KSCE Journal of Civil Engineering

, Volume 23, Issue 4, pp 1872–1880 | Cite as

Development of a Reliability Index Considering Flood Damage for Urban Drainage Systems

  • Eui Hoon Lee
  • Joong Hoon KimEmail author
Water Resources and Hydrologic Engineering


Urban drainage systems are used to safely drain rainwater and prevent urban inundation, and their reliability is usually calculated from the probability of failure, which includes the probability of the drainage facilities being destroyed. This study proposes a new reliability index that includes three factors (flood volume, nodes, and damage), with the aim of prioritizing the structural and nonstructural measures required to improve urban drainage systems. In this study, synthetic rainfall data are generated by the Huff distribution and are used as input data for runoff simulations. The Distance Measure Method that uses a utopian approach is employed here to generate a dimensionless reliability index, as the three factors use different units and no definitive criteria currently exist to determine the weights that should be assigned to each factor. The reliability indexes of flood volume, nodes, and damage determined in this study are 0.7226, 0.4584 and 0.9750, respectively, as the three factors are weighted equally in the reliability index calculation. Using the new method, the reliability index of the city of Jeongup is 0.6484. The new reliability index can be used to assess the effectiveness of various flood mitigation measures in preparation for extreme rainfall events.


flood damage reliability index distance measure method multi-dimensional flood damage analysis urban drainage systems 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Awumah, K., Goulter, I., and Bhatt, S. K. (1990). “Assessment of reliability in water distribution networks using entropy based measures.” Stochastic Hydrology and Hydraulics, Springer Berlin Heidelberg, Vol. 4, No. 4, pp. 309–320.CrossRefGoogle Scholar
  2. Baek, C. W., Jun, H. D., and Kim, J. H. (2010). “Development of a PDA model for water distribution systems using harmony search algorithm.” KSCE Journal of Civil Engineering, KCSE, Vol. 14, No. 4, pp. 613–62, DOI: 10.1007/s12205-010-0613-7.CrossRefGoogle Scholar
  3. Choi, H., Lee, E. H., Joo, J. G., and Kim, J. H. (2017) “Determining optimal locations for rainwater storage sites with the goal of reducing urban inundation damage costs.” KSCE Journal of Civil Engineering, KCSE, Vol. 21, No. 6, pp. 2488–2500, DOI: 10.1007/s12205-016-0922-6.CrossRefGoogle Scholar
  4. Choi, S. A., Yi, C. S., Shim, M. P., and Kim, H. S. (2006). “Multidimensional flood damage analysis (I): Principle and procedure.” Journal of Korea Water Resources Association, KWRA, Vol. 50, No. 8, pp. 1–9, DOI: 10.3741/JKWRA.2017.50.8.513.Google Scholar
  5. Cullinane, M. J. (1986). “Hydraulic reliability evaluation of water distribution systems.” Water forum 1986: World water issues in evolution, ASCE, San Francisco, CA, USA.Google Scholar
  6. Danielsson, P. E. (1980). “Euclidean distance mapping.” Computer Graphics and Image Processing, Elsevier, Vol. 14, No. 3, pp. 227–248, DOI: 10.1016/0146-664X(80)90054-4.CrossRefGoogle Scholar
  7. Farmani, R., Walters, G. A., and Savic, D. A. (2005). “Trade-off between total cost and reliability for Anytown water distribution network.” Journal of Water Resources Planning and Management, ASCE, Vol. 131, No. 3, pp. 161–171, DOI: 10.1061/(ASCE)0733-9496(2005)131:3(161).CrossRefGoogle Scholar
  8. Farmani, R., Walters, G., and Savic, D. (2006). “Evolutionary multiobjective optimization of the design and operation of water distribution network: Total cost vs. reliability vs. water quality.” Journal of Hydroinformatics, IWA Publishing, Vol. 8, No. 3, pp. 165–179, DOI: 10.2166/hydro.2006.019.CrossRefGoogle Scholar
  9. Fujiwara, O. and Ganesharajah, T. (1993). “Reliability assessment of water supply systems with storage and distribution networks.” Water Resources Research, AGU, Vol. 29, No. 8, pp. 2917–2924, DOI: 10.1029/93WR00857.CrossRefGoogle Scholar
  10. Gouri, R. L. and Srinivas, V. V. (2015). “Reliability assessment of a storm water drain network.” Aquatic Procedia, Elsevier, Vol. 4, pp. 772–779, DOI: 0.1016/j.aqpro.2015.02.160.CrossRefGoogle Scholar
  11. Griffin, R. C. and Mjelde, J. W. (2000). “Valuing water supply reliability.” American Journal of Agricultural Economics, Blackwell Publishing, Vol. 82, No. 2, pp. 414–426, DOI: 10.1111/0002-9092.00035.CrossRefGoogle Scholar
  12. Haghighi, A. and Bakhshipour, A. E. (2016). “Reliability-based layout design of sewage collection systems in flat areas.” Urban Water Journal, Taylor & Francis, Vol. 13, No. 8, pp. 790–802, DOI: 10.1080/1573062X.2015.1036085.CrossRefGoogle Scholar
  13. Hajani, E. and Rahman, A. (2014). “Reliability and cost analysis of a rainwater harvesting system in peri-urban regions of Greater Sydney, Australia.” Water, MDPI, Vol. 6, No. 4, pp. 945–960, DOI: 10.3390/w6040945.CrossRefGoogle Scholar
  14. Hashimoto, T., Stedinger, J. R., and Loucks, D. P. (1982). “Reliability, resiliency, and vulnerability criteria for water resource system performance evaluation.” Water Resources Research, AGU, Vol. 18, No. 1, pp. 14–20, DOI: 10.1029/WR018i001p00014.CrossRefGoogle Scholar
  15. Howe, C. W., Smith, M. G., Bennett, L., Brendecke, C. M., Flack, J. E., Hamm, R. M., Mann, R., Rozaklis, L., and Wunderlich, K. (1994). “The value of water supply reliability in urban water systems.” Journal of Environmental Economics and Management, Elsevier, Vol. 26, No. 1, pp. 19–30, DOI: 10.1006/jeem.1994.1002.CrossRefGoogle Scholar
  16. Huff, F. A. (1967). “Time distribution of rainfall in heavy storms.” Water Resources Research, AGU, Vol. 3, No. 4, pp. 1007–1019, DOI: 10.1029/WR003i004p01007.CrossRefGoogle Scholar
  17. Jin, Y. and Mukherjee, A. (2010). “Modeling blockage failures in sewer systems to support maintenance decision making.” Journal of Performance of Constructed Facilities, ASCE, Vol. 24, No. 6, pp. 622–633, DOI: 10.1061/(ASCE)CF.1943-5509.0000126.CrossRefGoogle Scholar
  18. Kaufmann, A., Cruon, R., and Grouchko, D. (1977). Mathematical models for the study of the reliability of systems, Elsevier, New York, NY, USA.Google Scholar
  19. Kwon, H. J. and Lee, C. E. (2010). “Safety analysis of storm sewer using probability of failure and multiple failure mode.” Journal of Korea Water Resources Association, KWRA, Vol. 43, No. 11, pp. 967–976, DOI: 10.3741/JKWRA.2010.43.11.967.CrossRefGoogle Scholar
  20. Lee, E. H. and Kim, J. H. (2017). “Development of resilience index based on flooding damage in urban areas.” Water, MDPI, Vol. 9, No. 6, p. 428, DOI: 10.3390/w9060428.CrossRefGoogle Scholar
  21. Lee, J. H. (2012). “Development of a reliability estimation method for the storm sewer network.” Journal of Korean Society of Hazard Mitigation, KOSHAM, Vol. 12, No. 2, pp. 225–230, DOI: 10.9798/kosham.2012.12.2.225.CrossRefGoogle Scholar
  22. Lee, J. H. and Park, M. J. (2012). “A reliability evaluation method of storm sewer networks for excessive rainfall events.” Journal of Korean Society of Hazard Mitigation, KOSHAM, Vol. 12, No. 4, pp. 195–201, DOI: 10.9798/kosham.2012.12.4.195.CrossRefGoogle Scholar
  23. Mahmoodian, M. and Alani, A. M. (2013). “Multi-failure mode assessment of buried concrete pipes subjected to time-dependent deterioration, using system reliability analysis.” Journal of Failure Analysis and Prevention, Vol. 13, No. 5, pp. 634–642, DOI: 10.1007/s11668-013-9727-9.CrossRefGoogle Scholar
  24. Ministry of Construction and Transportation (2004). Study on economical analysis method of flood control project, Seoul, Korea.Google Scholar
  25. Miszta-Kruk, K. (2016). “Reliability and failure rate analysis of pressure, vacuum and gravity sewer systems based on operating data.” Engineering Failure Analysis, Elsevier, Vol. 61, pp. 37–45, DOI: 10.1016/j.engfailanal.2015.07.034.CrossRefGoogle Scholar
  26. Rahman, A., Keane, J., and Imteaz, M. A. (2012). “Rainwater harvesting in Greater Sydney: Water savings, reliability and economic benefits.” Resources, Conservation and Recycling, Elsevier, Vol. 61, pp. 16–21, DOI: 10.1016/j.resconrec.2011.12.002.CrossRefGoogle Scholar
  27. Rodríguez, J. P., McIntyre, N., Díaz-Granados, M., and Maksimovic, C. (2012). “A database and model to support proactive management of sediment-related sewer blockages.” Water Research, Elsevier, Vol. 46, No. 15, pp. 4571–4586, DOI: 10.1016/j.watres.2012.06.037.CrossRefGoogle Scholar
  28. Shinstine, D. S., Ahmed, I., and Lansey, K. E. (2002). “Reliability/ availability analysis of municipal water distribution networks: Case studies.” Journal of Water Resources Planning and Management, ASCE, Vol. 128, No. 2, pp. 140–151, DOI: 10.1061/(ASCE)0733-9496(2002)128:2(140).CrossRefGoogle Scholar
  29. Song, Y. H. and Lee, J. H. (2014). “Analysis on the sedimentation characteristics according to slope variation of storm sewer pipe line.” Journal of Korean Society of Hazard Mitigation, KOSHAM, Vol. 14, No. 5, pp. 341–350, DOI: 10.9798/KOSHAM.2014.14.5.341.Statistics Korea, Available online at (accessed on 25 February 2017).CrossRefGoogle Scholar
  30. Su, Y. C., Mays, L. W., Duan, N., and Lansey, K. E. (1987). “Reliabilitybased optimization model for water distribution systems.” Journal of Hydraulic Engineering, ASCE, Vol. 113, No. 12, pp. 15391556, DOI: 10.1061/(ASCE)0733-9429(1987)113:12(1539).CrossRefGoogle Scholar
  31. Thorndahl, S. and Willems, P. (2008). “Probabilistic modelling of overflow, surcharge and flooding in urban drainage using the firstorder reliability method and parameterization of local rain series.” Water Research, Elsevier, Vol. 42, No. 1, pp. 455–466, DOI: 10.1016/j.watres.2007.07.038CrossRefGoogle Scholar
  32. Thorndahl, S., Schaarup-Jensen, K., and Jensen, J. B. (2008). “Probabilistic modelling of combined sewer overflow using the First Order Reliability Method.” Water Science and Technology, IWA Publishing, Vol. 57, No. 9, pp. 1337–1344, DOI: 10.2166/wst.2008.301.CrossRefGoogle Scholar
  33. Tolson, B. A., Maier, H. R., Simpson, A. R., and Lence, B. J. (2004). “Genetic algorithms for reliability-based optimization of water distribution systems.” Journal of Water Resources Planning and Management, ASCE, Vol. 130, No. 1, pp. 63–72, DOI: 10.1061/(ASCE)0733-9496(2004)130:1(63).CrossRefGoogle Scholar
  34. USEPA (2010). Storm water management model user’s manual version 5.0, United States Environmental Protection Agency, Washington, DC, USA.Google Scholar
  35. Wagner, J. M., Shamir, U., and Marks, D. H. (1988). “Water distribution reliability: Simulation methods.” Journal of Water Resources Planning and Management, ASCE, Vol. 114, No. 3, pp. 276–294, DOI: 10.1061/(ASCE)0733-9496(1988)114:3(276).CrossRefGoogle Scholar
  36. Wolff, G. (2008). “Calculating constant-reliability water supply unit costs.” Water Policy, IWA Publishing, Vol. 10, No. 1, pp. 95–104, DOI: 10.2166/wp.2007.032.CrossRefGoogle Scholar
  37. Xanthopulos, Z., Melachrinoudis, E., and Solomon, M. M. (2000). “Interactive multiobjective group decision making with interval parameters.” Management Science, INFORMS, Vol. 46, No. 12, pp. 1585–1601, DOI: 10.1287/mnsc.46.12.1585.12071.CrossRefGoogle Scholar
  38. Xu, C. and Goulter, I. C. (1999). “Reliability-based optimal design of water distribution networks.” Journal of Water Resources Planning and Management, ASCE, Vol. 125, No. 6, pp. 352–362, DOI: 10.1061/(ASCE)0733-9496(1999)125:6(352).CrossRefGoogle Scholar
  39. Yoon, Y. N., Jung, J. H., and Ryu, J. H. (2013). “Introduction of design flood estimation.” Journal of Korea Water Resources Association, KWRA, Vol. 46, No. 3, pp. 55–68.Google Scholar

Copyright information

© Korean Society of Civil Engineers 2019

Authors and Affiliations

  1. 1.School of Civil EngineeringChungbuk National UniversityCheongjuKorea
  2. 2.School of Civil, Environmental and Architectural EngineeringKorea UniversitySeoulKorea

Personalised recommendations