# CFD–DEM Simulations of Seepage-Induced Erosion

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Governing Equations

#### 2.1.1. Governing Equations for the Fluid System

#### 2.1.2. Governing Equations for the Particle System

#### 2.2. Fluid-Particle Interaction Force

_{p}are the drag force and volume of each particle respectively.

#### 2.3. Coupling Procedures of CFD–DEM

## 3. Validation of Developed Software

## 4. Observations of Seepage Failure

## 5. Micro-Scale Mechanisms of Seepage Failure and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**The evolution of fluid phases during simulation at t = (

**a**) 0.0, (

**b**) 0.1, (

**c**) 0.3 and (

**d**) 0.5 s.

**Figure 7.**The loss of fine particle content at t = 0.5 s for h = (

**a**) 0.06, (

**b**) 0.07, (

**c**) 0.08 and (

**d**) 0.09 m.

**Figure 8.**The evolution of porosity field for the test with h = 0.06 m at t= (

**a**) 0.0, (

**b**) 0.1, (

**c**) 0.3 and (

**d**) 0.5 s.

**Figure 9.**The evolution of porosity field for the test with h = 0.09 m at t = (

**a**) 0.0, (

**b**) 0.1, (

**c**) 0.3 and (

**d**) 0.5 s.

**Figure 12.**The behavior of soil weight at different local regions during erosion for h = (

**a**) 0.06, (

**b**) 0.07, (

**c**) 0.08 and (

**d**) 0.09 m.

**Figure 13.**The behavior for the ratio of $\raisebox{1ex}{${F}_{d}$}\!\left/ \!\raisebox{-1ex}{$W$}\right.$ at different local regions for h = (

**a**) 0.06, (

**b**) 0.07, (

**c**) 0.08 and (

**d**) 0.09 m.

Young’s Modulus | Density of Particles | Radii of Particles | Friction Coefficient | Poission’s Ratio | Restitution Coefficient |
---|---|---|---|---|---|

5 MPa | 2500 kg/m^{3} | ${r}_{\mathrm{min}}=0.25\mathrm{mm}$ ${r}_{\mathrm{max}}=1\mathrm{mm}$ | 0.85 | 0.45 | 0.1 |

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**MDPI and ACS Style**

Xiao, Q.; Wang, J.-P.
CFD–DEM Simulations of Seepage-Induced Erosion. *Water* **2020**, *12*, 678.
https://doi.org/10.3390/w12030678

**AMA Style**

Xiao Q, Wang J-P.
CFD–DEM Simulations of Seepage-Induced Erosion. *Water*. 2020; 12(3):678.
https://doi.org/10.3390/w12030678

**Chicago/Turabian Style**

Xiao, Qiong, and Ji-Peng Wang.
2020. "CFD–DEM Simulations of Seepage-Induced Erosion" *Water* 12, no. 3: 678.
https://doi.org/10.3390/w12030678