During recent years, the possibility that damage at the time of earthquake could change depending on the deterioration condition of infrastructure has been noted through analytical analyses. Faced with such a possibility, management policy should be optimized by internalizing the external elements of earthquake damage, evaluating the appropriateness of management policy for infrastructure, and optimizing the system. In this study, the deterioration process for infrastructure was modelled using the Markov process model, and a methodology to determine the optimal management policy is proposed by considering the two risks: i) the risk that infrastructure fails because of deterioration independent of external elements such as an earthquake, and ii) the risk that changes due to deterioration fails the infrastructure at the time of earthquake. Using an example of the application the following two points are demonstratively shown: i) the optimal management policy would change in the case in which earthquake risk is not considered, and ii) the optimal management policy would change depending on the earthquake occurrence probability in the case in which earthquake risk is considered.

1. [1] The Headquarters for Earthquake Research Promotion, Ministry of Education, Culture, Sports, Science and Technology, “National Seismic Hazard Maps for Japan,” 2005.
2. [2] S. Madanat, “Incorporating inspection decisions in pavement management,” Transportation Research Part B: Methodological, Vol.27, Issue 6, pp. 425-438, 1993.
3. [3] R. A. Howard, “Dynamic Programming and Markov Processes,” MIT Press, 1960.
4. [4] R. Bellman, “The theory of dynamic programming,” Bulletin of the American Mathematical Society, Vol.60, Issue 6, pp. 503-515, 1954.
5. [5] M. Jido, T. Otazawa, and K. Kobayashi, “Optimal repair and inspection rules under uncertainty,” J. of Infrastructure Systems, Vol.14, Issue 2, pp. 150-158, 2008.
6. [6] S. Madanat, “Optimizing sequential decisions under measurement and forecasting uncertainty: Application to infrastructure inspection, maintenance and rehabilitation,” Doctoral dissertation, Massachusetts Institute of Technology, 1991.
7. [7] S. Madanat and M. Ben-Akiva, “Optimal inspection and repair policies for infrastructure facilities,” Transportation Science, Vol.28, No.1, pp. 55-62, 1994.
8. [8] Y. Li and S. Madanat, “A steady-state solution for the optimal pavement resurfacing problem,” Transportation Research Part A: Policy and Practice, Vol.36, Issue 6, pp. 525-535, 2002.
9. [9] Y. Ouyang and S. Madanat, “An analytical solution for the finite-horizon pavement resurfacing planning problem,” Transportation Research Part B: Methodological, Vol.40, Issue 9, pp. 767-778, 2006.
10. [10] K. Aoki, K. Yamamoto, and K. Kobayashi, “An optimal inspection/rehabilitation model of multi-components systems with time-dependent deterioration processes,” J. of Japan Society of Civil Engineers, Series F, Vol. 62, No.2, pp. 240-257, 2006 (in Japanese).
11. [11] K. Kobayashi, K. Kaito, and N. Lethanh, “Deterioration forecasting model with multistage Weibull hazard functions,” J. of Infrastructure Systems, Vol.16, Issue 4, pp. 282-291, 2010.
12. [12] K. Kobayashi, M. Eguchi, A. Oi, K. Aoki, K. Kaito, and Y. Matsumura, “The optimal repair and replacement model of pavement structure,” J. of Japan Society of Civil Engineers, Series E1, Vol.68, No.2, pp. 54-68, 2012 (in Japanese).
13. [13] T. Otazawa, K. Yamamoto, K. Aoki, and K. Kobayashi, “Optimal synchronizing repair model of highway equipment facilities,” J. of Japan Society of Civil Engineers, Series F, Vol.64, No.2, pp. 200-217, 2008 (in Japanese).
14. [14] M. Hori, T. Tsuruta, K. Kaito, and K. Kobayashi, “Maintenance management accounting system of waste water disposal systems,” J. of Japan Society of Civil Engineers, Series F4, Vol.67, No.1, pp. 33-52, 2011 (in Japanese).
15. [15] K. Kaito, H. Kanaji, H. Kobayashi, N. Mashima, H. Ohishi, and K. Matsuoka, “Optimum inspection policy for long span bridge based on fault tree analysis with visual inspection data,” J. of Japan Society of Civil Engineers, Series F4, Vol.67, No.2, pp. 74-91, 2011 (in Japanese).
16. [16] K. Kobayashi, M. Eguchi, A. Oi, K. Aoki, and K. Kaito, “The optimal implementation policy of pavement inspection with deterioration uncertainty,” J. of Japan Society of Civil Engineers, Series E1, Vol.67, No.2, pp. 75-90, 2011 (in Japanese).
17. [17] K. Obama, K. Kaito, K. Aoki, K. Kobayashi, and T. Fukuda, “The optimal scrapping and maintenance model of infrastructure considering deterioration process,” J. of Japan Society of Civil Engineers, Series F4, Vol.68, No.3, pp. 141-156, 2012 (in Japanese).
18. [18] C. Torres-Machí, A. Chamorro, C. Videla, E. Pellicer, and V. Yepes, “An iterative approach for the optimization of pavement maintenance management at the network level,” The Scientific World J., Vol.2014, Article ID 524329, 2014.
19. [19] N. Lethanh, B. T. Adey, and M. Burkhalter, “Determining an Optimal Set of Work Zones on Large Infrastructure Networks in a GIS Framework,” J. of Infrastructure Systems, Vol.24, Issue 1, Article No.04017048, 2017.
20. [20] M. Burkhalter, C. Martani, and B. T. Adey, “Determination of Risk-Reducing Intervention Programs for Railway Lines and the Significance of Simplifications,” J. of Infrastructure Systems, Vol.24, Issue 1, Article No.04017038, 2017.
21. [21] D. Mizutani, M. Burkhalter, B. T. Adey, C. Martani, and V. Ramdas, “Initial investigations into the use of three heuristic algorithms to determine optimal intervention programs for multiple railway objects,” Int. J. of Architecture, Engineering and Construction, Vol.6, No.3, pp. 1-20, 2017.
22. [22] M. S. Dehghani, G. Flintsch, and S. McNeil, “Impact of Road Conditions and Disruption Uncertainties on Network Vulnerability,” J. of Infrastructure Systems, Vol.20, Issue 3, Article No.04014015, 2014.
23. [23] J. Simon, J. M. Bracci, and P. Gardoni, “Seismic response and fragility of deteriorated reinforced concrete bridges,” J. of Structural Engineering, Vol.136, Issue 10, pp. 1273-1281, 2010.
24. [24] L. Ibarra, B. Dasgupta, and K.-T. Chiang, “Seismic Performance of Degraded Shear Walls for Long-Term Compliance Periods,” J. Disaster Res., Vol.7, No.5, pp. 638-644, 2012.
25. [25] K. Hayashi, Y. Adachi, K. Komoto, H. Yatsumoto, A. Igarashi, J. Dang, and T. Higashide, “Experimental verification for remaining performance of lead rubber bearings with aging deterioration,” J. of Japan Society of Civil Engineers, Series A1, Vol.70, No.4, pp. I1032-I1042, 2014 (in Japanese).
26. [26] J. Dang, T. Higashide, A. Igarashi, Y. Adachi, and T. Hayashi, “Dynamic analysis to investigate the effect of aging deterioration of lead rubber bearings on the seismic performance of bridges,” J. of Japan Society of Civil Engineers, Series A1, Vol.71, No.4, pp. I713-I724, 2015 (in Japanese).
27. [27] M. Onodera, H. Matsuzaki, and M. Suzuki, “Effect of deteriorated isolators on the seismic response of reinforced concrete columns with isolator,” J. of Japan Society of Civil Engineers, Series A1, Vol.71, No.4, pp. I737-I748, 2015 (in Japanese).
28. [28] Y. Thanapol, M. Akiyama, and D. M. Frangopol, “Updating the seismic reliability of existing RC structures in a marine environment by incorporating the spatial steel corrosion distribution: Application to bridge piers,” J. of Bridge Engineering, Vol.21, Issue 7, Article No.04016031, 2016.
29. [29] Y. Tsuda, K. Kaito, K. Aoki, and K. Kobayashi, “Estimating Markovian transition probabilities for bridge deterioration forecasting,” Structural Eng./Earthquake Eng., Vol.23, No.2, pp. 241s-256s, 2006.
30. [30] S. Hirakawa, D. Mizutani, K. Obama, and K. Kaito, “An optimal inspection/replacement policy of expressway tunnel lighting systems in consideration of non-stationary inspection intervals,” J. of Japan Society of Civil Engineers, Series F4, Vol.71, No.3, pp. 162-181, 2015 (in Japanese).
31. [31] Road Bureau, Ministry of Land, Infrastructure, Transport and Tourism, “Guideline for Periodic Road Bridge Inspection,” 2014 (in Japanese).
32. [32] Osaka Prefecture, “Guideline for Bridge Inspection,” 2016 (in Japanese).
33. [33] D. O’Reilly, J. Hopkin, G. Loomes, M. Jones-Lee, P. Philips, K. McMahon, D. Ives, B. Soby, D. Ball, and R. Kemp, “The value of road safety: UK research on the valuation of preventing non-fatal injuries,” J. of Transport Economics and Policy, Vol.28, No.1, pp. 45-59, 1994.