# Quantitative Deterioration Assessment of Road Bridge Decks Based on Site Inspected Cracks

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Artificial Neural Network

## 3. Building Neural Networks

#### 3.1. Scope of Target

#### 3.2. Material Properties for Reference

#### 3.3. Loading Patterns

#### 3.4. Limit State Failure Criteria

_{L,N}is the central live load deflection at Nth of cycles, δ

_{1,N}is the total deflection of span center at Nth of cycles at the preceding stage of loading, δ

_{2,N}is the total deflection of span center at Nth of cycles at unloading stage, δ

_{L,0}is the initial live load deflection and N

_{f}is number of cycles corresponding to (δ

_{L,N}from Equation (2)).

#### 3.5. Standardized States for Numerical Model

#### 3.6. Crack Patterns Taken from Real Decks

## 4. Massive Life Simulation for ANN’s Learning

#### 4.1. Referential RC Deck “No Damage”

#### 4.2. Sensitivity Analysis for Crack Depth

#### 4.3. Cracked Cases

_{avg.}is the average strain on the bottom surface of RC deck, k indicates the kth element at the bottom surface of the deck, ε

_{xx}is the normal strain of concrete in X-direction for the kth element, ε

_{yy}is the normal strain of concrete in Y-direction for the kth element and n is the total number of elements.

#### 4.4. Statistical Correlation of Remaining Fatigue Life and Inspected Cracks

_{k}is the length of the kth crack at the bottom surface of the RC deck and W

_{k}is its width, A is the length of the RC deck in the longitudinal direction and B is its width in the transverse direction and β is crack type indicator; 1.0 for continuous crack and 0.44 for discrete one.

= − 0.266 × ln (CD) − 0.095 ≥ 0 → CD ≥ 0.15%

## 5. Training Artificial Neural Networks

#### 5.1. Methodology for Fatigue Life Identification

_{xx}, ε

_{yy}) and the shear strain (ε

_{xy}). For cases (3) & (4), the number of sub-elements of the deck’s bottom surface is intentionally reduced from 336 (see Figure 9) to 84 sub-elements (see Figure 12). The cracks information for case (3) & (4) is taken as a lump sum for each 500 × 500 mm

^{2}area instead of 250 × 250 mm

^{2}of the deck’s bottom surface.

_{1}is the maximum principal strain, θ is its principal directional angle (degrees) and ε

_{ij}is the strain tensors of concrete on the bottom surface of the RC deck.

#### 5.2. Requirements of Training Dataset

#### 5.3. Neural Network Platform and Structure

#### 5.4. Built ANN’s Performance and Input Variables

^{2}) of 0.964, 0.971, 0.975 and 0.962 for the studied cases (1), (2), (3) and (4), respectively. For the case (3), the mean squarer errors are stabilized (best performance) after 224 epochs with a value of 0.0021. Figure 14b shows that the mean square errors of the ANN estimate compared to the proposed statistical formulae in Section 4.3 is reduced from 0.0069 to 0.0028, 0.0022, 0.0019 and 0.0030 for the cases (1), (2), (3) and (4). The prediction interval variance of 95% is reduced from 14.8% to 10.5%, 9.5%, 8.9% and 10.9% for the cases (1), (2), (3) and (4), respectively.

#### 5.5. Significance of Cracks Direction

#### 5.6. ANN Performance Evaluation

^{2}) is 0.913 and the mean square errors’ (mse) value is 0.0073. The results demonstrate the generalization of the network, where it maps almost all the validation subsets with good accuracy.

#### 5.7. Structural Mechanistic Expressions of ANN’s Weights

_{1×84}× [W]

_{84×1})

_{1}

_{×84}× [W]

_{84×1}

## 6. Conclusions

- Two fast-truck quantitative assessment models for the magnitude of damages of in-situ RC bridge road decks in service were built based upon the training dataset created by numerical simulation as well as the real site inspection data. A quick and massive diagnosis, which is equivalent to the full 3D multi-scale simulation, is made possible.
- The statistical model is built on the basis of the mechanics-based parameter. Here, the conservative and safer-side assessment of the remaining fatigue life is practically made possible by avoiding the case where pre-cracking stops the preceding shear cracking.
- By examining the wide variety of crack orientation and their patterns over the bottom surfaces of RC decks, it is quantitatively proved that the geometrical patterns of cracking have much to do with the remaining fatigue life as well as crack width.
- By conduction k-fold cross-validation and testing the ANN model, the robustness and the generalization of the proposed ANN model are confirmed with the crack patterns observed at bridge construction site. Here, the numerically produced training dataset, which was offered by the multi-scale analysis, enables us to compensate the week spots of the training dataset.
- A hazard mapping to identify the high-risk location of cracking is created in use of the neuron’s weight and its sensitivity to the fatigue life. It is found that both RC deck’s central zone and their corners are the spots of caution. This map can be used as the guideline to train inspectors.
- It is proved that artificial intelligence is not just a tool for conducting predictive models but it can guide somehow to achieve physical expressions for a particular problem.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- NEXCO-Japan. Regarding Large-Scale Renewal and Large-Scale Repair on the Expressway Managed by Eastern, Central and West Japan Expressway Co., Ltd. 2014. Available online: https://www.c-nexco.co.jp/koushin/pdf/about.pdf (accessed on 17 May 2018).
- Japan Society of Civil Engineers. Standard Specifications for Concrete Structures—2017 “Maintenance”; JSCE Guidelines for Concrete; Japan Society of Civil Engineers: Tokyo, Japan, 2007. [Google Scholar]
- Maekawa, K.; Pimanmas, A.; Okamura, H. Nonlinear Mechanics of Reinforced Concrete; Spon Press: London, UK, 2003. [Google Scholar]
- Maekawa, K.; Ishida, T.; Kishi, T. Multi-Scale Modeling of Structural Concrete; Taylor & Francis: London, UK, 2009. [Google Scholar]
- Maekawa, K.; Toongoenthong, T.; Gebreyouhannes, E.; Kishi, T. Direct path-integral scheme for fatigue simulation of reinforced concrete in shear. J. Adv. Concr. Technol.
**2006**, 4, 159–177. [Google Scholar] [CrossRef] - Fujiyama, C.; Tang, X.J.; Maekawa, K.; An, X. Pseudo-cracking approach to fatigue life assessment of RC bridge decks in service. J. Adv. Concr. Technol.
**2013**, 11, 7–21. [Google Scholar] [CrossRef] - Tang, X.J.; Fujiyama, C.; An, X.H.; Maekawa, K. Pseudo cracking approach to fatigue life assessment of existing RC bridge decks based on crack inspection data. In Proceedings of the Thirteenth East Asia Pacific Conference on Structural Engineering and Construction (EASEC 13), Sapporo, Japan, 11–13 September 2013. [Google Scholar]
- Tanaka, Y.; Maekawa, K.; Maeshima, T.; Iwaki, I.; Nishida, T.; Shiotani, T. Data assimilation for fatigue life assessment of RC bridge decks coupled with hygro-mechanistic model and nondestructive inspection. J. Disaster Res.
**2017**, 12, 422–431. [Google Scholar] [CrossRef] - Fathalla, E.; Tanaka, Y.; Maekawa, K. Parametrical study on fatigue life of road bridge decks with pseudo-cracking analysis. In Proceedings of the 8th Asia and Pacific Young Researchers and Graduates Symposium, Tokyo, Japan, 7–8 September 2017. [Google Scholar]
- Fathalla, E.; Tanaka, Y.; Maekawa, K. Remaining fatigue life assessment of in-service road bridge decks based upon artificial neural networks. Eng. Struct.
**2018**, 171, 602–616. [Google Scholar] [CrossRef] - Fausett, L.V. Fundamentals of Neural Networks: Architectures, Algorithms, and Applications; Prentice-Hall: Englewood Cliffs, NJ, USA, 1994. [Google Scholar]
- M.I.T. Lincoln Laboratory. DARPA Neural Network Study; Defense Technical Information Center: Fort Belvoir, VA, USA, 1989. [Google Scholar]
- Grossberg, S. Studies of the Mind and Brain; Reidel Press: Drodrecht, The Netherlands, 1982. [Google Scholar]
- Hagan, M.T.; Demuth, H.B.; Beale, M.H.; Jesús, O.D. Neural Network Design; PWS Publishing: Boston, MA, USA, 1996. [Google Scholar]
- Japan Road Association. Specification for Highway Bridges—Part III Concrete Bridges; Japan Road Association: Tokyo, Japan, 2012. [Google Scholar]
- Matsui, S. Lifetime prediction of bridge. J. JSCE
**1996**, 30, 432–440. [Google Scholar] - Maeshima, T.; Koda, Y.; Tsuchiya, S.; Iwaki, I. Influence of corrosion of rebars caused by chloride induced deterioration on fatigue resistance in RC road deck. J. JSCE E2
**2014**, 70, 208–225. [Google Scholar] [CrossRef] - Kado, M.; Maeshima, T.; Koda, Y.; Nakano, S.; Fujiyama, C.; Iwaki, I. Study on a method of evaluating fatigue damage for RC bridge deck slab using long basis optical strand sensors. J. JSCE E2
**2015**, 71, 323–337. [Google Scholar] [CrossRef] - Okada, K.; Okamura, H.; Sonoda, K.; Shimada, I. Cracking and fatigue behavior of bridge deck RC slabs. J. JSCE
**1982**, 321, 49–61. [Google Scholar] [CrossRef] - Mizutani, T.; Nakamura, N.; Yamaguchi, T.; Tarumi, M.; Ando, Y. Signal processing for fast RC bridge slab damage detection by using UHF-band radar. In Proceedings of the 6th Asia Pacific Workshop on Structural Health Monitoring, Hobart, Australia, 7–9 December 2017. [Google Scholar]
- Kobayashi, Y.; Oda, K.; Shiotani, T. Three dimensional AE tomography with accurate source location technique. In Proceedings of the Structural Faults & Repair, London, UK, 8–10 July 2014. [Google Scholar]
- Nair, A.; Cai, C.S. Acoustic emission monitoring of bridges: Review and case studies. Eng. Struct.
**2010**, 32, 1704–1714. [Google Scholar] [CrossRef] - Takeuchi, H.; Ozawa, I.; Yano, R.; Mitsuya, Y.; Dobashi, K.; Uesaka, M.; Tanaka, Y.; Takahashi, Y.; Kusano, J.; Yoshida, E.; et al. Quantification of transmission X-ray imaging capability of portable X-ray source in concrete bridge inspection. J. JSCE E2
**2018**, 74, 66–79. [Google Scholar] [CrossRef] - Ikeda, Y.; Takamura, M.; Taketani, A.; Sunaga, H.; Otake, Y.; Suzuki, H.; Kumagai, M.; Oba, Y. Prospect for application of compact accelerator-based neutron source to neutron engineering diffraction. Nucl. Instrum. Methods Phys. Res. Sect. A
**2016**, 833, 61–67. [Google Scholar] [CrossRef] - Tanaka, Y.; Kishi, T.; Maekawa, K. Experimental research on the structural mechanism of RC members containing artificial crack in shear. JSCE
**2005**, 802, 109–121. [Google Scholar] [CrossRef] - Tanaka, Y.; Kishi, T.; Maekawa, K. Tied arch system and evaluation method of shear strength of RC members containing artificial crack or unbond zone. JSCE
**2005**, 788, 175–193. [Google Scholar] - Niwa, J.; Yamada, K.; Yokozawa, K.; Okamura, H. Revaluation of the equation for shear strength of reinforced concrete beams without web reinforcement. J. JSCE
**1986**, 372, 65–84. [Google Scholar] [CrossRef] - Murphy, K.P. Machine Learning: A Probabilistic Perspective; The MIT Press: Cambridge, MA, USA, 2012. [Google Scholar]
- Hagan, M.T.; Menhaj, M. Training feed-forward networks with the Marquardt algorithm. IEEE Trans. Neural Netw.
**1994**, 15, 989–993. [Google Scholar] [CrossRef] [PubMed] - Rumelhart, D.; Hinton, G.; Williams, R. Learning representations by back-propagating errors. Nature
**1986**, 323, 533–536. [Google Scholar] [CrossRef] - Burden, F.; Winkler, D. Bayesian Regularization of Neural Networks, in Artificial Neural Networks. Methods Mol. Biol.
**2008**, 458, 25–44. [Google Scholar] [PubMed] - Foresee, F.D.; Hagan, M.T. Gauss-Newton approximation to Bayesian regularization. In Proceedings of the International Joint Conference on Neural Networks, Nagoya, Japan, 23–29 August 1997. [Google Scholar]
- MacKay, D.J.C. Bayesian Interpolation. Neural Comput.
**1992**, 4, 415–447. [Google Scholar] [CrossRef] - Geisser, S. Predictive Inference; Chapman and Hall: New York, NY, USA, 1993. [Google Scholar]
- Picard, R.R.; Cook, R.D. Cross-Validation of Regression Models. J. Am. Stat. Assoc.
**1984**, 79, 575–583. [Google Scholar] [CrossRef] - Maekawa, K.; Zhu, X.; Chijiwa, N.; Tanabe, S. Mechanism of long-term excessive deformation and delayed shear failure of underground RC box culverts. J. Adv. Concr. Technol.
**2016**, 14, 183–204. [Google Scholar] [CrossRef]

**Figure 4.**Cyclic passage of moving wheel type load versus live-load deflection at span center for the referential RC deck.

**Figure 7.**Relationship between the average strain and the fatigue life of real crack patterns and randomized artificial crack pattern program (RACPs).

**Figure 11.**Proposed correlation for the remaining fatigue life prediction by using cracks density parameter.

**Figure 14.**Relationship between the fatigue life of “multiscale simulation program” & “ANN” for the training dataset.

**Figure 20.**Comparison of the remaining fatigue life between two crack patterns of the same cracks density.

Material Type | Concrete | Steel Reinforcement | |
---|---|---|---|

Young’s Modulus | N/mm^{2} | 24,750 | 205,000 |

Compressive Strength | N/mm^{2} | 30 | 295 |

Tensile Strength | N/mm^{2} | 2.2 | 295 |

Specific Weight | kN/m^{3} | 24 | 78 |

**Table 2.**Four sets of input variables for choosing the best performance artificial neural networks (ANN) model.

ANN Input Variables | Variables for Each FEM Element | No. of Elements | Total Number of Variables | Cracks Direction |
---|---|---|---|---|

Case (1) | ε_{xx}, ε_{yy}, ε_{xy} | 336 | 1008 | Included “Indirectly” |

Case (2) | ε_{1}, θ (Equations (6) and (7)) | 336 | 672 | Included “Directly” |

Case (3) | ε_{xx}, ε_{yy}, ε_{xy} | 84 | 252 | Included “Indirectly” |

Case (4) | ε_{1}, θ (Equations (6) and (7)) | 84 | 168 | Included “Directly” |

ANN Input Variables | Number of Hidden Layers | Number of Neurons |
---|---|---|

Case 1 | 1 | 1 |

Case 2 | 1 | 1 |

Case 3 | 1 | 2 |

Case 4 | 1 | 2 |

Case 5 Section 5.5 | 1 | 2 |

ANN Input Variables | Variables for Each FEM Element | No. of Elements | Total Number of Variables | Cracks Direction |
---|---|---|---|---|

Case (3) | ε_{xx}, ε_{yy}, ε_{xy} | 84 | 252 | Included “Indirectly” |

Case (5) | ε_{1} | 84 | 84 | Not included |

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**MDPI and ACS Style**

Fathalla, E.; Tanaka, Y.; Maekawa, K.; Sakurai, A.
Quantitative Deterioration Assessment of Road Bridge Decks Based on Site Inspected Cracks. *Appl. Sci.* **2018**, *8*, 1197.
https://doi.org/10.3390/app8071197

**AMA Style**

Fathalla E, Tanaka Y, Maekawa K, Sakurai A.
Quantitative Deterioration Assessment of Road Bridge Decks Based on Site Inspected Cracks. *Applied Sciences*. 2018; 8(7):1197.
https://doi.org/10.3390/app8071197

**Chicago/Turabian Style**

Fathalla, Eissa, Yasushi Tanaka, Koichi Maekawa, and Akito Sakurai.
2018. "Quantitative Deterioration Assessment of Road Bridge Decks Based on Site Inspected Cracks" *Applied Sciences* 8, no. 7: 1197.
https://doi.org/10.3390/app8071197