# Influence of Supports on the Low-Velocity Impact Response of Square RC Slab of Standard Concrete and Ultra-High Performance Concrete: FEM-Based Computational Analysis

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Modeling of RC Slabs under Drop Load Impact

#### 2.1. General Procedure

^{3}, shown in Figure 6. A control slab, designated as S-NSC-4s, is the same as tested by the authors of [13]. Noted that all of the slabs possess 0.88% tension steel reinforcement and are subjected to identical concentrated low-velocity drop load.

#### 2.2. Assumptions Involved in the FE Modeling

_{c}= concrete modulus, σ = stress, ε = strain, ${\epsilon}^{pl}$ = plastic strain, and d = damage coefficients (0.0–1.0).

^{2}and 10

^{3}s

^{−1}(Figure 7) [1,2,3]. For instance, this phenomenon has a significant influence on structures made of reinforced concrete. Their resistance might rise significantly, with dynamic coefficients of 3 for compression and 6 for tension, as reported in [2,3,41,42]. Note that the dynamic coefficients used to incorporate strain-rate effects are briefly discussed in refs. [2,3]. The striker does not penetrate through the slab when the load is applied, and following contact, it remains apart. The impact load is applied using the command “initial_velocity_generation” [2,3,38]. The concrete–steel reinforcement connection is defined using the constraint “embedded region” [2,3]. Altogether, five face-to-face interaction contacts [2,3,38] are used in the modeling: striker–concrete, striker–steel bars, steel bars–concrete, slab–steel beams, and beams–columns. Moreover, static and dynamic coefficients of friction considered are 0.20 and 0.10, respectively. Note that the striker can only cause translation in the global Y-direction (impact direction) while the X- and Y-translations as well as X-, Y-, and Z-rotations are all restricted. The nonreflecting constraint is imposed all around the slab model.

#### 2.3. Material Properties

#### 2.4. Application of Impact Load on Slab Top Face

^{2}) and H = impact height (in this case = 2500 mm) [2,3,13]. Note that the load is applied to the centroid of the slab using the explicit module of the software considering ${V}_{0}$ = 7.0 m/s, free-fall time of 0.71 s [2,3], and a total impact duration of 1.0 s. The applied energy to the impacting face of the slab can be calculated using Equation (5), [13]:

^{2}, and H = 2500 mm.

#### 2.5. Mesh-Sensitivity Analysis

## 3. Results and Discussion

## 4. Conclusions

- Simulation results show that the total energy dissipated through the damage of the slab supported on three edges is greater than that of the slab supported on all four edges, as well as the slab supported only on two opposite edges on account of the formation of a higher number of wider and deeper diagonal cracks and severe punching.
- Domination of the flexure in the slab S-NSC/UHPC-2s indicated by maximum tensile stress in the steel re-bars supplemented by their maximum displacement under the impacted area shows that damage due to shearing of concrete in this slab is less than that of the slab S-NSC/UHPC-3s. This is why the damage to the slab S-NSC/UHPC-3s is maximum.
- Damage in the form of the detachment of cover concrete at the corners consisting of free edge(s) of the slabs S-NSC/UHPC-3s and S-NSC/UHPC-2s occurs due to impulsive reaction at such corners, which makes the steel bars exposed. These slabs undergo severe diagonal cracking and de-bonding in the flexure zone as compared to the slab S-NSC/UHPC-4s.
- The depth of the diagonal cracks toward the restrained corners of slab S-NSC/UHPC-3s is a little higher than that of diagonal cracks toward the corners having one free edge. This shows that the supports’ effects have a significant influence on the dynamic response and failure mode of the RC slab under impact loading.
- UHPC replaced for NSC in the slabs with similar supports greatly improves the impact response and follows a similar trend of results as those of the slabs with NSC. UHPC slabs show identical behavior for 4s and 3s models with regard to maximum displacement and damage, while for the 2s model, it contributes more to control the displacement than damage.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 11.**Damage to the NSC slabs by applied impact load at t = 0.735 s, the time at which the slab attains maximum displacement.

**Figure 16.**Equivalent plastic strain distribution on the top surface of the NSC and UHPC slabs at t = 0.735 s.

S. No. | Specimen | *Δ_{y} (mm) | DDE (J) | α_{y} (g) | S_{t} (MPa) | |
---|---|---|---|---|---|---|

Slab | Bars | |||||

1 | S-NSC-4s | −27.31 | −21.27 | 190.97 | 294.72 | 426.39 |

2 | S-NSC-3s | −33.96 | −27.03 | 209.57 | 135.07 | 479.94 |

3 | S-NSC-2s | −34.82 | −29.22 | 204.88 | 129.26 | 525.22 |

4 | S-UHPC-4s | −4.39 | −3.85 | 92.76 | 395.15 | 421.56 |

5 | S-UHPC-3s | −5.27 | −5.0 | 104.78 | 197.77 | 427.0 |

6 | S-UHPC-2s | −8.49 | −7.93 | 98.12 | 189.61 | 466.24 |

_{y}= Max

^{m}displacement in Y-direction at the point of impact; DDE = damage dissipation energy; α

_{y}= peak acceleration in Y-direction; S

_{t}= Max

^{m}tensile stress in the steel bars at the point of impact; g = acceleration due to gravity.

Slab Supported On | Maximum Displacement Ratio | Damage (DDE) Ratio | Remark |
---|---|---|---|

Four edges (4s) | 1:0.160 | 1:0.485 | UHPC slabs respond (1) identically in the case of 4s and 3s models with regard to displacement and damage; (2) more contributes to control displacement than damage for the 2s model. |

Three edges (3s) | 1:0.155 | 1:0.499 | |

Two opposite edges (2s) | 1:0.243 | 1:0.478 |

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**MDPI and ACS Style**

Anas, S.M.; Shariq, M.; Alam, M.; Yosri, A.M.; Mohamed, A.; AbdelMongy, M.
Influence of Supports on the Low-Velocity Impact Response of Square RC Slab of Standard Concrete and Ultra-High Performance Concrete: FEM-Based Computational Analysis. *Buildings* **2023**, *13*, 1220.
https://doi.org/10.3390/buildings13051220

**AMA Style**

Anas SM, Shariq M, Alam M, Yosri AM, Mohamed A, AbdelMongy M.
Influence of Supports on the Low-Velocity Impact Response of Square RC Slab of Standard Concrete and Ultra-High Performance Concrete: FEM-Based Computational Analysis. *Buildings*. 2023; 13(5):1220.
https://doi.org/10.3390/buildings13051220

**Chicago/Turabian Style**

Anas, S. M., Mohd Shariq, Mehtab Alam, Ahmed M. Yosri, Ahmed Mohamed, and Mohamed AbdelMongy.
2023. "Influence of Supports on the Low-Velocity Impact Response of Square RC Slab of Standard Concrete and Ultra-High Performance Concrete: FEM-Based Computational Analysis" *Buildings* 13, no. 5: 1220.
https://doi.org/10.3390/buildings13051220