# Erosion Failure of a Soil Slope by Heavy Rain: Laboratory Investigation and Modified GA Model of Soil Slope Failure

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Test

#### 2.1. Experimental Materials and Facilities

#### 2.2. Experiment Results and Discussion

#### 2.2.1. Rainfall Infiltration

#### 2.2.2. Runoff and Soil Erosion

## 3. Rainfall Infiltration Model of the Soil Slope

_{s}is the saturated permeability coefficient of soil, S

_{f}is the matrix absorption water head in the wetting front, Z

_{w}is the vertical downward depth (cm) of the wetting front, and h

_{0}is the total water potential at the surface.

_{w}of rainwater is as follows:

_{s}and θ

_{i}are the saturation moisture content and initial moisture content, respectively, and F

_{w}is the cumulative infiltration.

_{p}= Z

_{w}cosa (Z

_{p}is the depth of wetting front perpendicular to the slope, and a is the slope angle), and the water head at the surface is very small (h

_{0}≈ 0). Therefore, the relationship between the depth of the wetting front and the time is as follows:

_{s}= 0.42, θ

_{i}= 0.12, k

_{s}= 4 cm/d, and S

_{f}= 20 cm. When a = 45°, other parameters were introduced into Equation (5) to obtain the theoretical value of the wetting peak depth perpendicular to the slope, which varied with time, as shown in Figure 9.

_{s}= 0.53, θ

_{i}= 0.3, k

_{s}= 0.0048 cm/min, S

_{f}= 150 cm, and a = 0°. The theoretical values of the test conditions were obtained using Equation (5), as shown in Figure 10.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**The characteristics of the 35° slope wetting front in rainfall conditions: (

**a**) 15 min, (

**b**) 45 min, (

**c**) 75 min, and (

**d**) 105 min.

**Figure 3.**The characteristics of the 40° slope wetting front in rainfall conditions: (

**a**) 15 min, (

**b**) 45 min, (

**c**) 75 min, and (

**d**) 105 min.

**Figure 4.**The characteristics of the 45° slope wetting front in rainfall conditions: (

**a**) 15 min, (

**b**) 45 min, (

**c**) 75 min, and (

**d**) 105 min.

**Figure 6.**The erosion of the 35° slope surface: (

**a**) 0 min, (

**b**) 15 min, (

**c**) 45 min, (

**d**) 75 min, (

**e**) 105 min, and (

**f**) 135 min.

**Figure 7.**The erosion of the 40° slope surface: (

**a**) 0 min, (

**b**) 15 min, (

**c**) 45 min, (

**d**) 75 min, (

**e**) 105 min, and (

**f**) 135 min.

**Figure 8.**The erosion of the 45° slope surface: (

**a**) 0 min, (

**b**) 15 min, (

**c**) 45 min, (

**d**) 75 min, (

**e**) 105 min, and (

**f**) 135 min.

Moisture ω (%) | Bulk Density ρ_{s} (g·cm^{−3}) | Void Ratio e | Saturation S_{r} | Liquid Limit w_{L} | Plastic Limit W_{p} | Cohesive Force c (kPa) | Internal Friction Angle φ(°) |
---|---|---|---|---|---|---|---|

12.5 | 2.73 | 0.8 | 0.414 | 32.8 | 23.56 | 23.9 | 12.51 |

Test Number | Slope Dimension (cm) | Slope Angles α (°) | Rainfall (mm/min) |
---|---|---|---|

1 | 45 × 35 × 20 | 35 | 1.7 |

2 | 45 × 35 × 20 | 40 | 1.7 |

3 | 45 × 35 × 20 | 45 | 1.7 |

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**MDPI and ACS Style**

Jing, X.; Chen, Y.; Pan, C.; Yin, T.; Wang, W.; Fan, X.
Erosion Failure of a Soil Slope by Heavy Rain: Laboratory Investigation and Modified GA Model of Soil Slope Failure. *Int. J. Environ. Res. Public Health* **2019**, *16*, 1075.
https://doi.org/10.3390/ijerph16061075

**AMA Style**

Jing X, Chen Y, Pan C, Yin T, Wang W, Fan X.
Erosion Failure of a Soil Slope by Heavy Rain: Laboratory Investigation and Modified GA Model of Soil Slope Failure. *International Journal of Environmental Research and Public Health*. 2019; 16(6):1075.
https://doi.org/10.3390/ijerph16061075

**Chicago/Turabian Style**

Jing, Xiaofei, Yulong Chen, Changshu Pan, Tianwei Yin, Wensong Wang, and Xiaohua Fan.
2019. "Erosion Failure of a Soil Slope by Heavy Rain: Laboratory Investigation and Modified GA Model of Soil Slope Failure" *International Journal of Environmental Research and Public Health* 16, no. 6: 1075.
https://doi.org/10.3390/ijerph16061075