# A New Method for the Determination of Fire Risk Zones in High-Bay Warehouses

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## Abstract

**:**

## 1. Introduction

_{2}, etc.), thick smoke, and an insufficient amount of oxygen [3,4]. The fire that occurred in August 2015 in the warehouse of the port of Tianjin in North China, due to the large number of victims and material damage caused, highlighted the importance of the issue of fire protection in warehouses. In this event, 173 people died, and several hundred were injured [5]. According to the conducted research, the cause of the accident was the improper storage of explosive materials (nitrocellulose) with 40 other flammable and explosive materials (for example, refined naphthalene, sodium sulfide, furfuryl alcohol, ammonium nitrate, etc.). Another fire with catastrophic consequences occurred in August 2020, in a port warehouse in Beirut (Lebanon) [6]. In this fire, 203 people died, more than 7000 were injured, and more than 300,000 people were left homeless. Based on the conducted investigation, the cargo of 2750 tons of ammonium nitrate was inadequately stored for 6 years without the application of appropriate safety and fire protection measures. In 2021, at least fourteen people died and twelve were seriously injured in a fire that occurred in a logistics warehouse located in Changchun [7], the capital of the northeastern province of Jilin. At least 49 people, including 9 firefighters, were killed in a major fire in 2022 at a container warehouse near a port city in southeastern Bangladesh [8], and more than 100 people were injured in total. The cause of such a large fire was the explosion of a container that was full of chemicals.

## 2. Materials and Methods

#### 2.1. Selection of Parameters for Multi-Criteria Analysis

_{2}[mg/g], smoke density [kg/m

^{3}], ignition temperature [°C], thermal conductivity [W/mK], specific heat capacity [J/(kg K)], and calorific value [MJ/kg]. Increasing the number of criteria in the COPRAS method impairs the quality and precision of the results obtained in the multi-criteria decision-making process [22].

#### 2.2. Determination of Simulation Parameters Using the COPRAS Method

- Step 1—Creation of the initial decision matrix

- Step 2—Normalization of the decision matrix

_{ij}—performance of the i-th alternative in relation to the j-th criterion; m—number of alternatives; n—number of criteria.

- Step 3—Forming the weighted normalized decision matrix $V={\left[{V}_{ij}\right]}_{m\times n}$

_{ij}is calculated using the weight vector and the normalized decision matrix, using Equation (4):

- Step 4—Sum of the weighted normalized values of criteria V
_{ij}

_{+i}(maximizing indices) and expenditure S

_{−i}(minimizing indices), the decision matrix first places the income and the expenditure criteria, and S

_{+i}and S

_{−i}are calculated using expressions (5) and (6):

- Step 5—Determining the relative importance (weight) of each alternative

_{−min}is the minimum value of S

_{−i}.

- Step 6—Ranking the alternatives

_{i}, and the best alternative is determined using the following formula:

_{i}[%], the better the alternative.

#### 2.3. Three-Dimensional Method for Determining Storage Parameters

#### 2.4. The Procedure for Determining the Coordinates of Potential Risk Zones

_{ci}, Y

_{ci}, and Z

_{ci}), as well as the weighting coefficient Q

_{i}, which contains the values of all relevant fire-related parameters.

Algorithm 1: Algorithm to find pointset of potential fire hazard zones |

INPUT: Pointset X_{ci}, Y_{ci}, Z_{ci}, Q_{i} |

OUTPUT: X, Y, Z |

Numerator = 0 |

Denominator = 0 |

for i = 1:n |

Numerator_x = Numerator + X_{ci}*Q_{i} |

Numerator_y = Numerator + Y_{ci}*Q_{i} |

Numerator_z = Numerator + Z_{ci}*Q_{i} |

Denominator = Denominator + Q_{i} |

end |

X = Numerator_X/Denominator |

Y = Numerator_Y/Denominator |

Z = Numerator_Z/Denominator |

Post-processing and presentation of results |

^{®}Core™ i5-11300H processor, 32GB DDR4 RAM memory and 512GB SSD disk.

## 3. Numerical Example

_{j}(j = 1, …, 5). After converting the qualitative attributes into quantitative ones, the decision matrix with assigned weighting coefficients formed based on Equation (1) is shown in Table 2.

_{i}and the corresponding ranking are obtained, as shown in Table 3. Identically, the parameters for case 2 can be determined when the decision matrix is replaced, so that parameters C4, C5, C6, and C7 are considered useful, and the other criteria, C1, C2, and C3, are considered useless, as shown in Table 3.

- -
- Variant 1: The first three racks on the left side of the warehouse are completely emptied and the filling of the warehouse with the remaining 840 transport units starts from rack number 4;
- -
- Variant 2: The last three racks on the right side of the warehouse are completely emptied and the filling of the warehouse with the remaining 840 transport units starts from rack number 1;
- -
- Variant 3: The content of each of the racks on the upper front side is reduced by 30%;
- -
- Variant 4: The content of each of the racks on the lower front side is reduced by 30%;
- -
- Variant 5: The content of each of the racks in the uppermost rows is reduced by 30%;
- -
- Variant 6: The content of each of the racks is reduced by 30% in the initial lower rows;
- -
- Variant 7: The content of each of the racks is reduced by 30% and the arrangement of transport units within the racks is carried out randomly.

- -
- Due to the significant difference in the parameters concentration of CO [mg/g] and smoke density [kg/m
^{3}] for tire compared to the other materials (case 1), the weight coefficient w_{e}_{5}= 0.45105 of the mentioned material has the highest value, in comparison to the weight coefficients of the other four materials. - -
- There is no big difference between the weight coefficients w
_{ci}in case 2 because there is no significant deviation in the values of the parameters related to the thermal characteristics of the stored materials.

## 4. Results and Discussion

_{e5}= 0.45105, while in the other case, when the dominant factors are related to combustion, the weighting coefficient is w

_{c5}= 0.155235. The mentioned difference in the weighting coefficient has the effect that in all variants in the first column, the fire risk zone gravitates toward the racks where tire is located, which directly indicates that the width and position of the fire risk zone depend on the arrangement and amount of material in the warehouse.

- -
- The X coordinate for variants 7.1 and 7.2 represents approximately the mean value of the X coordinate for pairs 1.1 and 2.1, that is, 1.2 and 2.2, respectively;
- -
- The Y coordinate for variants 7.1 and 7.2 represents approximately the mean value of the Y coordinate for pairs 3.1 and 4.1, that is, 3.2 and 4.2;
- -
- The Z coordinate of variants 7.1 and 7.2 represents approximately the mean value of the Z coordinate of pairs 5.1 and 6.1, that is, 5.2 and 6.2.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Schematic representation of the formation of a three-dimensional warehouse model and the procedure for obtaining the relevant parameters.

**Figure 4.**Layout of a high-bay warehouse with associated dimensions and materials (• wood, • cardboard, • chipboard, • PVC, and • rubber).

**Figure 5.**Graphic representation of the fire risk zones in the warehouse with isometric view, top view, and side view.

**Table 1.**Input parameters in the procedure of determining the weighting coefficients required for the simulation.

Material | CO [mg/g] | CO_{2} [mg/g] | Smoke Density [kg/m^{3}] | Ignition Temperature [°C] | Thermal Conductivity [W/mK] | Specific Heat Capacity [J/(kg K)] | Calorific Value [MJ/kg] |
---|---|---|---|---|---|---|---|

Wood | 6 | 1696 | 100 | 350 | 0.15 | 1360 | 14.4 |

Cardboard | 0.1 | 1450 | 39.8 | 427 | 0.061 | 1400 | 13.5 |

Plywood | 6 | 1774 | 400 | 150 | 0.13 | 2500 | 17 |

PVC | 71 | 657 | 55.03 | 391 | 0.185 | 900 | 41 |

Rubber (tire) | 600 | 1911 | 8000 | 315 | 1.85 | 1880 | 35 |

Criteria | C1 | C2 | C3 | C4 | C5 | C6 | C7 |
---|---|---|---|---|---|---|---|

Unit of Measure | [mg/g] | [mg/g] | [kg/m^{3}] | [°C] | [W/mK] | [J/(kg K)] | [MJ/kg] |

Goal | min | min | min | max | min | max | min |

Beneficial | Non-Beneficial | ||||||

Weights | 0.2 | 0.2 | 0.2 | 0.1 | 0.1 | 0.1 | 0.1 |

A1 | 6 | 1696 | 100 | 350 | 14.4 | 1360 | 0.15 |

A2 | 0.1 | 1450 | 3.8 | 427 | 13.5 | 1400 | 0.061 |

A3 | 6 | 1774 | 400 | 150 | 17 | 2500 | 0.13 |

A4 | 71 | 657 | 55.03 | 391 | 41 | 900 | 0.185 |

A5 | 600 | 1911 | 8000 | 315 | 35 | 1880 | 1.85 |

**Table 3.**Tabular representation of the entire procedure in the process of determining the weight of alternatives, steps 1–6.

STEP 1 | |||||||

A1 | 0.00878 | 0.22650 | 0.01168 | 0.21433 | 0.06313 | 0.16915 | 0.11911 |

A2 | 0.00015 | 0.19364 | 0.00044 | 0.26148 | 0.02567 | 0.17413 | 0.11166 |

A3 | 0.00878 | 0.23691 | 0.04674 | 0.09186 | 0.05471 | 0.31095 | 0.14061 |

A4 | 0.10394 | 0.08774 | 0.00643 | 0.23944 | 0.07786 | 0.11194 | 0.33912 |

A5 | 0.87835 | 0.25521 | 0.93471 | 0.19290 | 0.77862 | 0.23383 | 0.28950 |

STEP 2 | |||||||

A1 | 0.00878 | 0.22650 | 0.01168 | 0.21433 | 0.06313 | 0.16915 | 0.11911 |

A2 | 0.00015 | 0.19364 | 0.00044 | 0.26148 | 0.02567 | 0.17413 | 0.11166 |

A3 | 0.00878 | 0.23691 | 0.04674 | 0.09186 | 0.05471 | 0.31095 | 0.14061 |

A4 | 0.10394 | 0.08774 | 0.00643 | 0.23944 | 0.07786 | 0.11194 | 0.33912 |

A5 | 0.87835 | 0.25521 | 0.93471 | 0.19290 | 0.77862 | 0.23383 | 0.28950 |

STEP 3 | |||||||

A1 | 0.00176 | 0.04530 | 0.00234 | 0.02143 | 0.00631 | 0.01692 | 0.01191 |

A2 | 0.00003 | 0.03873 | 0.00009 | 0.02615 | 0.00257 | 0.01741 | 0.01117 |

A3 | 0.00176 | 0.04738 | 0.00935 | 0.00919 | 0.00547 | 0.03109 | 0.01406 |

A4 | 0.02079 | 0.01755 | 0.00129 | 0.02394 | 0.00779 | 0.01119 | 0.03391 |

A5 | 0.17567 | 0.05104 | 0.18694 | 0.01929 | 0.07786 | 0.02338 | 0.02895 |

CASE 1 | |||||||

STEP 4 | STEP 5 | STEP 6 | |||||

S_{+i} | S_{−i} | S_{−min}/S_{−i} | w_{ei} | U_{i} | Rank | ||

0.04939 | 0.0566 | 1 | 0.14821 | 32.8586 | 3 | ||

0.03885 | 0.0573 | 0.98738885 | 0.13642 | 30.2442 | 4 | ||

0.05849 | 0.0598 | 0.94582261 | 0.15195 | 33.6878 | 2 | ||

0.03962 | 0.0768 | 0.73626964 | 0.11238 | 24.9145 | 5 | ||

0.41365 | 0.1495 | 0.37844907 | 0.45105 | 100 | 1 | ||

CASE 2 | |||||||

STEP 4 | STEP 5 | STEP 6 | |||||

S_{+i} | S_{−i} | S_{−min}/S_{−i} | w_{ci} | U_{i} | Rank | ||

0.03364 | 0.07181 | 0.890464834 | 0.191791 | 82.62265 | 4 | ||

0.03168 | 0.06584 | 0.971262209 | 0.204186 | 87.96209 | 3 | ||

0.05135 | 0.06871 | 0.930749428 | 0.216658 | 93.33521 | 2 | ||

0.05452 | 0.06395 | 1 | 0.232129 | 100 | 1 | ||

0.12880 | 0.42969 | 0.148824442 | 0.155235 | 66.87452 | 5 |

**Table 4.**Coordinates of potential fire risk zones, distance r, and radius R for cases 1 and 2 (when tire occupies the last two racks).

Variant | X | Y | Z | r | R | View | Variant | X | Y | Z | r | R | View |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Variant 1.1 | 13.85 | 12.11 | 5.05 | 19.08 | 1.054 | Variant 1.2 | 12.19 | 11.98 | 4.76 | 17.74 | 1.038 | ||

Variant 2.1 | 7.94 | 12.11 | 5.05 | 15.34 | 0.742 | Variant 2.2 | 6.38 | 11.95 | 4.76 | 14.36 | 1.142 | ||

Variant 3.1 | 11.61 | 8.40 | 4.80 | 15.11 | 1.018 | Variant 3.2 | 9.23 | 8.40 | 4.80 | 13.37 | 1.584 | ||

Variant 4.1 | 11.61 | 15.60 | 4.8 | 20.03 | 1.018 | Variant 4.2 | 9.23 | 15.60 | 4.80 | 18.75 | 1.584 | ||

Variant 5.1 | 11.51 | 11.56 | 3.45 | 16.67 | 0.648 | Variant 5.2 | 9.12 | 11.57 | 3.47 | 15.14 | 1.249 | ||

Variant 6.1 | 11.61 | 12.46 | 6.21 | 18.13 | 0.654 | Variant 6.2 | 9.23 | 12.46 | 6.21 | 16.70 | 1.379 | ||

Variant 7.1 | 11.61 | 11.84 | 4.89 | 17.29 | 0.862 | Variant 7.2 | 9.23 | 11.84 | 4.87 | 15.78 | 1.493 |

**Table 5.**Coordinates of potential fire risk zones, distance r, and radius R for cases 1 and 2 (when tire occupies the first two racks).

Variant | X | Y | Z | r | R | View | Variant | X | Y | Z | r | R | View |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Variant 1.1 | 10.73 | 11.89 | 4.56 | 16.65 | 0.757 | Variant 1.2 | 12.56 | 12 | 4.82 | 18.03 | 1.242 | ||

Variant 2.1 | 4.82 | 11.90 | 4.56 | 13.62 | 0.976 | Variant 2.2 | 6.76 | 12 | 4.82 | 14.59 | 1.006 | ||

Variant 3.1 | 7.01 | 8.40 | 4.80 | 11.95 | 1 | Variant 3.2 | 9.78 | 8.40 | 4.80 | 13.76 | 1.426 | ||

Variant 4.1 | 7.01 | 15.60 | 4.8 | 17.76 | 1 | Variant 4.2 | 9.78 | 15.60 | 4.80 | 19.03 | 1.426 | ||

Variant 5.1 | 6.97 | 11.56 | 3.45 | 13.93 | 0.578 | Variant 5.2 | 9.66 | 11.57 | 3.48 | 15.47 | 1.262 | ||

Variant 6.1 | 7.01 | 12.46 | 6.21 | 15.59 | 0.626 | Variant 6.2 | 9.78 | 12.46 | 6.21 | 17.01 | 1.193 | ||

Variant 7.1 | 7.05 | 11.82 | 4.88 | 14.60 | 0.838 | Variant 7.2 | 9.78 | 11.84 | 4.87 | 16.11 | 1.322 |

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**MDPI and ACS Style**

Bošković, G.; Todorović, M.; Ubavin, D.; Stepanov, B.; Mihajlović, V.; Perović, M.; Čepić, Z.
A New Method for the Determination of Fire Risk Zones in High-Bay Warehouses. *Fire* **2024**, *7*, 149.
https://doi.org/10.3390/fire7040149

**AMA Style**

Bošković G, Todorović M, Ubavin D, Stepanov B, Mihajlović V, Perović M, Čepić Z.
A New Method for the Determination of Fire Risk Zones in High-Bay Warehouses. *Fire*. 2024; 7(4):149.
https://doi.org/10.3390/fire7040149

**Chicago/Turabian Style**

Bošković, Goran, Marko Todorović, Dejan Ubavin, Borivoj Stepanov, Višnja Mihajlović, Marija Perović, and Zoran Čepić.
2024. "A New Method for the Determination of Fire Risk Zones in High-Bay Warehouses" *Fire* 7, no. 4: 149.
https://doi.org/10.3390/fire7040149