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Probabilistic modeling of rainfall-induced shallow landslide using a point-estimate method

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Abstract

The assessment of rainfall-induced shallow landslides using a physical-based model requires accounting for the uncertainty of soil parameters that cannot be accurately quantified. In this study, the modified Iverson model was integrated with the Rosenblueth point-estimate method to probabilistically model rainfall-induced shallow landslides, while simultaneously considering the uncertainty and correlation of soil parameters. Using various soil parameters, hillslope conditions, and hydrological conditions, the applicability of the Rosenblueth point-estimate method was compared with that of the Monte Carlo simulation method. The simulated results indicated that the Rosenblueth point-estimate method can accurately and efficiently assess the probability of rainfall-induced shallow landslides. A lognormal distribution of the safety factor can be assumed when the soil parameters are lognormally distributed random variables. Accounting for the correlation of soil parameters decreases the standard deviation of the safety factor, but does not affect the mean of the safety factor. Neglecting the correlation of soil parameters could substantially misestimate the probability of rainfall-induced shallow landslides.

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Abbreviations

c :

Soil cohesion

d Z :

Water depth

d LZ :

Slope depth

E[]:

Expect value

FS:

Factor of safety

I Z :

Rainfall intensity

K sat :

Saturated hydraulic conductivity

p :

Weight factor

P r :

Probability

S S :

Specific storage

T :

Rainfall duration

X :

Point mass

\( Z \) :

The coordinate

\( \psi \) :

Groundwater pressure head

\( \theta \) :

Soil volumetric water content

\( \alpha \) :

Slope angle

\( \phi \) :

Soil friction angle

\( \varPhi \) :

Standard normally accumulative distribution function

\( \gamma_{\text{sat}} \) and \( \gamma_{\text{w}} \) :

The unit weights of saturated soil and water

\( \mu_{\text{x}} \) :

Mean of input random variable

\( \sigma_{\text{x}} \) :

Standard deviation of input random variable

\( \gamma_{\text{x}} \) :

Skewness coefficient of input random variable

\( \mu_{\text{FS}} \) :

Mean of safety factor

\( \sigma_{\text{FS}} \) :

Standard deviation of safety factor

\( \mu_{\text{x}} \) :

Mean of input random variable

\( \rho \) :

The correlation coefficient

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Authors and Affiliations

  1. Department of Civil and Water Resources Engineering, National Chiayi University, 300 Sefu Road, Chiayi, 60004, Taiwan

    Tung-Lin Tsai, Ping-Yu Tsai & Pei-Jhang Yang

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  1. Tung-Lin Tsai
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  2. Ping-Yu Tsai
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Correspondence to Tung-Lin Tsai.

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Tsai, TL., Tsai, PY. & Yang, PJ. Probabilistic modeling of rainfall-induced shallow landslide using a point-estimate method. Environ Earth Sci 73, 4109–4117 (2015). https://doi.org/10.1007/s12665-014-3696-5

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