Advertisement

Development and Comparison of Two New Methods for Quantifying Uncertainty in Analysis of Flow Through Rockfill Structures

  • Ali Yousefi
  • Seyed Mahmood Hosseini
Research paper
  • 4 Downloads

Abstract

Although extensive researches have been conducted in the analytical and numerical analysis of flow through rockfill structures, one of the main issues in these analyses which still needs attention is uncertainty quantification. In this research, first, it was investigated and shown that the nature and source of uncertainty in rockfill hydraulic parameters can be different indicating random and fuzzy parameters. Then, uncertainty analysis of gradually varied flow computations in rockfill structures was conducted using proposed hybrid and transformation methods in order to quantify the uncertainty in computed water surface profiles resulting from uncertainty in the model hydraulic parameters. Although the proposed methods can be applied to any equation that quantifies the head loss in flow through rockfill structures, two commonly used equations, i.e., Stephenson and Wilkins equations, were used in this study. The methods were applied to a laboratory-scale physical model, and the numerical results were compared with the corresponding measured water surface levels. Three main conclusions drawn from this study were: (1) the results of the two different uncertainty analysis methods did not show significant differences, but the transformation method was rather simple and computationally efficient in comparison with the hybrid method, (2) for both Wilkins and Stephenson equations, the experimental data were within the 90% confidence intervals resulting from both uncertainty analysis methods and (3) the proposed approach and methodologies in this study can be used by hydraulic engineers in analysis and design of real-life rockfill structures.

Keywords

Gradually varied flow Hybrid method Rockfill Transformation method Uncertainty analysis 

References

  1. Abebe AJ, Guinot V, Solomatine DP (2000) Fuzzy alpha-cut vs. Monte Carlo techniques in assessing uncertainty in model parameters. In: Proceedings of 4th Hydroinformatics conference, Iowa, USAGoogle Scholar
  2. Akan AO (2006) Open channel hydraulics. Elsevier, CanadaGoogle Scholar
  3. Alavi Moghaddam SMR, Hosseini SM (2008) Accuracy of energy and momentum principles for gradually varied analysis of flow through compound channels. Dam Eng 19(1):5–28Google Scholar
  4. Ascough JC II, Flanagan DC, Nearing MA, Engel BA (2013) Sensitivity and first-order/Monte Carlo uncertainty analysis of the WEPP hillslope erosion model. Trans ASABE 56(2):437–452CrossRefGoogle Scholar
  5. Bari R (1997) The hydraulics of buried streams. In: M.S. thesis, Department of Civil Engineering, Technical University of Nova Scotia, Halifax, Nova Scotia, CanadaGoogle Scholar
  6. Bari R, Hansen D (2003) Application of gradually-varied flow algorithms to simulate buried streams. J Hydraul Res 40(6):673–683.  https://doi.org/10.1080/00221680209499914 CrossRefGoogle Scholar
  7. Branisavljevic N, Ivetic M (2006) Fuzzy approach in the uncertainty analysis of the water distribution network of Becej. Civ Eng Environ Syst 23(3):221–236.  https://doi.org/10.1080/10286600600789425 CrossRefGoogle Scholar
  8. Chaudhry MH (2008) Open-channel flow. Springer Publishing Company, New YorkCrossRefGoogle Scholar
  9. CIRIA, CUR and CETMEF (2007) The rock manual: the use of rock in hydraulic engineering, C683. CIRIA, LondonGoogle Scholar
  10. Dubois D, Prade H, Sandri S (1993) On possibility/probability transformations. In: Lowen R, Roubens M (eds) Fuzzy Logic. Springer, Netherlands, pp 103–112CrossRefGoogle Scholar
  11. Faybishenko B (2010) Fuzzy-probabilistic calculations of water-balance uncertainty. Stoch Environ Res Risk Assess 24(6):939–952.  https://doi.org/10.1007/s00477-010-0379-y CrossRefGoogle Scholar
  12. Ganoulis J (2006) Fuzzy modelling for uncertainty propagation and risk quantification in environmental water systems. In: Proceedings of NATO advanced research workshop on computational models of risks to infrastructure. Primosten, CroatiaGoogle Scholar
  13. Garga VK, Hansen D, Townsend DR (1989) Considerations in the design of flow through rockfill drains. In: Proceedings of 14th annual British Columbia mine reclamation symposium. Cranbrook, British ColumbiaGoogle Scholar
  14. Golasowski M, Litschmannova M, Kuchar S, Podhorányi M, Martinovic J (2015) Uncertainty modelling on rainfall-runoff simulations based on parallel Monte Carlo method. Neural Netw World 25(3):267–286.  https://doi.org/10.14311/NNW.2015.25.014 CrossRefGoogle Scholar
  15. Greenly BT, Joy DM (1996) One-dimensional finite-element model for high flow velocities in porous media. J Geotech Eng 122(10):789–796.  https://doi.org/10.1061/(ASCE)0733-9410(1996)122:10(789) CrossRefGoogle Scholar
  16. Gupta R, Bhave PR (2007) Fuzzy parameters in pipe network analysis. Civ Eng Environ Syst 24(1):33–54.  https://doi.org/10.1080/10286600601024822 CrossRefGoogle Scholar
  17. Guyonnet D, Bourgine B, Dubois D, Fargier H, Come B, Chiles JP (2003) Hybrid approach for addressing uncertainty in risk assessments. J Environ Eng 128(1):68–78.  https://doi.org/10.1061/(ASCE)0733-9372(2003)129:1(68) CrossRefGoogle Scholar
  18. Hansen D, Bari R (2002) Uncertainty in water surface profile of buried stream flowing under coarse material. J Hydraul Eng 128(8):761–773.  https://doi.org/10.1061/(ASCE)0733-9429(2002)128:8(761) CrossRefGoogle Scholar
  19. Hansen D, Roshanfekr A (2012) Use of index gradients and default tailwater depth as aids to hydraulic modeling of flow-through rockfill dams. J Hydraul Eng 138(8):726–735.  https://doi.org/10.1061/(ASCE)HY.1943-7900.0000572 CrossRefGoogle Scholar
  20. Hansen D, Zhao WZ, Han SY (2005) Hydraulic performance and stability of coarse rockfill deposits. Water Manag 158(4):163–175.  https://doi.org/10.1680/wama.2005.158.4.163 CrossRefGoogle Scholar
  21. Hanss M (2005) Applied fuzzy arithmetic: an introduction with engineering applications. Springer, BerlinzbMATHGoogle Scholar
  22. Heydari M, Talaee PH (2011) Prediction of flow through rockfill dams using a neuro-fuzzy computing technique. J Math Comput Sci 2(3):515–528CrossRefGoogle Scholar
  23. Hosseini SM (2000) Statistical evaluation of the empirical equations that estimate hydraulic parameters for flow through rockfill. In: Wang ZY, Hu SX (eds) Stochastic hydraulics ‘00. Balkema, Rotterdam, The Netherlands, pp 547–552Google Scholar
  24. Hosseini SM, Joy DM (2006) Calibration of hydraulic parameters for flow through rockfill structures. Dam Eng 17(2):85–111Google Scholar
  25. Hosseini SM, Joy DM (2007) Development of an unsteady model for flow through coarse heterogeneous porous media applicable to valley fills. Int J River Basin Manag 5(4):253–265.  https://doi.org/10.1080/15715124.2007.9635325 CrossRefGoogle Scholar
  26. Jankovic-Nisic B, Maksimovic C, Graham NJD (2000) Using a Monte Carlo method for active leakage control in water supply networks. In: Proceedings of 4th Hydroinformatics conference, Iowa, USAGoogle Scholar
  27. Kang D, Lansey K (2010) Demand and roughness estimation in water distribution systems. J Water Resour Plan Manag 137(1):20–30.  https://doi.org/10.1061/(ASCE)WR.1943-5452.0000086 CrossRefGoogle Scholar
  28. Kang D, Pasha MFK, Lansey K (2009) Approximate methods for uncertainty analysis of water distribution systems. Urban Water J 6(3):233–249.  https://doi.org/10.1080/15730620802566844 CrossRefGoogle Scholar
  29. Kells JA (1993) Spatially varied flow over rockfill embankments. Can J Civ Eng 20(5):820–827.  https://doi.org/10.1139/l93-107 CrossRefGoogle Scholar
  30. Kumar V, Schuhmacher M (2005) Fuzzy uncertainty analysis in system modelling. In: Proceedings of 38th European symposium of the working party on computer aided process engineering. Barcelona, SpainGoogle Scholar
  31. Kunstmann H, Kinzelbach W, Siegfried T (2002) Conditional first-order second-moment method and its application to the quantification of uncertainty in groundwater modeling. Water Resour Res 38(4):1–14.  https://doi.org/10.1029/2000WR000022 CrossRefGoogle Scholar
  32. Leps TM (1973) Flow through rockfill. In: Hirschfeld R, Poulos S (eds) Embankment dam engineering. Wiley, New York, pp 87–97Google Scholar
  33. Li H, Zhang K (2010) Development of a fuzzy-stochastic nonlinear model to incorporate aleatoric and epistemic uncertainty. J Contam Hydrol 111(4):1–12.  https://doi.org/10.1016/j.jconhyd.2009.10.004 CrossRefGoogle Scholar
  34. Li B, Garga VK, Davies MH (1998) Relationship for non-Darcy flow in rockfill. J Hydraul Eng 124(2):206–212.  https://doi.org/10.1061/(ASCE)0733-9429(1998)124:2(206) CrossRefGoogle Scholar
  35. Liwei H, Zongkun L (2010) Back analysis of earth rockfill dam’s seepage property based on cloud reasoning. In: International conference on computer application and system modeling (ICCASM), IEEE, Taiyuan, ChinaGoogle Scholar
  36. Loveridge M, Rahman A (2014) Quantifying uncertainty in rainfall–runoff models due to design losses using Monte Carlo simulation: a case study in New South Wales, Australia. Stoch Environ Res Risk Assess 28(8):2149–2159.  https://doi.org/10.1007/s00477-014-0862-y CrossRefGoogle Scholar
  37. McCorquodale JA (1970) Variational approach to non-Darcy flow. J Hydraul Div 96(11):2265–2278Google Scholar
  38. Moller B, Beer M (2005) Fuzzy randomness: Uncertainty in civil engineering and computational mechanics, 1st edn. Springer, GermanyzbMATHGoogle Scholar
  39. Mpimpas H, Anagnostopoulos P, Ganoulis J (2008) Uncertainty of model parameters in stream pollution using fuzzy arithmetic. J Hydroinformatics 10(3):189–200.  https://doi.org/10.2166/hydro.2008.037 CrossRefGoogle Scholar
  40. Nasseri M, Ansari A, Zahraie B (2014) Uncertainty assessment of hydrological models with fuzzy extension principle: evaluation of a new arithmetic operator. Water Resour Res 50(2):1095–1111.  https://doi.org/10.1002/2012WR013382 CrossRefGoogle Scholar
  41. Nazemi A-R, Hosseini SM, Akbarzadeh-T M-R (2006) Soft computing-based nonlinear fusion algorithms for describing non-Darcy flow in porous media. J Hydraul Res 44(2):269–282.  https://doi.org/10.1016/j.jcp.2007.08.012 CrossRefGoogle Scholar
  42. Ng G-HC, McLaughlin D, Entekhabi D, Scanlon BR (2010) Probabilistic analysis of the effects of climate change on groundwater recharge. Water Resour Res 46(7):1–18.  https://doi.org/10.1029/2009WR007904 CrossRefGoogle Scholar
  43. Parkin AK (1991) Through and overflow rockfill dams. In: Maranha das Neves E (ed) Advances in Rockfill Structures. Kluver Academic Publishers, The Netherlands, pp 571–592CrossRefGoogle Scholar
  44. Peng C, Xu G, Wu W, Yu H-S, Wang C (2017) Multiphase SPH modeling of free surface flow in porous media with variable porosity. Comput Geotech 81:239–248.  https://doi.org/10.1016/j.compgeo.2016.08.022 CrossRefGoogle Scholar
  45. Revelli R, Ridolfi L (2002) Fuzzy approach for analysis of pipe networks. J Hydraul Eng 128(1):93–101.  https://doi.org/10.1061/(ASCE)0733-9429(2002)128:1(93) CrossRefzbMATHGoogle Scholar
  46. Ross TJ (2016) Fuzzy logic with engineering applications, 4th edn. Wiley, EnglandGoogle Scholar
  47. Samani JMV, Solimani A (2008) Uncertainty analysis of routed outflow in rockfill dams. J Agric Sci Technol 10(1):55–66Google Scholar
  48. Samani H, Samani J, Shaiannejad M (2003) Reservoir routing using steady and unsteady flow through rockfill dams. J Hydraul Eng 129(6):448–454.  https://doi.org/10.1061/(ASCE)0733-9429(2003)129:6(448) CrossRefGoogle Scholar
  49. Sedghi-Asl M, Farhoudi J, Rahimi H, Hartmann S (2014) An analytical solution for 1-D non-Darcy flow through slanting coarse deposits. Transp Porous Media 104(3):565–579.  https://doi.org/10.1007/s11242-014-0350-3 CrossRefGoogle Scholar
  50. Shokri M, Sabour M (2014) Experimental study of unsteady turbulent flow coefficients through granular porous media and their contribution to the energy losses. KSCE J Civ Eng 18(2):706–717.  https://doi.org/10.1007/s12205-014-0590-3 CrossRefGoogle Scholar
  51. Sivakumar P, Prasad RK (2016) Analysis of water distribution network using EPANET and vertex method. Urban Hydrol Watershed Manag Socio-Econ Asp 73:227–239.  https://doi.org/10.1007/978-3-319-40195-9_18 CrossRefGoogle Scholar
  52. Smith E (2002) Uncertainty analysis. In: El-Shaarawi AH, Piegorsch WW (eds) Encyclopedia of environmetrics. Wiley, UK, pp 2283–2297Google Scholar
  53. Song X, Zhang J, Zhan C, Xuan Y, Ye M, Xu C (2015) Global sensitivity analysis in hydrological modeling: review of concepts, methods, theoretical framework, and applications. J Hydrol 523:739–757.  https://doi.org/10.1016/j.jhydrol.2015.02.013 CrossRefGoogle Scholar
  54. Soualmia A, Jouini M, Masbernat L, Dartus D (2015) An analytical model for water profile calculations in free surface flows through rockfills. J Theor Appl Mech 53(1):215–219.  https://doi.org/10.15632/jtam-pl.53.1.209 CrossRefGoogle Scholar
  55. Stephenson D (1978) Hydraulics of gabions and rockfill. In: Proceedings of XVI Convegno di Idraulica e Costruzioni Idrauliche, Torino, Italy, pp B31-1–B31-11Google Scholar
  56. Stephenson D (1979) Rockfill in hydraulic engineering. Elsevier Scientific Publishing Co., AmsterdamGoogle Scholar
  57. Talaee P, Heydari M, Fathi P, Marofi S, Tabari H (2012) Numerical model and computational intelligence approaches for estimating flow through rockfill dam. J Hydrol Eng 17(4):528–536.  https://doi.org/10.1061/(ASCE)HE.1943-5584.0000446 CrossRefGoogle Scholar
  58. Townsend RD, Garga VK, Hansen D (1991) Finite difference modelling of the variation in piezometric head within a rockfill embankment. Can J Civ Eng 18(2):254–263.  https://doi.org/10.1139/l91-030 CrossRefGoogle Scholar
  59. Tung Y-K (1996) Uncertainty analysis in water resources engineering. In: Tickle KS, Goulter IC, Xu C, Wasimi SA, Bouchart F (eds) Stochastic hydraulics’96. Balkema, Rotterdam, The Netherlands, pp 29–46Google Scholar
  60. Tung Y-K, Yen BC (1993) Some recent progress in uncertainty analysis for hydraulic design. In: Yen BC, Tung Y-K (eds) Reliability and uncertainty analysis in hydraulic design. ASCE Publications, USA, pp 17–34Google Scholar
  61. Volker RE (1969) Nonlinear flow in porous media by finite elements. J Hydraul Div 95(6):2093–2114.  https://doi.org/10.1016/0045-7825(85)90041-6 CrossRefGoogle Scholar
  62. Volker RE (1975) Solutions for unconfined non-Darcy seepage. J Irrig Drain Div 101(1):53–65Google Scholar
  63. Ye M, Pohlmann KF, Chapman JB, Pohll GM, Reeves DM (2009) A model-averaging method for assessing groundwater conceptual model uncertainty. Ground Water 48(5):716–728.  https://doi.org/10.1111/j.1745-6584.2009.00633 CrossRefGoogle Scholar
  64. Zadeh LA (1965) Fuzzy Sets. Inf Control 8(3):338–353.  https://doi.org/10.1016/S0019-9958(65)90241-X CrossRefzbMATHGoogle Scholar
  65. Zhang K, Achari G (2010) Correlation between uncertainty theories and their application in uncertainty propagation. In: Proceedings of 10th international conference on structure safety and reliability, Osaka, JapanGoogle Scholar
  66. Zhang K, Achari G, Li H (2009) A comparison of numerical solutions of partial differential equations with probabilistic and possibilistic parameters for the quantification of uncertainty in subsurface solute transport. J Contam Hydrol 110(1–2):45–59.  https://doi.org/10.1016/j.jconhyd.2009.08.005 CrossRefGoogle Scholar
  67. Zhao Z, Zhao J, Xin P, Jin G, Hua G, Li L (2016) A hybrid sampling method for the fuzzy stochastic uncertainty analysis of seawater intrusion simulations. J Coast Res 32(3):725–734.  https://doi.org/10.2112/JCOASTRES-D-15-00084.1 CrossRefGoogle Scholar

Copyright information

© Shiraz University 2018

Authors and Affiliations

  1. 1.Civil Engineering DepartmentFerdowsi University of MashhadMashhadIran

Personalised recommendations