Uncertainties and Optimization in Geotechnical Engineering
Keywords:
uncertainties, optimization, metering algorithms, L.A.S., autocorrelation, cross-correlation, reliability.Abstract
The needs of modern times for more economical, more efficient construction lead to a move away from the one-dimensional concept of "security" and are now turning towards the search for the "optimum" in search of the best solution through a set of secure options. Recognition of this need led to the creation of original mathematical programming techniques that focus on solving optimization problems. They include finding a set of variables that optimize the objective function and satisfy some predefined design constraints. Their capabilities have now been widely recognized, resulting in applications of genetic and other evolutionary algorithms, as well as neural networks extending not only to nonlinear problems but also to all aspects of geotechnical engineering. Studies of metaheuristic optimization algorithms have shown that they can provide appreciable results in geotechnical applications, such as the example of generating random fields of soil properties using the following L.A.S. method. It is estimated that their wider application to practical and theoretical geotechnical problems can bring beneficial results and become a particularly useful tool in the hands of civil engineers.
References
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[1] https://en.wikipedia.org/wiki/History_of_randomness.
[2] Kolmogorov A.N. (1980). Foundation of the theory of probability. Chelsea Publishing Company. N.Y. 1980.
[3] https://en.wikipedia.org/wiki/Normal_distribution
[3] Koutras B. M., (2002). Introduction to Probability. Theory and applications. Athens 2002.
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[7] https://www.google.gr/search?q=Kulhawy+1992&sa
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[9] Lacasse S. 1994. Reliability and probabilistic methods. In 13th International Conference on Soil Mechanics and Foundation Engineering, 1994. New Delhi, India, pp. 225-227.
[9] Lacasse S., Nadim F, (1997). Uncertainties in characterising soil properties. Norwegian Geotech Inst.201 (2): p.p. 49-75.
[10] Suchomel R. and Masin D. (2010). Comparison of different probabilistic methods for predicting stability of a slope in spatially variable c-phi soil. Computers and Geotechnics 37, No 1-2, p.p. 132-140.
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[11] Komodromos A., (2008). Computational Geotechnical Engineering. Soil-Construction Interaction. Klidarithmos Publications, Athens, P.27-28, 88-92, 157-162 and 341-397.
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[17] Li K.S. and Lumb P. (1987). Probabilistic design of slopes. Canadian Geotechnical Journal,24( 4), p.p 520-535.
[17] Li K.S. and White W. (1987). Probabilistic Approaches to Slope Design. Research Report No.20, Civil Engineering Department, Australian Defence Force Academy, Canberra. Australia, p.p. 54
[18] Smith I.M. and Griffiths D.V. (2004). Programming the Finite Element Method, 4th ed., Wiley, New York.
[19] Hicks M.A. and Samy K. (2002). Influence of heterogeneity of undrained clay slope stability. Quarterly Journal of Engineering Geology and Hydrogeology, 35 (1), p.p. 41-49.
[20] Wang Y., Zijun C., Siu-Kui A. (2010) Practical reliability analysis of slope stability by advanced Monte Carlo simulations in a spreadsheet. Canadian Geotechnical Journal, 2011, 48(1): 162-172, 10.1139/T10-044
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[22] Vorechovsky M., (2007). Simulation of simply cross correlated random fields by series expansions methods. Science Direct. Elsevier LTD, p.p.337-362.
[23] Forrest WS, Orr TL. (2010). Reliability of shallow foundations designed to Eurocode 7. Georisk 4(4): 186-207
[23] Orr T.L.L., and Breysse., D. (2008). Eurocode 7 and reliability-based design in geotechnical engineering. Edited by K.K. Phoon. Taylor and Francis, Oxon, UK. p.p. 298–343.
[24] Hara T., Honjo Y. et al. (2011) Application of reliability based design (RBD) to Eurocode 7 Reference: ISGSR 2011 - Vogt, Schuppener, Straub & Bräu (eds) 2011 Bundesanstalt für Wasserbau mit State Design in Geotechnical Engineering Practice.
[25] Lumb P. (1970). Probability of failure in earth works., Proc. Of the 2nd Southeast Asian Conference of Soil Engineering, Singapore.
[26] Matsuo M., Kuroda K. (1974) Probabilistic approach to the design of embankments. 19F, 6T, 13R Soils Found. V14, N2, June 1974, p-17.
[27] Wolff T.F. (1996). “Probabilistic slope stability in theory and practice” in Uncertainty in the Geological Environment: From Theory to Practice, Geotechnical Special Publication No 58, C.D. Shackelford et al. Eds., American Society of Civil Engineers, New York, p.p 419-433.
[28] Babu S.G.L, Srirastava A, Murthy D.S.N (2006) Reliability analysis of the bearing capacity of a shallow foundation resting on cohesive soil. Can Geotech J 43:217–2
[29] Chowdhury R.N, Xu D.W. (1995). Geotechnical system reliability of slopes. Reliability Engineering and System Safety 47(3): 141-151
[30] Low, B.K. and Wilson H. Tang (1997). "Probabilistic slope analysis using Janbu's generalized procedure of slices." Computers and Geotechnics, Elsevier, U.K., Vol. 21, No. 2, 121-142.
[31] Wu Xing Zheng (2013). Trivariate analysis of soil ranking correlated characteristics and its application to probabilistic stability assessments in geotechnical engineering problems, Soils and Foundations, Volume 53, Issue 4, August 2013, p.p. 540-556.
[32] Huber M. (2013). Soil variability and its consequences. Institut für Geotechnik der Universität Stuttgart, Germany. pp. 1-9.
[33] Pochtman, Yu M. and Kolesnichenko, A. L. (1972), Application of the Dynamic Programming Method to the Solution of Some Problems of Soil mechanics, Soil Mechanics and Foundation Engineering, Translated from Russian, 430-432.
[34] Krugman, P. K. and Krizek, R. J. (1973), Stability Charts for Inhomogeneous Soil Conditions, Geotechnical Engineering, Journal of South East Asian Society of Soil Engineering, 4, 1-13.
[35] Chen W.F. (1975). Limit Analysis and Soil Plasticity. Elsevier, Amsterdam.
[36] Cui L., & Sheng D. (2005). Genetic algorithms in probabilistic finite element analysis of geotechnical problems. Computers and Geotechnics 32:555-563 December 2005.?
[37] Honjo Y. (2002). Reliability based design of geotechnical structures. Keynote 003 p.p 1-6.
[38] Baecher G. and Christian J. (2003): Geotechnical reliability: playing cards with the universe, Proc. Pan-American Conf. on SMGE (Soil and Rock America 2003), Vol.2, p.p. 2751-2755
[39] Fortsakis P., Stylianidis E. and Kavvadas M. (2010). Stability of Slope Slopes using Stochastic Methods. 6th Panhellenic Conference of Geotechnical and Geoenvironmental Engineering, TEE, P.1-8.
[40] Piliounis G., (2011). Reliability Analysis of Geotechnical Problems using metaheuristic optimization methods. NTUA, Athens. p.p.9-11,15-23
[40] Comodromos E, Pitilakis K. and Hatzigogos T. (1992a). Procédure Numérique pour la Simulation des Excavations des Sols Elastoplastiques. Revue Française de Géotechnique, 58, 51-66.
[40] Comodromos E., Hatzigogos T. and Pitilakis K. (1992b). Finite Element Algorithm for Analysing Geotechnical Problems with Variable Domain and Boundaries. In proc.IV Numer.Mod. in Geomech. 577-587, Swansea.
[41] Fenton and Griffiths (2003). Bearing- capacity prediction of spatially random c-phi soils. Canadian Geotechnical Journal, p.p 40, 54-65.
[42] Christian J.T., Ladd C. Ch, Baecher B. Gr (1994). Reliability Applied to Slope Analysis J. Geotech Engrg 10, 1061(ASCE) 0733-9410(1994) 120:12 (2180), p.p. 2180-2207.
[42] Griffiths, D.V. and Lane P.A. (1999). Slope stability Analysis by finite Elements, Geothechnique, vol.49, No 3 p.p. 387-403.
[42] Griffiths D.V. and Fenton G.A. (2004) Probabilistic slope stability analysis by finite elements. NSF Grant No CMS-9877189, p.p. 1-27.
[42] Hicks M.A. and Samy K (2004). Stochastic evaluation of heterogeneous slope stability. Italian Geotechnical Journal, p.p.38 (2), 54-66.
[42] Tang W.H. (1984). Principles of probabilistic characterization of soil properties. Symposium of probabilistic Characterization of Soil Properties, ASCE, Reston, VA, p.p. 74-89.
[43] Dakoulas P. (1991). Stability of slopes and Earth Dams Under Earthquakes: Concluding Remarks, Proceedings of the Second International Conference on Geotechnical Earthquake Engineering and Soil dynamics, St. Louis, Missouri, March 11-15, Vol 3, p.p. 2157.
[43] Dakoulas P. (2005). Advanced Soil Mechanics (Elasto-plastic Constitutive Models for soils). Notes for the Graduate Course Advanced Soil Mechanics, University of Thessaly, Greece, 400 pages.
[43] Fenton A.G. and Vanmarcke E.H (1990). Simulation of Random Fields via Local Average Subdivision, Journal of Engineering Mechanics, Vol.116, No 8 p.p. 1733-1749
[43] Fenton G.A., Griffiths D.V. and Urquhart A. (2003). A slope stability model for spatially random soils. In Proc. 9th Int. Conf. Applications of Statistics and Probability in Civil Engineering (ICASP9), A. Kiureghian et al. Eds Millpress, San Francisco, CA, p.p 1263-1269.
[44] Themelis N., (2008). Notes on the Mathematica program. NTUA Athens.
[44] Theodorou G. and Theodorou H. (2004). Practical Guide to Mathematica. Aristotle University of Thessaloniki
[45] Fenton GA, Griffiths DV. (2007). Random field generation and local average subdivision method. New York. CISM Courses and Lectures.
[45] Griffiths D.V. and Fenton G.A. (2004) Probabilistic slope stability analysis by finite elements. NSF Grant No CMS-9877189, p.p. 1-27.
[45] Griffiths D.V. Huang J. (2009) Influence of Spatial Variability on Slope Reliability Using 2-D Random Fields. Journal of Geotechnical and geoenvironmental engineering ASCE/October 2009/ p.p 1367-1375.
[45] Griffiths D.V., Huang J. and Fenton G.A. (2010). Probabilistic infinite slope analysis. (Infoslope 2010), p.p. 1-3.
[46] Alamanis N.O (2017), Effect of spatial variability of soil properties in permanent seismic displacements of road slopes. Doctoral dissertation: University of Thessaly. Department of Civil Engineering, Geotechnical Engineering Sector p.p. 8-19, 99-102.
[1] Koutras B. M., (2002). Introduction to Probability. Theory and applications. Athens 2002
[1] https://en.wikipedia.org/wiki/History_of_randomness.
[2] Kolmogorov A.N. (1980). Foundation of the theory of probability. Chelsea Publishing Company. N.Y. 1980.
[3] https://en.wikipedia.org/wiki/Normal_distribution
[3] Koutras B. M., (2002). Introduction to Probability. Theory and applications. Athens 2002.
[4] Fenton A.G. and Griffiths D.V. (2008). Risk Assessment in Geotechnical Engineering. John Viley and Sons, Inc. ISBN: 978-0-470-17820-1 p.p. 91-235, 381-392.
[4] Griffiths D.V. and Fenton G.A (2007). Probabilistic methods in geotechnical engineering. CISM courses and lectures No 491, International center for mechanical sciences, Springer Wien, New York.
[5] Fenton, G.A. and Griffiths, D, V. (2002). Probabilistic foundation Settlement on spatially random Soil. Journal of Geotechnical and Geoenvironmental, p.p.128(S),
[6] Harr M.E. (1987). Reliability-based design in civil engineering. Mc- Graw-Hill, New York.
[7] https://www.google.gr/search?q=Kulhawy+1992&sa
[8] Phoon K.K, Kulhawy F.H. (1999). Characterization of geotechnical variability. Canadian Geotechnical Journal 36(4): 612-624
[8] Phoon K.K., Kulhawy F.H., Grigoriu M.D. (1995). Reliability-based design for transmission line structure foundations. Computers and geotechnics, 2000, 26(3): p.p. 169-185.
[9] Lacasse S. 1994. Reliability and probabilistic methods. In 13th International Conference on Soil Mechanics and Foundation Engineering, 1994. New Delhi, India, pp. 225-227.
[9] Lacasse S., Nadim F, (1997). Uncertainties in characterising soil properties. Norwegian Geotech Inst.201 (2): p.p. 49-75.
[10] Suchomel R. and Masin D. (2010). Comparison of different probabilistic methods for predicting stability of a slope in spatially variable c-phi soil. Computers and Geotechnics 37, No 1-2, p.p. 132-140.
[11] Duncan J.M., (2000). Factors of safety and reliability in geotechnical engineering. Geotech Geoenvironmental Eng. 126(4) 307-16.
[11] Komodromos A., (2008). Computational Geotechnical Engineering. Soil-Construction Interaction. Klidarithmos Publications, Athens, P.27-28, 88-92, 157-162 and 341-397.
[11] Boukovalas G., (2006). Computational Methods in Geotechnics. NTUA Athens.
[12] Jeremic B. and Sett K. (2007). Uncertain soil properties and elastic-plastic simulations in geomechanics, Geotechnical Special Publications 2007, p.p. 9.
[13] Griffiths, D.V., Fenton G.A. and Tveten, D.E. (2002). Probabilistic geotechnical analysis how difficult does it need to be? (Keynote paper). Proc. of Int. Conf. on Probabilistic in Geotechnics-technical and economic risk estimation, Gratz, Austria, p.p.3-20.
[14] El-Ramly H., Morgestern N.R. and Cruden D.M (2002). Probabilistic slope stability analysis for practice. Canadian Geotechnical Journal, 39, p.p.665-683.
[15] Schweiger H.F and Peschl G.M., (2005). Reliability analysis in geotechnics with a random set finite element method. Comput Geotech 32, p.p. 422-435.
[16] Cherubini C. (1997). Data and considerations on the variability of geotechnical properties of soils. In. Proceedings of the Conference on Advances in Safety and Reliability, ESREL: 1583-1591.
[17] Li K.S. and Lumb P. (1987). Probabilistic design of slopes. Canadian Geotechnical Journal,24( 4), p.p 520-535.
[17] Li K.S. and White W. (1987). Probabilistic Approaches to Slope Design. Research Report No.20, Civil Engineering Department, Australian Defence Force Academy, Canberra. Australia, p.p. 54
[18] Smith I.M. and Griffiths D.V. (2004). Programming the Finite Element Method, 4th ed., Wiley, New York.
[19] Hicks M.A. and Samy K. (2002). Influence of heterogeneity of undrained clay slope stability. Quarterly Journal of Engineering Geology and Hydrogeology, 35 (1), p.p. 41-49.
[20] Wang Y., Zijun C., Siu-Kui A. (2010) Practical reliability analysis of slope stability by advanced Monte Carlo simulations in a spreadsheet. Canadian Geotechnical Journal, 2011, 48(1): 162-172, 10.1139/T10-044
[21] Rackwitz R., (2000). Reviewing probabilistic soils modelling. Elsevier Science Ltd. Computers and Geotechnics 26 (2000) p.p. 199-223.
[22] Vorechovsky M., (2007). Simulation of simply cross correlated random fields by series expansions methods. Science Direct. Elsevier LTD, p.p.337-362.
[23] Forrest WS, Orr TL. (2010). Reliability of shallow foundations designed to Eurocode 7. Georisk 4(4): 186-207
[23] Orr T.L.L., and Breysse., D. (2008). Eurocode 7 and reliability-based design in geotechnical engineering. Edited by K.K. Phoon. Taylor and Francis, Oxon, UK. p.p. 298–343.
[24] Hara T., Honjo Y. et al. (2011) Application of reliability based design (RBD) to Eurocode 7 Reference: ISGSR 2011 - Vogt, Schuppener, Straub & Bräu (eds) 2011 Bundesanstalt für Wasserbau mit State Design in Geotechnical Engineering Practice.
[25] Lumb P. (1970). Probability of failure in earth works., Proc. Of the 2nd Southeast Asian Conference of Soil Engineering, Singapore.
[26] Matsuo M., Kuroda K. (1974) Probabilistic approach to the design of embankments. 19F, 6T, 13R Soils Found. V14, N2, June 1974, p-17.
[27] Wolff T.F. (1996). “Probabilistic slope stability in theory and practice” in Uncertainty in the Geological Environment: From Theory to Practice, Geotechnical Special Publication No 58, C.D. Shackelford et al. Eds., American Society of Civil Engineers, New York, p.p 419-433.
[28] Babu S.G.L, Srirastava A, Murthy D.S.N (2006) Reliability analysis of the bearing capacity of a shallow foundation resting on cohesive soil. Can Geotech J 43:217–2
[29] Chowdhury R.N, Xu D.W. (1995). Geotechnical system reliability of slopes. Reliability Engineering and System Safety 47(3): 141-151
[30] Low, B.K. and Wilson H. Tang (1997). "Probabilistic slope analysis using Janbu's generalized procedure of slices." Computers and Geotechnics, Elsevier, U.K., Vol. 21, No. 2, 121-142.
[31] Wu Xing Zheng (2013). Trivariate analysis of soil ranking correlated characteristics and its application to probabilistic stability assessments in geotechnical engineering problems, Soils and Foundations, Volume 53, Issue 4, August 2013, p.p. 540-556.
[32] Huber M. (2013). Soil variability and its consequences. Institut für Geotechnik der Universität Stuttgart, Germany. pp. 1-9.
[33] Pochtman, Yu M. and Kolesnichenko, A. L. (1972), Application of the Dynamic Programming Method to the Solution of Some Problems of Soil mechanics, Soil Mechanics and Foundation Engineering, Translated from Russian, 430-432.
[34] Krugman, P. K. and Krizek, R. J. (1973), Stability Charts for Inhomogeneous Soil Conditions, Geotechnical Engineering, Journal of South East Asian Society of Soil Engineering, 4, 1-13.
[35] Chen W.F. (1975). Limit Analysis and Soil Plasticity. Elsevier, Amsterdam.
[36] Cui L., & Sheng D. (2005). Genetic algorithms in probabilistic finite element analysis of geotechnical problems. Computers and Geotechnics 32:555-563 December 2005.?
[37] Honjo Y. (2002). Reliability based design of geotechnical structures. Keynote 003 p.p 1-6.
[38] Baecher G. and Christian J. (2003): Geotechnical reliability: playing cards with the universe, Proc. Pan-American Conf. on SMGE (Soil and Rock America 2003), Vol.2, p.p. 2751-2755
[39] Fortsakis P., Stylianidis E. and Kavvadas M. (2010). Stability of Slope Slopes using Stochastic Methods. 6th Panhellenic Conference of Geotechnical and Geoenvironmental Engineering, TEE, P.1-8.
[40] Piliounis G., (2011). Reliability Analysis of Geotechnical Problems using metaheuristic optimization methods. NTUA, Athens. p.p.9-11,15-23
[40] Comodromos E, Pitilakis K. and Hatzigogos T. (1992a). Procédure Numérique pour la Simulation des Excavations des Sols Elastoplastiques. Revue Française de Géotechnique, 58, 51-66.
[40] Comodromos E., Hatzigogos T. and Pitilakis K. (1992b). Finite Element Algorithm for Analysing Geotechnical Problems with Variable Domain and Boundaries. In proc.IV Numer.Mod. in Geomech. 577-587, Swansea.
[41] Fenton and Griffiths (2003). Bearing- capacity prediction of spatially random c-phi soils. Canadian Geotechnical Journal, p.p 40, 54-65.
[42] Christian J.T., Ladd C. Ch, Baecher B. Gr (1994). Reliability Applied to Slope Analysis J. Geotech Engrg 10, 1061(ASCE) 0733-9410(1994) 120:12 (2180), p.p. 2180-2207.
[42] Griffiths, D.V. and Lane P.A. (1999). Slope stability Analysis by finite Elements, Geothechnique, vol.49, No 3 p.p. 387-403.
[42] Griffiths D.V. and Fenton G.A. (2004) Probabilistic slope stability analysis by finite elements. NSF Grant No CMS-9877189, p.p. 1-27.
[42] Hicks M.A. and Samy K (2004). Stochastic evaluation of heterogeneous slope stability. Italian Geotechnical Journal, p.p.38 (2), 54-66.
[42] Tang W.H. (1984). Principles of probabilistic characterization of soil properties. Symposium of probabilistic Characterization of Soil Properties, ASCE, Reston, VA, p.p. 74-89.
[43] Dakoulas P. (1991). Stability of slopes and Earth Dams Under Earthquakes: Concluding Remarks, Proceedings of the Second International Conference on Geotechnical Earthquake Engineering and Soil dynamics, St. Louis, Missouri, March 11-15, Vol 3, p.p. 2157.
[43] Dakoulas P. (2005). Advanced Soil Mechanics (Elasto-plastic Constitutive Models for soils). Notes for the Graduate Course Advanced Soil Mechanics, University of Thessaly, Greece, 400 pages.
[43] Fenton A.G. and Vanmarcke E.H (1990). Simulation of Random Fields via Local Average Subdivision, Journal of Engineering Mechanics, Vol.116, No 8 p.p. 1733-1749
[43] Fenton G.A., Griffiths D.V. and Urquhart A. (2003). A slope stability model for spatially random soils. In Proc. 9th Int. Conf. Applications of Statistics and Probability in Civil Engineering (ICASP9), A. Kiureghian et al. Eds Millpress, San Francisco, CA, p.p 1263-1269.
[44] Themelis N., (2008). Notes on the Mathematica program. NTUA Athens.
[44] Theodorou G. and Theodorou H. (2004). Practical Guide to Mathematica. Aristotle University of Thessaloniki
[45] Fenton GA, Griffiths DV. (2007). Random field generation and local average subdivision method. New York. CISM Courses and Lectures.
[45] Griffiths D.V. and Fenton G.A. (2004) Probabilistic slope stability analysis by finite elements. NSF Grant No CMS-9877189, p.p. 1-27.
[45] Griffiths D.V. Huang J. (2009) Influence of Spatial Variability on Slope Reliability Using 2-D Random Fields. Journal of Geotechnical and geoenvironmental engineering ASCE/October 2009/ p.p 1367-1375.
[45] Griffiths D.V., Huang J. and Fenton G.A. (2010). Probabilistic infinite slope analysis. (Infoslope 2010), p.p. 1-3.
[46] Alamanis N.O (2017), Effect of spatial variability of soil properties in permanent seismic displacements of road slopes. Doctoral dissertation: University of Thessaly. Department of Civil Engineering, Geotechnical Engineering Sector p.p. 8-19, 99-102.
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2017-11-22
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Alamanis, N. (2017). Uncertainties and Optimization in Geotechnical Engineering. American Scientific Research Journal for Engineering, Technology, and Sciences, 38(1), 92–111. Retrieved from https://asrjetsjournal.org/index.php/American_Scientific_Journal/article/view/3601
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