# Blast Resistance of Reinforced Concrete Slabs Based on Residual Load-Bearing Capacity

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Study

#### 2.1. Test Specimen Design

#### 2.2. Experimental Results and Analysis

#### 2.2.1. Blast-Load Measurement

#### 2.2.2. Displacement Response-Time History

#### 2.2.3. Comparison of Damage Modes

## 3. Numerical Simulation

#### 3.1. Finite Element Model

#### 3.2. Material Model

_{1}, R

_{2}, and ω are the EOS parameters. The JWL EOS parameters of the TNT explosive can be found in reference [25].

_{0}~C

_{6}are the coefficients of the polynomial equation, E

_{1}is the internal energy density, and V

_{0}is the initial relative volume. The parameters for air can be seen in reference [25].

^{−3}, uniaxial compressive strength ${f}_{c}^{\prime}=30$ MPa, and Poisson’s ratio $\nu =0.2$. Under blast loading, the strain rate of the reinforced concrete is up to 100~10,000 s

^{−1}. The strength of the materials under dynamic loading is fundamentally different from that under quasi-static loading. Therefore, the strain-rate effect of materials needs to be considered for blast-loading analysis. In the material model, the defined strain-rate curve can be called by LCRATE.

#### 3.3. Finite Element Model Verification

^{3}, the peak overpressure is highly sensitive to grid size and has great discreteness, indicating that the grids need to be fine enough to ensure the computational accuracy. Considering the size of the three-dimensional model, and the computational accuracy and efficiency, the 10 mm grid size is selected for the subsequent finite element modeling and analysis.

#### 3.4. Analysis of Finite Element Calculation Results

#### 3.4.1. Explosion Load Analysis

^{1/3}is obtained, as shown in Figure 12. In the figure, the X-axis and Y-axis represent the directions of the short span and long span of the slab, respectively.

#### 3.4.2. Damage Analysis of RC Slab

#### 3.4.3. Residual Displacement Analysis

#### 3.4.4. Residual Bearing Capacity Analysis

## 4. Conclusions

- The load distribution in the RC slabs under close-in blast loading was extremely uneven. The peak overpressure on the impact surface of the slabs was large in the center along the long-span direction and gradually decreased at both ends. The specific impulse was gradually reduced along the long-span direction. The impulse near the ground was about two times that at the top.
- The damage distribution of the two RC slabs with different reinforcement ratios was similar, but the degree of damage differed markedly. A large rectangular plastic strain zone appeared in the center of the back surface of the slab with a low reinforcement ratio, several plastic strands along the short-span direction could be observed, and the concrete in some areas almost completely failed, and the damage range and degree are significantly higher than those of the slab with a high reinforcement ratio.
- Compared with the undamaged slabs, the shape of the resistance curves of the damaged RC slabs saw significant changes, and their load-bearing capacity and bending stiffness were irreversibly degraded. Increasing the reinforcement ratio can not only inhibit the crack extension and reduce the residual displacement of components, but also reduce the decrease of bearing capacity after damage.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Layout of pressure and displacement measuring points, (

**a**) the layout of the pressure sensors, (

**b**) the layout of the acceleration and displacement sensors, and (

**c**) overall survey point distribution.

**Figure 4.**Comparison between measured overpressure curves of shock waves at different measuring points and ConWep calculation results: (

**a**) the blast loading−time history of the measuring point P1, (

**b**) the blast loading−time history of the measuring point P2, and (

**c**) the blast loading−time history of the measuring point P3.

**Figure 7.**Comparison of damage modes of the two RC slabs: (

**a**) damage effect of slab A (low reinforcement ratio), and (

**b**) damage effect of slab B (high reinforcement ratio).

**Figure 10.**Comparison of pressure−time history, (

**a**) the comparison of pressure−time history of the measuring point P2, (

**b**) The comparison of pressure−time history of the measuring point P3.

**Figure 11.**Comparison of displacement−time history: (

**a**) the comparison of displacement−time history of the measuring point D3, and (

**b**) the comparison of displacement−time history of the measuring point D4.

**Figure 12.**Contour plots of load distribution in RC slab: (

**a**) peak overpressure, (

**b**) specific impulse.

**Figure 17.**Comparison of load−bearing capacity between undamaged and damaged slabs: (

**a**) slab A with low reinforcement ratio, and (

**b**) slab B with high reinforcement ratio.

Measuring Point | X/m | Y/m | Distance from Explosion Source/m | Scaled Distance/m/kg^{1/3} | Angle of Incidence/° |
---|---|---|---|---|---|

P1 | 0 | 0 | 1.2 | 0.557 | 90 |

P2 | 0.16 | 0 | 1.211 | 0.562 | 82.4 |

P3 | 0 | 0.3 | 1.237 | 0.574 | 75.96 |

P4 | 0.16 | 0.3 | 1.247 | 0.579 | 74.18 |

Measuring Point | Scaled Distance/m/kg^{1/3} | Peak Positive Pressure/MPa | Shock Wave Arrival Time/ms | Specific Impulse/MPa × ms | Angle of Incidence/° |
---|---|---|---|---|---|

P1 | 0.557 | 32.32 | 0.36 | 3.35 | 90 |

P2 | 0.562 | 26.47 | 0.363 | 3.02 | 82.4 |

P3 | 0.574 | 23.58 | 0.38 | 2.93 | 75.96 |

Displacement Measuring Point | D1 | D2 | D3 | D4 | D5 |
---|---|---|---|---|---|

Peak displacement/cm | 0.51 | 1.18 | 1.97 | 1.98 | 0.89 |

Residual displacement/cm | −0.37 | 1.18 | 1.97 | 1.73 | 0.38 |

Displacement Measuring Point | D6 | D7 | D8 | D9 | D10 |
---|---|---|---|---|---|

Peak displacement/cm | 0.67 | 0.92 | 1.41 | 1.09 | 0.79 |

Residual displacement/cm | 0.03 | 0.31 | 0.58 | 0.80 | 0.08 |

Parameter | ρ/kg·m^{−3} | E/GPa | V_{s} | σ_{y}/MPa | E_{t}/GPa | C/s^{−1} | P_{s} | F_{s} |
---|---|---|---|---|---|---|---|---|

HRB400 | 7850 | 210 | 0.28 | 400 | 2.1 | 40 | 5 | 0.2 |

HPB235 | 235 | |||||||

Clamp | 300 | 0 | 0 |

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**MDPI and ACS Style**

Wang, L.; Cheng, S.; Liao, Z.; Yin, W.; Liu, K.; Ma, L.; Wang, T.; Zhang, D.
Blast Resistance of Reinforced Concrete Slabs Based on Residual Load-Bearing Capacity. *Materials* **2022**, *15*, 6449.
https://doi.org/10.3390/ma15186449

**AMA Style**

Wang L, Cheng S, Liao Z, Yin W, Liu K, Ma L, Wang T, Zhang D.
Blast Resistance of Reinforced Concrete Slabs Based on Residual Load-Bearing Capacity. *Materials*. 2022; 15(18):6449.
https://doi.org/10.3390/ma15186449

**Chicago/Turabian Style**

Wang, Lijun, Shuai Cheng, Zhen Liao, Wenjun Yin, Kai Liu, Long Ma, Tao Wang, and Dezhi Zhang.
2022. "Blast Resistance of Reinforced Concrete Slabs Based on Residual Load-Bearing Capacity" *Materials* 15, no. 18: 6449.
https://doi.org/10.3390/ma15186449