Advances in Civil Engineering

Volume 2018, Article ID 2120854, 12 pages

https://doi.org/10.1155/2018/2120854

## Probabilistic Analysis of Weathered Soil Slope in South Korea

^{1}Oregon State University, 101 Kearney Hall, Corvallis, OR 97331, USA^{2}Department of Rural Systems Engineering and Research Institute for Agriculture and Life Sciences, Seoul National University, Seoul, Republic of Korea

Correspondence should be addressed to Younghwan Son; rk.ca.uns@68hys

Received 4 April 2018; Revised 25 May 2018; Accepted 25 June 2018; Published 18 July 2018

Academic Editor: Tiago Ferreira

Copyright © 2018 Taeho Bong and Younghwan Son. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Rainfall is a major trigger of shallow slope failures, and it is necessary to consider the spatial correlation of soil properties for probabilistic analysis of slope stability in heterogeneous soil. In this study, a case study of a weathered soil slope in Korea was performed to identify the rainfall-induced landslides considering the spatial variability of the soil properties and the probabilistic rainfall intensity depending on the return period and the rainfall duration. Various laboratory tests were performed to determine the physical properties of the site, and an electrical resistivity survey was carried out to understand the soil strata. Cohesion, friction angle, and permeability were considered as random variables considering the spatial variability, and the probabilistic rainfall intensities for return period of 2, 5, 10, 50, 100, and 200 years were used to consider the effects of rainfall infiltration. The results showed that a probabilistic framework can be used to efficiently consider the spatial variability of soil properties, and various slope failure patterns were identified according to the spatial variability of the soil properties and the probabilistic rainfall intensity.

#### 1. Introduction

Shallow slope failure (typically 1–3 m deep) due to heavy rainfall during rainstorms and typhoons is common in mountain areas and take the form of translational slides, which form parallel to the original surface [1, 2]. Over the past decade, many studies on rainfall pattern changes due to climate change have been carried out, and climate change has resulted in changes in rainfall patterns that can cause less frequent, but more intense rainfall events [3, 4].

One of the main triggering factors for landslides is heavy rainfall [5–8], and the abnormal climate and localized heavy rainfall caused by climate change may lead to more frequent landslides [4, 8–12]. For this reason, the prediction of rainfall-induced landslides is becoming more important, and the infinite slope model is usually implemented for the stability analysis of natural slopes; this model is appropriate when the horizontal dimensions of the surface are relatively much larger than the vertical depth of the potential failure slope. In addition, physically-based models have frequently been used in the framework of early warning systems devoted to rainfall-induced landslide hazard monitoring [13], and infinite slope model is commonly used to assess the factor of safety. However, the traditional infinite slope equation assumes homogeneous or averaged soil properties, and the potential failure surface is always fixed at the base of the slope [14] or wetting front depth (WFD). Although the uncertainties of the soil can be considered through the probabilistic analysis, the potential failure surface is still fixed and the probability of failure can be underestimated if the soil properties are treated as random variables without considering the spatial variability.

Geomorphological processes can lead to soil regions characterized by a degree of spatial heterogeneity [15], and the spatial variation can occur at various scales depending on the soil forming factors such as parent material, climate, topography, time, and so on. Describing and understanding the complexity of the interacting processes of soil formation has been a challenge, and geostatistics assumes that the variation of a property such as soil is continuous, which is generally more realistic for soil [16]. If the spatial variability of soil properties is considered in the probabilistic analysis, the soil strength can vary depending on the depth considering the spatial correlation structure, and the potential failure surface can occur at various depths. Considering these features, some recent studies focused on the probabilistic analysis of slope stability in heterogeneous soil considering the spatial variability.

For example, Cho [17] identified the effect of spatial variability of unit weight and shear strength parameters using a limit equilibrium method, also, Griffiths et al. [18] investigated the effect of the spatial variability of shear strength parameters using the random finite-element method (RFEM), and Griffiths et al. [14] performed infinite slope analysis considering spatial variability of soil and showed that the potential failure surface can occur at various depths depending on spatial variability. Jiang et al. [19] identified the effect of spatial variability of shear strength parameters using a nonintrusive stochastic finite element method. Cho [20] discussed the effect of spatial variability of permeability on infinite slope stability and the distribution of failure depth due to rainfall infiltration. However, the saturated permeability is often depth-dependent, and Dou et al. [21] investigated the effect of spatial variability of permeability considering nonstationary random field of the saturated permeability as an extension of Cho’s [20]. In a similar vein, Li et al. [22] conducted reliability analysis of an infinite slope considering the linear trend of shear strength parameters in a random field. Li et al. [23] also proposed a multiple response-surface method for efficient slope reliability analysis considering spatial variability, and Cai et al. [24] conducted a cross-correlation analysis to determine the impact of heterogeneity of permeability, soil cohesion, and soil friction angle on slope stability.

In previous studies, the random variables most frequently considered when analyzing spatial variability of the soil properties are shear strength parameters (cohesion, and friction angle, ), and the permeability has also been considered in slope stability analysis due to rainfall infiltration. In practice, other important factors for estimating the probability of landslides occurrence are the intensity of rainfall and duration time [25], which are climatic factors. Rainfall is a major cause of landslides, and it is known that spatial and temporal variability is very high [26]. Therefore, it is important to consider and evaluate the appropriate probabilistic rainfall intensity for predicting the actual probability of landslide occurrence. However, little is known about the role of spatial variability of soil properties in probabilistic analysis of slope stability considering the probability rainfall intensity.

The purpose of this study was to identify the probability of failure of rainfall-induced landslides considering the spatial variability of soil properties and probabilistic rainfall intensity. A case study of shallow slope failure of weathered residual soil slope in Jangheung, Korea, was performed to verify the probabilistic analysis framework. The soil strata of the slope were identified, and the site investigation point was selected through electrical resistivity survey. Then, the soil physical properties and infiltration characteristics of unsaturated soil on natural slope were investigated, and two shear strength parameters ( and ) and permeability were considered as random fields. A slope stability analysis was performed using an infinite slope model, and the probabilistic rainfall intensity for 2, 5, 10, 50, 100, and 200 years frequency for the study area was considered. A series of Latin hypercube sampling- (LHS-) [27] based Monte Carlo simulations was conducted to investigate the effect of the spatial variability of soil properties on the mechanism of slope failure during periods of rain infiltration. Consequently, the probability of slope failure according to the probabilistic rainfall intensity and spatial variability of soil properties was estimated. How soil properties and climatic factors affect slope stability were then discussed.

#### 2. Random Field

Nearly all natural soils are highly variable in their properties, and their variability shows a spatial correlation. The spatial variability of soil properties can be effectively considered using random field theory, and probabilistic analyses that incorporate the spatial variability of soil properties as random fields are more appropriate to consider the uncertainty of soil than those considering soil properties as a single random variable.

##### 2.1. Spatial Variability of Soil

Because of complex geological and environmental processes, soil is inherently heterogeneous, and its properties can be highly variable and spatially correlated in the vertical and horizontal directions. The spatial correlation of soil properties is known to influence the geotechnical response of soil, and it brings unavoidable uncertainty in design, leading to unexpected soil responses [15, 28]. These uncertain spatial properties can be characterized using random field theory [29, 30]. Vanmarcke [29] used a scale of fluctuation (SOF, *δ*) to describe the extent of how soil properties are spatially correlated. Various methods are available to estimate the SOF, and the simplest approach is to fit the theoretical autocorrelation function (ACF, *ρ*) to the empirical ACF [31–34]. However, determining a theoretical ACF may not be easily implemented because a large amount of data is required. Therefore, some theoretical ACFs are usually used to characterize the spatial correlation of soil properties, and the single exponential ACF has been widely used to model the inherent spatial variability of soil properties in probabilistic analysis of slope stability [23]:where represents the autocorrelation distance and reflects the rate at which the correlation decays between two points (). The SOF implied by the single exponential autocorrelation function is equal to twice the value of the autocorrelation distance ().

##### 2.2. Random Fields

In this study, the Karhunen–Loève expansion (KLE) was adopted to generate random fields because it is an efficient method for random field discretization with a desired level of accuracy and provides the greatest accuracy when an exponential ACF is used [35].

The KLE of a random field with a mean value () and a variance () is given by Spanos and Ghanem [36]:where and are the eigenvalues and eigenfunctions of the covariance function, respectively, and represents the uncorrelated zero mean random variables. For practical implementation, the discretization of the random field is obtained by truncating the series expansion at the term:

The accuracy of the represented random field depends on the number of terms used in the KLE expansion, and the number of required terms is determined according to the ratio of the correlation length and the domain size [37].

Normal random fields are often used for modeling uncertainties with spatial variability for mathematical convenience and due to a lack of available data, but they are not applicable in many situations where the random variable is always non-negative. Therefore, the assumption of a log-normal distribution is appropriate as the soil properties used in this study are always non-negative [38, 39]. In (3), if is zero and is one, standard normal random fields are generated by KLE, and it can be transformed into log-normal random fields using (4) as follows:where and are equal to the mean and standard deviation of of the underlying normal distribution.

#### 3. Rainfall-Induced Landslide

In this section, the rainfall infiltration model and slope stability analysis model for unsaturated soils were described to assess the vulnerability of rainfall-induced landslides caused by rainfall, and then the probabilistic analysis procedure considering the spatial variability of soil properties was presented.

##### 3.1. Rainfall Infiltration

In order to perform infiltration analysis considering spatial variability, the flow of water in multilayered soils should be considered, and this can be performed using differential equations that satisfy Darcy’s law [20, 21, 24, 40]. Alternatively, semianalytical and areal-averaged infiltration models have been established to study field-scale infiltration over soils with the variability of permeability based on the Green-Ampt [41] model [42, 43]. Chu and Marino [44] present a modified Green-Ampt model considering infiltration in multilayered soils. This model is able to deal with unsteady and steady rainfall events as well as ponding and nonponding conditions. Therefore, in this study, the infiltration model by Chu and Marino [44] was adopted to consider the spatial variability of permeability. Figure 1 shows infiltration of rainfall into an -layered soil profile with permeability () and initial volumetric water content () for each layer.