A method for estimating rainfall-induced slope failure probability considering climate change

Abstract

The present application relates to a kind of considering climate change's rainfall slope instability probability estimation method, which includes following five steps: (I) the collection and downscaling processing of future daily rainfall data in global climate model;(II) the time-varying characteristic quantification of non-stationary rainfall variable under the influence of climate change;(III) the establishment of rainfall interval-rainfall duration alternative random process updating model considering climate change;(IV) rainfall slope vulnerability analysis considering rock-soil parameter uncertainty;(V) estimate the slope instability probability based on total probability theorem convolution rainfall disaster curve and slope vulnerability curve in future predefined time.Compared with prior art, the present application proposes a kind of considering climate change's rainfall slope instability probability estimation new method, realizes the quantitative characterization of non-stationary rainfall caused by climate change effect, and provides an effective method for more accurate estimation of future rainfall slope instability probability.

Description

Technical Field

[0001] This invention belongs to the field of engineering geology, and in particular relates to a method for estimating the probability of slope instability due to rainfall, taking into account climate change. Background Technology

[0002] With the intensification of global climate change, the frequency and intensity of rainfall events are showing a non-stationary upward trend. Therefore, establishing a method for estimating the probability of slope instability due to rainfall that takes into account climate change is of great significance for reducing future landslide risks.

[0003] However, existing methods for estimating the probability of slope instability due to rainfall typically focus on the probability of slope instability under a single rainfall event or the annual probability of slope instability, failing to fully consider the time-varying characteristics of rainfall caused by climate change, i.e. ignoring the non-stationary increase in the frequency and intensity of rainfall events over time. Summary of the Invention

[0004] Aiming to address the lack of consideration for non-stationary rainfall variations caused by climate change in existing methods for estimating slope instability probability, and given the background technology, there is an urgent need to develop a new method for estimating the probability of slope instability due to rainfall that takes into account climate change. This method would quantify the impact of climate change on the non-stationary growth effect of rainfall, achieve an accurate assessment of the probability of slope instability due to rainfall, and provide a solid theoretical foundation and practical guidance for the effective management of landslide risks in the future.

[0005] The purpose of this invention is to provide a new method for estimating the probability of slope instability due to rainfall that takes into account climate change, thereby solving the problem that the existing technology does not take into account the non-stationary increase in rainfall frequency and intensity caused by climate change.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for estimating the probability of slope instability due to rainfall while taking into account climate change includes the following steps:

[0008] (I) Collection and downscaling of daily rainfall data to obtain daily-scale rainfall data;

[0009] (II) Quantification of the time-varying characteristics of non-stationary rainfall variables under the influence of climate change:

[0010] (III) Establish an update model for a stochastic process of alternating rainfall intervals and durations that takes into account climate change:

[0011] The rainfall process within the future scheduled time period can be described as: "Rainfall interval ( D ) — Duration of rainfall ( W —Rainfall intensity during rainfall duration ( I The loop of ")";

[0012] An alternating stochastic process update model for rainfall events, taking into account climate change, was constructed, where the rainfall interval ( D ) and duration of rainfall ( W Alternately;

[0013] (IV) Vulnerability analysis of rain-affected slopes considering uncertainties in geotechnical parameters;

[0014] (V) Estimation of slope instability probability based on the law of total probability during rainfall:

[0015] Based on the law of total probability, by convolving the rainfall disaster curve and the slope vulnerability curve, the slope vulnerability curve can be obtained in the future within a predefined time interval. t 0, t inv The probability of failure within ] .

[0016] Details are as follows:

[0017] A method for estimating the probability of slope instability due to rainfall while taking into account climate change includes the following steps:

[0018] (I) Collection and downscaling of future daily precipitation data in the Global Climate Model (GCM):

[0019] First, diurnal precipitation data for a predetermined future time period were collected from multiple global climate models (GCMs) during the Sixth Coupled Model Intercomparison Project (CMIP6). While GCMs simulate large-scale global climate models, their low spatial resolution (typically 100 to 300 kilometers between grid points) makes it difficult to capture local-scale climate change. Therefore, this invention employs bias correction and statistical downscaling methods using quantile mapping (QM) and quantile increment mapping (QDM) to reduce the bias between GCM predicted data and local observational data, thereby obtaining bias-corrected future diurnal precipitation data for the local study area.

[0020] To estimate the bias-corrected GCM data, it is necessary to estimate the cumulative distribution function (CDF) corresponding to the historical and future predicted daily rainfall data from the GCM simulation, denoted as [description of CDF]. F s,h,m and F s,p,m The CDF of historical daily rainfall data from local rain gauges is denoted as... F o,h,m , where subscript m This refers to a specific month. Based on the QM method, the bias-corrected daily rainfall data for GCM can be calculated as follows:

[0021] (1)

[0022] In the formula, This indicates that the bias-corrected climate variables (e.g., daily rainfall as described in this invention) associated with future GCM forecasts correspond to time variables. t ,in t Defined as a date vector, represented as t = { t year , t month , t day},in, t ∈ [ t 0, t d ]. In the date vector t month Equal to the aforementioned subscript m .

[0023] Furthermore, the relative changes Δ of climate variables in the GCM output between historical and future data. s It can be quantified as:

[0024] (2)

[0025] Based on the above equations (1) and (2), the deviation correction GCM according to the QDM method can be expressed as:

[0026] (3)

[0027] The bias-corrected daily precipitation data of GCM obtained based on the QDM method is used to quantify the time-varying characteristics of non-stationary precipitation under the influence of climate change in step (II) below.

[0028] (II) Quantification of the time-varying characteristics of non-stationary rainfall variables under the influence of climate change:

[0029] Based on the future diurnal rainfall data obtained in step (I), the duration of rainfall for each rainfall event is calculated. W ), corresponding rainfall intensity ( I ) and the time interval between two rainfall events ( D Since the future diurnal precipitation data in the GCMs used have fully accounted for the impacts of climate change, subsequent analysis of the obtained precipitation characteristics ( D、W , I The processing of rainfall data can effectively reflect the non-stationary growth characteristics of rainfall caused by climate change.

[0030] The rainfall characteristics ( D、W , IThe data were separated by month, and time-varying statistical parameters for each month across the year were calculated using moving average and standard deviation methods. A linear model was then fitted to obtain the rainfall characteristics under the influence of climate change. D、W , I The monthly variation trend across years.

[0031] Furthermore, in order to represent rainfall characteristics ( D、W , I The seasonality of rainfall is described by using a step function to describe the monthly variation of rainfall characteristics in a specific year, which assumes that rainfall characteristics remain constant in a certain month of a specific year.

[0032] Therefore, the non-stationary increase in rainfall caused by climate change, in which the rainfall interval ( D ) and duration of rainfall ( W The time-varying statistical characteristics of ) can be expressed by mathematical formulas (4) and (5) as follows:

[0033] (4)

[0034] (5)

[0035] In the formula, l D ( t )and l W ( t ) respectively represent the rainfall interval ( D ) and duration of rainfall ( W The time-varying average recurrence rate of ) l D and l W 0 represents the rainfall interval at the start of the future scheduled time period ( D ) and duration of rainfall ( W The initial average recurrence rate; F D and F W These represent the intervals with and from rainfall ( D ) and duration of rainfall ( W The increase or decrease in the recurrence rate. Furthermore, to clearly describe the relationship with the rainfall interval ( D ) and duration of rainfall ( W The relevant time-varying statistical parameters, in formulas (4) and (5), are time-varying statistical parameters at different... t day The following can have the same value.

[0036] Furthermore, the intensity of rainfall caused by climate change ( I The time-varying statistical characteristics of ) can be expressed by mathematical formulas (6) and (7) as follows:

[0037] (6)

[0038] (7)

[0039] In the formula, m I (t) and s I (t) These represent the initial mean and standard deviation of rainfall intensity within the analyzed time period, respectively; while F μI and F σI These represent the rates of change of the mean and standard deviation of rainfall intensity, respectively.

[0040] (III) Establish an update model for a stochastic process of alternating rainfall intervals and durations that takes into account climate change:

[0041] The rainfall process within the future scheduled time period can be described as: "Rainfall interval ( D ) — Duration of rainfall ( W —Rainfall intensity during rainfall duration ( I The invention further constructs an alternating stochastic process update model for rainfall processes that considers climate change, wherein the rainfall interval ( D ) and duration of rainfall ( W ) alternately. Based on the rainfall interval quantified by formulas (4) and (5) in step (II) D ) and duration of rainfall ( W The time-varying characteristics of rainfall intervals due to climate change ( D ) and duration of rainfall ( W probability distribution of ) f D ( t )and f W ( t ) can be represented as time-varying exponential distributions, as expressed by formulas (8) and (9) as follows:

[0042] (8)

[0043] (9)

[0044] Furthermore, based on the rainfall intensity quantified by formulas (6) and (7) in step (II), I Time-varying statistical characteristics (mean) m I (t) and standard deviation sI (t) ), taking into account the rainfall intensity during rainfall duration due to climate change ( I probability distribution of ) f I(t) ( i It can be represented as a non-homogeneous Gamma distribution with time-varying characteristics, as expressed by formula (10) as follows:

[0045] (10)

[0046] In the formula, α I (t ) = [ m I ( t ) / s I ( t )] 2 For time-varying shape parameters of a non-homogeneous Gamma distribution; β I ( t ) = [ s I ( t )] / m I ( t ) represents the time-varying scale parameter.

[0047] Therefore, this alternating stochastic update process model can effectively take into account the rainfall characteristics in step (II). D、W , I The time-varying statistical characteristics of precipitation processes reflect the impact of climate change on precipitation processes.

[0048] Under the influence of climate, the maximum rainfall intensity within a predetermined future period is defined as I max = { I 1, I 2, …, I n The cumulative distribution function (CDF) of time-varying maximum rainfall intensity can be described as follows:

[0049] (11)

[0050] Furthermore, under the condition of non-stationary time-varying rainfall caused by climate change, the probability distribution of the maximum rainfall intensity in formula (11) is related to the rainfall frequency, i.e., the number of rainfall events. n The frequency of rainfall is related to the arrival time of each rainfall event. According to the law of total probability, the cumulative distribution function (CDF) of the time-varying maximum rainfall intensity can be obtained as:

[0051] (12)

[0052] (IV) Vulnerability analysis of rainfall-affected slopes considering uncertainties in geotechnical parameters:

[0053] Safety factor of slope under rainfall Fs The calculation can be performed using the Bishop method, as shown in formula (13):

[0054] (13)

[0055] In the formula, the sliding body of the slope is divided into N x A strip of earth; W j For soil strips j Total weight; B j For soil strips j The width; U j ( I max , k s () indicates the maximum rainfall intensity I max and saturated hydraulic conductivity k s Affected soil strips j The pore air and water pressure at the bottom midpoint can be obtained using Richards' seepage theorem; d j It is a type of earthen strip. j The slope angle at the bottom. It is worth noting that the safety factor of the slope is calculated using formula (13). F s It needs to be iterated.

[0056] Furthermore, considering the uncertainty of soil and rock parameters, the log-normal distribution is used to account for the uncertainty of soil and rock parameters (i.e., cohesion, internal friction angle, unit weight and hydraulic conductivity). Monte Carlo simulation (MCS) is used to calculate the slope instability probability under a given rainfall disaster intensity, and the commonly used log-normal distribution is used for fitting, as shown in formula (14):

[0057] (14)

[0058] In the formula, F s(X) is the safety factor of the slope under rainfall, which can be calculated by formula (13), where X is a random variable (i.e., cohesion, internal friction angle, unit weight and hydraulic conductivity); Φ(·) represents the cumulative distribution function of the standard normal distribution; m s and s s These represent the mean and standard deviation of the slope vulnerability curve, respectively.

[0059] (V) Estimation of the probability of slope instability due to rainfall based on the law of total probability

[0060] Based on the law of total probability, convolving the rainfall disaster curve and the slope vulnerability curve, we can obtain the slope's vulnerability over a predefined time interval in the future. t 0, t inv The failure probability within ] is specifically expressed mathematically as shown in formula (15):

[0061] (15)

[0062] In the formula, U i Rainfall intensity i The maximum number of points; It is the vulnerability curve of the slope under the action of rainfall; This is equivalent to the differential of the rainfall disaster curve.

[0063] In summary, the beneficial effects of this invention are as follows: By extracting and processing diurnal rainfall data affected by climate change in CMIP6, time-varying statistical parameters of future rainfall characteristics are obtained, thereby establishing an alternating stochastic process update model of rainfall interval-rainfall duration considering climate change. This enables accurate assessment of non-stationary rainfall hazards caused by climate change. Furthermore, based on the law of total probability, the non-stationary rainfall hazard curve is convolved with the slope vulnerability curve, achieving accurate assessment of the probability of slope instability due to rainfall considering climate change. Compared with traditional methods, this invention can dynamically reflect the impact of future climate change on rainfall, providing more accurate input data for rainfall-induced landslide hazard risk assessment. Simultaneously, it cleverly combines short-term slope instability under rainfall with long-term climate change impacts, providing a solid theoretical foundation and practical guidance for effective management of future landslide risks and adaptive responses to climate change. Attached Figure Description

[0064] Figure 1 A schematic diagram of the process of this invention.

[0065] Figure 2 Assessment results of rainfall-related disasters in Lishui City, Zhejiang Province.

[0066] Figure 3Results of slope vulnerability assessment during rainfall.

[0067] Figure 4 Table 1. Probability distribution types of slope soil and rock parameters and related parameter values.

[0068] Figure 5 Table 2. Estimated probability of slope instability due to rainfall considering climate change. Detailed Implementation

[0069] The technical solution of the present invention will be described in detail below with specific examples. Parts not described, such as the values ​​of slope soil and rock parameters, the number of times random rainfall sequences are generated, and the number of times slope seepage stability is calculated, need to be designed in combination with the actual situation. Under the guidance of the present invention, those skilled in the art can carry out construction through experiments and calculations according to existing conditions without affecting the implementation of the invention.

[0070] This invention verifies the feasibility and effectiveness of its method in estimating the probability of slope instability caused by rainfall through a practical application on a generalized slope in Lishui City, Zhejiang Province.

[0071] This implementation method is specifically divided into five steps, see Figure 1 As shown, the specific content is as follows:

[0072] (I) Collection and downscaling of future daily rainfall data in GCM:

[0073] First, daily precipitation data for predetermined future time periods (e.g., 2030, 2050, and 2100) from multiple global climate models (GCMs) were collected from the Sixth Coupled Model Intercomparison Project (CMIP6). In this example, data from three GCM models—ACCESS-ESM1-5, CESM2-WACCM, and CMCC-CM2-SR5—were selected for analysis.

[0074] Secondly, based on formulas (1), (2) and (3), bias correction and statistical downscaling methods such as quantile mapping (QM) and quantile increment mapping (QDM) are used to process these GCM data to obtain bias-corrected future daily-scale rainfall data for Lishui City, Zhejiang Province.

[0075] (II) Quantification of the time-varying characteristics of non-stationary rainfall variables under the influence of climate change:

[0076] By processing bias-corrected future diurnal rainfall data, the time-varying statistical parameters of the rainfall variable are calculated. Specifically, the rainfall interval is calculated based on formula (4). D Time-varying average recurrence rate l D ( t The duration of rainfall is calculated based on formula (5).W Time-varying average recurrence rate l W ( t ), and calculate rainfall intensity based on formulas (6) and (7) respectively. I mean and standard deviation m I ( t )and s I ( t These time-varying statistical parameters effectively reflect the impact of climate change on rainfall patterns, particularly the non-stationary increase in rainfall frequency and intensity.

[0077] (III) Establish an update model for a stochastic process of alternating rainfall intervals and durations that takes into account climate change:

[0078] Based on the alternating stochastic process update model, in this invention, the rainfall process is modeled as "rainfall interval ( D - Duration of rainfall ( W Rainfall intensity () I The cyclic process of ")" is described. Based on formulas (8), (9), and (10), the probability distribution of rainfall intervals is calculated. f D ( t ), Probability distribution of rainfall duration f W ( t ) and probability distribution of rainfall intensity f I(t) ( i From these, a series of rainfall intervals were generated by sampling. t n,D The rainfall lasted for a long time t n,W and rainfall intensity I n,k This generates a random rainfall sequence for a predetermined future time period.

[0079] Furthermore, the maximum rainfall intensity within the predicted time period. I max = max{ I 1, I 2, …, I n} is defined as the rainfall disaster intensity of the current random rainfall sequence.

[0080] By repeating the above steps for 10,000 simulations, the probability distribution of maximum rainfall intensity can be obtained, and the assessment results of non-stationary rainfall disasters can be finally obtained. Figure 2As shown: Rainfall disaster assessment results in Lishui City, Zhejiang Province: (a) Comparison and verification of historical daily rainfall data from Lishui rain gauge station with downscaled and undownscaled CDF data from three GCM models; (b) Historical and future rainfall disaster curves based on downscaled daily rainfall data from three GCM models.

[0081] (IV) Vulnerability analysis of rainfall-affected slopes considering uncertainties in geotechnical parameters:

[0082] Define the range of maximum rainfall intensity and determine the random variables of soil and rock parameters (such as cohesion, angle of internal friction, unit weight, and hydraulic conductivity). Select an appropriate probability distribution type for these soil and rock parameters and determine their distribution parameters, such as... Figure 4 As shown in Table 1.

[0083] Next, for each selected maximum rainfall intensity I max Based on GeoStudio software, slope seepage stability analysis was performed, and the results were calculated for a given maximum rainfall intensity. I max Safety factor of the lower slope.

[0084] Repeat this process 10,000 times to obtain each maximum rainfall intensity. I max Failure probability of the lower slope. The vulnerability curve of the slope is obtained using formula (14) and the log-normal distribution fitting method, see... Figure 3 As shown: Results of slope vulnerability assessment during rainfall: (a) Slope model; (b) Rainfall vulnerability curve.

[0085] (V) Estimation of slope instability probability based on the law of total probability during rainfall:

[0086] Based on the total probability formula (15), the non-stationary rainfall disaster assessment results obtained in step (III) and the rainfall slope vulnerability analysis results obtained in step (IV) are convolved to calculate the slope instability probability within a predetermined future time period, such as... Figure 5 The slope instability probability is shown in Table 2. This probability takes into account the impact of future climate change.

[0087] The above-described embodiments are examples of the present invention. The present invention is not limited to these examples and may be combined with, or partially replaced by, known, conventional or publicly known techniques. Furthermore, the present invention includes variations readily apparent to those skilled in the art.

Claims

1. A method for estimating the probability of slope instability considering climate change, characterized in that, Comprising the following steps: (I) Collection and downscaling of daily rainfall data, obtaining daily scale rainfall data; (II) Quantification of time-varying characteristics of non-stationary rainfall variables under the influence of climate change: (III) Establishment of a rainfall interval-rainfall duration alternating random process updating model considering climate change: The future rainfall process in a predetermined time period can be described as a cycle of "rainfall interval (D) - rainfall duration (W) - rainfall intensity (I) " in the rainfall duration; A rainfall process alternating random process updating model considering climate change is constructed, in which rainfall interval (D) and rainfall duration (W) are alternated; (IV) Rainfall slope vulnerability analysis considering uncertainty of rock-soil parameters; (V) Rainfall slope instability probability estimation based on the total probability theorem: Based on the total probability theorem, the convolution of the rainfall hazard curve and the slope vulnerability curve is obtained, and the failure probability of the slope in the future predefined time interval [t0, t inv ] is obtained. In step (II): Based on the daily scale rainfall data obtained in step (I), the rainfall duration (W) of each rainfall event, the corresponding rainfall intensity (I), and the time interval (D) between two rainfall events are calculated to obtain the rainfall characteristics (D, W, I); The rainfall characteristics (D, W, I) data are separated by month, and the moving average and standard deviation method is used to calculate the time-varying statistical parameters of each month across years, and a linear model is used for fitting, thereby obtaining the cross-year monthly variation trend of rainfall characteristics (D, W, I) under the influence of climate change; Further, to represent the seasonality of rainfall characteristics (D, W, I), a step function is used to describe the monthly variation of rainfall characteristics in a specific year, i.e. it is assumed that in a certain month of a certain year, the rainfall characteristics remain constant; Thus, the non-stationary growth of rainfall caused by climate change, in which the time-varying statistical characteristics of rainfall interval (D) and rainfall duration (W) can be expressed by mathematical formulas (4) and (5) as follows: where λ D (t) and λ W (t) represent the time-varying average return periods of the rainfall interval (D) and the rainfall duration (W), respectively; λ D and λ W0 represent the initial average return periods of the rainfall interval (D) and the rainfall duration (W) at the beginning of the future predetermined time period, respectively; Φ D and Φ W represent the increasing / decreasing amplitudes associated with the return periods of the rainfall interval (D) and the rainfall duration (W), respectively, in which the time-varying statistical parameters can have the same values at different t day . Further, the time-varying statistical characteristics of rainfall intensity (I) caused by climate change are expressed by mathematical formulas (6) and (7) as follows: where μ I (t) and σ I (t) are the initial mean and standard deviation of the rainfall intensity in the analyzed time period, respectively; while Φ μI and Φ σI are the rates of change of the mean and standard deviation of the rainfall intensity, respectively. In step (III): Based on the time-varying characteristics of the rainfall interval (D) and the rainfall duration (W) quantified in Equations (4) and (5) in Step (II), the probability distribution f D (t) and f W (t) can be expressed as time-varying exponential distributions, as expressed in Equations (8) and (9) as follows: Further, based on the time-varying statistical characteristics (mean μ I (t) and standard deviation σ I (t)) of the rainfall intensity (I) quantified in step (II) by equations (6) and (7), the probability distribution f I(t) (i) of the rainfall intensity (I) within the rainfall duration considering climate change can be represented as a non-homogeneous Gamma distribution with time-varying characteristics, as expressed in equation (10) as follows: where α I (t) = [μ I (t) / σ I (t)] 2 is the time-varying shape parameter of the non-homogeneous Gamma distribution; β I (t) = [σ I (t)] / μ I (t) is the time-varying scale parameter; Thus, this alternating random updating process model can effectively consider the time-varying statistical characteristics of rainfall characteristics (D, W, I) in step (II), reflecting the influence of climate change on the rainfall process; Under the climate impact, the maximum rainfall intensity is defined as I max = {I1, I2,..., In} over a predetermined time period in the future, and the cumulative distribution function (CDF) of the time-varying maximum rainfall intensity is described as: n F(I) = {F(I1), F(I2),..., F(In)}. Further, under the condition of non-stationary time-varying rainfall caused by climate change, the probability distribution of the maximum rainfall intensity of formula (11) is related to the rainfall frequency, i.e. the number of rainfall events n, and the rainfall frequency depends on the arrival time of each rainfall event; according to the total probability theorem, the cumulative distribution function CDF of the time-varying maximum rainfall intensity is: 2.The method of claim 1, wherein, In step (I): Daily scale rainfall data in a future predetermined time period is collected from multiple global climate models (GCMs) in the sixth international coupled model intercomparison project (CMIP6).

3. The method of claim 2, wherein, In step (I): The bias correction and statistical downscaling method of quantile mapping (QM) and quantile delta mapping (QDM) is used to reduce the bias between the prediction data of global climate models (GCMs) and local observation data, obtaining the future daily scale rainfall data in the local study area after bias correction.

4. The method of claim 3, wherein, In step (I): To estimate bias-corrected global climate model (GCM) prediction data, it is necessary to estimate the cumulative distribution functions (CDFs) corresponding to the historical and future predicted daily rainfall data simulated by the global climate model (GCM), denoted as F s,h,m and F s,p,m respectively, and the CDF of the observed historical daily rainfall data from local rain gauges, denoted as F o,h,m where the subscript m refers to a specific month; the bias-corrected GCM daily rainfall data is calculated according to the QM method as: where θ s,p (t) denotes the bias-corrected climate variable corresponding to time variable t associated with future GCM predictions, where t is defined as a date vector, denoted as t = {t year ,t month ,t day}, where t e [t0, t d ], t month in the date vector is equal to the aforementioned subscript m; Further, the relative change Δ of the climate variable in the Global Climate Model (GCM) output between historical and future data s may be quantified as:

5. The method of claim 4, wherein, In step (I): Based on the above equations (1) and (2), the bias-corrected global climate model (GCM) according to the QDM method is represented as: The bias-corrected GCM daily rainfall data obtained based on the QDM method is used for quantifying the time-varying characteristics of non-stationary rainfall under climate change in the following step (II).

6. The method of claim 1, wherein, In step (IV): Safety factor F of a slope under rainfall action s The calculation is made by the Bishop method, as shown in equation (13): In the formula, the sliding body of the slope is divided into N x soil strips; W j is the total weight of the soil strip j; B j is the width of the soil strip j; U j (I max ,k s ) represents the pore air and water pressure at the midpoint of the bottom of the soil strip j, which is affected by the maximum rainfall intensity I max and the saturated hydraulic conductivity k s ; δ j is the inclination angle of the bottom of the soil strip j, and it is worth noting that the safety factor F s of the slope is calculated by formula (13) and needs to be iterated; Furthermore, considering the uncertainty of geotechnical parameters, the Monte Carlo Simulation (MCS) is used to calculate the slope instability probability under a given rainfall disaster intensity by using the lognormal distribution to consider the uncertainty of geotechnical parameters, and the commonly used lognormal distribution is used for fitting, as shown in equation (14): where F s (X) is the safety factor of the slope under rainfall action, calculated by equation (13), where X is a random variable; Φ(·) represents the cumulative distribution function of the standard normal distribution; μ s and σ s represent the mean and standard deviation of the slope vulnerability curve, respectively.

7. The method of claim 1, wherein, In step (V): The mathematical expression of the failure probability of the slope in a predefined time interval [t0, t inv ] in the future is shown in equation (15): where U i is the upper limit of integration of the rainfall intensity i; P(F s (X)-1 < 0 | I max = i) is the vulnerability curve of the slope under rainfall action; is equivalent to the derivative of the rainfall disaster curve.

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