Geomechanics and Engineering

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Partial safety factors for retaining walls and slopes: A reliability based approach

  • Received : 2012.06.27
  • Accepted : 2013.09.04
  • Published : 2014.02.25
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Abstract

Uncertainties in design variables and design equations have a significant impact on the safety of geotechnical structures like retaining walls and slopes. This paper presents a possible framework for obtaining the partial safety factors based on reliability approach for different random variables affecting the stability of a reinforced concrete cantilever retaining wall and a slope under static loading conditions. Reliability analysis is carried out by Mean First Order Second Moment Method, Point Estimate Method, Monte Carlo Simulation and Response Surface Methodology. A target reliability index ${\beta}$ = 3 is set and partial safety factors for each random variable are calculated based on different coefficient of variations of the random variables. The study shows that although deterministic analysis reveals a safety factor greater than 1.5 which is considered to be safe in conventional approach, reliability analysis indicates quite high failure probability due to variation of soil properties. The results also reveal that a higher factor of safety is required for internal friction angle ${\varphi}$, while almost negligible values of safety factors are required for soil unit weight ${\gamma}$ in case of cantilever retaining wall and soil unit weight ${\gamma}$ and cohesion c in case of slope. Importance of partial safety factors is shown by analyzing two simple geotechnical structures. However, it can be applied for any complex system to achieve economization.

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References

  1. AASHTO (1997), LRFD Highway Bridge Design Specifications, SI Units, American Association of State Highway and Transportation Officials, Washington D.C., USA.
  2. AASHTO (2007), LRFD Bridge Design Specifications, (4th Ed.), American Association of State Highway and Transportation Officials, Washington D.C., USA.
  3. Babu, G.L.S. and Basha, B.M. (2006), "Inverse reliability based design optimisation of cantilever retaining walls", The 3rd International ASRANET Collquium, Glasgow, UK, July.
  4. Baecher, G.B. and Christian, J.T. (2003), Reliability and Statistics in Geotechnical Engineering. Wiley, New York.
  5. Becker, D.E. (1996), "Limit State Design for Foundations: Part I. An overview of the foundation design process". 18th Canadian Geotechnical Colloquium, Canadian Geotechnical Journal, 33: 956-983.
  6. Bhattacharya, G., Jana, D., Ojha, S. and Chakroborty, S. (2003), "Direct Search for minimum Reliability Index of Earth Slopes", Comput. Geotech., 30(6), 455-462. https://doi.org/10.1016/S0266-352X(03)00059-4
  7. Biernatowski, K, and Pula, W. (1988), "Probabilistic analysis of the stability of massive bridge abutments using simulation methods", Struct. Safety, 5(1), 1-15. https://doi.org/10.1016/0167-4730(88)90002-1
  8. Bishop, A.W. (1955), "The use of the slip circle in the stability analysis of slopes", Geotechnique, 5(1), 7-17. https://doi.org/10.1680/geot.1955.5.1.7
  9. Castillo, E., Munguez, R., Teran, A.R. and Canteli, A.F. (2004), "Design and sensitivity analysis using the probability-safety-factor method: An application to retaining walls", Struct. Safety, 26(2), 156-179.
  10. CEN (2001), Eurocode 7, part 1: Geotechnical Design: General Rules, Final Draft prEN 1997-1. Brussels: European Committee for Standardisation (CEN).
  11. Chalermyanont, T. and Benson, C.H. (2004), "Reliability based design for internal stability of mechanically stabilised Earth walls", J. Geotech. Geoenviron. Eng., ASCE, 130(2), 163-173. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:2(163)
  12. Chalermyanont, T. and Benson, C.H. (2005), "Reliability based design for external stability of mechanically stabilised Earth walls", Int. J. Geomech., ASCE, 5(3), 196-205. https://doi.org/10.1061/(ASCE)1532-3641(2005)5:3(196)
  13. Cherubini, C. (2000), "Probabilistic approach to the design of anchored sheet pile walls", Comput. Geotech., 26(4), 309-330. https://doi.org/10.1016/S0266-352X(99)00044-0
  14. Christian, J.T., Ladd, C.C. and Baecher, G.B. (1994), "Reliability applied to slope stability analysis", J. Geotech. Eng., ASCE, 120(12), 2180-2207. https://doi.org/10.1061/(ASCE)0733-9410(1994)120:12(2180)
  15. Devaraj, V., Sriram, A.V. and Srinivasa, M. (2004), "Reliability analysis of concrete gravity dam: A case study", GEORISK-2004, Bangalore, India, November.
  16. Ellingwood, B., Galambos, T.V., MacGregor, J.G. and Cornell, C.A. (1980), "Development of a probability based load criterion for American National Standard A58-Building Code requirements for minimum design loads in buildings and other structures", National Bureau of Standards, Washington, D.C., USA.
  17. Eurocode 7 (1997), Geotechnical Design, General Rules, European Committee for Standardisation (CEN). Prestandard (ENV), Danish Geotechnical Institute, Copenhagen, Denmark.
  18. Fellenius, W. (1936), "Calculation of stability of Earth dams", Trans. 2nd Congress on Large Dams.
  19. Foye, K., Scott, B., and Salgado, R. (2006), "Assessment of variable uncertainties for reliability-based design of foundations", J. Geotech. Geoenviron. Eng., ASCE, 132(9), 1197-1207. https://doi.org/10.1061/(ASCE)1090-0241(2006)132:9(1197)
  20. Guharay, A. and Baidya, D.K. (2011), "Probabilistic analysis of a cantilever retaining wall", Proceedings of The 3rd Indian Young Geotechnical Engineers Conference 3IYGEC, New Delhi, pp. 115-120.
  21. Harr, M.E. (1984), "Reliability-based design in civil engineering", (Henry M. Shaw Lecture), Dept. of Civil Engineering, North Carolina State University, Raleigh, NC, USA.
  22. Harr, M.E. (1987), Reliability-Based Design in Civil Engineering, McGraw-Hill, New York.
  23. Hassan, A.M. and Wolff, T.F. (1999), "Search algorithm for minimum reliability index of Earth slopes". J. Geotech. Geoenviron. Eng., 125(4), 301-308. https://doi.org/10.1061/(ASCE)1090-0241(1999)125:4(301)
  24. Hoeg, K. and Murarka, R.P. (1974), "Probabilistic analysis and design of a retaining wall", J. Geotech. Eng. Div., ASCE, 100(3), 349-366.
  25. Honjo, Y. and Kusakabe, O. (2002), Proposal of a Comprehensive Foundation Design Code: Geo-Code 21 Ver. 2, Proceeding of the International Workshop on Foundation Design Codes and Soil Investigation in View of International Harmonization and Performance Based Design, Kamakura, pp. 95-103.
  26. Kulhawy, F.H. (1992), "On the evaluation of static soil properties", (Stability and performance of slopes and embankments II, In: Seed RB, Boulanger RW, Editors), Geotechnical Special Publication 31, ASCE, Berkeley, California, June-July, pp. 95-115.
  27. Low, B.K. (2005), "Reliability analysis based design applied to retaining walls", Geotechnique, 55(1), 63-75. https://doi.org/10.1680/geot.2005.55.1.63
  28. Meyerhof, G.G. (1970), "Safety factors in soil mechanics", Can. Geotech. J., 7(4), 349-355 https://doi.org/10.1139/t70-047
  29. Meyerhof, G.G. (1982), "Limit state design in geotechnical engineering", Struct. Safety, 1(1), 67-71. https://doi.org/10.1016/0167-4730(82)90015-7
  30. Orr, T.L.L. (2000), "Selection of characteristic values and partial factors in geotechnical designs to Eurocode 7", Comput. Geotech., 26(3-4), 263-279. https://doi.org/10.1016/S0266-352X(99)00042-7
  31. Paikowsky, S.G. (2004), "Load and resistance factor design for deep foundations", NCHRP Report 507, Transportation Research Board, Washington D.C., USA.
  32. Rankine, W.J.M. (1857), On the Stability of Loose Earth, Philosophical Transactions of the Royal Society of London, Vol. 147, London, UK.
  33. Rosenblueth, E. (1975), "Point estimates for probability moments", Proceeding of National Academy of Sciences of the United States of America, 72(10), 3812-3814. https://doi.org/10.1073/pnas.72.10.3812
  34. Sayed, S., Dodagoudar, G.R. and Rajagopal, K. (2008), "Reliability analysis of reinforced soil walls under static and seismic forces", Geosynth. Int., 15(4), 246-257. https://doi.org/10.1680/gein.2008.15.4.246
  35. Simpson, B., Thompson, R., Findlay, J. and Bolton, M. (1997), "Eurocode 7: Geotechnical Design 1. General Design Rules: What happens now?", Proceeding of Institution of Civil Engineers Geotechnical Engineering, 125(1), 55-59. https://doi.org/10.1680/igeng.1997.28998
  36. Srivastava, A. and Babu, G.L.S. (2010), "Reliability analysis of gravity retaining wall system using response surface methodology", Ind. Geotech. J., 40(2), 124-128.
  37. Tang, W.H., Yucemen, M.S. and Ang, A.H. (1976), "Probability based short term design of Slopes", Can. Geotech. J., 13(3), 201-215. https://doi.org/10.1139/t76-024
  38. Taylor, D.W. (1948), Fundamentals of Soil Mechanics, John Wiley & Sons, New York, USA.
  39. USACE (1997), Risk-based Analysis in Geotechnical Engineering for Support of Planning Studies, Engineering and Design, U.S. Army Corps of Engineers, Department of Army, Washington D.C., 20314-100.
  40. Venmarcke, E.H. (1977), "Reliability of Earth slopes", J. Geotech. Eng. Div., ASCE, 103(11), 1227-1246.
  41. Wu, T.H. and Kraft, L.M. (1970), "Safety analysis of slopes", J. Soil Mech. Found. Div., ASCE, 96(2), 609-630.
  42. Xue, J.F. and Gavin, K. (2007), "Simultaneous determination of critical slip surface and reliability index for slopes", J. Geotech. Geoenviron. Eng., ASCE, 133(7), 878-886. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:7(878)
  43. Zevgolis, I.E. and Bourdeau, P.L. (2010), "Probabilistic analysis of retaining walls", Comput. Geotech., 37(3), 359-373. https://doi.org/10.1016/j.compgeo.2009.12.003

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