Abstract
Providing precise estimations of soil deformation modulus is very difficult due to its dependence on many factors. In this study, gene expression programming (GEP) and multi-expression programming (MEP) systems are presented to derive empirical equations for the prediction of the pressuremeter soil deformation modulus. The employed expression programming (EP) systems formulate the soil deformation modulus in terms of the soil physical properties. Selection of the best models is on the basis of developing and controlling several models with different combinations of the affecting parameters. The proposed EP-based models are established upon 114 pressuremeter tests on different soil types conducted in this study. The generalization capabilities of the models are verified using several statistical criteria. Contributions of the variables influencing the soil modulus are evaluated through a sensitivity analysis. The GEP and MEP approaches accurately characterize the soil deformation modulus resulting in a very good prediction performance. The result indicates that moisture content and soil dry unit weight can efficiently represent the initial state and consolidation history of soil for determining its modulus.
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Karmakar S, Sharma J, Kushwaha RL (2004) Critical state elasto-plastic constitutive models for soil failure in tillage—A review. Can Biosyst Eng 46:19–23
Briaud JL (2001) Introduction to soil moduli. Geotech. News, June 2001, BiTech Publishers, Richmond, BC
Briaud JL, Li Y, Rhee K (2006) BCD: a soil modulus device for compaction control. J Geotech Geoenviron Eng (ASCE) 132(1):108–115
Mollahasani A, Alavi AH, Gandomi AH (2011) Empirical modeling of plate load test moduli of soil via gene expression programming. Comput Geotech 38(2):281–286
Rashed A, Bolouri Bazaz J, Alavi AH (2012) Nonlinear modeling of soil deformation modulus through LGP-based interpretation of pressuremeter test results. Eng Appl Artif Intel. doi:10.1016/j.engappai.2011.11.008
Reznik YM (1995) Comparison of results of oedometer and plate load tests performed on collapsible soils. Eng Geol 39:17–30
Murthy S (2008) Geotechnical engineering: principles and practices of soil mechanics, 2nd edn. CRC Press, Taylor & Francis, UK
Koza JR (1992) Genetic programming: on the programming of computers by means of natural selection. MIT Press, Cambridge MA
Alavi AH, Ameri M, Gandomi AH, Mirzahosseini MR (2011) Formulation of flow number of asphalt mixes using a hybrid computational method. Constr Build Mater 25(3):1338–1355
Chakraverty S, Gupta P (2008) Comparison of neural network configurations in the long-range forecast of southwest monsoon rainfall over India. Neural Comput Appl 17(2):187–192
El-Shafie A, Abdelazim T, Noureldin A (2010) Neural network modeling of time-dependent creep deformations in masonry structures. Neural Comput Appl 19:583–594
Chakraverty S, Gupta P, Sharma S (2010) Neural network-based simulation for response identification of two-storey shear building subject to earthquake motion. Neural Comput Appl 19:367–375
Kraslawski A, Pedrycz W, Nyström L (1999) Fuzzy neural network as instance generator for case-based reasoning system: an example of selection of heat exchange equipment in mixing. Neural Comput Appl 8(2):106–113
Cao M, Qiao P (2008) Neural network committee-based sensitivity analysis strategy for geotechnical engineering problems. Neural Comput Appl 17:509–519
Yang XS, Gandomi AH, Talatahari S, Alavi AH (2012) Metaheuristics in water resources, geotechnical and transportation engineering, 1st edn. Elsevier. ISBN:9780123982964
Gandomi AH, Alavi AH (2011) Multi-stage genetic programming: a new strategy to nonlinear system modeling. Inf Sci 181(23):5227–5239
Cabalar AF, Cevik A, Guzelbey IH (2009) Constitutive modeling of Leighton Buzzard sands using genetic programming. Neural Comput Appl 19(5):657–665
Mousavi SM, Alavi AH, Gandomi AH, Mollahasani A (2011) A hybrid computational approach to formulate soil deformation moduli obtained from PLT. Eng Geol 123:324–332
Ferreira C (2001) Gene expression programming: a new adaptive algorithm for solving problems. Complex Syst 13(2):87–129
Oltean M, Dumitrescu D (2002) Multi expression programming. Technical report, UBB-01-2002, Babeş-Bolyai University, Cluj-Napoca, Romania
Oltean M, Grosşan C (2003) A comparison of several linear genetic programming techniques. Adv Complex Syst 14(4):1–29
Gandomi AH, Alavi AH, Mirzahosseini MR, Moqhadas Nejad F (2011) Nonlinear genetic-based models for prediction of flow number of asphalt mixtures. J Mater Civil Eng ASCE 23(3):248–263
Alavi AH, Gandomi AH (2011) A robust data mining approach for formulation of geotechnical engineering systems. Eng Computations 28(3):242–274
Baykasoglu A, Oztas A, Ozbay E (2009) Prediction and multi-objective optimization of high-strength concrete parameters via soft computing approaches. Exp Syst Appl 36(3):6145–6155
Baykasoglu A, Gullu H, Canakcı H, Ozbakır L (2008) Prediction of compressive and tensile strength of limestone via genetic programming. Exp Syst Appl 35(1–2):111–123
Alavi AH, Gandomi AH, Sahab MG, Gandomi M (2010) Multi expression programming: a new approach to formulation of soil classification. Eng Comput 26(2):111–118
Alavi AH, Aminian P, Gandomi AH, Arab Esmaeili M (2011) Genetic-based modeling of uplift capacity of suction caissons. Exp Syst Appl 38(10):12608–12618
Cevik A, Arslan MH, Köroğlu MH (2010) Genetic-programming-based modeling of RC beam torsional strength. KSCE J Civil Eng 14(3):371–384
Cevik A (2007) A new formulation for web crippling strength of cold-formed steel sheeting using genetic programming. J Constr Steel Res 63:867–883
Weise T (2009) Global optimization algorithms—theory and application. Germany: it-weise.de (self-published). [Online]. Available: http://www.it-weise.de
Friedberg RM (1958) A learning machine: part i. IBM J Res Develop 2:2–13
Cramer NL (1985) A representation for the adaptive generation of simple sequential programs. In: Proceedings of genetic algorithms and their applications, pp 183–187
Gandomi AH, Alavi AH, Yun GJ (2011) Nonlinear modeling of shear strength of SFRCB beams using linear genetic programming. Struct Eng Mech 38(1):1–25
Banzhaf W, Nordin P, Keller R, Francone F (1998) Genetic programming—an introduction. On the automatic evolution of computer programs and its application. Dpunkt/Morgan Kaufmann, Heidelberg/San Francisco
Poli R, Langdon WB, McPhee NF, Koza JR (2007) Genetic programming: an introductory tutorial and a survey of techniques and applications; Technical report [CES-475], University of Essex, UK
Brameier M, Banzhaf W (2007) Linear genetic programming. Springer Science + Business Media, New York
Miller J, Thomson P (2002) Cartesian genetic programming. In: Proceedings of genetic programming. Springer, Berlin
Patterson N (2002) Genetic programming with context-sensitive grammars. PhD Thesis, School of Computer Science, University of Scotland
Reznik YM (2007) Influence of physical properties on deformation characteristics of collapsible soils. Eng Geol 92:27–37
Look BG (2007) Handbook of geotechnical investigation and design tables. Taylor & Francis, London
ASTM D4719–87 (1987) Standard test method for pressuremeter testing in soils. STM International, Sydney
Farrar DE, Glauber RR (1967) Multicollinearity in regression analysis: the problem revisited. Review Econ Stat 49(1):92–107
Dunlop P, Smith S (2003) Estimating key characteristics of the concrete delivery and placement process using linear regression analysis. Civil Eng Environ Syst 20:273–290
Smith GN (1986) Probability and statistics in civil engineering. Collins, London
GEPSOFT (2006), GeneXproTools Owner’s Manual. Version 4.0. Available online: http://www.gepsoft.com/
Oltean M (2004) Multi expression programming source code. Available at: http://www.mep.cs.ubbcluj.ro/
Frank IE, Todeschini R (1994) The data analysis handbook. Elsevier, Amsterdam
Golbraikh A, Tropsha A (2002) Beware of q2. J Mole Graph Model 20:269–276
Roy PP, Roy K (2008) On some aspects of variable selection for partial least squares regression models. QSAR Comb Sci 27:302–313
Chakraverty S, Singh VP, Sharma RK (2006) Regression based weight generation algorithm in neural network for estimation of frequencies of vibrating plates. J Comput Meth Appl Mech Eng 195:4194–4202
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Alavi, A.H., Gandomi, A.H., Nejad, H.C. et al. Design equations for prediction of pressuremeter soil deformation moduli utilizing expression programming systems. Neural Comput & Applic 23, 1771–1786 (2013). https://doi.org/10.1007/s00521-012-1144-6
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DOI: https://doi.org/10.1007/s00521-012-1144-6