# Discrete Element Simulation of the Road Slope Considering Rainfall Infiltration

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{3D}) was used to establish a novel rainfall infiltration model, which integrates water transfer, intensity decay and seepage force into the calculation of the moisture field. By applying this model to the rainfall infiltration analysis of a road slope in Nanping City, Fujian Province, China, the distribution law of water content, the functional relationship between shear strength and water content, and the calculation of permeability at different times can be obtained. The model was verified by comparing simulated results of water content with field monitoring data. The simulation error of water content is lower than 10%. Furthermore, this model application was validated by reproducing the pressure variation of the retaining wall on 12 May 2022. To obtain the accuracy of this model application, it was compared with saturated water content model and seepage force model. The comparison results of the three models showed that the simulation results of this model are best matching with the observation data. Moreover, the verification and validation indicate that our proposed model can be used to effectively analyze the rainfall infiltration of road slope.

## 1. Introduction

^{3D}software [36] was used to develop a rainfall infiltration model for slopes by integrating moisture transfer, intensity decay, and seepage force methods. The model is validated by comparing moisture content monitoring data with simulation results. In addition, to obtain the applicability of the infiltration model, retaining wall pressure monitoring is conducted on a road slope in Nanping City, Fujian Province, China [37]. Ultimately, the simulation results of our proposed model are compared with saturated water content model and seepage force model.

## 2. Materials and Methods

#### 2.1. Moisture Diffusion Model

#### 2.2. Strength Calculation between Particles

- (1)
- Samples are taken at the slope site, and 5–10 groups of samples with different water content are designed;
- (2)
- An indoor direct shear test is conducted for each group of experiments. The vertical pressure is divided into 50 kPa, 100 kPa and 200 kPa. The horizontal shear stress is applied under different vertical pressures to obtain the shear stress at failure;
- (3)
- A numerical model is established in PFC to simulate the direct shear test. Based on the water content grouping in step (1) and the shear strength obtained in step (2), the numerical simulation inversion can obtain the mapping relationship between the water content and friction coefficient;
- (4)
- Draw curves. Take the water content as the abscissa and the friction coefficient as the ordinate;
- (5)
- Fit the curve. A mathematical equation is obtained, which takes the water content as independent variable and friction coefficient as dependent variable;
- (6)
- Based on the fitting equation, the program in PFC is used to map the moisture transfer and friction coefficient of the particles.

#### 2.3. Strength Calculation between Particles

^{3}. $\mathrm{I}$ is the hydraulic gradient, $\mathrm{V}$ is the equivalent continuous space volume, and the hydraulic gradient $\mathrm{I}$ can be calculated by the following formula:

## 3. Application

#### 3.1. Study Area

^{2}. It governs 13 administrative villages and a timber yard. Here, the climate is mild and rainfall is abundant throughout the year.

#### 3.2. Slope Model and Boundary Conditions

^{3D}software to formative sliding bodies and sliding beds (Figure 4).

^{3D}is limited by slope volume and computer performance. Considering the size effect and computer operation, the particle radius of this model was set to 0.25~0.4 m. The number of particles reaches 22,816 when the slope is calculated to be in equilibrium.

#### 3.3. Parameter Calibration

^{3D}[53,54,55].

## 4. Results and Discussion

#### 4.1. Comparison of Moisture Content

#### 4.2. Earth Pressure Comparison

#### 4.3. Highlights and Prospects

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Location map of the Nanping road slope. (

**a**) The location of Fujian in the whole country; (

**b**) Nanping terrain; (

**c**) The location of slope.

**Figure 3.**Topography and surrounding layout of the Nanping road slope. (

**a**) Two sections of the slope in the north-south and east-west directions; (

**b**) Slope size; (

**c**) Distribution around the slope.

**Figure 5.**Parameter calibration process and results. (

**a**) Numerical model of the direct shear test; (

**b**) Parameter calibration result.

**Figure 6.**Water diffusion mechanism and seepage force direction. (

**a**) is the water flow direction in the numerical model; (

**b**) is the direction of seepage force and the distribution of water content of slope infiltration.

**Figure 7.**Comparison of field monitoring values and numerical simulation values of seven water content monitoring points. (

**a**) Distribution of water content at the initial stage of rainfall; (

**b**) Variation in water content on-site during a rainfall event; (

**c**) Distribution of water content at the end of rainfall; (

**d**) Water content change of numerical simulation during a rainfall event.

**Figure 8.**Comparison of the soil pressure results obtained by the three models. (

**a**) The monitoring data; (

**b**) The simulated data from three models.

Parameters | Definition | Parameter Value |
---|---|---|

$R$ | Radius (m) | 0.25–0.4 |

$\mathrm{\rho}$ | Density (kg/m^{3}) | 1600 |

${k}_{s}$ | Tangential stiffness (Pa) | 5 × 10^{7} |

${k}_{n}$ | Normal stiffness (Pa) | 5 × 10^{7} |

${\mathsf{\theta}}_{\mathrm{s}}$ | Saturated volume moisture content | 0.4 |

${\mathsf{\theta}}_{\mathrm{r}}$ | Residual moisture content | 0.008 |

${\mathrm{K}}_{\mathrm{s}}$ | Saturated permeability coefficient | 2.46 × 10^{−6} |

α, m, n | Fitting parameters | 1.76, 4.53, 0.22 |

Rainfall Time | Rainfall Duration | Moisture Content Monitoring Point | No.1 | No.2 | No.3 | No.4 | No.5 | No.6 | No.7 |
---|---|---|---|---|---|---|---|---|---|

27 April 2022 | 21 mm/4 h | Field monitoring (%) | 24.00 | 36.40 | 25.50 | 17.80 | 21.20 | 2.50 | 20.30 |

Numerical simulation (%) | 25.00 | 33.37 | 26.02 | 17.62 | 21.62 | 2.50 | 22.29 | ||

Relative error * (%) | 4.17 | 8.32 | 2.04 | 1.01 | 1.98 | 0 | 9.8 |

Value | Monitoring Data | Simulated Data | Relative Error * | ||||
---|---|---|---|---|---|---|---|

This Model | Saturated Water Content Model | Seepage Force Model | This Model | Saturated Water Content Model | Seepage Force Model | ||

Start value | 3.99667 | 3.99639 | 3.99857 | 3.99667 | 11.5% | 17.82% | 38.99% |

Peak value | 4.02214 | 4.01891 | 4.02858 | 4.01221 | |||

Difference value | 0.02547 | 0.02252 | 0.03001 | 0.01554 |

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**MDPI and ACS Style**

Gu, X.; Nie, W.; Li, Q.; Geng, J.; Zhou, T.; Yuan, C. Discrete Element Simulation of the Road Slope Considering Rainfall Infiltration. *Water* **2022**, *14*, 3663.
https://doi.org/10.3390/w14223663

**AMA Style**

Gu X, Nie W, Li Q, Geng J, Zhou T, Yuan C. Discrete Element Simulation of the Road Slope Considering Rainfall Infiltration. *Water*. 2022; 14(22):3663.
https://doi.org/10.3390/w14223663

**Chicago/Turabian Style**

Gu, Xiao, Wen Nie, Qihang Li, Jiabo Geng, Tao Zhou, and Canming Yuan. 2022. "Discrete Element Simulation of the Road Slope Considering Rainfall Infiltration" *Water* 14, no. 22: 3663.
https://doi.org/10.3390/w14223663