# Statistical Analysis of Ice Load on Icebreaker Ship Based on Stochastic Ice Fields

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## Abstract

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## 1. Introduction

## 2. Establishment of a Stochastic Ice Field

#### 2.1. Probability Density Function of Sea Ice Thickness

#### 2.2. Goodness-of-Fit Test

#### 2.3. Construction of a Stochastic Ice Field

## 3. Numerical Simulation of the Ice Failure Process by an Icebreaker

#### 3.1. Establishment of Numerical Model

#### 3.2. Numerical Model Validation

#### 3.3. Numerical Model Results

#### 3.3.1. Straight Navigation

#### 3.3.2. Rotation Navigation

## 4. Distribution of Ice Loads on the Hull

#### 4.1. Straight-Line Icebreaking Case

#### 4.2. Ship’s Turning Icebreaking Case

## 5. Estimation of Ship Ice Load Extreme Values

#### 5.1. Asymptotic Method

#### 5.2. Estimation of Ice Load Extremes in Straight-Line Motion

#### 5.3. Estimation of Ice Load Extremes in the Rotational Case

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Comparison of the sea ice thickness distribution function f and the empirical cumulative distribution function f based on the sample data.

**Figure 11.**Time history curve of the overall ice load on the icebreaker in straight navigation in a certain stochastic ice field.

Parameters | Value | Units |
---|---|---|

Density | 850 | ${\mathrm{kg}/\mathrm{m}}^{3}$ |

Elastic modulus | 3 | GPa |

Poisson ratio | 0.33 | |

Compressive strength | 3 | MPa |

Bending strength | 1.2 | MPa |

Frictional coefficient | 0.15 |

Grid Partitioning Accuracy | Number of Units 137312 | Number of Units 145984 | Number of Units 156576 |
---|---|---|---|

Average of peaks ($\times {10}^{6}\phantom{\rule{3.33333pt}{0ex}}\mathrm{N}$) | 7.998 | 8.219 | 8.357 |

Error (%) | 2.69 | 1.68 | |

Computer time (h) | 26 | 30 | 45 |

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**MDPI and ACS Style**

Li, L.; Han, G.; Ji, S.
Statistical Analysis of Ice Load on Icebreaker Ship Based on Stochastic Ice Fields. *J. Mar. Sci. Eng.* **2024**, *12*, 448.
https://doi.org/10.3390/jmse12030448

**AMA Style**

Li L, Han G, Ji S.
Statistical Analysis of Ice Load on Icebreaker Ship Based on Stochastic Ice Fields. *Journal of Marine Science and Engineering*. 2024; 12(3):448.
https://doi.org/10.3390/jmse12030448

**Chicago/Turabian Style**

Li, Liang, Guangchun Han, and Shunying Ji.
2024. "Statistical Analysis of Ice Load on Icebreaker Ship Based on Stochastic Ice Fields" *Journal of Marine Science and Engineering* 12, no. 3: 448.
https://doi.org/10.3390/jmse12030448