Open Access

Predictive Modelling of Pavement Quality Fibre-Reinforced Alkali-Activated Nano-Concrete Mixes through Artificial Intelligence

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Mar 24, 2025

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Figure 1:

The yearly growth of National Highways in India [15].
The yearly growth of National Highways in India [15].

Figure 2:

The detailed flowchart for the experimental programme and analysis.
The detailed flowchart for the experimental programme and analysis.

Figure 3:

Compaction factor values of PQAC mixes: (a) PQAC+NA and PQAC+NS and (b) PQAC+PVA and PQAC+PPF.
Compaction factor values of PQAC mixes: (a) PQAC+NA and PQAC+NS and (b) PQAC+PVA and PQAC+PPF.

Figure 4:

Split tensile strength and percentage variation in split tensile strength: (a) PQAC+NS, (b) PQAC+NA, (c) PQAC+PVAF and (d) PQAC+PPF.
Split tensile strength and percentage variation in split tensile strength: (a) PQAC+NS, (b) PQAC+NA, (c) PQAC+PVAF and (d) PQAC+PPF.

Figure 5:

Pair plots for the input parameters and observed responses.
Pair plots for the input parameters and observed responses.

Figure 6:

Correlation heatmap of input parameters and observed responses.
Correlation heatmap of input parameters and observed responses.

Figure 7:

Relative frequency distribution of the prediction-to-test STS ratio.
Relative frequency distribution of the prediction-to-test STS ratio.

Figure 8:

The violin plot illustrating the relative error percentages of different models.
The violin plot illustrating the relative error percentages of different models.

Figure 9:

Comparative analysis between actual and predicted values: a) MLR, b)DT, c) RF, d) SVR, e) AdaBoost and f) GBR.
Comparative analysis between actual and predicted values: a) MLR, b)DT, c) RF, d) SVR, e) AdaBoost and f) GBR.

Figure 10:

Correlation between expected and experimental values of STS for PQAC.
Correlation between expected and experimental values of STS for PQAC.

Figure 11:

Effect of the number of estimators on RF’s performance in terms of (a) MAE, (b) MSE, (c) RMSE, (d) R2 and (e) cross-validation mean.
Effect of the number of estimators on RF’s performance in terms of (a) MAE, (b) MSE, (c) RMSE, (d) R2 and (e) cross-validation mean.

Figure 12:

Effect of the number of estimators on AdaBoost’s performance in terms of (a) MAE, (b) MSE, (c) RMSE, (d) R2 and (e) cross-validation mean.
Effect of the number of estimators on AdaBoost’s performance in terms of (a) MAE, (b) MSE, (c) RMSE, (d) R2 and (e) cross-validation mean.

Figure 13:

Effect of the number of estimators on GBR’s performance in terms of (a) MAE, (b) MSE, (c) RMSE, (d) R2 and (e) cross-validation mean.
Effect of the number of estimators on GBR’s performance in terms of (a) MAE, (b) MSE, (c) RMSE, (d) R2 and (e) cross-validation mean.

Mix Design of PQAC mixes with fibres_

Mix ID APVA-0.4 APVA-0.8 APVA-1.2 APVA-1.6 APVA-2.0 APF-0.4 APF-0.8 APF-1.2 APF-1.6 APF-2.0
% Addition of fibres (by volume of binder) 0.4% 0.8% 1.2% 1.6% 2.0% 0.4% 0.8% 1.2% 1.6% 2.0%
Materials in kg/m3
GGBS 493 493 493 493 493 493 493 493 493 493
NaOH flakes 11.2 11.2 11.2 11.2 11.2 11.2 11.2 11.2 11.2 11.2
Liquid sodium silicate 75.12 75.12 75.12 75.12 75.12 75.12 75.12 75.12 75.12 75.12
Water 157.56 157.56 157.56 157.56 157.56 157.56 157.56 157.56 157.56 157.56
Natural coarse aggregate 1071.4 1071.4 1071.4 1071.4 1071.4 1071.4 1071.4 1071.4 1071.4 1071.4
River sand fine aggregate 577.84 577.84 577.84 577.84 577.84 577.84 577.84 577.84 577.84 577.84
PVA 0.748 1.49 2.24 2.99 3.74 - - - - -
PPF - - - - - 0.612 1.224 1.836 2.448 3.06

Mix Design of PQAC mixes with nano-additives_

Mix ID A-0 AS-0.5 AS-1.0 AS-1.5 AS-2.0 AA-0.5 AA-0.75 AA-1.0 AA-1.25
% Addition of nano-additives (by weight of binder) 0% 0.5% 1.0% 1.5% 2.0% 0% 0.75% 1.0% 1.25%
Materials in kg/m3
GGBS 493 493 493 493 493 493 493 493 493
NaOH flakes 11.2 11.2 11.2 11.2 11.2 11.2 11.2 11.2 11.2
Liquid sodium silicate 75.12 75.12 75.12 75.12 75.12 75.12 75.12 75.12 75.12
Water 157.56 157.56 157.56 157.56 157.56 157.56 157.56 157.56 157.56
Natural coarse aggregate 1071.4 1071.4 1071.4 1071.4 1071.4 1071.4 1071.4 1071.4 1071.4
River sand fine aggregate 577.84 577.84 577.84 577.84 577.84 577.84 577.84 577.84 577.84
Nano-silica 0 2.47 4.93 7.39 9.86 - - - -
Nano-alumina - - - - - 2.47 3.69 4.93 6.16

Performance results of the predictive models_

Model RMSE MAE MSE R2 score CV mean
Linear Regression 0.629266 0.488546 0.395976 0.608906 0.445094
Decision Tree 0.452297 0.382320 0.204573 0.797950 0.713217
Random Forest 0.453657 0.383848 0.205805 0.796733 0.707697
Support Vector 0.636715 0.492057 0.405406 0.599593 0.454470
ADA Boost 0.454821 0.384150 0.206862 0.795688 0.714149
Gradient Boosting 0.459522 0.390104 0.211160 0.791443 0.71143811

Statistical summary of the dataset_

Count Mean Std Min 25% 50% 75% Max
GGBS 570 493 0 493 493 493 493 493
NaOH 570 11.2 0 11.2 11.2 11.2 11.2 11.2
LSS 570 75.12 0 75.12 75.12 75.12 75.12 75.12
Water 570 157.56 0 157.56 157.56 157.56 157.56 157.56
NCA 570 1071.4 0 1071.4 1071.4 1071.4 1071.4 1071.4
RSFA 570 577.84 0 577.84 577.84 577.84 577.84 577.84
NS 570 1.3 2.81 0 0 0 0 9.86
NA 570 0.91 1.87 0 0 0 0 6.16
PVAF 570 0.59 1.13 0 0 0 0.75 3.74
PPF 570 0.48 0.92 0 0 0 0.61 3.06
STS 570 5.34 0.94 3.69 4.64 5.17 5.81 8.2

Relative frequency distribution of the prediction-to-test STS ratio_

Model Mean Median Standard deviation Skew
Linear Regression 1.003337 0.99848 0.108407 0.154706
Decision Tree 1.002638 0.98704 0.0855 0.399816
Random Forest 1.002764 0.98737 0.085843 0.40379
Support Vector 1.004801 0.99847 0.109484 0.076785
ADA Boost 0.999269 0.98854 0.084598 0.367988
Gradient Boosting 1.004576 0.99069 0.08731 0.416545
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