The Life-Cycle Cost (LCC) concept and methods have remarkably advanced in the field of civil infrastructure [1]. Many international symposia and workshops have been held all over the world. The basic concept and methodology of LCC itself are not so new and were already adopted several decades ago in the fields of electrical and mechanical engineering. In the field of civil engineering, seismic risk analysis was established on the basis of LCC. However, it is noted that the seismic risk analysis has not paid much attention to the structural maintenance activities.
LCC analysis and design are formulated as an optimization problem, which aims to implement an optimal inspection/repair strategy for the minimum expected total life-cycle cost that includes initial, preventive maintenance, inspection, repair and failure cost, while the civil structure maintains the target safety. As a representative civil structure, highway bridges follow the life-cycle that consists of design, construction, inspection, repair and failure. At present, it is desirable to develop an optimal strategy for the bridge management through the lifetime in order to reduce the overall cost.
An efficient method that provides adequate inspection/repair strategies was proposed by Frangopol et al [2]. This method can determine how many inspections are appropriate for lifetime, and at what time inspections and repairs should be done, while taking into account all bridge repair possibilities based on an event tree.
However, if the number of design variables increases, it is difficult to solve the problem. Therefore, an attempt was made to extend and improve the work by Frangopol et al. [2] using Genetic Algorithm (GA) [3, 4]. Using GA, it is possible to easily decide the number of lifetime inspections, the time of each inspection, and which inspection has to be used. LCC is a useful measure for evaluating the structural performance of deteriorating structures. Then, the optimal strategy obtained by LCC optimization can be different according to the prescribed level of structural performance and required service life. The relationships among several performance measures are discussed and attempted to provide rational balances of these measures by using the Multi-Objective Genetic Algorithm (MOGA). So far the authors have discussed the relationships among the minimization of LCC, the optimal extension of structural service life, and the target safety level by using MOGA [5]. By introducing MOGA, it is possible to obtain several available solutions that have different structural life spans, safety levels, and LCC values.
Furthermore, LCC is evaluated focusing on the effects of earthquakes that are major natural disasters in Japan [6]. At first, LCC analysis is formulated to consider the social and economical effects due to the collapse of structures occurred by the earthquake as well as the minimization of maintenance cost. The loss by the collapse of structures due to the earthquake can be defined in terms of an expected cost and introduced into the calculation of LCC. A stochastic model of structural response is proposed, which accounts for the variation due to the uncertain characteristics of earthquake. Then, the probability of failure due to the earthquake excitation is calculated based on the reliability theory. In addition, LCC evaluations are performed not only for a single bridge but also for many bridges forming road networks [7, 8].

References

1. Frangopol, D. M.. & Furuta, H. (eds.). Life-Cycle Cost Analysis and Design of Civil Infrastructure Systems, ASCE, Reston Virginia, 336 pages, 2001.
2. Frangopol, D. M, Lin, K-Y, and Estes, A. C., Life-Cycle Cost Design of Deteriorating Structures, Journal of Structural Engineering, ASCE, Vol.123 (10), pp.1390-1401, 1997.
3. Goldberg, D. E., Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Publishing Company, Inc. 1989
4. Furuta, H., Frangopol, D. M. & Saito, M. Application of Genetic Algorithm to Life-Cycle Cost Maintenance of Bridges, Proc. of KKNN Symposium, Seoul, Korea, 1998.
5. Furuta, H., Kameda, T., Fukuda, Y., and Frangopol, D. M. Life-Cycle Cost Analysis for Infrastructure Systems: Life-Cycle Cost vs. Safety Level vs. Service life, Proc. of 3rd Life-Cycle Cost Analysis and Design of Infrastructure Systems, Lausanne, Switzerland, 2003.
6. Furuta, H. and Koyama, K. Optimal Maintenance Planning of Bridge Structures Considering Earthquake Effects, Proc. of IFIP TC7 Conference, Antipolis, France, 2003.
7. Furuta, H., Nose, Y., Dogaki, M. & Frangopol, D. M. Bridge Maintenance System of Road Network Using Life-Cycle Cost and Benefit, Proc. of IABMAS, Barcelona, Spain, July, 2002.
8. Liu, M. & Frangopol, D.M. Optimal Bridge Maintenance Planning Based on Probabilistic Performance Prediction, Engineering Structures, Elsevier, Vol. 26, No. 7, pp.991-1002, 2004.