# Using Artificial Intelligence Techniques to Predict Punching Shear Capacity of Lightweight Concrete Slabs

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Database

^{3}; (2) column width (short side) ($\mathit{a}$) in m; (3) column length (long side) ($\mathit{b}$) in m, (for circular columns $\mathit{a}=\mathit{b}=0.785columndiameter$); (4) slab depth ($\mathit{d}$) in m; (5) 28-day cylinder compressive strength of concrete (${\mathit{f}}_{\mathit{c}}^{\prime}$) in MPa; (5) longitudinal reinforcement ratio x yield strength of steel ($\mathit{\mu}{\mathit{f}}_{\mathit{y}}$) in MPa; (6) ultimate punching capacity (${\mathit{V}}_{\mathit{u}}$) in kN. These collected records were divided into a training set (90 records) and a validation set (26 records). Table 1 summarizes their statistical characteristics. In addition, Figure 1 shows the histograms for both inputs and outputs.

## 3. Selected Design Model

^{3}.

## 4. Correlation and Effective Parameters

## 5. AI Model Development

**V**in kN) using the concrete density (γ in kN/m3), column width (a in m), column length (b in m), slab depth (d in m), 28-day concrete cylinder strength (${\mathit{f}}_{\mathit{c}}^{\prime}$ in MPa), and reinforcement ratio by steel yield stress ($\mathit{\mu}{\mathit{f}}_{\mathit{y}}$in MPa).

_{u}#### 5.1. GP Model

**V**), whereas Figure 5a shows its fitness. The average error % of total dataset is (32.4%), while the (R

_{u}^{2}) value is (0.823).

#### 5.2. ANN Model

^{2}) value was (0.890). The relative importance values for each input parameter are illustrated in Figure 7, which indicates that the slab thickness is the most important factor, whereas the concrete strength and flexure reinforcement ratio is second after the depth. The relationship between the calculated and predicted values are shown in Figure 5b.

#### 5.3. EPR Model

^{2}) values were (26.4%—0.888) for the total datasets.

## 6. Safety of Proposed and Existing Models

#### 6.1. Overall Safety of Various Models

#### 6.2. Safety of Various Models Versus Slab Size

#### 6.3. Safety of Various Models Versus Concrete Compressive Strength

#### 6.4. Safety of Various Models Versus Concrete Density

#### 6.5. Safety of Various Models Versus Column Dimension to Depth Ratio

#### 6.6. Safety of Various Models Versus Flexure Reinforcements

## 7. Future Studies

- Design code development for cases of tension forces [48].
- The behavior of full-scale slabs with thickness larger than 180 mm.
- The effect of using fibers in the concrete mix of lightweight concrete on the punching shear strength.

## 8. Conclusions

**V**) using the concrete density (γ), columns dimensions (a & b), slab depth (d), concrete strength (${\mathit{f}}_{\mathit{c}}^{\prime}$), and reinforcement ratio by steel yield stress ($\mathit{\mu}{\mathit{f}}_{\mathit{y}}$). Although concluding remarks are limited to the range of parameter values in the database, which can improve with more testing of slabs, concluding remarks are as follows:

_{u}- Both (ANN) and (EPR) have the greatest prediction accuracy (73.9% and 73.6%, respectively), whereas the (GP) model has the lowest prediction accuracy (67.6%);
- (GP) and (EPR) have almost the same level of accuracy (65.3% and 68.1%, respectively);
- Although the error% of the (ANN) and (EPR) models are so close, the output of (EPR) is closed-form equations, which could be used manually or as software, unlike the (ANN) output, which cannot be used manually;
- The summation of the absolute weights of each neuron in the input layer of the developed (ANN) model indicates that the slab depth (d) has a major influence on the punching capacity; other parameters have a minor effect, especially the compressive strength of the concrete;
- The formula developed using (EPR) did not include the parameter ($\mathit{\mu}{\mathit{f}}_{\mathit{y}}$), which indicates its minor effect on the punching capacity.
- The GA technique successfully reduced the 210 terms of the conventional polynomial regression quadrilateral formula to only ten terms without significant impact on its accuracy.
- AI models captured the true behavior and overcame the variability of the traditional design codes concerning the effective parameters.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**General schematic for the artificial neural network [47], reproduced with permission from Elsevier.

**Figure 3.**Presentation of mathematical formula in tree and genetic form [47], reproduced with permission from Elsevier.

**Figure 4.**Typical flow diagram of the evolutionary polynomial regression (EPR) procedure [46], reproduced with permission from Springer Nature.

**Figure 5.**Relative relationship between predicted and calculated (

**V**) values using the developed models, (

_{u}**a**) GP, (

**b**) ANN, (

**c**) EPR

**Figure 11.**SF calculated using various models versus $\raisebox{1ex}{$b$}\!\left/ \!\raisebox{-1ex}{$d$}\right.$.

γ | $\mathit{a}$ | $\mathit{b}$ | $\mathit{d}$ | ${\mathit{f}}_{\mathit{c}}^{\prime}$ | $\mathit{\mu}{\mathit{f}}_{\mathit{y}}$ | ${\mathit{V}}_{\mathit{u}}$ | |
---|---|---|---|---|---|---|---|

kN/m^{3} | m | m | m | MPa | MPa | kN | |

Training set | |||||||

Min. | 15.60 | 0.10 | 0.10 | 0.04 | 12.96 | 1.05 | 29.00 |

Max. | 23.40 | 0.40 | 0.46 | 0.18 | 78.40 | 9.48 | 914.00 |

Avg. | 18.00 | 0.19 | 0.22 | 0.10 | 37.98 | 4.52 | 245.38 |

SD | 1.38 | 0.07 | 0.11 | 0.04 | 18.43 | 2.13 | 181.90 |

VAR | 0.08 | 0.39 | 0.49 | 0.37 | 0.49 | 0.47 | 0.74 |

Validation set | |||||||

Min. | 15.60 | 0.11 | 0.11 | 0.04 | 21.10 | 0.00 | 46.59 |

Max. | 21.56 | 0.41 | 0.46 | 0.18 | 72.00 | 8.56 | 1354.00 |

Avg. | 17.79 | 0.19 | 0.24 | 0.10 | 37.93 | 4.79 | 282.99 |

SD | 1.51 | 0.09 | 0.13 | 0.04 | 14.08 | 2.11 | 256.77 |

VAR | 0.08 | 0.49 | 0.56 | 0.39 | 0.37 | 0.44 | 0.91 |

Mechanism | EC2 | ACI |
---|---|---|

Friction across crack in terms of ${f}_{c}^{\prime}$. | √ | √ |

Dowel action mechanism in terms of $\mu $. | √ | × |

Concrete type in terms of $\mathit{\gamma}$. | √ | √ |

Column dimension in terms of a, b | × | × |

Direct shear mechanism in terms of compression zone depth in the strength. | × | × |

Size effect in terms of $d$. | √ | √ |

Aggregate interlock mechanism in terms of aggregate size and type. | × | × |

Arch action mechanism in terms of shear span to depth ratio. | × | × |

Flexure capacity of the slab cross section. | × | × |

γ | $\mathit{a}$ | $\mathit{b}$ | $\mathit{d}$ | ${\mathit{f}}_{\mathit{c}}^{\prime}$ | $\mathit{\mu}{\mathit{f}}_{\mathit{y}}$ | ${\mathit{V}}_{\mathit{u}}$ | |
---|---|---|---|---|---|---|---|

Γ | 1.00 | ||||||

$a$ | 0.07 | 1.00 | |||||

$b$ | −0.15 | 0.55 | 1.00 | ||||

$d$ | 0.34 | 0.21 | 0.30 | 1.00 | |||

${f}_{c}^{\prime}$ | 0.39 | 0.28 | −0.03 | 0.44 | 1.00 | ||

$\mu {f}_{y}$ | −0.02 | 0.15 | 0.15 | −0.15 | −0.16 | 1.00 | |

${V}_{u}$ | 0.38 | 0.46 | 0.39 | 0.78 | 0.40 | 0.05 | 1.00 |

Technique | Model | SSE | Avg. Error % | R^{2} |
---|---|---|---|---|

GP | Equation (1) | 780,494 | 32.4 | 0.823 |

ANN | Figure 2 | 506,732 | 26.1 | 0.890 |

EPR | Equation (2) | 518,119 | 26.4 | 0.888 |

Hidden Layer | ||||||||||||

H (1:1) | H (1:2) | H (1:3) | H (1:4) | H (1:5) | H (1:6) | H (1:7) | H (1:8) | H (1:9) | H (1:10) | |||

Input Layer | (Bias) | 1.10 | −0.50 | 0.07 | −0.09 | −0.23 | 0.14 | 0.26 | −0.12 | −0.53 | 0.15 | |

γ | −0.22 | −0.19 | 0.02 | −0.51 | −0.38 | −0.04 | 0.68 | −1.42 | −0.06 | 0.05 | ||

a | −0.24 | −0.03 | 0.47 | 0.14 | −0.19 | 0.35 | −0.84 | 0.05 | 0.43 | 0.23 | ||

b | −0.79 | −0.81 | −0.18 | −0.14 | −0.13 | −0.16 | −0.19 | 0.13 | −0.67 | −0.03 | ||

d | −0.51 | 1.57 | 0.16 | 0.01 | −0.13 | −0.52 | 0.22 | 0.43 | 0.38 | 0.33 | ||

${\mathit{f}}_{\mathit{c}}^{\prime}$ | 0.40 | −0.73 | −0.19 | 0.13 | −0.16 | −0.47 | −0.16 | −0.75 | −0.24 | 0.14 | ||

$\mathit{\mu}{\mathit{f}}_{\mathit{y}}$ | 0.33 | −0.30 | 0.07 | 0.09 | 0.15 | −0.11 | −0.29 | −0.59 | −0.32 | −0.71 | ||

Hidden Layer | ||||||||||||

Output layer | H (1:1) | H (1:2) | H (1:3) | H (1:4) | H (1:5) | H (1:6) | H (1:7) | H (1:8) | H (1:9) | H (1:10) | (Bias) | |

${\mathit{V}}_{\mathit{u}}$ | −0.15 | −0.69 | 0.82 | −0.15 | 0.23 | 0.13 | −0.36 | −0.67 | −0.48 | −0.79 | 0.26 |

GP | ANN | EPR | ACI | EC2 | |

Maximum | 1.81 | 1.90 | 2.10 | 2.93 | 3.94 |

Minimum | 0.36 | 0.35 | 0.42 | 0.31 | 0.43 |

Average | 0.97 | 0.95 | 0.98 | 1.24 | 1.49 |

C.O.V. | 25% | 31% | 29% | 43% | 44% |

Lower 95% | 0.92 | 0.9 | 0.93 | 1.14 | 1.37 |

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**MDPI and ACS Style**

Ebid, A.; Deifalla, A.
Using Artificial Intelligence Techniques to Predict Punching Shear Capacity of Lightweight Concrete Slabs. *Materials* **2022**, *15*, 2732.
https://doi.org/10.3390/ma15082732

**AMA Style**

Ebid A, Deifalla A.
Using Artificial Intelligence Techniques to Predict Punching Shear Capacity of Lightweight Concrete Slabs. *Materials*. 2022; 15(8):2732.
https://doi.org/10.3390/ma15082732

**Chicago/Turabian Style**

Ebid, Ahmed, and Ahmed Deifalla.
2022. "Using Artificial Intelligence Techniques to Predict Punching Shear Capacity of Lightweight Concrete Slabs" *Materials* 15, no. 8: 2732.
https://doi.org/10.3390/ma15082732