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 rainfallinduced 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.
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 [
One of the main triggering factors for landslides is heavy rainfall [
Geomorphological processes can lead to soil regions characterized by a degree of spatial heterogeneity [
For example, Cho [
In previous studies, the random variables most frequently considered when analyzing spatial variability of the soil properties are shear strength parameters (cohesion,
The purpose of this study was to identify the probability of failure of rainfallinduced 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 (
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.
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 [
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 [
The KLE of a random field with a mean value (
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 [
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 nonnegative. Therefore, the assumption of a lognormal distribution is appropriate as the soil properties used in this study are always nonnegative [
In this section, the rainfall infiltration model and slope stability analysis model for unsaturated soils were described to assess the vulnerability of rainfallinduced landslides caused by rainfall, and then the probabilistic analysis procedure considering the spatial variability of soil properties was presented.
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 [
Infiltration into a layered soil profile under an initially ponded condition.
When the wetting front is over layer
The travel time to depth
Rainfallinduced landslides usually have shallow surface failure depth, being the main cause of the reduction of negative pore water pressure in unsaturated soil due to rainfall infiltration [
Infinite slope analysis model.
The shear strength contribution due to matric suction of unsaturated soil can be expressed as described by Fredlund and Rahardjo [
The schematic view of the probabilistic slope analysis considering the spatial variability of soil properties and probabilistic rainfall intensity is shown in Figure
Flow chart for the probabilistic slope analysis.
The study area is located in Jangheung, Gyeonggido, South Korea (37°45′03″N, 126°56′21″E). This area is underlain by a Gyeonggi gneiss complex that belongs to the Gyeonggi massif, and the bedrock is intensely weathered. The surface is covered by
Location of the study area and surface plot.
Electrical resistivity survey was carried out in order to identify soil strata from the resistivity distribution and to select the site investigation point. Resistar RS100M equipment with multielectrode system ME100 (Geofyzika A.s.) was used for a multielectrode survey using a Wenner–Schlumberger electrode array with electrode spacing of 2.5 m. Primary data were processed into resistivity cross sections by a 2D inverse method using the software Res2DInv [
Resistivity tomography of the slope.
As shown in Figure
Location of sampling points.
Summary of basic soil properties and slope conditions.
Parameter  Value  

Soil property  Specific gravity, 
2.62 
Water content (%)  19.1  
Dry unit weight, 
14.7  
Porosity (%)  43.1  
Plastic limit (%)  15.7  
USCS  SM, SC  


Slope  Length (m)  50 
Angle (°)  31  
Depth (m)  2.8 
In accordance with the United Soil Classification System (USCS), the soil is classified as SM or SC, and the specific gravity (
Statistical properties of shear strength parameters.
Soil property  Mean  Standard deviation  COV (%)  Scale of fluctuation  

Cohesion, 
14.7  4.41  30  Lognormal  0.1 
Friction angle, 
17.9  3.58  20  Lognormal  0.4 
Permeability, 
1.64 × 10^{−6}  8.19 × 10^{−7}  50  Lognormal  1.5 
Rainfall infiltration into the soil begins from unsaturated conditions, and it is necessary to identify the permeability characteristics under unsaturated conditions. Therefore, a laboratory test for SWCC was conducted, and parameters of the van Genuchten [
Conditions of infiltration analysis.


Fitting parameters of van Genuchten’s SWCC 







28.1  41.2  0.0286  0.3580  1.5576  0.89 
Soilwater characteristic curve.
Rainfall information on the study area is very important because rainfall has a high spatial and temporal variability, and its probabilistic characteristics are very different depending on the region. The information of probability rainfall intensity at the study area was obtained from the Korea precipitation frequency data server of the Ministry of Land, Infrastructure and Transport (MOLIT,
IDF curves for study site.
Rainfall intensity for the IDF curve increased as the return period increased, and the smaller the duration, the greater the difference in rainfall intensity. In this study, the probabilistic rainfall intensity for a return period (
Probabilistic rainfall intensity (mm/h) of the study area.
Return period (year)  Duration time (hour)  

1  2  3  6  9  12  15  18  24  
2  45.1  32.3  26.1  17.4  13.4  11.0  9.4  8.3  6.7 
5  61.8  45.3  36.9  24.6  19.0  15.6  13.4  11.8  9.6 
10  72.9  53.9  43.9  29.4  22.6  18.6  16.0  14.1  11.5 
50  97.2  72.8  59.6  39.9  30.7  25.3  21.7  19.2  15.7 
100  107.5  80.8  66.2  44.3  34.1  28.1  24.2  21.3  17.5 
200  117.7  88.8  72.7  48.7  37.5  30.9  26.6  23.5  19.3 
Figure
Change in wetting front depth and factor of safety depending on rainfall duration using a deterministic approach.
The gray line indicates the WDF changes and the dotted lines the changes of FS at the baseline and at the WFD. WFD increases approximately 2 m when rainfall duration is equal to 24 h, and the factor of safety at WFD was drastically reduced due to the dissipation of negative pore water pressure in unsaturated soil as the rainfall began to penetrate into the ground. The factor of safety at the baseline showed a very small reduction rate considering only an increase in unit weight due to the rainfall infiltration. In the deterministic approach, the factor of safety until a rainfall of 24 h was greater than 1. The change in the WFD with the rainfall duration and normalized SOF is shown in Figure
Change in wetting front depth depending on rainfall duration and normalized SOF.
The average WFD showed a significant increase with increasing rainfall duration, but it increased very slightly with normalized SOF. When the return period was low, the difference in average WFD according to the return period was not significant even though there was a large difference in rainfall intensity, whereas the average WFD significantly changed with the return period for high rainfall durations. Although there was no significant difference in average WFD with normalized SOF, there was a large variation in standard deviation. The WFD appeared at various depths depending on the spatial variability of the permeability, and the distribution exhibited a wider range as the rainfall duration increased (Figure
Distribution of WFD according to normalized SOF for rainfall duration of (a) 6 hours and (b) 18 hours.
In this study, the potential failure surface was defined as the deepest depth with a factor of safety of less than 1, and if the factor of safety is less than 1 at any depth, the slope failure was considered to have occurred. The probability of failure is significantly affected by the return period and the rainfall duration as shown in Figure
Change in the probability of failure depending on the return period and the rainfall duration.
The variation of the probability of failure according to normalized SOF for the return period of 2 and 100 years is shown in Figure
Change in the probability of failure depending on normalized SOF for (a)
Figure
Histograms for the frequency of the critical depth and the cumulative failure probability along with the depth (
The probability of failure according to the normalized SOF and the rainfall duration for 2 and 100 years return periods were compared with the case where the spatial variability of soil properties was not considered (i.e., homogeneous soil) for each return period, and the differences in probability of failure (
Difference in probability of failure with the results for homogeneous soil (
The purpose of this study was to identify the failure of rainfallinduced landslides considering the spatial variability of soil properties and the probabilistic rainfall intensity through a case study of a weathered soil slope in Korea. An electrical resistivity survey was performed to understand the stratum of the slope. Although the electrical resistivity survey has some inherent limitations as it cannot provide direct information such as shear strength, the distribution of soil strata can be confirmed with images, and information can be provided on soil survey location and direction of random field generation. Herein, three soil properties (i.e., cohesion, friction angle, and permeability) were considered as random fields, and the IDF curves with a 2, 5, 10 50, 100, and 200year return period were applied to identify the effects of probabilistic rainfall intensity. An infinite slope equation for unsaturated soil and multilayer infiltration model by Chu and Marino [
Probability of failure was significantly affected by the spatial variability of soil properties, and the results are similar to those of previous studies. The return period and rainfall duration also have a significant impact on slope stability due to the wetting front development. Although the rainfall conditions are the same, their effects on the slope stability were different according to the spatial variability of soil properties, and their effects were more sensitive with decreasing normalized SOF. The probability of failure increased as the return period and the rainfall duration increased. However, the increase rate of the probability of failure decreased as the return period increased, and there was no significant difference in probability of failure when the return period is over 100 years because rainfall infiltration is dominated by the infiltration capability of the soil.
Compared with the results of traditional probabilistic analysis without consideration of the spatial variability of soil properties, the difference in probability of failure was found to be approximately 24∼30% when the normalized SOF was small (i.e.,
The data used to support the findings of this study are included within the article.
The authors declare that they have no conflicts of interest.
The work of this research had been conducted in the Department of Rural System Engineering, Seoul National University, and the authors would like to thank them for their technical and laboratory support.