# Prediction of Fracture Toughness of Intermediate Layer of Asphalt Pavements Using Artificial Neural Network

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Measurement, Collection, and Pretreatment of Data

#### 2.2. ANN Modeling for FT Prediction

#### 2.3. Selection and Evaluation of Candidate ANN Models

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

- KEC. Highway Pavement Maintenance System Operation Manual; Korea Expressway Corporation: Gimcheon-si, Korea, 1996. [Google Scholar]
- Lee, G.H.; Gang, M.S.; Jo, M.J. Damage status and reduction method of asphalt pavement. Korean Soc. Road Eng.
**2012**, 14, 5–11. [Google Scholar] - Harold, L.; Von, Q.; Thomas, W.K. Mixture properties related to pavement performance. Proc. Assoc. Asph. Asph. Paving Technol.
**1989**, 58, 553–570. [Google Scholar] - Zafrul, K.; Hasan, M.F. Fracture toughness measurement of asphalt concrete by nanoindentation. In Proceedings of the 2017 International Mechanical Congress and Exposition, Tampa, FL, USA, 3–9 November 2017. [Google Scholar]
- Kruzic, J.J.; Kim, D.K.; Koester, K.J.; Ritchie, R.O. Indentation techniques for evaluating the fracture toughness of biomaterials and hard tissues. J. Mech. Behav. Biomed. Mater.
**2009**, 2, 384–395. [Google Scholar] [CrossRef] [PubMed] - Kim, D.H.; Lee, S.J.; Moon, K.H.; Jeong, J.H. Prediction of indirect tensile strength of intermediate layer of asphalt pavement using artificial neural network model. Arab. J. Sci. Eng.
**2021**, 46, 4911–4922. [Google Scholar] [CrossRef] - Choi, J.H.; Adams, T.M.; Bahia, H.U. Pavement roughness modeling using back-propagation neural networks. Comput.-Aided Civ. Infrastruct. Eng.
**2004**, 19, 295–303. [Google Scholar] [CrossRef] - Gandhi, T.; Xiao, F.; Amirkhanian, S.N. Estimating indirect tensile strength of mixtures containing anti-stripping agents using an artificial neural network approach. Int. J. Pavement Res. Technol.
**2009**, 2, 1–12. [Google Scholar] - Josipa, D.; Hrvoje, D.; Tatjana, R.; Sanja, D. Application of an artificial neural network in pavement management system. Teh. Vjesn.
**2018**, 25, 466–473. [Google Scholar] [CrossRef] - Graves, A.; Liwicki, M.; Fernandez, S.; Bertolami, R.; Bunke, H.; Schmidhuber, J.; Nobel, A. Connectionist system for improved unconstrained handwriting recognition. IEEE Trans. Pattern Anal. Mach. Intell.
**2009**, 31, 855–868. [Google Scholar] [CrossRef] [Green Version] - Achanta, A.S.; Kowalski, J.G.; Rhodes, C.T. Artificial neural networks: Implications for pharmaceutical sciences. Drug Dev. Ind. Pharm.
**1995**, 21, 119–155. [Google Scholar] [CrossRef] - Kim, S.; Gopalakrishnan, K.; Ceylan, H. Neural networks application in pavement infrastructure materials. Intell. Soft Comput. Infrastruct. Syst. Eng.
**2009**, 259, 47–66. [Google Scholar] [CrossRef] - Lushinga, N.; Cao, L.; Dong, Z. Effect of silicone oil on dispersion and low-temperature fracture performance of crumb rubber asphalt. Adv. Mater. Sci. Eng.
**2019**, 2019, 8602562. [Google Scholar] [CrossRef] [Green Version] - McDaniel, R.; Shah, A. Asphalt Additives to Control Rutting and Cracking; Federal Highway Administration: IN/JTRP-2002/29; Federal Highway Administration: Washington, DC, USA, 2002. [Google Scholar]
- Melesse, A.M.; Ahmad, S.; McClain, M.E.; Wang, X.; Lim, Y.H. Suspended sediment load prediction of river systems: An artificial neural network approach. Agric. Water Manag.
**2011**, 98, 855–866. [Google Scholar] [CrossRef] - Abramowitz, M.; Stegun, I.A. Hanbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th ed.; Dover: New York, NY, USA, 1972; p. 928. ISBN 0-486-61272-4. [Google Scholar]
- Kenney, J.F.; Keeping, E.S. Mathematics of Statistics, 3rd ed.; D. Van Nostrand Company: New York, NY, USA, 1962; pp. 102–103. ISBN 978-1114612600. [Google Scholar]
- Kline, R.B. Principles and Practice of Structural Equation Modeling, 2nd ed.; Guilford Press: New York, NY, USA, 2005; ISBN 978-1606238769. [Google Scholar]
- Wilson, E.B.; Hilferty, M.M. The distribution of chi-square. Proc. Natl. Acad. Sci. USA
**1931**, 17, 684–688. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Maclean, C.J.; Morton, N.E.; Elston, R.C.; Yee, S. Skewness in commingled distributions. Biometrics
**1976**, 32, 695–699. [Google Scholar] [CrossRef] [PubMed] - William, H.K.; Judith, M.T. International Encyclopedia of Statistics, 1st ed.; Free Press: New York, NY, USA, 1978; pp. 523–541. ISBN 002917970X. [Google Scholar]
- McCulloch, W.; Walter, P. A logical calculus of ideas immanent in nervous activity. Bull. Math. Biophys.
**1943**, 5, 115–133. [Google Scholar] [CrossRef] - Lagaris, I.E.; Likas, A.; Fotiadis, D.I. Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans. Neural Netw.
**1998**, 9, 987–1000. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Ramachandran, P.; Barret, Z.; Quoc, V.L. Searching for activation functions. Comput. Sci. Neural Evol. Comput.
**2017**. Available online: https://openreview.net/forum?id=SkBYYyZRZ (accessed on 23 May 2022). - Claesen, M.; Bart, D.M. Hyperparameter search in machine learning. In Proceedings of the XI Metaheuristics International Conference, Agadir, Morocco, 7–10 June 2015. [Google Scholar]
- Probst, P.; Boulesteix, A.L.; Bischl, B. Tunability: Importance of hyperparameters of machine learning algorithms. J. Mach. Learn. Res.
**2018**, 20, 1–32. [Google Scholar] - Lydia, A.A.; Francis, F.S. Adagrad—An optimizer for stochastic gradient descent. Int. J. Inf. Comput. Sci.
**2019**, 6, 566–568. [Google Scholar] - Diederik, P.K.; Jimmy, L.B. Adam: A method for stochastic optimization. In Proceedings of the International Conference on Learning Represent, 2015 Workshop Track, San Diego, CA, USA, 7–9 May 2015. [Google Scholar]
- Dozat, T. Incorporating Nesterov momentum into Adam. In Proceedings of the International Conference on Learning Represent, 2016 Workshop Track, San Juan, Puerto Rico, 2–4 May 2016. [Google Scholar]
- Ruder, S. An overview of gradient descent optimization algorithms. Comput. Sci. Mach. Learn.
**2016**. [Google Scholar] [CrossRef] - KASCON. Hot Mix Asphalt; SPS-KAI0002-F2349-5687; Korea Asphalt Concrete Industrial Cooperative Association: Seoul, Korea, 2018. [Google Scholar]

**Figure 4.**Frequency distribution of raw data of variables. (

**a**) FT, (

**b**) IRI, (

**c**) RD, (

**d**) SD, (

**e**) ESAL.

**Figure 5.**Frequency distribution of data of FT and SD with different forms. (

**a**) FT

^{1/2}, (

**b**) SD

^{1/2}, (

**c**) FT

^{1/3}, (

**d**) SD

^{1/3}, (

**e**) ln(FT + 1), (

**f**) ln(SD + 1).

**Figure 6.**Distribution of the maximum, minimum, and average adjusted variables. (

**a**) Dataset 1, (

**b**) Dataset 2.

**Figure 7.**Distribution of the maximum, minimum, and average standardized variables. (

**a**) Dataset 1, (

**b**) Dataset 2.

**Figure 10.**Minimum MSE calculated by trained model according to ANN structures and optimizers. (

**a**) Dataset 1 and one hidden layer, (

**b**) Dataset 2 and one hidden layer, (

**c**) Dataset 1 and two hidden layers, (

**d**) Dataset 2 and two hidden layers.

**Figure 11.**MSE according to the amount of learning for training and validation dataset. (

**a**) Rp136 model, (

**b**) Am253 model, (

**c**) Nd144 model.

**Figure 12.**Scatter plot of measured and predicted FT for Rp136 model. (

**a**) Training dataset, (

**b**) test dataset.

**Figure 13.**Scatter plot of measured and predicted FT for Am253 model. (

**a**) Training dataset, (

**b**) test dataset.

**Figure 14.**Scatter plot of measured and predicted FT for Nd144 model. (

**a**) Training dataset, (

**b**) test dataset.

**Figure 15.**Frequency distribution of actual and predicted FT. (

**a**) Measured data, (

**b**) prediction of Rp136 model, (

**c**) prediction of Am253 model, (

**d**) prediction for Nd144 model.

Variables | Dataset 1 | Dataset 2 |
---|---|---|

FT | Cube Root | Logarithm |

IRI | Raw | Raw |

RD | Raw | Raw |

SD | Cube Root | Logarithm |

ESAL | Raw | Raw |

Dataset | Number of Hidden Layers | Number of Nodes in 1st Hidden Layer | Number of Nodes in 2nd Hidden Layer | Number of Hyper-Parameters | Optimizer |
---|---|---|---|---|---|

Dataset 1 | 1 | 4 | - | 25 | Adagrad (Ag) Adam (Ad) Adamax (Am) Nadam (Nd) RMSprop (Rp) |

5 | - | 31 | |||

6 | - | 37 | |||

7 | - | 43 | |||

8 | - | 49 | |||

2 | 3 | 6 | 46 | ||

3 | 7 | 51 | |||

4 | 4 | 45 | |||

4 | 5 | 51 | |||

5 | 3 | 47 | |||

Dataset 2 | 1 | 4 | - | 25 | |

5 | - | 31 | |||

6 | - | 37 | |||

7 | - | 43 | |||

8 | - | 49 | |||

2 | 3 | 6 | 46 | ||

3 | 7 | 51 | |||

4 | 4 | 45 | |||

4 | 5 | 51 | |||

5 | 3 | 47 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kim, D.-H.; Kim, H.-Y.; Moon, K.-H.; Jeong, J.-H.
Prediction of Fracture Toughness of Intermediate Layer of Asphalt Pavements Using Artificial Neural Network. *Sustainability* **2022**, *14*, 7927.
https://doi.org/10.3390/su14137927

**AMA Style**

Kim D-H, Kim H-Y, Moon K-H, Jeong J-H.
Prediction of Fracture Toughness of Intermediate Layer of Asphalt Pavements Using Artificial Neural Network. *Sustainability*. 2022; 14(13):7927.
https://doi.org/10.3390/su14137927

**Chicago/Turabian Style**

Kim, Dong-Hyuk, Ha-Yeong Kim, Ki-Hoon Moon, and Jin-Hoon Jeong.
2022. "Prediction of Fracture Toughness of Intermediate Layer of Asphalt Pavements Using Artificial Neural Network" *Sustainability* 14, no. 13: 7927.
https://doi.org/10.3390/su14137927