Stochastic Reliability Analysis of Armor Units of Rubble-Mound Breakwaters Subject to Multiple Loads

다중하중에 따른 경사제 피복재의 추계학적 신뢰성 해석

  • Lee, Cheol-Eung (Department of Civil Engineering, Kangwon National University)
  • 이철응 (강원대학교 토목공학과)
  • Received : 2012.03.16
  • Accepted : 2012.04.19
  • Published : 2012.04.30


A stochastic reliability analysis model has been developed for evaluating the time-dependent stability performance of armor units of rubble-mound breakwaters subjected to the multiple loads of arbitrary magnitudes which could be occurred randomly. The initial structural capacities and the damage rates of armor units of rubble-mound breakwaters could be estimated as a function of the incident wave height with a given return period by using the modified Hudson's formula and Melby's formula. The structural stability performances of armor units of rubble-mound breakwaters could be analyzed in detail through the lifetime reliability investigations according to the limit states such as the serviceability or ultimate limit state and the conditions of multiple loads. Finally, repair intervals for the structural management of armor units of rubble-mound breakwaters could quantitatively be evaluated by a new approach suggested in this paper that has been based on the target probability for repair and the accumulated probabilities of failure obtained from the present stochastic reliability analysis model.


  1. Aven, T.J. and Jensen, U. (1999). Stochastic models in reliability. Applications of mathematics; stochastic modelling and applied probability series, 41, Springer, N.Y., USA.
  2. Frangopol, D.M., Kallen, M.J. and Noortwijk, M. (2004). Probabilistic models for life-cycle performance of deteriorating structures: review and future directions, Prog. Struct. Eng. Mater., 6. 197-212.
  3. Guillaumot, V.M., Durango, P.L. and Madanat, S. (2003). Adaptive optimization of infrastructure maintenance and inspection decisions under performance model uncertainty, J. Inf. Syst. ASCE, 9(4), 133-139.
  4. Hasofer, A.M. (1974). Design for infrequent overloads, Earthquake Eng. Struct. Dynam., 2(4), 387-388.
  5. Kleiner, Y. (2001). Scheduling inspection, renewal of large infrastructure asserts, J. Inf. Syst. ASCE, 7(4), 136-143.
  6. Kubler, O. and Faber, M.H., Optimal design of infrastructure facilities subject to deterioration, Proc. ICASP'03, 1031-1039.
  7. Li, C.Q. (2003). Life cycle modelling of corrosion affected concrete structures-Propagation, J. of Struct. Eng., ASCE, 15(4), 753-761.
  8. Li, C.Q. and Zhao, J.M. (2010). Time-dependent risk assessment of combined overtopping and structural failure for reinforced concrete coastal structures, J. Waterway, Port, Coast., and Ocn. Eng., ASCE, 136(2), 97-103.
  9. Liu, Y. and Wyers, R.E. (1988). Modelling the time-to-corrosion cracking of the cover concrete in chloride contaminated reinforced concrete structures, ACI Master J., 95, 675-681.
  10. Madsen, H.O., Krenk, S. and Lind, N.C., 1986, Methods of structural safety, Prentice-Hall, N.J., USA.
  11. Melby, J.A. (1999). Damage progression on breakwaters, Ph.D. thesis, Dept. of Civ. Engrg., Univ. of Delware, USA.
  12. Mishalani, R.G. and Madanat, S.M. (2002), Computation of infrastructure state transition probabilities using stochastic duration models, J. Inf. Syst., ASCE, 8(4), 139-148.
  13. Nagakawa, T. On a replacement problem of cumulative damage model, Oper. Res. Quart., 27(4), 895-900.
  14. Parzen, E. (1962). Stochastic processes, Holden-Day, S.F., USA.
  15. PIANC (1992). Analysis of rubble mound breakwaters, Supplement to Bull., N. 78/79, Brussels, Belgium.
  16. Rosenblueth, E. (1976). Optimum design for infrequent disturbances, J. Struct. Div., ASCE, 102(ST9), 1807-1825.
  17. Rosenblueth, E. and Mendoza, E. (1971). Reliability optimization in isostatic structures, J. Eng. Mech. Div., ASCE, 97(EM6), 1625-1642.
  18. Sanchez-Silva, M. and Rackwitz, R. (2004). Implications of the high quality index in the design of optimum structures to withstand earthquake, J. Struct. Eng., ASCE, 130(6), 969-977.
  19. Sanchez-Silva, M., Klutke, G.A. and Rosowsky, D.V. (2011). Lifecycle performance of structures subject to multiple deterioration mechanisms, Struct. Safety, 33, 206-217.
  20. Sherif, Y. and Smith, M. (1981). Optimal maintenance models for systems subject to failure-a review, Naval Res. Logist. Quart., 28, 47-74.
  21. Val. D. and Stewart, M. (2005). Decision analysis for deteriorating structures, Reliab. Eng. Syst. Safety, 87, 377-387.
  22. Wortman, M.A., Klutke, G.-A. and Ayhan, H. (1994). A maintenance strategy for systems subjected to deterioration governed by random shocks, IEEE Trans. Reliab., 43(3), 439-445.
  23. Yang, Y. and Klutke, G. A. (2000). Improved inspection schemes for deteriorating equipment, Probab. Eng. Inform. Sci., 14, 445-460.

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