# Damage Zone of the Reinforced Concrete Beam under Rectangular Explosive Contact Explosions

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Test Overview and Results Analysis

#### 2.1. RC Beam Model

#### 2.2. Test Conditions

^{3}, respectively. TNT with a mass of 1, 2, 3, 4, and 6 kg was selected for the damaged test. The dimension of TNT is shown in Figure 4a. TNT is placed on the surface of the beam and in direct contact with the concrete, as shown in Figure 4b.

#### 2.3. Analysis of Test Results

## 3. Numerical Simulation

#### 3.1. Finite Element Model

#### 3.2. Material Model and Parameters

_{1}, R

_{2}, and ω are fitting coefficients. Specific parameter values are presented in Table 2

#### 3.3. Results and Analysis of Numerical Simulation

#### 3.4. Damage Curve Fitting

#### 3.5. Effects of Concrete and Steel Grade

#### 3.6. Effects of Explosive Stand-off Distance

^{−1/3}; only the concrete on the front side of the beam showed slight damage and there were no obvious cracks on the side when the stand-off distance increased to 50 cm. The degree of damage to the beam caused by TNT contact explosions of the same mass increases sharply compared to near-field explosions. The damage to the beam will be significantly reduced when the scaled distance is 0.208 m·kg

^{−1/3}.

## 4. Discussion

#### 4.1. Beam Surface Load

#### 4.2. Analysis of Concrete Failure Effect of the Beam

#### 4.3. Calculation of Damage to the Beam

^{1/3}. The equation is conservative in calculating the explosion crater, spall, and penetration of the beam, and appropriately increasing the right coefficient is consistent with the test results of this study when the height of the beam is equivalent to the thickness of the plate.

#### 4.4. Resistance Function of Beam

^{3}. The dead weight of the test beam is 2900 kg after calculation. $x(t)$ is the change of displacement of the single degree-of-freedom system with time, and $F(t)$ is the external load on the single degree-of-freedom system.

#### 4.5. Calculation of Blasting Crater of the Beam

## 5. Conclusions

^{−1/3}.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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Mass of Explosive/kg | Explosive Size/mm^{3} | Damage Span of Front Face/cm | Damage Span of Back Face/cm | Depth of Blasting Crater/cm |
---|---|---|---|---|

1 | 125 × 50 × 100 | 52.4 | 0 | 3 |

2 | 125 × 100 × 100 | 82.8 | 80.2 | 13 |

3 | 150 × 125 × 100 | 91.7 | 97 | 25.5 |

4 | 200 × 125 × 100 | 106.5 | 132 | 33.4 |

6 | 200 × 125 × 150 | 126 | 138 | 42 |

Material Type | Material Model | Main Parameters | |||
---|---|---|---|---|---|

Explosive | MAT_HIGH_EXPLOSIVE_BURN | ρ/(g/cm^{3}) | C/(m/s) | A/GPa | B/Gpa |

1.63 | 6930 | 373.77 | 3.75 | ||

R1 | R2 | ω | E0/KJ/m^{3} | ||

4.5 | 0.9 | 0.35 | 6.0 × 10^{6} | ||

air | MAT_NULL | ρ/(g/cm^{3}) | T/K | γ | c/(J/kg·K) |

1.225 × 10^{−3} | 288.2 | 1.4 | 717.6 | ||

reinforcement | MAT_PLASTIC_KINEMATIC | ρ/(g/cm^{3}) | E/GPa | ν | σ_{y} |

7.8 | 200 | 0.3 | 400 |

Density (g/cm ^{3}) | Compressive Strength (MPa) | Tensile Strength (MPa) | Shear Modulus (MPa) | A | N |
---|---|---|---|---|---|

2.314 | 35 | 3.5 | 16,700 | 1.6 | 0.61 |

Af | Nf | ${\mathrm{Q}}_{0}$ | B | ${\mathrm{D}}_{1}$ | ${\mathrm{D}}_{2}$ |

1.6 | 0.61 | 0.6805 | 0.0105 | 0.04 | 1.0 |

EMP | ${\mathrm{A}}_{1}$ (MPa) | ${\mathrm{A}}_{2}$ (MPa) | ${\mathrm{A}}_{3}$ (MPa) | ${\mathrm{B}}_{0}$ | ${\mathrm{B}}_{1}$ |

0.01 | 35,270 | 39,580 | 9040 | 1.22 | 1.22 |

Mass of TNT/kg | Length of Failure Zone of Front Face/cm | Error | Length of Failure Zone of Back Face/cm | Error | ||
---|---|---|---|---|---|---|

Test | Numerical Simulation | Test | Numerical Simulation | |||

1 | 52.4 | 54 | 3.05% | — | — | — |

2 | 82.8 | 82 | 0.97% | 80.2 | 84 | 4.74% |

3 | 91.7 | 88 | 4.03% | 97 | 104 | 7.22% |

4 | 106.5 | 111 | 4.23% | 132 | 117 | 11.36% |

6 | 126 | 116 | 7.94% | 138 | 126 | 8.70% |

Grade | Density (kg/m^{3}) | ${\mathit{f}}_{\mathit{c}}$ (MPa) | ${\mathit{\beta}}_{\mathit{c}}$ | ${\mathit{\beta}}_{\mathit{t}}$ |
---|---|---|---|---|

C40 | 2400 | 40 | 0.029 | 0.033 |

C50 | 2420 | 50 | 0.024 | 0.029 |

C60 | 2440 | 60 | 0.02 | 0.025 |

C70 | 2460 | 70 | 0.017 | 0.022 |

Stand-off Distance (m) | Mass of TNT (kg) | Scaled Distance (m·kg^{−1/3}) |
---|---|---|

0.1 | 3 | 0.069 |

0.15 | 3 | 0.104 |

0.2 | 3 | 0.139 |

0.3 | 3 | 0.208 |

0.4 | 3 | 0.277 |

0.5 | 3 | 0.347 |

${\mathit{Q}}_{\mathit{v}}$ (J/kg) | ${\mathit{\rho}}_{\mathit{w}}$ (kg/m^{3})
| ${\mathit{P}}_{\mathit{w}}$ (MPa) | $\mathit{h}$ (cm) | $\mathit{b}$ (cm) |
---|---|---|---|---|

5.44 × 10^{6} | 1600 | 8.83 × 10^{3} | 10 | 7.5 |

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**MDPI and ACS Style**

Zhao, L.; Hao, Y.; Wang, Q.; Yang, C.; Yao, H.; Jia, X.
Damage Zone of the Reinforced Concrete Beam under Rectangular Explosive Contact Explosions. *Buildings* **2023**, *13*, 1403.
https://doi.org/10.3390/buildings13061403

**AMA Style**

Zhao L, Hao Y, Wang Q, Yang C, Yao H, Jia X.
Damage Zone of the Reinforced Concrete Beam under Rectangular Explosive Contact Explosions. *Buildings*. 2023; 13(6):1403.
https://doi.org/10.3390/buildings13061403

**Chicago/Turabian Style**

Zhao, Lijun, Yongping Hao, Qiuyang Wang, Chaozhi Yang, Huangwei Yao, and Xin Jia.
2023. "Damage Zone of the Reinforced Concrete Beam under Rectangular Explosive Contact Explosions" *Buildings* 13, no. 6: 1403.
https://doi.org/10.3390/buildings13061403