# Using Detailing Concept to Assess Railway Functional Safety

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## Abstract

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## 1. Introduction

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- Change of force impulses over time;
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- Changes in the deformability process over time.

## 2. Research Methods

## 3. Research Results

#### 3.1. The First Direction of Detailing

- 1.
- Since energy exchange occurs during the impact, one of its characteristics is the law of change of the acting physical quantity over time. This value characterizes the intensity of the impact of the force impulse and allows describing such characteristics of the impact as “legato” and “staccato” in music or “soft” and “hard/sharp” in mechanical systems.

- 2.
- The action of a constant force per unit time on an object, regardless of the time of its impact, is characterized by the same value of the amount of motion per unit time, which serves as a potential for performing the same amount of work of the object per unit time. This means that it transfers the same amount of energy per unit time during the action of the force. If the force has a variable value in time, then the impulses of the variable forces cause the exchange of a variable amount of energy per unit time during the duration of the force.

#### 3.2. The Second Direction of Detailing

## 4. Discussion, Conclusions and Future Recommendation

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- Modeling of time-space processes occurring both inside each element of the structure and in the track structure as a whole under the influence of both external and internal influences;
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- Modifying of models by changing the geometric and physical-mechanical characteristics of structural elements for certain operating conditions;
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- Optimizing the risks associated with unsuccessful trials;
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- Controlling deformability parameters in dynamic processes;
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- Expanding existing methods for diagnosing dynamic systems;
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- Optimizing costs for the manufacture and operation of simulation objects, as well as damage prediction during continued operation.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The dependence of oscillation amplitudes of the track structure section over time with a motion speed of 80 km/h under the single force impact of the section’s different loads.

**Figure 2.**Ratio of deformability work and intensity of use for section of track construction under different axle loads and speed of rolling stock.

**Figure 3.**Ratio of deformability work and intensity of use for pad under different axle loads and speed of rolling stock.

**Figure 4.**Ratio of deformability work and intensity of use for sleeper under different axle loads and speed of rolling stock.

**Figure 5.**Ratio of deformability work and intensity of use for ballast under different axle loads and speed of rolling stock.

**Figure 6.**Ratio of deformability work and intensity of use for ground base under different axle loads and speed of rolling stock.

**Figure 7.**Ratio of intensity of use for railway track structure and its elements under different axle loads and speed of rolling stock.

Element | Density, kg/m^{3} | Poisson’s Coefficient | Young’s Module E, MPa | Cl, m/s ^{1} | Ct, m/s ^{2} |
---|---|---|---|---|---|

Rail | 7830 | 0.24 | 2.1 × 105 | 5622 | 3288 |

Pad | 918 | 0.3 | 100 | 382 | 204 |

Sleeper | 2200 | 0.1 | 36,000 | 4090 | 2727 |

Ballast | 1900 | 0.2 | 100 | 241 | 148 |

Ground base | 170 | 0.3 | 30 | 487 | 260 |

^{1}—the speed of longitudinal;

^{2}—the speed of transverse waves in the material.

Force Ratios at Different Speeds F_{i}/F = 225 kN and V = 80 km/h | |||||||||

F = 225 kN | F = 294 kN | F = 450 kN | |||||||

V = 50 km/h | V = 80 km/h | V = 110 km/h | V = 50 km/h | V = 80 km/h | V = 110 km/h | V = 50 km/h | V = 80 km/h | V = 110 km/h | |

0.896 | 1.000 | 1.110 | 1.205 | 1.341 | 1.491 | 1.838 | 2.054 | 2.279 | |

Deformability work A_{i}/A = 225 kN and V = 80 km/h | |||||||||

Object | F = 225 kN | F = 294 kN | F = 450 kN | ||||||

V = 50 km/h | V = 80 km/h | V = 110 km/h | V = 50 km/h | V = 80 km/h | V = 110 km/h | V = 50 km/h | V = 80 km/h | V = 110 km/h | |

Track structure | 1.212 | 1.000 | 0.770 | 2.855 | 2.371 | 2.021 | 9.401 | 7.522 | 7.081 |

Pad | 0.873 | 1.000 | 1.205 | 1.791 | 2.024 | 2.422 | 5.048 | 5.692 | 6.597 |

Sleeper | 1.244 | 1.000 | 0.907 | 2.760 | 2.188 | 2.018 | 8.539 | 6.799 | 6.306 |

Ballast | 1.199 | 1.000 | 0.706 | 2.874 | 2.513 | 2.014 | 9.776 | 8.249 | 7.641 |

Ground base | 1.246 | 1.000 | 0.932 | 2.933 | 2.200 | 2.038 | 9.041 | 6.847 | 6.364 |

Intensity of use I_{i}/I = 225 kN and V = 80 km/h | |||||||||

Object | F = 225 kN | F = 294 kN | F = 450 kN | ||||||

V = 50 km/h | V = 80 km/h | V = 110 km/h | V = 50 km/h | V = 80 km/h | V = 110 km/h | V = 50 km/h | V = 80 km/h | V = 110 km/h | |

Track structure | 0.786 | 1.000 | 1.022 | 1.677 | 2.150 | 2.432 | 4.796 | 5.918 | 7.394 |

Pad | 0.566 | 1.000 | 1.601 | 1.052 | 1.836 | 2.915 | 2.575 | 4.478 | 6.889 |

Sleeper | 0.807 | 1.000 | 1.205 | 1.621 | 1.984 | 2.429 | 4.356 | 5.349 | 6.585 |

Ballast | 0.777 | 1.000 | 0.938 | 1.688 | 2.279 | 2.424 | 4.988 | 6.490 | 7.979 |

Ground base | 0.808 | 1.000 | 1.238 | 1.723 | 1.995 | 2.453 | 4.613 | 5.387 | 6.646 |

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## Share and Cite

**MDPI and ACS Style**

Bondarenko, I.; Campisi, T.; Tesoriere, G.; Neduzha, L.
Using Detailing Concept to Assess Railway Functional Safety. *Sustainability* **2023**, *15*, 18.
https://doi.org/10.3390/su15010018

**AMA Style**

Bondarenko I, Campisi T, Tesoriere G, Neduzha L.
Using Detailing Concept to Assess Railway Functional Safety. *Sustainability*. 2023; 15(1):18.
https://doi.org/10.3390/su15010018

**Chicago/Turabian Style**

Bondarenko, Iryna, Tiziana Campisi, Giovanni Tesoriere, and Larysa Neduzha.
2023. "Using Detailing Concept to Assess Railway Functional Safety" *Sustainability* 15, no. 1: 18.
https://doi.org/10.3390/su15010018