# Numerical Simulation Study on Factors Influencing Anti-Explosion Performance of Steel Structure Protective Doors under Chemical Explosion Conditions

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## Abstract

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## 1. Introduction

^{1/3}, and they proposed a failure evaluation criterion for one-way slabs based on their test results. Fang et al. [3] used the LS-DYNA finite element analysis software to conduct a comparative study on the anti-explosion capabilities of two types of protective doors (ordinary steel protective doors and protective doors with high-damping rubber filler layers) under typical shock wave loads. Their numerical simulation results showed that using high-damping rubber filler layers in steel protective doors can effectively improve the stress distribution of the door sash panel and avoid the stress concentration phenomena in local areas of the door sash. The door deformation could be reduced by 62% by the rubber filler layers, showing good attenuation resistance to shock waves. Guo et al. [4] used finite element software to establish a model for typical beam–plate steel-structure protective doors and carried out analysis on the factors influencing the anti-explosion performance of the protective door under shock wave loads. Due to the significant stress concentration around the four corners of the doorframe under shock waves, Zhao et al. [5] established a finite element model of the door and the doorframe wall structure based on cantilever beam theory. To effectively reduce the stress concentration, local stress alleviation measures were proposed, which were carried out by establishing artificial weak layers at the doorframe wall and its lining. Li et al. [6] used LS-DYNA to analyze the effect of the explosion shock wave loads of a thermal-pressure bomb on the failure modes of reinforced concrete protective doors. Dong et al. [7] used the ABAQUS finite element software to analyze the dynamic responses of a protective door with a cable and membrane structure under explosion loads and evaluated the anti-explosion performance of the protective door based on the simulation results.

## 2. Anti Explosion Test Condition of Protective Door

#### 2.1. Test Conditions

#### 2.2. Layout of Measuring Points

## 3. Shock Wave Load Analysis for Protective Door

#### 3.1. Finite Element Model and Material Parameters

#### 3.1.1. Finite Element Model

#### 3.1.2. Mesh Size Effect Analysis

^{3}times that of the former, and its calculation time cost increased significantly. Based on the above analysis, it is reasonable to set the cell mesh size of the 3D model in this paper to 10 cm. This cell size can ensure good calculation accuracy and high calculation efficiency during the analysis process.

#### 3.1.3. Air

_{0}is initial air density, value 1.225 kg/m

^{3}; γ is adiabatic index, value 1.4; E

_{0}is the initial specific internal energy of the air, the value is 2.068 e5 J/kg.

#### 3.1.4. Explosives

_{0}, ρ and ρ

_{0}is the initial density of explosive and the density of detonation products, kg/m

^{3}; e is the initial internal energy per unit mass explosive, J/kg; A, B, R

_{1}, R

_{2}and ω are the five constants of the equation of state that need to be determined by cylinder test and two-dimensional hydrodynamic program [14,15]. The equation of state parameters of TNT explosives are selected, as shown in Table 2. The dominant pressure term in the equation of state changes at different stages of the loading explosion. Three terms in the right end of the upper formula (From left to right, it is represented by PH, PM and PL) play the main role in the high, medium, and low pressure ranges, respectively, while in the late stage of the detonation product expansion, the pressure of the detonation product is mainly determined by PL, the first two roles are negligible.

#### 3.2. Layout of the Observation Points

**Figure 7.**Layout of observation points: (

**a**) Front view (X axis); (

**b**) Right view (Y axis); (

**c**) Oblique axonometric drawing.

#### 3.3. Comparison of Numerical Simulations and Experimental Results

#### Overpressure Time-History Curves of Observation Point on Doorframe Wall

**Figure 8.**Comparison of overpressure time-history curves of door frame wall measuring points under test condition 2: (

**a**) Observation point 1 (Measuring point P1); (

**b**) Observation point 2 (Measuring point P3); (

**c**) Observation point 3 (Measuring point P2).

**Figure 9.**Comparison of overpressure time-history curves of door frame wall measuring points under test condition 3: (

**a**) Observation point 1 (Measuring point P1); (

**b**) Observation point 2 (Measuring point P3).

#### 3.4. Calculation Load on Protective Door

**Figure 10.**Calculation of overpressure time-history curve of measuring points on the door leaf of protective door: (

**a**) Test condition 2; (

**b**) Test condition 3.

_{n}and F

_{8}are the peak overpressure or impulse at observation points No. n and No. 8, respectively.

**Figure 11.**Distribution of shock wave load parameters of protective door under test condition 2: (

**a**)Peak overpressure; (

**b**) Impulse.

**Figure 12.**Distribution of shock wave load parameters of protective door under test condition 3: (

**a**) Peak overpressure; (

**b**) Impulse.

## 4. Failure Effect Analysis of Steel Structure Protective Door

#### 4.1. Finite Element Model and Material Parameters of Steel Structure Protective Door

#### 4.1.1. Finite Element Model

**Figure 14.**Finite element calculation model of protective door: (

**a**) 1/2 finite element model of skeleton; (

**b**) Connection mode between skeleton and panel; (

**c**) Finite element model of protective door and door frame (front); (

**d**) Finite element model of protective door and door frame (back).

#### 4.1.2. Steel

_{y}is the dynamic yield stress, σ

_{0}is the initial yield stress, $\dot{\epsilon}$ is the strain rate, C and P are strain rate parameters, ${\epsilon}_{p}^{eff}$ is the effective plastic strain, β is the hardening parameter, and E

_{p}is the plastic hardening modulus. The values of C and P are related to the steel type. Table 6 shows the strain rate data of different types of steel. The C and P values used in this paper were 40.4 s

^{−1}and 5, respectively.

#### 4.1.3. Doorframe

#### 4.2. Shock Wave Loading Pattern

**Figure 15.**Velocity and acceleration curve of the central node of the blast face of the protective door: (

**a**) Velocity curve; (

**b**) Acceleration curve.

#### 4.3. Comparison between Simulation and Measurements

#### 4.3.1. Comparative Analysis of Displacement

^{−4}

_{1}= 0.1 s as the dividing line. The displacement curve of a given node has similar variation processes in different stages, i.e., reaching the peak displacement rapidly under the load and then reaching a stable residual deformation condition after a process of small oscillations and rebounds. A larger peak overpressure resulted in a shorter oscillation period. A smaller displacement rebound resulted in a larger residual displacement. In stage I, the displacement rebounds of these two nodes were approximately 30.0%, while they were only approximately 5% in stage II. This was because the peak load in stage II was greater, and the door had already sustained damage in stage I. Therefore, the deformation recovery capability of the door in stage II was significantly less than that in stage I, resulting in a larger residual deformation.

#### 4.3.2. Comparative Analysis of Failure Modes

## 5. Analysis on Influence Factors of Anti-Explosion Performance of Protective Door

#### 5.1. Overview of Finite Element Analysis

#### 5.2. Effect of Steel Strength

#### 5.3. Effect of Geometric Dimensions

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**2D finite element model with different element mesh sizes: (

**a**) 2D axisymmetric model; (

**b**) 10 mm; (

**c**) 5 mm; (

**d**) 2.5 mm; (

**e**) 1 mm.

**Figure 5.**Overpressure time-history curves of measuring points calculated with different mesh sizes: (

**a**) x = 0.5 m; (

**b**) x = 1.0 m; (

**c**) x = 1.5 m.

**Figure 6.**Influence of different mesh sizes on calculation results of tunnel shock wave: (

**a**) Influence of mesh size on overpressure peaks; (

**b**) Influence of mesh size on impulse.

**Figure 18.**The failure pattern of the two anti-explosion tests of the protective door: (

**a**) Stage I; (

**b**) Stage II.

**Figure 21.**Displacement time-history curves of protective doors with different material strengths: (

**a**) Outer panel; (

**b**) Skeleton; (

**c**) Inner panel.

**Figure 22.**Relationship between the peak displacement of the protective door and the steel strength.

**Figure 23.**Relationship between the decreasing amplitude of the displacement peak value of the protective door and the increasing amplitude of the steel strength.

**Figure 24.**Influence of outer panel thickness ${h}_{1}$ on displacement response of protective door: (

**a**) Displacement time-history curve; (

**b**) Relationship between peak displacement and thickness of outer panel.

**Figure 25.**Influence of inner panel thickness ${{h}^{\prime}}_{1}$ on displacement response of protective door: (

**a**) Displacement time-history curve; (

**b**) Relationship between peak displacement and inner panel thickness.

**Figure 26.**Influence of flange thickness ${h}_{2}$ on displacement response of protective door: (

**a**) Displacement time-history curve; (

**b**) Relationship between peak displacement and flange thickness.

**Figure 27.**Influence of web thickness ${h}_{3}$ on displacement response of protective door: (

**a**) Displacement time-history curve; (

**b**) Relationship between peak displacement and web thickness.

**Figure 28.**Influence of skeleton height ${h}_{4}$ on displacement response of protective door: (

**a**) Displacement time-history curve; (

**b**) Relationship between displacement peak and skeleton height.

Test Conditions | Charge Quantity (W/kg) | Horizontal Distance between Charging Center and Protective Door (S/m) | Suspension Height of Charging Center (h/m) |
---|---|---|---|

1 | 1.36 | 11.0 | 0.9 |

2 | 10.2 | 11.0 | 0.9 |

3 | 20.0 | 7.0 | 0.9 |

Explosive | ρ_{0}/(kg·m^{−3}) | A/Pa | B/Pa | R_{1} | R_{2} | $\mathit{\omega}$ | Detonation Velocity D/(m·s^{−1}) | Explosion Pressure P_{CJ}/Pa | Internal Energy per Unit Volume E_{0}/(J·m^{−3}) |
---|---|---|---|---|---|---|---|---|---|

TNT | 1630 | 3.74 × 10^{11} | 3.75 × 10^{9} | 4.15 | 0.9 | 0.35 | 6930 | 2.1 × 10^{10} | 6.0 × 10^{9} |

Number | Position Coordinates | Remarks | ||
---|---|---|---|---|

X/mm | Y/mm | Z/mm | ||

1 | 18,200 | 0 | 2350 | Observation points on the door frame wall: observation points 1, 2 and 3 correspond to measurement points P1, P3 and P2 in the test respectively. |

2 | 18,200 | −825 | 1100 | |

3 | 18,200 | 825 | 1100 | |

4 | 18,100 | 700 | 100 | Observation point on the protective gate |

5 | 18,100 | 700 | 1150 | |

6 | 18,100 | 700 | 2200 | |

7 | 18,100 | 0 | 100 | |

8 | 18,100 | 0 | 1150 | |

9 | 18,100 | 0 | 2200 |

**Table 4.**Comparison between experimental and calculated values of shock wave parameters at measuring points.

Test Conditions | Observation Point | Peak Overpressure/MPa | Impulse/Pa·s | ||||
---|---|---|---|---|---|---|---|

Test Value | Calculated Value | Error/% | Test Value | Calculated Value | Error/% | ||

2 | 1 | 1.52 | 1.42 | −6.6 | 11,727.0 | 12,347.4 | 5.3 |

2 | 2.39 | 2.45 | 2.5 | 15,267.9 | 16,467.5 | 7.9 | |

3 | 2.48 | 2.45 | −1.2 | × | 12,254.8 | × | |

3 | 1 | 3.48 | 3.12 | −10.3 | × | 18,445.1 | × |

2 | 6.13 | 7.73 | 26.1 | ◊ | 25,956.7 | ◊ | |

3 | ◊ | 7.73 | ◊ | ◊ | 25,956.7 | ◊ |

Position | Test Point Number | Test Conditions 2 | Test Conditions 3 | ||
---|---|---|---|---|---|

Peak Overpressure/MPa | Impulse Value/Pa·s | Peak Overpressure/MPa | Impulse Value/Pa·s | ||

Lower part | 4 | 2.30 | 21,183.5 | 5.84 | 33,980.3 |

7 | 1.51 | 21,056.4 | 4.67 | 33,827.7 | |

Middle part | 5 | 1.63 | 20,133.4 | 4.75 | 32,614.6 |

8 | 1.67 | 20,148.5 | 4.93 | 32,641.0 | |

Upper part | 6 | 1.57 | 20,285.0 | 4.06 | 32,338.2 |

9 | 1.34 | 20,292.2 | 3.07 | 32,496.2 |

Material | C/s^{−1} | P | literature |
---|---|---|---|

Mild steel | 40.4 | 5 | Cowper and Symonds [18] |

Aluminium alloy | 6500 | 4 | Bodner and Symonds [19] |

α-titanium (Ti50A) | 120 | 9 | Symonds and Chon [20] |

304 Stainless steel | 100 | 10 | Forrestal and Sagartz [21] |

High-strength steel | 3200 | 5 | Paik and Chung [22] |

Assembly | Density/(kg/m^{3}) | Poisson Ratio | Elastic Modulus/GPa | Yield Strength/MPa | Hardening Modulus/GPa | Strain Rate Parameter | Failure Strain | |
---|---|---|---|---|---|---|---|---|

C | P | |||||||

Skeleton, panel, backing plate | 7800 | 0.3 | 206 | 235 | 0.21 | 40.4 | 5 | 0.3 |

Screw rod, sleeve | 7800 | 0.3 | 200 | 355 | 0.21 | 40.4 | 5 | 0.3 |

Door frame | 2500 | 0.2 | 32.5 | - | - | - | - | - |

Calculation Condition Number | Outer Panel | Inner Panel | Skeleton | Maximum Displacement/mm | Maximum Displacement Reduction Amplitude/% |
---|---|---|---|---|---|

1 | Q235 | Q235 | Q235 | 97.4 | 0 |

2 | Q275 | 96.5 | 0.9 | ||

3 | Q345 | 95.8 | 1.6 | ||

5 | Q235 | Q275 | Q235 | 70.2 | 27.9 |

6 | Q345 | 55.7 | 42.8 | ||

7 | Q235 | Q235 | Q275 | 95.3 | 2.2 |

8 | Q345 | 92.7 | 4.8 |

**Table 9.**Calculation condition table for the analysis of the influencing factors of geometric dimensions.

Calculation Condition Number | ${\mathit{h}}_{1}/\mathbf{mm}$ | ${{\mathit{h}}^{\prime}}_{1}/\mathbf{mm}$ | ${\mathit{h}}_{2}/\mathbf{mm}$ | ${\mathit{h}}_{3}/\mathbf{mm}$ | ${\mathit{h}}_{4}/\mathbf{mm}$ |
---|---|---|---|---|---|

1 | 6 | 8 | 8 | 6 | 100 |

2 | 8 | ||||

3 | 10 | ||||

4 | 12 | ||||

5 | 14 | ||||

6 | 8 | 6 | 8 | 6 | 100 |

7 | 10 | ||||

8 | 12 | ||||

9 | 14 | ||||

10 | 8 | 8 | 6 | 6 | 100 |

11 | 10 | ||||

12 | 12 | ||||

13 | 14 | ||||

14 | 8 | 8 | 8 | 8 | 100 |

15 | 10 | ||||

16 | 12 | ||||

17 | 14 | ||||

18 | 8 | 8 | 8 | 6 | 60 |

19 | 80 | ||||

20 | 120 | ||||

21 | 140 |

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**MDPI and ACS Style**

Wang, H.; Li, Z.; Wu, Y.; Shao, L.; Yao, M.; Liao, Z.; Tang, D.
Numerical Simulation Study on Factors Influencing Anti-Explosion Performance of Steel Structure Protective Doors under Chemical Explosion Conditions. *Materials* **2022**, *15*, 3880.
https://doi.org/10.3390/ma15113880

**AMA Style**

Wang H, Li Z, Wu Y, Shao L, Yao M, Liao Z, Tang D.
Numerical Simulation Study on Factors Influencing Anti-Explosion Performance of Steel Structure Protective Doors under Chemical Explosion Conditions. *Materials*. 2022; 15(11):3880.
https://doi.org/10.3390/ma15113880

**Chicago/Turabian Style**

Wang, Haiteng, Zhizhong Li, Yingxiang Wu, Luzhong Shao, Meili Yao, Zhen Liao, and Degao Tang.
2022. "Numerical Simulation Study on Factors Influencing Anti-Explosion Performance of Steel Structure Protective Doors under Chemical Explosion Conditions" *Materials* 15, no. 11: 3880.
https://doi.org/10.3390/ma15113880