Rainfall slope instability probability estimation method considering climate change

Abstract

The invention relates to a rainfall slope instability probability estimation method considering climate change. The method comprises the following five steps: (I) collection and downscaling processing of rainfall data of a future day in a global climate model; (II) time-varying characteristic quantification of a non-stationary rainfall variable under the influence of climate change; (III) establishing a rainfall interval-rainfall duration alternating random process updating model capable of considering climate change; (IV) analyzing the vulnerability of the rainfall side slope by considering the uncertainty of rock and soil parameters; and (V) estimating the slope instability probability based on the total probability theorem convolution rainfall disaster curve and the slope vulnerability curve in the future predefined time. Compared with the prior art, the new rainfall slope instability probability estimation method considering the climate change is provided, quantitative characterization of non-stationary rainfall caused by the climate change effect is achieved, and an effective method is provided for more accurate estimation of the rainfall slope instability probability in the future.

Description

Technical Field

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

[0002] In recent years, extreme rainfall events have occurred frequently, resulting in frequent slope instability disasters, causing casualties and property losses. With the intensification of global climate change, the frequency and intensity of rainfall events have shown a non-steady growth trend, and the probability of slope instability caused by rainfall in the future will increase significantly. Therefore, establishing a method for estimating the probability of slope instability caused by rainfall considering climate change is of great significance for reducing the risk of landslides in the future.

[0003] However, existing methods for estimating the probability of slope instability due to rainfall usually focus on the probability of slope instability under a single rainfall event or the annual probability of slope instability, and fail to fully consider the time-varying characteristics of rainfall caused by climate change, that is, they ignore the characteristics that the frequency and intensity of rainfall events increase non-steadily over time. Summary of the invention

[0004] The aim is to solve the problem that the existing slope instability probability estimation methods lack consideration of the non-stationary changes in rainfall caused by climate change. In view of the background technology, there is an urgent need to develop a new method for estimating the probability of rainfall slope instability taking into account climate change, so as to quantify the impact of climate change on the non-stationary growth effect of rainfall and achieve an accurate assessment of the probability of rainfall slope instability, which will provide a solid theoretical basis and practical guidance for the effective management of landslide risks in the future.

[0005] The purpose of the present invention is to provide a new method for estimating the probability of slope instability caused by rainfall taking into account climate change, so as to solve the problem that the existing technology does not take into account the non-steady growth of rainfall frequency and intensity caused by climate change.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

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

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

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

[0010] (III) Establish a random process update model of rainfall interval-rainfall duration alternation that can take climate change into account:

[0011] The rainfall process in the future predetermined time period can be described as a cycle of “rainfall interval (D) – rainfall duration (W) – rainfall intensity within the rainfall duration (I)”;

[0012] An alternating random process update model of rainfall process considering climate change is constructed, in which the rainfall interval (D) and rainfall duration (W) are alternating;

[0013] (IV) Rainfall slope vulnerability analysis considering geotechnical parameter uncertainties;

[0014] (V) Estimation of the probability of slope instability due to rainfall based on the total probability theorem:

[0015] Based on the total probability theorem, the rainfall hazard curve and the slope vulnerability curve are convolved to obtain the slope in the future predefined time interval [t0,t inv ] within the failure probability.

[0016] Details are as follows:

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

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

[0019] First, daily-scale rainfall data of multiple global climate models (GCMs) in a predetermined time period in the future are collected from the sixth international coupled model intercomparison project (CMIP6). GCMs simulate large-scale global climate patterns, but due to the low spatial resolution (usually 100 to 300 kilometers between grid points), it is difficult to capture climate change at the local scale. To this end, the present invention adopts the bias correction and statistical downscaling methods of quantile mapping (QM) and quantile delta mapping (QDM) to reduce the deviation between GCM prediction data and local observation data, thereby obtaining bias-corrected future daily-scale rainfall data in the local study area.

[0020] In order 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 simulated by GCM, denoted by F s,h,m and F s,p,m , and the CDF of the observed historical daily rainfall data from the local rain gauge, denoted as F o,h,m , where the subscript m refers to a specific month. According to the QM method, the bias-corrected GCM daily rainfall data can be calculated as:

[0021]

[0022] In the formula, The bias-corrected climate variable associated with the future GCM prediction (e.g., daily rainfall in the present invention) corresponds to the time variable t, where t is defined as a date vector, represented by t = {tyear ,t month ,t day}, where t∈[t0,t d ]. t in the date vector month Equal to the aforementioned subscript m.

[0023] In addition, the relative change in climate variables in GCM output between historical and future data Δ s It can be quantified as:

[0024]

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

[0026]

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

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

[0029] Based on the future daily 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. Since the future daily rainfall data in the GCMs used have fully considered the impact of climate change, the subsequent processing of the obtained rainfall characteristics (D, W, I) can effectively reflect the non-stationary growth characteristics of rainfall caused by climate change.

[0030] The rainfall characteristics (D, W, I) data are separated by month, and the time-varying statistical parameters of each month across the year are calculated using the moving average and standard deviation methods. The linear model is then used to fit the data, thereby obtaining the monthly variation trends of the rainfall characteristics (D, W, I) across the year under the influence of climate change.

[0031] Furthermore, 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 within a certain month in a specific year, the rainfall characteristics remain constant.

[0032] Therefore, 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:

[0033]

[0034] In the formula, λ D(t) and λ W (t) represents the time-varying average recurrence rate of rainfall interval (D) and rainfall duration (W), respectively; λ D and λ W0 They represent the initial average recurrence rates of rainfall interval (D) and rainfall duration (W) at the beginning of the future scheduled time period; Φ D and Φ W They represent the increase or decrease of the recurrence rate of rainfall interval (D) and rainfall duration (W). In addition, in order to clearly describe the time-varying statistical parameters related to rainfall interval (D) and rainfall duration (W), in formulas (4) and (5), the time-varying statistical parameters are expressed at different t day The following can have the same value.

[0035] Furthermore, the time-varying statistical characteristics of rainfall intensity (I) caused by climate change can be expressed by mathematical formulas (6) and (7) as follows:

[0036]

[0037] In the formula, μ I (t) and σ I (t) represent the initial mean and standard deviation of rainfall intensity during the analyzed period; and Φ μI and Φ σI represent the rate of change of the mean and standard deviation of rainfall intensity, respectively.

[0038] (III) Establish a random process update model of rainfall interval-rainfall duration alternation that can take climate change into account:

[0039] The rainfall process in the future predetermined time period can be described as a cycle of "rainfall interval (D) - rainfall duration (W) - rainfall intensity within the rainfall duration (I)". The present invention further constructs an alternating random process update model for the rainfall process considering climate change, in which the rainfall interval (D) and rainfall duration (W) are alternating. Based on the time-varying characteristics of the rainfall interval (D) and rainfall duration (W) quantified by formulas (4) and (5) in step (II), the probability distribution f of the rainfall interval (D) and rainfall duration (W) considering climate change is D (t) and f W (t) can be expressed as time-varying exponential distributions, such as formulas (8) and (9) as follows:

[0040]

[0041] Furthermore, based on the time-varying statistical characteristics (mean μ I (t) and standard deviation σ I(t)), the probability distribution of rainfall intensity (I) within the rainfall duration considering climate change f I(t) (i) can be expressed as a non-homogeneous Gamma distribution with time-varying characteristics, as shown in formula (10):

[0042]

[0043] In the formula, α I (t) = [μ I (t) / σ I (t)] 2 is the time-varying shape parameter of the nonhomogeneous Gamma distribution; β I (t) = [σ I (t)] / μ I (t) is the time-varying scale parameter.

[0044] Therefore, the alternating random update process model can effectively consider the time-varying statistical characteristics of rainfall characteristics (D, W, I) in step (II), reflecting the impact of climate change on the rainfall process.

[0045] Under the influence of climate, the maximum rainfall intensity in the future predetermined period is defined as I max ={I1,I2,…,I n}. The cumulative distribution function (CDF) of the time-varying maximum rainfall intensity can be described as:

[0046] F Imax( t ) (i) = P[Imax(t)≤i]

[0047] =P[max(I1(t1),I1(t1),...,I1(t1))≤i] (11)

[0048] =P[I1(t1)≤i,I2(t2)≤i,...,I n (t n )]

[0049] Furthermore, under the non-stationary time-varying conditions of rainfall caused by climate change, the probability distribution of the maximum rainfall intensity in formula (11) is related to the rainfall frequency, that is, 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 can be obtained as:

[0050]

[0051] (IV) Rainfall slope vulnerability analysis considering geotechnical parameter uncertainty:

[0052] The safety factor Fs of the slope under rainfall can be calculated by the Bishop method, as shown in formula (13):

[0053]

[0054] In the formula, the sliding body of the slope is divided into N x A soil strip; W j is the total weight of soil strip j; B j is the width of soil strip j; U j (I max ,k s ) indicates the maximum rainfall intensity I max and saturated hydraulic conductivity k s The pore air and water pressures at the bottom midpoint of the affected soil strip j can be obtained by Richards’ seepage theorem; δ j is the inclination angle of the bottom of soil strip j. It is worth noting that the safety factor F of the slope is calculated by formula (13): s Iteration is required.

[0055] Furthermore, taking into account the uncertainty of geotechnical parameters, the log-normal distribution is used to consider the uncertainty of geotechnical parameters (ie, cohesion, internal friction angle, gravity and hydraulic conductivity), and Monte Carlo simulation (MCS) is used to calculate the probability of slope instability under a given rainfall disaster intensity, and the commonly used log-normal distribution is used for fitting, as shown in formula (14):

[0056]

[0057] 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 (ie, cohesion, internal friction angle, gravity and hydraulic conductivity); 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 fragility curve, respectively.

[0058] (V) Estimation of the probability of slope instability due to rainfall based on the total probability theorem

[0059] Based on the total probability theorem, the convolution rainfall hazard curve and the slope vulnerability curve can be used to obtain the slope vulnerability curve in the future predefined time interval [t0,t inv ], the specific mathematical expression is shown in formula (15):

[0060]

[0061] Where U iis the integral upper limit of rainfall intensity i; P(F s (X)-1<0|I max =i) is the vulnerability curve of the slope under rainfall; It is equivalent to the differential of the rainfall hazard curve.

[0062] In summary, the beneficial effects of the present invention are as follows: by extracting and processing the daily-scale rainfall data affected by climate change in CMIP6, the time-varying statistical parameters of future rainfall characteristics are obtained, thereby establishing an alternating random process update model of rainfall interval-rainfall duration considering climate change, and realizing an accurate assessment of the non-stationary rainfall disaster caused by climate change. Furthermore, based on the total probability theorem, the non-stationary rainfall disaster curve is convolved with the slope vulnerability curve, and an accurate assessment of the probability of rainfall slope instability considering climate change is realized. Compared with traditional methods, the present invention can dynamically reflect the impact of future climate change on rainfall, and provide more accurate input data for rainfall landslide disaster risk assessment; at the same time, it can cleverly combine the slope instability under short-term rainfall with the long-term climate change impact, and provide a solid theoretical basis and practical guidance for the effective management of future landslide risks and adaptive response to climate change. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 Schematic diagram of the process of the present invention.

[0064] Figure 2 Rainfall disaster assessment results in Lishui City, Zhejiang Province.

[0065] Figure 3 Results of rainfall slope vulnerability assessment.

[0066] Figure 4 Table 1 Probability distribution types of slope geotechnical parameters and related parameter values.

[0067] Figure 5 Table 2 Estimation results of the probability of slope instability due to rainfall considering climate change. DETAILED DESCRIPTION

[0068] The technical solution of the present invention is described in detail below in conjunction with specific examples. Parts not described, such as the values ​​of slope geotechnical parameters, the number of times random rainfall sequences are generated, the number of times the slope seepage stability is calculated, etc., need to be designed in combination with actual conditions. 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.

[0069] The present invention verifies the feasibility and effectiveness of the method in estimating the probability of slope instability caused by rainfall by applying it to the generalized slopes in Lishui City, Zhejiang Province.

[0070] This implementation method is specifically divided into five steps. Figure 1 The specific contents are as follows:

[0071] (I) Collection and downscaling of future daily rainfall data in GCM:

[0072] First, daily rainfall data of multiple global climate models (GCMs) in the future predetermined time periods (e.g., 2030, 2050, and 2100) are collected from the sixth international coupled model intercomparison project (CMIP6). In this example, data from three GCM models, ACCESS-ESM1-5, CESM2-WACCM, and CMCC-CM2-SR5, are selected for analysis.

[0073] Secondly, based on formulas (1), (2) and (3), bias correction and statistical downscaling methods such as quantile mapping (QM) and quantile delta mapping (QDM) were used to process these GCM data to obtain the bias-corrected future daily-scale rainfall data for Lishui City, Zhejiang Province.

[0074] (II) Quantification of time-varying characteristics of non-stationary rainfall variables under the influence of climate change:

[0075] By processing the bias-corrected future daily rainfall data, the time-varying statistical parameters of the rainfall variable are calculated. Specifically, the time-varying average recurrence rate λ of the rainfall interval D is calculated based on formula (4): D (t), the time-varying average recurrence rate λ of rainfall duration W is calculated based on formula (5) W (t), and the mean and standard deviation μ of rainfall intensity I are calculated based on formulas (6) and (7) respectively. I (t) and σ I (t). These time-varying statistical parameters effectively reflect the impact of climate change on rainfall patterns, especially the non-stationary increase in rainfall frequency and intensity.

[0076] (III) Establish a random process update model of rainfall interval-rainfall duration alternation that can take climate change into account:

[0077] Based on the alternating random process update model, in the present invention, the rainfall process is modeled as a cyclic process of "rainfall interval (D)-rainfall duration (W)-rainfall intensity (I)". Based on formulas (8), (9) and (10), the rainfall interval probability distribution f is obtained by calculation D (t), probability distribution of rainfall duration f W (t) and the probability distribution of rainfall intensity f I(t) (i) A series of rainfall intervals t are generated by sampling n,D , rainfall duration t n,W and rainfall intensity I n,k, thereby generating a random rainfall sequence within a predetermined time period in the future.

[0078] Furthermore, the maximum rainfall intensity I in the future predetermined time period max =max{I1,I2,…,I n} is defined as the rainfall hazard intensity of the current random rainfall sequence.

[0079] By repeating the above steps for 10,000 simulations, the probability distribution of the maximum rainfall intensity can be obtained, and finally the assessment results of non-stationary rainfall disasters can be obtained, see Figure 2 Shown: Results of rainfall disaster assessment in Lishui City, Zhejiang Province: (a) Comparison and verification of downscaled and un-downscaled CDF of historical daily rainfall data of Lishui rain gauge station and historical daily rainfall data of three GCM models; (b) Historical and future rainfall disaster curves of downscaled daily rainfall data based on three GCM models.

[0080] (IV) Rainfall slope vulnerability analysis considering geotechnical parameter uncertainty:

[0081] Define the maximum rainfall intensity range and determine the random variables of geotechnical parameters (such as cohesion, internal friction angle, density and hydraulic conductivity, etc.). Select appropriate probability distribution types for these geotechnical parameters and determine their distribution parameters, such as Figure 4 As shown in Table 1.

[0082] Next, for each selected maximum rainfall intensity I max , based on GeoStudio software, slope seepage stability analysis was performed and the given maximum rainfall intensity I was calculated. max Safety factor of the lower slope.

[0083] Repeat this process 10,000 times to obtain the maximum rainfall intensity I max The failure probability of the slope below is obtained by using formula (14) and the log-normal distribution fitting method, see Figure 3 Shown: Results of rainfall slope vulnerability assessment: (a) slope model; (b) rainfall vulnerability curve.

[0084] (V) Estimation of the probability of slope instability due to rainfall based on the total probability theorem:

[0085] According to 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 convoluted to obtain the probability of slope instability within a predetermined time period in the future, as follows: Figure 5 As shown in Table 2. The slope failure probability takes into account the impact of future climate change.

[0086] The above-mentioned embodiment is an example of the present invention, and the present invention is not limited to these examples, and can also be combined with known, customary or known technologies, or partially replaced with these examples. In addition, the present invention also includes modified inventions that can be easily thought of by those skilled in the art.

Claims

1. A method for estimating the probability of slope instability under rainfall considering climate change, characterized in that: The following steps are involved: (I) Collection and downscaling of daily rainfall data to obtain daily rainfall data; (II) Quantification of time-varying characteristics of non-stationary rainfall variables under the influence of climate change: (III) Establish a random process update model of rainfall interval-rainfall duration alternation that can take climate change into account: The rainfall process in the future predetermined time period can be described as a cycle of "rainfall interval (D) - rainfall duration (W) - rainfall intensity within the rainfall duration (I)"; An alternating random process update model of rainfall process considering climate change is constructed, in which the rainfall interval (D) and rainfall duration (W) are alternating; (IV) Rainfall slope vulnerability analysis considering geotechnical parameter uncertainties; (V) Estimation of the probability of slope instability due to rainfall based on the total probability theorem: Based on the total probability theorem, the rainfall hazard curve and the slope vulnerability curve are convolved to obtain the slope in the future predefined time interval [t0,t inv ] within the failure probability.

2. The method for estimating the probability of slope instability under rainfall considering climate change according to claim 1 is characterized in that: In step (I): Daily-scale rainfall data from multiple global climate models (GCMs) for a predetermined time period in the future are collected from the sixth international Coupled Model Intercomparison Project (CMIP6).

3. The method for estimating the probability of slope instability under rainfall considering climate change according to claim 1 is characterized in that: In step (I): The bias correction and statistical downscaling methods of quantile mapping (QM) and quantile delta mapping (QDM) were used to reduce the bias between the global climate model (GCM) prediction data and the local observation data, and to obtain bias-corrected future daily-scale rainfall data in the local study area.

4. The method for estimating the probability of slope instability under rainfall considering climate change according to claim 1 is characterized in that: In step (I): In order to estimate the bias-corrected GCM forecast data, it is necessary to estimate the cumulative distribution function (CDF) corresponding to the historical and future forecast daily rainfall data simulated by the GCM, denoted by F s,h,m and F s,p,m , and the CDF of the observed historical daily rainfall data from the local rain gauge, denoted as F o,h,m , where the subscript m refers to a specific month; according to the QM method, the bias-corrected GCM daily rainfall data is calculated as: In the formula, The bias-corrected climate variables associated with future GCM projections correspond to time variables t, where t is defined as a date vector, denoted as t = {t year ,t month ,t day }, where t∈[t0,t d ], t in the date vector month is equal to the aforementioned subscript m; In addition, the relative changes in climate variables in the output of global climate models (GCMs) between historical and future data, Δ s It can be quantified as:

5. The method for estimating the probability of slope instability under rainfall considering climate change according to claim 1 is characterized in that: In step (I): Based on the above equations (1) and (2), the bias-corrected global climate model (GCM) according to the QDM method is expressed as: The bias-corrected GCM daily rainfall data obtained based on the QDM method are used to quantify the time-varying characteristics of non-stationary rainfall under the influence of climate change in the following step (II).

6. The method for estimating the probability of slope instability under rainfall considering climate change according to claim 1 is characterized in that: In step (II): Based on the daily 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 rainfall characteristics (D, W, I); The rainfall characteristics (D, W, I) data are separated by month, and the time-varying statistical parameters of each month across the year are calculated using the moving average and standard deviation methods, and are fitted through a linear model to obtain the monthly variation trend of the rainfall characteristics (D, W, I) across the year under the influence of climate change; Furthermore, 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 particular year, i.e., it is assumed that within a month in a particular year, the rainfall characteristics remain constant; Therefore, 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: In the formula, λ D (t) and λ W (t) represents the time-varying average recurrence rate of rainfall interval (D) and rainfall duration (W), respectively; λ D and They represent the initial average recurrence rates of rainfall interval (D) and rainfall duration (W) at the beginning of the future scheduled time period; Φ D and Φ W They represent the increase and decrease of the rainfall interval (D) and rainfall duration (W) recurrence rate. In formulas (4) and (5), the time-varying statistical parameters are day The following can have the same value; Furthermore, the time-varying statistical characteristics of rainfall intensity (I) caused by climate change can be expressed by mathematical formulas (6) and (7) as follows: In the formula, μ I (t) and σ I (t) represent the initial mean and standard deviation of rainfall intensity during the analyzed period; and Φ μI and Φ σI represent the rate of change of the mean and standard deviation of rainfall intensity, respectively.

7. The method for estimating the probability of slope instability under rainfall considering climate change according to claim 1 is characterized in that: In step (III): Based on the time-varying characteristics of rainfall interval (D) and rainfall duration (W) quantified by equations (4) and (5) in step (II), the probability distribution of rainfall interval (D) and rainfall duration (W) considering climate change is f D (t) and f W (t) can be expressed as time-varying exponential distributions, such as formulas (8) and (9) as follows: Furthermore, based on the time-varying statistical characteristics (mean μ I (t) and standard deviation σ I (t)), the probability distribution of rainfall intensity (I) within the rainfall duration considering climate change f I(t) (i) can be expressed as a non-homogeneous Gamma distribution with time-varying characteristics, as shown in formula (10): In the formula, α I (t) = [μ I (t) / σ I (t)] 2 is the time-varying shape parameter of the nonhomogeneous Gamma distribution; β I (t)=[σ I (t)] / μ I (t) is the time-varying scale parameter; Therefore, the alternating random update process model can effectively consider the time-varying statistical characteristics of rainfall characteristics (D, W, I) in step (II), reflecting the impact of climate change on the rainfall process; Under the influence of climate, the maximum rainfall intensity in the future predetermined period is defined as I max ={I1,I2,…,I n }, the cumulative distribution function (CDF) of the time-varying maximum rainfall intensity is described as: Furthermore, under the non-stationary time-varying conditions of rainfall caused by climate change, the probability distribution of the maximum rainfall intensity in formula (11) is related to the rainfall frequency, that is, 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 obtained as:

8. The method for estimating the probability of slope instability under rainfall considering climate change according to claim 1 is characterized in that: In step (IV): Safety factor F of slope under rainfall s The calculation is performed using the Bishop method, as shown in formula (13): In the formula, the sliding body of the slope is divided into N x A soil strip; W j is the total weight of soil strip j; B j is the width of soil strip j; U j (I max ,k s ) indicates the maximum rainfall intensity I max and saturated hydraulic conductivity k s The pore air and water pressures at the bottom midpoint of the affected soil strip j are obtained by Richards’ seepage theorem; δ j is the inclination angle of the bottom of soil strip j. It is worth noting that the safety factor F of the slope is calculated by formula (13): s Iteration is required; Taking into account the uncertainty of geotechnical parameters, the log-normal distribution is used to consider the uncertainty of geotechnical parameters. Monte Carlo simulation (MCS) is used to calculate the probability of slope instability under a given rainfall disaster intensity, and the commonly used log-normal distribution is used for fitting, as shown in formula (14): In the formula, F s (X) is the safety factor of the slope under rainfall, which is calculated by formula (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 fragility curve, respectively.

9. The method for estimating the probability of slope instability under rainfall considering climate change according to claim 1, characterized in that: In step (V): Obtain the slope in the future predefined time interval [t0,t inv The mathematical expression of the failure probability within ] is shown in formula (15): Where U i is the integral upper limit of rainfall intensity i; P(F s (X)-1<0|I max =i) is the vulnerability curve of the slope under rainfall; It is equivalent to the differential of the rainfall hazard curve.

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