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Reliability-based optimum design of hydraulic water retaining structure constructed on heterogeneous porous media: utilizing stochastic ensemble surrogate model-based linked simulation optimization model

  • Muqdad Al-JubooriEmail author
  • Bithin Datta
Original Research
  • 35 Downloads

Abstract

Seepage characteristics under hydraulic water retaining structures (HWRSs) significantly affect the hydraulic serviceability and stability of such structures. The expected hydraulic conductivity value and its spatial and directional variation substantially influence seepage characteristics. Furthermore, the uniform and homogenous hydraulic conductive is rarely seen in the real field. To study the effects of uncertainty and variation in hydraulic conductivity, a random field concept was used to generate different realizations of heterogeneous hydraulic conductivity with constant mean and varied standard deviation. Consequently, the seepage characteristics stochastically varied, creating uncertainty in seepage characteristics which influenced the HWRS design. Therefore, the objective of this paper was to integrate the reliability concept in the linked simulation optimization (S-O) model to address the uncertainty of hydraulic conductivity. Hence, the safest and most cost-effective HWRS design could be attained considering the effects of the uncertainty of hydraulic conductivity. The reliability-based optimum design (RBOD) concept was implemented utilizing the multiple realization optimization technique based on stochastic ensemble surrogate models. The reliability degree of each candidate design was measured based on the number of stochastic constraints satisfying the design requirements to the total number of constraints. The S-O model-based RBOD was formulated to find the most cost-effective HWRS design satisfying a beforehand desired degree of reliability. Each surrogate model was trained utilizing several (input–output) data sets simulated using numerical seepage modeling code (SEEPW). The Gaussian process regression machine learning technique was used to train several surrogate models to imitate the responses of the numerical seepage modeling. Each single input data set was solved (4 × 5) times to simulate four different realizations of spatial variation resulting from one of the five different standard deviation values (0.85, 1.55, 2.25, 2.95, 3.65 m/day) with constant mean (2 m/day). Each group of data for single standard deviation was utilized to train a single surrogate model. The genetic algorithm-based S-O model was utilized as an efficient optimization solver for such complex optimization task. The results of this study demonstrated that the reliability significantly influenced the design of HWRS. Further, the deterministic optimum design of HWRS was insufficient to be considered a reliable design, especially when a high degree of uncertainty due to the hydraulic conductivity estimation is included. Hence, RBOD for such problem is essential and helps the designer make a decision.

Keywords

Reliability-based optimum design Gaussian process regression Seepage analysis Stochastic simulation–optimization Heterogeneous hydraulic conductivity Multiple realization optimization 

References

  1. ACI Committee American Concrete Institute & International Organization for Standardization (2011) Building code requirements for structural concrete (ACI 318-11 m) and commentary. American Concrete Institute, Framington HillsGoogle Scholar
  2. ACI_Committee_318 Building Code Requirements for Structural Concrete (ACI 318-11 M) and Commentary. In, 2011. American Concrete InstituteGoogle Scholar
  3. Ahmed AA (2012) Stochastic analysis of seepage under hydraulic structures resting on anisotropic heterogeneous soils. J Geotech Geoenviron Eng 139(6):1001–1004.  https://doi.org/10.1061/%28asce%29gt.1943-5606.0000813 CrossRefGoogle Scholar
  4. Al-Juboori M, Datta B (2017) Artificial neural networn modeling and genetic algorithm based optimization of hydraulic design related to seepage under concrete gravity dams on permeable soils. Int J Civ Environ Struct Constr Architect Eng 11(2):64–70.  https://doi.org/10.1999/1307-6892/10006237 CrossRefGoogle Scholar
  5. Al-Juboori M, Datta B (2018a) Linked simulation-optimization model for optimum hydraulic design of water retaining structures constructed on permeable soils. Int J GEOMATE 14(44):39–46.  https://doi.org/10.21660/2018.44.7229 CrossRefGoogle Scholar
  6. Al-Juboori M, Datta B (2018b) Performance evaluation of a genetic algorithm-based linked simulation-optimization model for optimal hydraulic seepage-related design of concrete gravity dams. J Appl Water Eng Res.  https://doi.org/10.1080/23249676.2018.1497558 CrossRefGoogle Scholar
  7. Baecher GB, Christian JT (2005) Reliability and statistics in geotechnical engineering. Wiley, West SussexGoogle Scholar
  8. Baroni G, Zink M, Kumar R, Samaniego L, Attinger S (2017) Effects of uncertainty in soil properties on simulated hydrological states and fluxes at different spatio-temporal scales. Hydrol Earth Syst Sci 21(5):2301.  https://doi.org/10.5194/hess-21-2301-2017 CrossRefGoogle Scholar
  9. Bayer P, de Paly M, Bürger CM (2010) Optimization of high-reliability-based hydrological design problems by robust automatic sampling of critical model realizations. Water Resour Res.  https://doi.org/10.1029/2009wr008081 CrossRefGoogle Scholar
  10. Bligh WG (1915) Dams and weirs: an analytical and practical treatise on gravity dams and weirs; arch and buttress dams; submerged weirs; and barrages. American Technical Society, ChicagoGoogle Scholar
  11. Bornschlegell A, Pelle J, Harmand S, Bekrar A, Chaabane S, Trentesaux D (2012) Thermal optimization of a single inlet T-junction. Int J Therm Sci 53:108–118CrossRefGoogle Scholar
  12. Chan N (1993) Robustness of the multiple realization method for stochastic hydraulic aquifer management. Water Resour Res 29(9):3159–3167.  https://doi.org/10.1029/93wr01410 CrossRefGoogle Scholar
  13. Christian JT, Ladd CC, Baecher GB (1994) Reliability applied to slope stability analysis. J Geotech Eng 120(12):2180–2207.  https://doi.org/10.1061/(asce)0733-9410(1994)120:12(2180) CrossRefGoogle Scholar
  14. Cojocaru C, Duca G, Gonta M (2013) Chemical kinetic model for methylurea nitrosation reaction: computer-aided solutions to inverse and direct problems. Chem Eng J 217:385–397.  https://doi.org/10.1016/j.cej.2012.11.130 CrossRefGoogle Scholar
  15. Datta B, Chakrabarty D, Dhar A (2011) Identification of unknown groundwater pollution sources using classical optimization with linked simulation. J Hydro Environ Res 5(1):25–36CrossRefGoogle Scholar
  16. Deng Z-P, Li D-Q, Qi X-H, Cao Z-J, Phoon K-K (2017) Reliability evaluation of slope considering geological uncertainty and inherent variability of soil parameters. Comput Geotech 92:121–131.  https://doi.org/10.1016/j.compgeo.2017.07.020 CrossRefGoogle Scholar
  17. Dhar A, Datta B (2009) Saltwater intrusion management of coastal aquifers. I: linked simulation-optimization. J Hydrol Eng 14(12):1263–1272CrossRefGoogle Scholar
  18. Dorsey R, Mayer W (1995a) Genetic algorithms for estimation problems with multiple optima, nondifferentiability, and other irregular features. J Bus Econ Stat 13(1):53–66.  https://doi.org/10.1080/07350015.1995.10524579 CrossRefGoogle Scholar
  19. Dorsey Robert E, Mayer WJ (1995b) Genetic algorithms for estimation problems with multiple optima, nondifferentiability, and other irregular features. Bus Econ Stat 13(1):53–66Google Scholar
  20. Duncan JM (2000) Factors of safety and reliability in geotechnical engineering. J Geotech Geoenviron Eng 126(4):307–316.  https://doi.org/10.1061/(asce)1090-0241(2000)126:4(307) CrossRefGoogle Scholar
  21. European Committee for Standardization (2004) Eurocode 7: geotechnical design-part 1: general rules. CEN, British Standards, UK. doi:https://www.ngm2016.com/uploads/2/1/7/9/21790806/eurocode_7_-_geotechnical_designen.1997.1.2004.pdf
  22. European_Committee_for_Standardization (1997) 1 (2004). Eurocode 7: geotechnical design-part 1: general rules. British Standards, UKGoogle Scholar
  23. Feyen L, Gorelick SM (2005) Framework to evaluate the worth of hydraulic conductivity data for optimal groundwater resources management in ecologically sensitive areas. Water Resour Res 41:3.  https://doi.org/10.1029/2003wr002901 CrossRefGoogle Scholar
  24. Freeze RA (1975) A stochastic-conceptual analysis of one-dimensional groundwater flow in nonuniform homogeneous media. Water Resour Res 11(5):725–741CrossRefGoogle Scholar
  25. Garg SK (1987) Irrigation engineering and hydraulic structures. Khanna publishers, Nai Sarak Delhi, IndiaGoogle Scholar
  26. Griffiths D, Fenton GA (1993a) Seepage beneath water retaining structures founded on spatially random soil. Géotechnique 43(4):577–587.  https://doi.org/10.1680/geot.1993.43.4.577 CrossRefGoogle Scholar
  27. Griffiths DV, Fenton GA (1993b) Seepage beneath water retaining structures founded on spatially random soil. Gektechnique 43(4):577–587.  https://doi.org/10.1680/geot.1993.43.4.577 CrossRefGoogle Scholar
  28. Griffiths D, Fenton GA (1997) Three-dimensional seepage through spatially random soil. J Geotech Geoenviron Eng 123(2):153–160.  https://doi.org/10.1061/(asce)1090-0241(1997)123:2(153) CrossRefGoogle Scholar
  29. Griffiths D, Fenton GA (2004) Probabilistic slope stability analysis by finite elements. J Geotech Geoenviron Eng 130(5):507–518.  https://doi.org/10.1061/(asce)1090-0241(2004)130:5(507) CrossRefGoogle Scholar
  30. Gupta HV, Sorooshian S, Yapo PO (1999) Status of automatic calibration for hydrologic models: comparison with multilevel expert calibration. J Hydrol Eng 4(2):135–143.  https://doi.org/10.1061/(asce)1084-0699(1999)4:2(135) CrossRefGoogle Scholar
  31. Harr ME (2012) Groundwater and seepage. McGraw Hill, New YorkGoogle Scholar
  32. Hassan WH (2015) Application of a genetic algorithm for the optimization of a cutoff wall under hydraulic structures. J Appl Water Eng Res.  https://doi.org/10.1080/23249676.2015.1105161 CrossRefGoogle Scholar
  33. He P, Li S-C, Xiao J, Zhang Q-Q, Xu F, Zhang J (2017a) Shallow sliding failure prediction model of expansive soil slope based on Gaussian process theory and its engineering application. KSCE J Civ Eng 22(5):1–11Google Scholar
  34. He P, Li S-C, Xiao J, Xu F, Zhang Q-Q, Zhang J (2017b) Shallow sliding failure prediction model of expansive soil slope based on Gaussian process theory and its engineering application. KSCE J Civ Eng 22(5):1–11.  https://doi.org/10.1007/s12205-017-1934-6 CrossRefGoogle Scholar
  35. Hicks MA, Spencer WA (2010) Influence of heterogeneity on the reliability and failure of a long 3D slope. Comput Geotech 37(7):948–955.  https://doi.org/10.1016/j.compgeo.2010.08.001 CrossRefGoogle Scholar
  36. Hicks MA, Nuttall JD, Chen J (2014) Influence of heterogeneity on 3D slope reliability and failure consequence. Comput Geotech 61:198–208.  https://doi.org/10.1016/j.compgeo.2014.05.004 CrossRefGoogle Scholar
  37. Housh M, Ostfeld A, Shamir U (2012) Box-constrained optimization methodology and its application for a water supply system model. J Water Resour Plan Manag 138(6):651–659.  https://doi.org/10.1061/(asce)wr.1943-5452.0000229 CrossRefGoogle Scholar
  38. Innal F, Dutuit Y, Chebila M (2015) Safety and operational integrity evaluation and design optimization of safety instrumented systems. Reliab Eng Syst Saf 134:32–50.  https://doi.org/10.1016/j.ress.2014.10.001 CrossRefGoogle Scholar
  39. Islam M, Buijk A, Rais-Rohani M, Motoyama K (2015) Process parameter optimization of lap joint fillet weld based on FEM–RSM–GA integration technique. Adv Eng Softw 79:127–136CrossRefGoogle Scholar
  40. Jha MK, Datta B (2011) Simulated annealing based simulation-optimization approach for identification of unknown contaminant sources in groundwater aquifers. Desalination Water Treat 32(1–3):79–85.  https://doi.org/10.5004/dwt.2011.2681 CrossRefGoogle Scholar
  41. Jiang S-H, Li D-Q, Zhang L-M, Zhou C-B (2014) Slope reliability analysis considering spatially variable shear strength parameters using a non-intrusive stochastic finite element method. Eng Geol 168:120–128.  https://doi.org/10.1016/j.enggeo.2013.11.006 CrossRefGoogle Scholar
  42. Kang F, Han S, Salgado R, Li J (2015) System probabilistic stability analysis of soil slopes using Gaussian process regression with Latin hypercube sampling. Comput Geotech 63:13–25.  https://doi.org/10.1016/j.compgeo.2014.08.010 CrossRefGoogle Scholar
  43. Kang F, Xu B, Li J, Zhao S (2017) Slope stability evaluation using Gaussian processes with various covariance functions. Appl Soft Comput 60:387–396.  https://doi.org/10.1016/j.asoc.2017.07.011 CrossRefGoogle Scholar
  44. Khosla AN, Bose NK, Taylor EM (1936) Design of weirs on permeable foundations. Central Board of Irrigation, New DelhiGoogle Scholar
  45. Krahn J (2012) Seepage modeling with SEEP/W: an engineering methodology. GEO-SLOPE International Ltd., CalgaryGoogle Scholar
  46. Lambe TW, Whitman RV (2008a) Soil mechanics. Wiley, New YorkGoogle Scholar
  47. Lambe TW, Whitman RV (2008b) Soil mechanics SI version. Wiley, West SussexGoogle Scholar
  48. Lane EW (1935a) Security from under-seepage-masonry dams on earth foundations. In: Proceedings of ASCEGoogle Scholar
  49. Lane EW (1935b) Security from under-seepage-masonry dams on earth foundations. Trans Am Soc Civ Eng 100(1):1235–1272Google Scholar
  50. Le TMH, Gallipoli D, Sanchez M, Wheeler SJ (2012) Stochastic analysis of unsaturated seepage through randomly heterogeneous earth embankments. Int J Numer Anal Methods Geomech 36(8):1056–1076.  https://doi.org/10.1002/nag.1047 CrossRefGoogle Scholar
  51. Li S-C, He P, Li L-P, Shi S-S, Zhang Q-Q, Zhang J, Hu J (2017) Gaussian process model of water inflow prediction in tunnel construction and its engineering applications. Tunn Undergr Space Technol 69:155–161.  https://doi.org/10.1016/j.tust.2017.06.018 CrossRefGoogle Scholar
  52. Loyola D, Pedergnana M, García SG (2016) Smart sampling and incremental function learning for very large high dimensional data. Neural Netw 78:75–87.  https://doi.org/10.1016/j.neunet.2015.09.001 zbMATHCrossRefGoogle Scholar
  53. MathWorks (2015) Global optimization toolbox user’s guide R2015b. www.mathworks.com. Accessed 10 Dec 2018
  54. Mollon G, Dias D, Soubra A-H (2009) Probabilistic analysis of circular tunnels in homogeneous soil using response surface methodology. J Geotech Geoenviron Eng 135(9):1314–1325.  https://doi.org/10.1061/(asce)gt.1943-5606.0000060 CrossRefGoogle Scholar
  55. Mollon G, Dias D, Soubra A-H (2010) Probabilistic analysis of pressurized tunnels against face stability using collocation-based stochastic response surface method. J Geotech Geoenviron Eng 137(4):385–397.  https://doi.org/10.1061/(asce)gt.1943-5606.0000443 CrossRefGoogle Scholar
  56. Moriasi DN, Arnold JG, Van Liew MW, Bingner RL, Harmel RD, Veith TL (2007) Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans ASABE 50(3):885–900.  https://doi.org/10.13031/2013.23153 CrossRefGoogle Scholar
  57. Pal M, Deswal S (2010) Modelling pile capacity using Gaussian process regression. Comput Geotech 37(7–8):942–947.  https://doi.org/10.1016/j.compgeo.2010.07.012 CrossRefGoogle Scholar
  58. Popescu R, Deodatis G, Nobahar A (2005) Effects of random heterogeneity of soil properties on bearing capacity. Probab Eng Mech 20(4):324–341.  https://doi.org/10.1016/j.probengmech.2005.06.003 CrossRefGoogle Scholar
  59. Rajper S, Amin IJ (2012) Optimization of wind turbine micrositing: a comparative study. Renew Sustain Energy Rev 16(8):5485–5492.  https://doi.org/10.1016/j.rser.2012.06.014 CrossRefGoogle Scholar
  60. Rasmussen CE (2004) Gaussian processes in machine learning. In: Bousquet O, von Luxburg U, Rätsch G (eds) Advanced lectures on machine learning. Springer, Berlin, pp 63–71.  https://doi.org/10.1007/978-3-540-28650-9_4 CrossRefGoogle Scholar
  61. Roberts S, Osborne M, Ebden M, Reece S, Gibson N, Aigrain S (2013) Gaussian processes for time-series modelling. Philos Trans R Soc A 371(1984):20110550MathSciNetzbMATHCrossRefGoogle Scholar
  62. Ross S (2014) A first course in probability. Pearson, BostonzbMATHGoogle Scholar
  63. Samui P, Jagan J (2013) Determination of effective stress parameter of unsaturated soils: a Gaussian process regression approach. Front Struct Civil Eng 7(2):133–136.  https://doi.org/10.1007/s11709-013-0202-1 CrossRefGoogle Scholar
  64. Shahrbanozadeh M, Barani G-A, Shojaee S (2015) Simulation of flow through dam foundation by isogeometric method. Int J Eng Sci Technol 18(2):185–193.  https://doi.org/10.1016/j.jestch.2014.11.001 CrossRefGoogle Scholar
  65. Shi JQ, Choi T (2011) Gaussian process regression analysis for functional data. Chapman and Hall, CRC Press, New YorkzbMATHCrossRefGoogle Scholar
  66. Shourian M, Mousavi SJ, Menhaj M, Jabbari E (2008) Neural-network-based simulation-optimization model for water allocation planning at basin scale. J Hydroinformatics 10(4):331–343CrossRefGoogle Scholar
  67. Singh RM (2010) Design of barrages with genetic algorithm based embedded simulation optimization approach. Water Resour Manage 25(2):409–429.  https://doi.org/10.1007/s11269-010-9706-9 CrossRefGoogle Scholar
  68. Singh RM (2011a) Genetic algorithm based optimal design of hydraulic structures with uncertainty characterization. In: Swarm, evolutionary, and memetic computing. Springer, pp 742–749Google Scholar
  69. Singh RM (2011b) Genetic algorithm based optimal design of hydraulic structures with uncertainty characterization. In: International conference on swarm, evolutionary, and memetic computing. Berlin, Heidelberg, Springer, pp 742–749.  https://doi.org/10.1007/978-3-642-27172-4_87
  70. Singh RM, Datta B (2006) Identification of groundwater pollution sources using GA-based linked simulation optimization model. J Hydrol Eng 11(2):101–109.  https://doi.org/10.1061/(ASCE)1084-0699(2006)11:2(101) CrossRefGoogle Scholar
  71. Singh A, Minsker BS (2008) Uncertainty-based multiobjective optimization of groundwater remediation design. Water Resour Res.  https://doi.org/10.1029/2005WR004436 CrossRefGoogle Scholar
  72. Sreekanth J, Datta B (2011) Coupled simulation-optimization model for coastal aquifer management using genetic programming-based ensemble surrogate models and multiple-realization optimization. Water Resour Res.  https://doi.org/10.1029/2010WR009683 CrossRefGoogle Scholar
  73. Sreekanth J, Datta B (2015) Review: simulation-optimization models for the management and monitoring of coastal aquifers. Hydrogeol J 23(6):1155–1166.  https://doi.org/10.1007/s10040-015-1272-z CrossRefGoogle Scholar
  74. Tee KF, Khan LR, Chen HP, Alani AM (2014) Reliability based life cycle cost optimization for underground pipeline networks. Tunn Undergr Space Technol 43:32–40.  https://doi.org/10.1016/j.tust.2014.04.007 CrossRefGoogle Scholar
  75. U.S. Army Corps of Engineers (1987) Engineering and design flotation stability criteria for concrete hydraulic structures. http://www.dtic.mil/dtic/tr/fulltext/u2/a403467.pdf
  76. U.S. Army Corps of Engineers (2006) Reliability analysis and risk assessment for seepage and slope stability failure modes for embankment damsGoogle Scholar
  77. Zhang J, Zhang L, Tang WH (2011) Reliability-based optimization of geotechnical systems. J Geotech Geoenviron Eng 137(12):1211–1221.  https://doi.org/10.1061/(ASCE)GT.1943-5606.0000551 CrossRefGoogle Scholar
  78. Zhu X, Wang X, Li X, Liu M, Cheng Z (2017) A new dam reliability analysis considering fluid structure interaction. Rock Mech Rock Eng.  https://doi.org/10.1007/s00603-017-1369-x CrossRefGoogle Scholar

Copyright information

© Society for Reliability and Safety (SRESA) 2019

Authors and Affiliations

  1. 1.College of Science and EngineeringJames Cook UniversityTownsvilleAustralia
  2. 2.College of EngineeringWasit UniversityWasitIraq
  3. 3.Discipline of Civil Engineering, College of Science and EngineeringJames Cook UniversityTownsvilleAustralia

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