# Numerical Simulation of the Liquefaction Phenomenon by MPSM-DEM Coupled CAES

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Background of the Analysis of Liquefaction

## 3. MPSM-DEM Coupled CAES

#### 3.1. Computer-Aided Engineering System (CAES)

#### 3.2. Particle-Based Method (PBM) and Moving Particle Semi-Implicit Method (MPSM)

#### 3.3. Discrete Element Method (DEM)

#### 3.4. MPSM-DEM Coupled CAES

## 4. Simulation Model and Conditions

#### 4.1. Simulation Model

#### 4.2. Setting of External Acceleration

^{2}), which corresponds to an earthquake with a seismic intensity of 5 or higher, as shown in Figure 7. The reason for setting this seismic intensity is that the liquefaction phenomenon often occurs from an earthquake that has a seismic intensity of 5 or higher.

**Figure 5.**Cross-section of Case 3, targeted for analysis (characteristic display of a liquefaction countermeasure part by grid-shaped piles).

#### 4.3. MPSM-DEM Coupled CAES Settings

^{3}, respectively. In this study, the diameter and density of the sand particles modeled by the DEM were set so that the particle sedimentation velocity of the Stokes fluid [38,39] was equal to that of typical sand particles and the sand particles modeled by the DEM. In this paper, the authors focus on the void ratio and express the sandy ground via the void ratio, using the maximum and minimum void ratios of a typical sandy ground. The void ratios for three case studies are shown in Table 3. The void ratio for Case 1 is 1.19, that for Case 2 is 0.71, and that for Case 3, with the piles, is 1.19.

## 5. Results and Discussion

## 6. Conclusions

- (1)
- Through the use of the MPSM-DEM coupled CAES, the liquefaction phenomenon was successfully visualized by applying an external acceleration that simulated seismic waves in the ground, modeled three-dimensionally.
- (2)
- The effect of the soil conditions, such as the void ratio, on the behavior of the particles in the soil during an earthquake was clarified. It was shown that, by employing the MPSM-DEM coupled CAES, it is possible to evaluate the behavior of the particles below the surface during an earthquake and to examine whether liquefaction is likely to occur.
- (3)
- The liquefaction phenomenon of a ground model with piles, simulating liquefaction countermeasures, was visualized. This visualization of the liquefaction phenomenon can be expected to contribute to the design and accountability of efficient and economical liquefaction countermeasures.
- (4)
- A MPSM-DEM coupled CAES model was constructed, in which the MPSM was used for the pore water below the surface and the DEM was used for the sand particles in the ground. In order to examine the validity of the constructed model, the authors conducted a numerical simulation with a model for the liquefaction phenomenon in a saturated sandy soil on which seismic waves acted, demonstrating the effectiveness of this model. From this, it was shown that an MPSM-DEM coupled CAES may be a method that can visualize various phenomena below the surface.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 8.**Liquefaction occurrence from 0 to 60 s in Case 1, when external acceleration is applied (void ratio: 1.19).

**Figure 9.**Liquefaction occurrence from 0 to 60 s in Case 2, when external acceleration is applied (void ratio: 0.71).

**Figure 10.**Liquefaction occurrence from 0 to 60 s in Case 3, when external acceleration is applied (void ratio: 1.19).

Density $\rho $ (kg/m^{3}) | Coefficient of Kinematic Viscosity $\upsilon $ (m^{2}/s) | |

Pore water | 998 | 0.000001 |

Sand Particles | |
---|---|

Particle density
$\rho $ (kg/m^{3}) | 2634 |

Normal spring constant ${k}^{n}$ (N/m) | 1.0 × 10^{8} |

Tangent spring constant ${k}^{t}$ (N/m) | 2.5 × 10^{7} |

Normal attenuation constant ${\eta}^{n}$ | 0.7 |

Tangent attenuation constant ${\eta}^{t}$ | 0.7 |

Frictional coefficient $\mu $ | 0.5 |

Void Ratio | Liquefaction Countermeasure | |
---|---|---|

Case 1 | 1.19 | Without countermeasure |

Case 2 | 0.71 | Without countermeasure |

Case 3 | 1.19 | With countermeasure |

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**MDPI and ACS Style**

Nakao, K.; Inazumi, S.; Takahashi, T.; Nontananandh, S.
Numerical Simulation of the Liquefaction Phenomenon by MPSM-DEM Coupled CAES. *Sustainability* **2022**, *14*, 7517.
https://doi.org/10.3390/su14127517

**AMA Style**

Nakao K, Inazumi S, Takahashi T, Nontananandh S.
Numerical Simulation of the Liquefaction Phenomenon by MPSM-DEM Coupled CAES. *Sustainability*. 2022; 14(12):7517.
https://doi.org/10.3390/su14127517

**Chicago/Turabian Style**

Nakao, Koki, Shinya Inazumi, Tsuyoshi Takahashi, and Supakij Nontananandh.
2022. "Numerical Simulation of the Liquefaction Phenomenon by MPSM-DEM Coupled CAES" *Sustainability* 14, no. 12: 7517.
https://doi.org/10.3390/su14127517