# Improving the Blast Resistance of Large Steel Gates—Numerical Study

^{*}

## Abstract

**:**

## 1. Introduction

^{2}). The manufacturer confirms that the door has resistance against multiple blast loads ranging from 9–18 bars (0.9–1.8 MPa) peak reflected overpressure, and that the steel material behaves within the elastic range.

## 2. Site Plan and Assumptions

- The gate is outside the explosion fireball. In other words, the interaction with the produced gases can be neglected and there is no afterburning effect. Afterburning (combustion of the detonation products following an explosion) can increase the duration of the positive phase and thus the impulse on near field structure.
- As a blast wave propagates in the air, atmospheric pressure is an important factor which varies with the altitude of the location. Therefore, it is assumed here that the blast occurs at sea level.
- The charge was uncased with no additional loading from fragmentation (for more information about fragmentation, refer to Szymczyk et al. [34].

## 3. Geometrical and Material Properties of the Gate

## 4. Threat Assessment and Blast Loading

## 5. Numerical Modelling

## 6. Uniaxial Graded Auxetic Damper (UGAD)

## 7. Gate Response (without UGAD)

#### 7.1. Peak Nodal Reaction Forces

_{m}/RF

_{100}) is presented in Figure 10b. Results show that the quarterly-decreasing mass of TNT did not reduce peak RF in the same pattern. For instance, a reduction from 100 kg to 50 kg in the mass of TNT led to only 24% fall in the peak RF at the same support (RF

_{m}/RF

_{100}= 76%). In other words, the blast level–reaction force relation is not proportional. Hence, the performance of passive dampers should be analysed for each blast level separately.

#### 7.2. Deformation and Operability Analysis

_{limit}= 750 sin2° = 26.2 mm. If permanent deformation exceeds that limit, then the gate can be considered as inoperable. As an example, Figure 13 shows the catastrophic failure of gate G2.5.

_{limit}). In other words, G10 was the only gate that can be considered as operable after the blast event, with permanent frame deformation d

_{frame}= 4.4 mm. The addition of passive dampers in Section 8 may reduce $d$ values for G5 or G7.5 to D

_{limit}, i.e., a lighter and hence more economical gate may be used (which is one objective of this study).

^{6}J of energy at the position of detonation. However, the gate receives much less energy depending on stand-off distance and exposed area of the gate. Figure 15 shows energy components for the four gates, namely G2.5, G5, G7.5, and G10, under a blast of 6.6 MPa (from 100 kg of TNT, R = 5 m, explosive location A). The following points can be highlighted; The more is the mass of the gate, the less the kinetic energy is (e.g., peak kinetic energy for G2.5 is 4 times higher than G10). Plastic dissipation energy and strain energy are the main components of internal energy in the gate. The plastic dissipation energy is found to be decreasing with increasing the thickness $t$. This is linked to the plastic deformations that are normally less for higher values of $t$. The plastic dissipation energy was as high as 1200 × 10

^{3}J for G2.5, and as low as 90 × 10

^{3}J for G10. In other words, light gates provide better energy absorption at the cost of more permanent deformation. Strain energy found to be increasing with increasing the thickness $t$. Damage dissipation energy was zero as damage criteria were not met. Viscous and creep dissipation energies were also zero. Artificial strain energy was very small (up to 2% of the total internal energy), which reflects the accuracy of the numerical model.

## 8. Gate Behavior with the Proposed Auxetic Damper

_{frame}= 4.4 mm, less than D

_{limit}(26.2 mm).

_{frame}< D

_{limit}(26.2 mm). The frame permanent deformation of G7.5 dropped from 28.4 to 4mm with the addition of the UGADs. Furthermore, the frame permanent deformation of G5 decreased from 40.5 to 22 mm with the addition of the UGADs, making G5 the lightest-operable option that can withstand the peak reflected overpressure target of 6.6 MPa.

^{6}to 0.51 × 10

^{6}N (49% of reduction).

^{3}J) constitute of major plastic dissipation (164 × 10

^{3}J) and minor frictional dissipation (10 × 10

^{3}J), with no dissipation due to damage. Based on that successful damping, the kinetic energy is mitigated. It is also important to highlight that the value of artificial energy is near zero, which reflects that the numerical model of the system was accurate to high extent. In addition, Figure 25 shows that 56% of the total PDE in the system was achieved from the UGADs, while 44% from the gate. The additional PDE gained from those light weight auxetic cores justifies the significant reduction in permanent deformations and reaction forces.

^{3}MPa. Moment of inertia I = $\frac{b{h}^{3}}{12}=\frac{{35}^{4}}{12}=125,052$ mm

^{4}. The effective length factor K is $2$ for free-end column, and the unsupported length of the column is 310 mm. Then, critical load ${P}_{cr}$ is 642 150 N, greater than the applied axial load. In other words, the piston rod would stay in elastic range with no lateral buckling, when subjected to peak reaction forces generated from 100 kg TNT at 5 m. In addition, numerical results showed no local buckling or eventual crippling in the piston rod.

## 9. Conclusions

- In-plane reaction forces are very small compared to those out-of-plane (direction of blast). Therefore, RFz is the considered component in this paper as it is the prominent one.
- The UGAD dampers may work for G5, G7.5, or G10 in the same efficiency, as the mass shown to have slight effect on RFs (Figure 11).
- G10 was the only gate (without external damping systems) that satisfied operability condition after the blast event, with peak permanent deformation, d
_{frame}= 4.4 mm. - With the application of the proposed UGAD, both G7.5 and G5 passed the operability requirement. The frame permanent deformation of G5 decreased from 40.5 to 22 mm, making G5 the lightest-operable option that can withstand the peak reflected overpressure target of 6.6 MPa. In addition, a 49% reduction in peak reaction forces was recorded which can reduce the required cross section and strength of the concrete supports.
- Internal energy in the whole model composed mainly of plastic dissipation, small frictional dissipation, and no dissipation due to damage. Moreover, 56% of the total plastic dissipation energy in the system was achieved from the UGADs, while 44% from the gate. Based on that successful energy dissipation, the kinetic energy was mitigated.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Peak reflected overpressure and impulse history of 4 blast levels (25 kg, 50 kg, 75 kg and 100 kg, R = 5 m), (

**a**) peak reflected overpressure, (

**b**) impulse.

**Figure 4.**Schematic of explosive centroid effective locations, situated on the gate projection, M = 100 kg, R = 5 m.

**Figure 8.**Uniaxial Graded Auxetic Damper (UGAD). (

**a**) Components of the UGAD. (

**b**) Cross-section. (

**c**) 3D.

**Figure 9.**The proposed gate system in reality, and the numerical modeling of quarter the system (due to symmetry).

**Figure 10.**Effect of blast levels (changing mass of TNT) on peak nodal reaction forces, RFs. (

**a**) RF time history. (

**b**) RF

_{m}/RF

_{100}.

**Figure 11.**Reaction forces for the 4 gates G2.5, G5, G7.5 and G10, under a blast of 100 kg of TNT, R = 5 m.

**Figure 14.**Spatial displacement of front and back plates of gate G5 after 6.6 MPa peak reflected overpressure. (

**a**) Front view. (

**b**) Side view.

**Figure 15.**Energy components for the 4 gates G2.5, G5, G7.5 and G10, under blast of 6.6 MPa (from 100 kg of TNT, R = 5 m).

**Figure 16.**Displacement of Gate G5 and the Auxetic damper after a blast peak reflected overpressure of 1.65 MPa from 25 kg TNT at R = 5 m.

**Figure 17.**Displacement of Gate G5 and the Auxetic damper after a blast peak reflected overpressure of 3.3 MPa from 50 kg TNT at R = 5 m.

**Figure 18.**Displacement of Gate G5 and the Auxetic damper after a blast peak reflected overpressure of 4.95 MPa from 75 kg TNT at R = 5 m.

**Figure 19.**Displacement of Gate G5 and the Auxetic damper after a blast peak reflected overpressure of 6.6 MPa from 100 kg TNT at R = 5 m.

**Figure 20.**Displacements of Pistons’ heads (i.e., compressed length of auxetic cores) at supports S1–S5, after peak reflected overpressure of 6.6 MPa from 100 kg TNT at R = 5 m, Gate G5.

**Figure 21.**Velocity of Pistons’ heads (i.e., velocity of compressing auxetic cores) at supports S1–S5, after a peak reflected overpressure of 6.6 MPa from 100 kg TNT at R = 5 m, Gate G5.

**Figure 22.**Reaction forces RF at supports S1–S5 without external dampers, after peak reflected overpressure of 6.6 MPa from 100 kg TNT at R = 5 m, Gate G5.

**Figure 23.**Reaction forces RFd at supports S1–S5 with the auxetic dampers, after peak reflected overpressure of 6.6 MPa from 100 kg TNT at R = 5 m, Gate G5.

**Figure 24.**Energy components of the model (shown in Figure 9E), after peak reflected overpressure of 6.6 MPa from 100 kg TNT at R = 5 m, Gate G5.

**Figure 25.**PDE by dampers, gate and the total PDE in the model (shown in Figure 9E), after peak reflected overpressure of 6.6 MPa from 100 kg TNT at R = 5 m, Gate G5.

**Figure 26.**Displacement of Gate G5 and the Auxetic damper after a blast peak reflected overpressure of 9.9 MPa from 150 kg TNT at R = 5 m.

**Table 1.**Material parameters for Weldox 460E Steel (adopted from [32]).

Category | Constant | Description | Unit | Value |
---|---|---|---|---|

Elastic Constants | E | Modulus of Elasticity | MPa | 200 × 10^{3} |

ν | Poisson’s ratio | - | 0.33 | |

Density | ρ | Mass density | t/mm^{3} | 7.85 × 10^{−9} |

Yield stress and strain hardening | A | Yield Strength | MPa | 490 |

B | Ultimate Strength | MPa | 807 | |

n | Work-hardening exponent | - | 0.73 | |

Strain-rate hardening | $\dot{{\epsilon}_{0}}$ | Reference Strain rate | S^{−1} | 5 × 10^{−4} |

C | Strain rate factor | - | 0.0114 | |

Damage evolution | ${D}_{c}$ | Critical Damage | - | 0.3 |

${p}_{d}$ | Damage threshold | - | 0 | |

Adiabatic heating and temperature softening | ${C}_{p}$ | Specific heat | mm^{2}K/S^{2} | 452 × 10^{6} |

χ | Taylor Quinney empirical constant/inelastic heat fraction | - | 0.9 | |

α | Coefficient of thermal expansion | K^{−1} | 1.1 × 10^{−5} | |

${T}_{m}$ | Melting Temperature | K | 1800 | |

${T}_{0}$ | Room Temperature | K | 293 | |

m | Thermal-softening exponent | - | 0.94 | |

K | - | - | 0.74 | |

Fracture Strain Constants | ${d}_{1}$ | - | - | 0.0705 |

${d}_{2}$ | - | - | 1.732 | |

${d}_{3}$ | - | - | −0.54 | |

${d}_{4}$ | - | - | −0.015 | |

${d}_{5}$ | - | - | 0 |

Mesh = 50 mm | Mesh = 20 mm | Mesh = 10 mm | |
---|---|---|---|

Plastic dissipation Energy | 12.84 | 2.85 | 0.84 |

Peak reaction force | 46.79 | 32.52 | 0.80 |

**Table 3.**The 3 auxetic cores of the Uniaxial Graded Auxetic Damper (UGAD), with their geometric and mechanical properties, adopted from [31].

Aux.1 | Aux.2 | Aux.3 | |
---|---|---|---|

Shape | |||

Shared parameters | L = 10 mm, cell angle $\theta $ = 60°, Grade AL3 (${\rho}_{s}$ = 2.703 × 10^{−9} t/mm^{3}),Size = 140 mm × 200 mm × 200 mm, volume of one core V = 5.6 × 10 ^{6} mm^{3} | ||

$t$ (mm) | 1.4 | 1.8 | 2.2 |

t/L | 0.14 | 0.18 | 0.22 |

Mass (ton) | 0.00338 | 0.00434 | 0.00530 |

Mass (kg) | 3.38 | 4.34 | 5.30 |

Density $\rho $ (t/mm^{3}) | 6.036 × 10^{−10} | 7.75 × 10^{−10} | 9.46 × 10^{−10} |

Relative Density ${\rho}^{*}=\rho /{\rho}_{s}$ | 0.223 | 0.287 | 0.35 |

Void ratio % | 77.7 | 71.3 | 65 |

Gate | G2.5 | G5 | G7.5 | G10 |
---|---|---|---|---|

Total Mass (ton) | 1.10 | 2.19 | 3.29 | 4.38 |

Mass/Area (kg/m^{2}) | 81.12 | 162.23 | 243.35 | 324.47 |

**Table 5.**Plastic strain, permanent deformation and operability for the 4 gates under consideration, subjected to 6.6 MPa peak reflected overpressure from 100 kg TNT at R = 5 m.

Peak Plastic Strain | Permanent Deformation d (mm) | Operable | ||||||
---|---|---|---|---|---|---|---|---|

Gate | t (mm) | Frame | Front Plate | Back Plate | Frame | Front Plate | Back Plate | (Yes/No) |

G2.5 | 2.5 | 0.89 | 0.82 | 0.17 | 551.0 | 489.0 | 490.0 | No |

G5 | 5 | 0.29 | 0.17 | 0.25 | 40.5 | 65.6 | 40.0 | No |

G7.5 | 7.5 | 0.20 | 0.13 | 0.17 | 28.4 | 30.0 | 28.0 | No |

G10 | 10 | 0.02 | 0.07 | 0.05 | 4.4 | 11.6 | 10.5 | Yes |

**Table 6.**Plastic strain, permanent deformation and operability of the gates with the proposed auxetic damper, subjected to 6.6 MPa blast peak reflected overpressure from 100 kg TNT at R = 5 m.

Peak Plastic Strain | Permanent Deformation d (mm) | Operable | ||||||
---|---|---|---|---|---|---|---|---|

Gate | t (mm) | Frame | Front Plate | Back Plate | Frame | Front Plate | Back Plate | (Yes/No) |

G2.5 | 2.5 | 0.93 | 0.89 | 0.19 | 676 | 613 | 609 | No |

G5 | 5 | 0.1 | 0.17 | 0.156 | 22 | 51 | 24 | Yes |

G7.5 | 7.5 | 0.03 | 0.16 | 0.1 | 4 | 19 | 8 | Yes |

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**MDPI and ACS Style**

Al-Rifaie, H.; Sumelka, W.
Improving the Blast Resistance of Large Steel Gates—Numerical Study. *Materials* **2020**, *13*, 2121.
https://doi.org/10.3390/ma13092121

**AMA Style**

Al-Rifaie H, Sumelka W.
Improving the Blast Resistance of Large Steel Gates—Numerical Study. *Materials*. 2020; 13(9):2121.
https://doi.org/10.3390/ma13092121

**Chicago/Turabian Style**

Al-Rifaie, Hasan, and Wojciech Sumelka.
2020. "Improving the Blast Resistance of Large Steel Gates—Numerical Study" *Materials* 13, no. 9: 2121.
https://doi.org/10.3390/ma13092121