# Microscale Modeling of Frozen Particle Fluid Systems with a Bonded-Particle Model Method

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- Flexibility in agglomerate generation, in which all particles and bonds can have their unique material or geometrical properties;
- Capability in mimicking the breakage behavior of agglomerate, such as the crack initiation, propagation, failure plane, etc.;
- Diversity in functional model usage, with numerous choices of rheological models in the particle-particle, particle-wall relationship, and solid bond models.

#### 1.1. Ice Rheology

^{−8}s

^{−1}to 10

^{−3}s

^{−1}, the compressive strength increases with an increase in strain rate, surpassing 10

^{−3}s

^{−1}compressive strength decreases with an increase in strain rate [29].

#### 1.2. Rheology of Frozen Soil

## 2. Materials and Methods

#### 2.1. Uniaxial Compression Test

#### 2.2. Specimen Preparation

#### 2.3. Investigated Parameter Space

^{−3}s

^{−1}was applied for a low strain rate, and 10

^{−2}s

^{−1}was used for a high strain rate. The strain rate is controlled by the compression speed, specified according to specimen height. The compression speed of 0.02 mm/s, which is two times larger than the minimal compression speed of the Texture Analyzer, was chosen as the low strain rate for all specimens. For high strain rate, compression speed is calculated by $specimenheight\times 0.01$. All experiments have been performed at a temperature of around −10 °C. The possibility of unfrozen water inside the agglomerate can be minimized with such a temperature.

#### 2.4. Ice Creep Behavior

#### 2.5. Fracture Patterns of Frozen PFS

^{−2}s

^{−1}). The fully saturated PFS samples can better transmit the pressure through the specimen. Thus, the cracks propagate from top to bottom, breaking the specimen into relatively large fragments containing numerous primary particles. In this case, the complete failure of the specimen occurred vigorously. In contrast, no large fragments were formed for PFS samples with 75% saturation. Only tiny pieces with several primary particles detached from the main structure during loading.

#### 2.6. Mechanical Behavior of Frozen PFS

#### 2.7. Bonded-Particle Model Approach

#### 2.8. Solid Bond Model Considering Creep Behavior

## 3. Result and Discussion

#### 3.1. Experimental Result

#### 3.2. Simulation Setup

#### 3.3. Comparison of Simulation and Experimental Results

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Texture Analyzer system equipped with a climate chamber: (

**Left**) Climate chamber coupled with Texture Analyzer; (

**Right**) CAD design.

**Figure 2.**Two exemplary samples of frozen PFS: (

**Left**) aggregate with alpha-alumina primary particles at 75% saturation level; (

**Right**): glass bead PFS with 100% saturation.

**Figure 3.**Polycrystalline ice specimen subjected to constant force load for 240 s under three different forces.

**Figure 4.**Representative stress-strain curve of polycrystalline ice during creep experiment (primary loading phase).

**Figure 5.**The fracture pattern for agglomerates at the strain rate is 10

^{−2}s

^{−1}: (

**a**) 100% saturation, alpha-alumina PFS (Supplementary material: Video S1); (

**b**) 75% saturation, glass PFS (Supplementary material: Video S2).

**Figure 6.**Representative stress-strain characteristics for different frozen PFS under a high strain (HS) rate of 10

^{−2}s

^{−1}and low strain (LS) rate of 10

^{−3}s

^{−1}.

**Figure 8.**Average Young’s modulus and breakage stress of different PFS: (

**a**) Young’s modulus; (

**b**) Breakage stress.

**Figure 9.**Representative agglomerate with diameter 10 mm, height 16 mm (

**upper**part: agglomerates in complete form;

**lower**part: agglomerates’ internal structure).

**Figure 10.**Experimental and simulation results for 100% saturation level for high strain (HS) rates (10

^{−2}s

^{−1}) and low strain (LS) rates (10

^{−3}s

^{−1}).

**Figure 11.**Comparison of experimental and simulation results for 100% saturation at −10 °C: (

**a**) Young’s modulus; (

**b**) Breakage stress.

**Figure 12.**Comparison of experimental and simulation results for 75% saturation at −10 °C: (

**a**) Young’s modulus; (

**b**) Breakage stress.

Stiffness | Shape | Surface Roughness | Particle Size (mm) | ||||
---|---|---|---|---|---|---|---|

Soft | Hard | Spherical | Non-Spherical | Ra | Rz | ||

Polyethene | X | X | 12.808 | 50.723 | 1.8 | ||

Glass bead | X | X | 1.767 | 11.462 | 1.65 | ||

Alpha-alumina | X | X | 49.262 | 187.453 | 1.72 | ||

Quartz sand | X | X | 13.416 | 49.623 | 0.5 |

**Table 2.**Mechanical behavior overview concerning saturation levels, temperatures, strain rates, and particle properties.

Saturation Level | Strain Rate | Smooth Particles (Polymer and Glass) | Rough Particles (Sand and Alpha-Alumina) |
---|---|---|---|

100% | Low | Mostly brittle with failure just after the yield point | Dilatant with slight strain softening or hardening |

High | Brittle failure | Brittle behavior with failure just after yield or brittle failure | |

75% | Low | Brittle failure | Dilatant with vast strain softening |

High | Brittle failure | Brittle failure |

**Table 3.**Main agglomerates properties used for simulation of different types of PFS with 100% saturation level.

Parameter | Polyethene/Glass/ Alpha-Alumina (Spherical) | Sand (Non-Spherical) |
---|---|---|

Particle diameter (mm) | 1.8/1.7/1.65 | 0.5 |

Bond diameter (mm) | 1.0 | 0.3 |

Particle density (kg/m^{3}) | 960/2500/3960 | 2640 |

Particle Young’s modulus (GPa) | 0.8/72.3/150 | 72 |

Particle Poisson’s ratio (-) | 0.36/0.22/0.22 | 0.2 |

$\mathrm{Maximal}\text{}\mathrm{bond}\text{}\mathrm{generation}\text{}\mathrm{distance}\text{}{L}_{gen}^{max}$ (mm) | 0.7 | 0.2 |

Numbers of particles (-) | ≈230 | ≈11,200 |

No. of bonds (-) | ≈1100 | ≈66,000 |

Porosity (-) | 0.44 | 0.42 |

Particle-wall sliding friction (-) | 0.45/0.45/0.45 | 0.45 |

Particle-wall rolling friction (-) | 0.05/0.05/0.05 | 0.5 |

Particle-particle sliding friction (-) | 0.45/0.4/0.45 | 0.45 |

Particle-particle rolling friction (-) | 0.05/0.05/0.05 | 0.5 |

Restitution coefficient (-) | 0.1 | 0.1 |

**Table 4.**Material properties for ice bonds used for modeling different agglomerates at different loading rates.

Primary Particles | ||||
---|---|---|---|---|

Polyethene | Glass | Alpha-Alumina | Natural Sand | |

Normal and shear strengths | ||||

- -
- High strain rate (MPa)
| 3.5 | 4.2 | 20 | 20 |

- -
- Low strain rate (MPa)
| 6 | 2.7 | 20 | 20 |

Creep parameter A (-) | 0.1 | 0.1 | 0.3 | 0.1 |

Creep factor m (-) | 0.1 | 0.1 | 0.16 | 0.1 |

Parameter | Polyethylene/Glass/Alpha-Alumina (Spherical) | Sand (Non-Spherical) |
---|---|---|

Bond diameter (mm) | 0.75 | 0.22 |

$\mathrm{Maximal}\text{}\mathrm{bond}\text{}\mathrm{generation}\text{}\mathrm{distance}\text{}{L}_{gen}^{max}$ (mm) | 0.01 | 0.01 |

Number of particles | ≈230 | ≈11,200 |

Number of bonds | ≈550 | ≈34,000 |

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**MDPI and ACS Style**

Chan, T.T.; Heinrich, S.; Grabe, J.; Dosta, M.
Microscale Modeling of Frozen Particle Fluid Systems with a Bonded-Particle Model Method. *Materials* **2022**, *15*, 8505.
https://doi.org/10.3390/ma15238505

**AMA Style**

Chan TT, Heinrich S, Grabe J, Dosta M.
Microscale Modeling of Frozen Particle Fluid Systems with a Bonded-Particle Model Method. *Materials*. 2022; 15(23):8505.
https://doi.org/10.3390/ma15238505

**Chicago/Turabian Style**

Chan, Tsz Tung, Stefan Heinrich, Jürgen Grabe, and Maksym Dosta.
2022. "Microscale Modeling of Frozen Particle Fluid Systems with a Bonded-Particle Model Method" *Materials* 15, no. 23: 8505.
https://doi.org/10.3390/ma15238505