Abstract
Three genetic programming models are developed for determining the ultimate bearing capacity of shallow foundations. The proposed genetic programming system (GPS), which comprises genetic programming (GP), weighted genetic programming (WGP), and soft-computing polynomials (SCP), simultaneously provides accurate prediction and visible formulas. Some improvements are achieved for GP and WGP. The SCP is also designed to model the ultimate bearing capacity of shallow foundations with polynomials. Laboratory experimental tests of shallow foundations on cohesionless soils are used with parameters of the angle of shearing resistance, the unit weight of the soil, and the geometry of a foundation considers depth, width, and length to determine the ultimate bearing capacity. Analytical results confirm that all GPS models perform well with acceptable prediction accuracy. Visible formulas of GPS models also facilitate parameter studies, sensitivity analysis, and application of pruning techniques. Notably, SCP gives concise representations for the ultimate bearing capacity and identifies the significant parameters. Although shear resistance angles have the largest impact on ultimate bearing capacity, foundation width and depth are also significant.
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References
Terzaghi K (1943) Theoretical soil mechanics. Wiley, New York
Meyerhof GG (1963) Some recent research on the bearing capacity of foundations. Can Geotech J 1(1):16–26
Vesic AS (1973) Analysis of ultimate loads of shallow foundations. J Soil Mech Found Div 99(1):45–73
Silvestri V (2003) A limit equilibrium solution for bearing capacity of strip foundations on sand. Can Geotech J 40:351–361
Bolton MD, Lau CK (1993) Vertical bearing capacity factors for circular and strip footings on Mohr–Coulomb. Can Geotech J 30:1024–1033
Soubra AH (1999) Upper-bound solutions for bearing capacity of foundations. J Geotech Geoenviron Eng 125(1):59–68
Griffiths DV (1982) Computation of bearing capacity factors using finite elements. Géotechnique 32:195–202
Young-Su K, Byung-Tak KJ (2006) Use of artificial neural networks in the prediction of liquefaction resistance of sands. J Geotech Geoenviron Eng 132(11):1502–1504
Mehrjoo M, Khaji N, Moharrami H, Bahreininejad A (2008) Damage detection of truss bridge joints using Artificial Neural Networks. Expert Syst Appl 35(3):1122–1131
Pal M, Deswal S (2008) Modeling pile capacity using support vector machines and generalized regression neural network. J Geotech Geoenviron Eng 134(7):1021–1024
Behzad M, Asghari K, Eazi M, Palhang M (2009) Generalization performance of support vector machines and neural networks in runoff modeling. Expert Syst Appl 36(4):7624–7629
Tsai CC, Hashash YMAJ (2009) Learning of dynamic soil behavior from downhole arrays. J Geotech Geoenviron Eng 135(6):745–757
Tsai HC (2009) Hybrid high order neural networks. Appl Soft Comput 9:874–881
Arditi D, Pulket T (2010) Predicting the outcome of construction litigation using an integrated artificial intelligence model. J Comput Civil Eng 24(1):73–80
Rezaiee-Pajand M, Akbarzadeh TMR, Nikdel A (2009) Direct adaptive neurocontrol of structures under earth vibration. J Comput Civil Eng 23(5):299–307
Dash NB, Panda SN, Remesan R, Sahoo N (2010) Hybrid neural modeling for groundwater level prediction. Neural Comput Appl 19(8):1251–1263
Tran DH, Perera BJC, Ng AWM (2010) Hydraulic deterioration models for storm-water drainage pipes: ordered probit versus probabilistic neural network. J Comput Civil Eng 24(2):140–150
Tsai HC (2010) Predicting strengths of concrete-type specimens using hybrid multilayer perceptrons with center-unified particle swarm optimization. Expert Syst Appl 37:1104–1112
Zhang Y, Zhou GC, Xiong Y, Rafiq MY (2010) Techniques for predicting cracking pattern of masonry wallet using artificial neural networks and cellular automata. J Comput Civil Eng 24(2):161–172
Nazari A, Khalaj G, Riahi S (2011) ANFIS-based prediction of the compressive strength of geopolymers with seeded fly ash and rice husk-bark ash. Neural Comput Appl 1–13
Sezer A (2011) Simple models for the estimation of shearing resistance angle of uniform sands. Neural Comput Appl 1–13
Yaprak H, Karaci A, Demir I (2011) Prediction of the effect of varying cure conditions and w/c ratio on the compressive strength of concrete using artificial neural networks. Neural Comput Appl 1–9
Koza JR (1992) Genetic programming: on the programming of computers by means of natural selection. MIT Press, Cambridge
Baykasoglu A, Güllü H, Çanakçi H, Ozbakir L (2008) Prediction of compressive and tensile strength of limestone via genetic programming. Expert Syst Appl 35(1–2):111–123
Oltean M, Dumitrescu D (2002) Multi expression programming, technical report, UBB-01-2002. Babes-Bolyai University, Cluj-Napoca
Ferreira C (2001) Gene expression programming: a new adaptive algorithm for solving problems. Complex Syst 13(2):87–129
Nazari A, Riahi S (2011) Prediction split tensile strength and water permeability of high strength concrete containing TiO2 nanoparticles by artificial neural network and genetic programming. Compos B Eng 42:473–488
Nazari A (2012) Experimental study and computer-aided prediction of percentage of water absorption of geopolymers produced by waste fly ash and rice husk bark ash. Int J Miner Process 110–111:74–81
Nazari A, Riahi A, Khalaj G, Bohlooli H, Kaykha MM (2012) Prediction of compressive strength of geopolymers with seeded fly ash and rice Husk_Bark ash by gene expression programming. Int J Damage Mech. doi:10.1177/1056789511431991
Milani AA, Nazari A (2012) Modeling ductile to brittle transition temperature of functionally graded steels by gene expression programming. Int J Damage Mech 21(4):465–492
Bhattacharya M, Abraham A, Nath B (2001) A linear genetic programming approach for modeling electricity demand prediction in Victoria. In: Proceedings of the hybrid information systems, first international workshop on hybrid intelligent systems, Adelaide, Australia, pp 379–393
Baykasoglu A, Oztas A, Ozbay E (2009) Prediction and multi-objective optimization of high-strength concrete parameters via soft computing approaches. Expert Syst Appl 36(3):6145–6155
Yeh IC, Lien LC (2009) Knowledge discovery of concrete material using genetic operation trees. Expert Syst Appl 36(3):5807–5812
Tsai HC (2011) Using weighted genetic programming to program squat wall strengths and tune associated formulas. Eng Appl Artif Intell 24:526–533
Lee IM, Lee JH (1996) Prediction of pile bearing capacity using artificial neural networks. Can Geotech J 18:189–200
Padmini DK, Ilamparuthi K, Sudheer KP (2007) Ultimate bearing capacity prediction of shallow foundations on cohesionless soils using neurofuzzy models. Can Geotech J 35:33–46
Kalinli A, Acar MC, Gündüz Z (2011) New approaches to determine the ultimate bearing capacity of shallow foundations based on artificial neural networks and ant colony optimization. Eng Geol 117(1–2):29–38
Tsai HC (2011) Weighted operation structures to program strengths of concrete-typed specimens using genetic algorithm. Expert Syst Appl 38:161–168
Tsai HC, Lin YH (2011) Predicting high-strength concrete parameters using weighted genetic programming. Eng Comput 27(4):347–355
Holland JH (1975) Adaptation in neural and artificial systems. The University of Michigan Press, Ann Arbor
Gen M, Cheng R (1997) Genetic algorithms and engineering design. Wiley, New York
Michalewicz Z (1996) Genetic algorithms + data structures = evolution programs, 3rd edn. Springer, New York
Hansen JB (1970) A revised and extended formula for bearing capacity. Dan Geotech Inst Bull 28:5–11
Foye KC, Salgado R, Scott B (2006) Assessment of variable uncertainties for reliability-based design of foundations. J Geotech Geoenviron Eng 132(9):1197–1207
Gandhi GN (2003) Study of bearing capacity factors developed from lab. Experiments on shallow footings on cohesionless soils. PhD thesis, Shri G.S. Institute of Technology and Science, Indore
Scardi M, Harding LW (1999) Developing an empirical model of phytoplankton primary production: a neural network case study. Ecol Modell 120(2):213–223
Peng CH, Yeh IC, Lien LC (2009) Modeling strength of high-performance concrete using genetic operation trees with pruning techniques source. Comput Concr 6(3):203–223
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Tsai, HC., Tyan, YY., Wu, YW. et al. Determining ultimate bearing capacity of shallow foundations using a genetic programming system. Neural Comput & Applic 23, 2073–2084 (2013). https://doi.org/10.1007/s00521-012-1150-8
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DOI: https://doi.org/10.1007/s00521-012-1150-8