for the random variables of soil parameters range from [x...]. u -3x σ ,x u +3x σ ], where x u and x σ The values ​​are 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 [0.65, 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 F is calculated using a finite element model under conditions of 1000 parameter vectors. s (θ,r), and based on the safety factor F s The samples are divided into two classes based on whether (θ,r) is greater than 1 (if the safety factor is greater than 1, it indicates that the slope is stable; otherwise, it indicates that the slope is unstable and a landslide event has occurred). The classified training samples are divided into test sample set and training sample set in a 1:9 ratio to construct a landslide classification surrogate prediction model based on random forest.

[0069] The schematic diagram of the random forest algorithm is as follows: Figure 3As shown, a random forest consists of multiple decision trees, and there is no association between different decision trees. When performing a classification task, after a new input sample enters, each decision tree makes a judgment and classification respectively, obtaining a classification result. The result with the largest number among the classification results of all decision trees is the final output classification result. Assume that each sample has M attributes. When each node of the decision tree needs to be split, m attributes are randomly selected from the M attributes (m << M), and then one attribute is selected from the m attributes using a certain strategy (such as information gain) as the splitting attribute of this node.

[0070] The trained landslide classification agent prediction model can evaluate its classification accuracy based on the confusion matrix. In this embodiment, the AUC value calculated based on the confusion matrix of the test sample set is equal to 0.99, indicating that the landslide classification agent prediction model has a high prediction accuracy.

[0071] S4. Randomly sample geotechnical parameters and independent rainfall events during the service period of the slope, and predict landslide events based on the landslide classification agent model.

[0072] During the service period (one year), the schematic diagram of the distribution of multiple rainfall events is as Figure 2 shown. Through Monte Carlo simulation, a group of geotechnical parameters θ is sampled based on the probability density distribution function of the geotechnical parameters, and a group of rainfall events r during the service period is sampled based on the random rainfall model. F s (θ, r) is the slope safety factor when the rainfall condition is r under the given soil parameters θ, and S[F s (θ, r)] is the indicator function of whether the slope is unstable, obtained through the landslide classification agent prediction model, and is defined as follows:

[0073]

[0074] Through the landslide classification agent prediction model, the evolution diagram of the slope performance under multiple landslide events during the service period as shown in Figure 4 can be obtained. Among them, the indicator function S[F s (θ, r)] = 1 indicates that the slope is stable, and becoming 0 indicates that the slope is unstable, that is, a landslide event occurs. δ 1n and δ 2n respectively represent the start time and end time of the nth landslide event, and δ rn represents the recovery time corresponding after the nth landslide event occurs.

[0075] S5. Randomly extract the recovery time corresponding after the landslide event occurs, and calculate the slope resilience index.

[0076] The recovery time corresponding after the landslide event occurs follows a triangular distribution, and is described as follows:

[0077]

[0078] Where, δ r Indicates recovery time, δ r,min δ r,m and δ r,max These represent the lower limit, mode, and upper limit of the recovery time triangle distribution, respectively.

[0079] The slope resilience index is calculated based on the ratio of total instability time to service life, using the following formula:

[0080]

[0081] Among them, R e δ represents the slope resilience index. ri Let T represent the recovery time after the i-th landslide event, T represent the service life, and n represent the number of landslide events.

[0082] It should be noted that if a new landslide occurs within the recovery period following a landslide, the new landslide will not be used to calculate the slope resilience index.

[0083] Based on a literature review, the recovery time δ after a landslide event is... r Treated as independent random variables, they follow a lower limit δ r,min =24 days, mode δ r,m =30 days, maximum δ r,max =A triangular distribution over 36 days.

[0084] S6. Repeat steps S4 and S5 multiple times to calculate the mean and standard deviation of all slope resilience indices and assess the slope resilience level.

[0085] Mean value of slope resilience index and standard deviation The calculation formulas are as follows:

[0086]

[0087]

[0088] Where T ej Let J represent the soil and rock parameters of the j-th group and the slope toughness index under the rainfall event, and N represent the number of repetitions of steps S4 and S5.

[0089] In this embodiment, repeating steps S4 and S5 10,000 times yields 10,000 sets of geotechnical parameters and slope resilience indices under rainfall events. With a service life of one year, the average slope recovery time is 5.75 days. The histogram showing the distribution of slope resilience indices under multiple landslide events within one year is shown below. Figure 5 As shown, the mean value of the slope resilience index is 0.984, and the standard deviation is 0.096.

[0090] 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.

[0091] 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 probabilistic assessment of slope resilience under rainfall conditions, characterized in that, Includes the following steps: S1. Collect historical rainfall data of the area where the slope is located, identify independent rainfall events, and construct a stochastic rainfall model; S2. Statistically calculate the mean and coefficient of variation of soil and rock parameters of the slope, and calibrate the probability density distribution function of soil and rock parameters; S3. Based on the random rainfall model and the probability density distribution function of the soil and rock parameters, uniformly sample multiple independent rainfall events and soil and rock parameters and calculate the corresponding slope safety factor. Classify the sampled samples into two categories and construct a landslide classification proxy prediction model. S4. Randomly sampled soil and rock parameters and independent rainfall events during the slope's service life, and predict landslide events based on the landslide classification proxy model; S5. Randomly select the recovery time corresponding to the landslide event and calculate the slope resilience index. S6. Repeat steps S4 and S5 multiple times to calculate the mean and standard deviation of all slope resilience indices and assess the slope resilience level. In step S1, the construction process of the random rainfall model is as follows: S101. Collect historical rainfall data for the area where the slope is located, define rainfall event interval thresholds and rainfall intensity thresholds, and identify independent rainfall events; S102. Statistically analyze the intensity and duration frequency distribution characteristics of independent rainfall events, and fit the joint probability density distribution function of rainfall intensity and duration based on Copula theory; S103. Statistically analyze the frequency distribution characteristics of the interval time of independent rainfall events, describe the interval time distribution function of rainfall events based on the Poisson process, and combine the joint probability density distribution function of rainfall intensity and duration to calibrate the interval time distribution of rainfall events and construct the random rainfall model. In step S5, the recovery time following a landslide event is based on a triangular distribution, as described below: in, Indicates recovery time. , and These represent the lower limit, mode, and upper limit of the recovery time triangle distribution, respectively; In step S5, the slope toughness index is calculated based on the ratio of total instability time to service life, using the following formula: in, This represents the slope resilience index. Indicates the first The recovery time corresponding to a landslide event. Indicates the period of service. This indicates the number of landslide events.

2. The method for probabilistic assessment of slope resilience under rainfall conditions according to claim 1, characterized in that, In step S102, univariate marginal distributions of rainfall intensity and duration are constructed based on the generalized Pareto distribution, and then connected using the FrankCopula function to obtain the joint probability density distribution function of rainfall intensity and duration.

3. The method for probabilistic assessment of slope resilience under rainfall conditions according to claim 1, characterized in that, In step S103, the expression for the rainfall event interval distribution function is as follows: in, Indicates the interval between rainfall events. This indicates the probability of a rainfall event occurring at intervals. This indicates the average rate of occurrence of rainfall events.

4. The method for probabilistic assessment of slope resilience under rainfall conditions according to claim 1, characterized in that, In step S2, the probability density distribution function of the soil and rock parameters is calibrated using a log-normal distribution.

5. The method for probabilistic assessment of slope resilience under rainfall conditions according to claim 1, characterized in that, In step S3, uniform sampling is performed within a 95% confidence interval, and the slope safety factor is calculated using numerical analysis to construct a landslide classification proxy prediction model based on random forest.

6. The method for probabilistic assessment of slope resilience under rainfall conditions according to claim 1, characterized in that, In step S4, random sampling is simulated using Monte Carlo simulation.

7. The method for probabilistic assessment of slope resilience under rainfall conditions according to claim 6, characterized in that, If a new landslide occurs within the recovery period following a landslide, that new landslide will not be used to calculate the slope resilience index.

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