# Investigation of the Influence of Rainfall Runoff on Shallow Landslides in Unsaturated Soil Using a Mathematical Model

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Mathematical Model

#### 2.1. Hydrological Module

#### 2.1.1. Rainfall Infiltration

#### 2.1.2. Surface Flow (Shallow Water Equations)

_{z}denotes the water table in the vertical direction. Initially, water completely infiltrates the soil before ponding starts to occur. In addition, the surface of the hillslope subjected to the rainfall yields:

#### 2.2. Soil Failure Module

## 3. Numerical Model Verification

^{3}) was packed with an 80 mm thickness for each rainfall event. The median diameter of the soil was 2.0 × 10

^{−5}m.

^{−6}m/s and 5.0 × 10

^{−6}m/s, respectively, following the results of Nord and Esteves [26].

^{3}) with a constant water flux (q

_{z}= 13.69 cm/h) at the soil surface and a constant water pressure at the end of the soil column. The changes of water content at different depths were obtained. This verification has also been made by other numerical models, for example, Hills et al. [28]. The experimental water content profiles and the simulation results are presented in Figure 3 and the pressure head profiles in Figure 4. The comparisons show good agreement, and no significant difference from the measured water contents is found.

## 4. Description of Case Study

^{2}) and a real storm hyetograph were applied. Figure 5 shows the topography of Beng-Ping-Keng (Kaohsiung), a mountainous area in southern Taiwan that is hit by, on average, 3–4 typhoons per year.

## 5. Results

#### 5.1. Water Depth

#### 5.2. Factor of Safety

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 6.**Meteorological data of Typhoon Meigi: (

**a**) Hyetograph in the study area; (

**b**) spatial distribution of accumulated rainfall amount (Source: National Science and Technology Center for Disaster Reduction, Taiwan).

**Figure 7.**Simulation results of water depth on slope surface at Locations A and B during Typhoon Meigi.

**Figure 9.**Simulated results of the factor of safety (FS) varying with time during the Typhoon Meigi (gray color represents FS > 1.2).

**Figure 11.**Simulated results of groundwater (pressure head varied with time, 1 m below ground at Locations A and B during Typhoon Meigi).

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**MDPI and ACS Style**

Chiu, Y.-Y.; Chen, H.-E.; Yeh, K.-C.
Investigation of the Influence of Rainfall Runoff on Shallow Landslides in Unsaturated Soil Using a Mathematical Model. *Water* **2019**, *11*, 1178.
https://doi.org/10.3390/w11061178

**AMA Style**

Chiu Y-Y, Chen H-E, Yeh K-C.
Investigation of the Influence of Rainfall Runoff on Shallow Landslides in Unsaturated Soil Using a Mathematical Model. *Water*. 2019; 11(6):1178.
https://doi.org/10.3390/w11061178

**Chicago/Turabian Style**

Chiu, Yen-Yu, Hung-En Chen, and Keh-Chia Yeh.
2019. "Investigation of the Influence of Rainfall Runoff on Shallow Landslides in Unsaturated Soil Using a Mathematical Model" *Water* 11, no. 6: 1178.
https://doi.org/10.3390/w11061178