Please wait a minute...

Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2018, Vol. 12 Issue (4) : 594-608
ANN-based empirical modelling of pile behaviour under static compressive loading
Abdussamad ISMAIL()
Department of Civil Engineering, Bayero University, Kano, Nigeria
Download: PDF(2211 KB)   HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Artificial neural networks have been widely used over the past two decades to successfully develop empirical models for a variety of geotechnical problems. In this paper, an empirical model based on the product-unit neural network (PUNN) is developed to predict the load-deformation behaviour of piles based SPT values of the supporting soil. Other parameters used as inputs include particle grading, pile geometry, method of installation as well as the elastic modulus of the pile material. The model is trained using full-scale pile loading tests data retrieved from FHWA deep foundations database. From the results obtained, it is observed that the proposed model gives a better simulation of pile load-deformation curves compared to the Fleming’s hyperbolic model and t-z approach.

Keywords piles in compression      load-deformation behaviour      product-unit neural network     
Corresponding Author(s): Abdussamad ISMAIL   
Online First Date: 14 December 2017    Issue Date: 20 November 2018
 Cite this article:   
Abdussamad ISMAIL. ANN-based empirical modelling of pile behaviour under static compressive loading[J]. Front. Struct. Civ. Eng., 2018, 12(4): 594-608.
E-mail this article
E-mail Alert
Articles by authors
Abdussamad ISMAIL
Fig.1  BP-PSO training flow diagram
Type of pile material Driven Bored
dry excavation wet excavation
Concrete piles 38 49 5
H-Steel piles 14 - -
Pipe piles 9 - -
Tab.1  Number and type of piles in the database
Length (m) Perimeter (m) Base area (m2) Elastic modulus (GPa)
Concrete Steel
Set Training Testing Training Testing Training Testing Training Testing Training Testing
x ¯ 11.785 15.782 1.5627 1.3405 0.37230 0.26920 28.93 28.93 200 200
xmin 30.480 31.590 3.8023 2.3939 2.63885 0.51890 28.975 28.975 200 200
xmax 3.650 6.240 0.3990 0.6384 0.00033 0.00032 28.9 28.9 200 200
Tab.2  Number and type of piles in the database
No. of
BP 2 0.34338 0.85678 0.35488 0.83603
3 0.29353 0.86996 0.36032 0.80784
PSO 2 0.34134 0.84912 0.37485 0.78259
3 0.35212 0.84419 0.38264 0.81474
BP-PSO (I) 2 0.45053 0.80113 0.46770 0.74878
3 0.28873 0.87660 0.24173 0.86268
BP-PSO (II) 2 0.16947 0.90233 0.22429 0.89563
3 0.36282 0.85703 0.38482 0.80109
Tab.3  Summary of training and testing results
Parameter Training method
Duration (s) 223 279 236 211
No. of evaluations 350 720 430 310
Tab.4  Time and number of epochs to convergence for various models
Parameter Concrete pile Steel pile
Driven Bored (dry) Bored (wet) H-steel Pipe
C1* -1.2617 -1.5265 -3.158 -0.4825 -1.2477
C2* 7.4131 4.0196 9.417 1.2000 9.8365
C3* -1156.7931 -2773.5869 -1743.864 -497.4374 -778.0912
C4* 12.5277 1.8631 0.086 58.9117 9.7524
C5* 843.1412 2280.6517 1520.356 520.3886 586.0043
C6* -0.0544 -0.0035 -0.006 -0.1629 -0.1430
Tab.5  Values of C-parameters for piles in non-cohesive soils
Piles in silt Piles in clay
C1= C1* ( fm+1 ) α1| ( f P+1) 1.1674 C1= C1* ( fc+1 ) β1| ( f P+1) 1.1674
C2= C2* ( fm+1 ) α2| ( f P+1) 1.0706 C2= C2* ( fc+1 ) β2| ( f P+1) 1.0706
C3= C3* ( fm+1 ) α3| ( f P+1) 0.1185 C3= C3* ( fc+1 ) β3| ( f P+1) 0.1185
C4= C4* ( fm+1 ) α4| ( f P+1) 1.8514 C4= C4* ( fc+1 ) β4| ( f P+1) 1.8514
C5= C5* ( fm+1 ) α5| ( f P+1) 0.1248 C5= C5* ( fc+1 ) β5| ( f P+1) 0.1248
C6= C6* ( fm+1 ) α6| ( f P+1) 1.4099 C6= C6* ( fc+1 ) β6| ( f P+1) 1.4099
Tab.6  Modified values of C-parameters for piles in clayey and silty soils
Parameter Pile type Parameter Pile type
Driven Bored Driven Bored
α1 1.2116 0.0954 β1 -0.0544 -0.2202
α2 -3.5895 0.9541 β2 -6.4958 0.4383
α3 -0.9161 0.1716 β3 -0.6348 -0.1101
α4 3.7225 3.7366 β4 2.0345 2.2703
α5 -0.1026 2.0021 β5 0.1708 0.0957
α6 1.0802 2.3988 β6 0.6985 6.8073
Tab.7  Values of α and β parameters
Fig.2  ANN representation of shaft component
Fig.3  ANN representation of base component
Fig.4  Comparison of actual versus predicted loads (a) proposed PUNN model versus training data; (b) proposed PUNN model versus testing data
Fig.5  Comparison of actual versus predicted loads (Bored piles)
Fig.6  Comparison of actual versus predicted loads (Driven concrete piles)
Fig.7  Comparison of actual versus predicted loads (H-steel piles)
Fig.8  Comparison of actual versus predicted loads (Steel pipe piles)
Fig.9  Performance comparison of PUNN, Hyperbolic and t-z methods (Driven concrete square pile, AB = 0.1265 m2, L=23.16 m)
Fig.10  (Performance comparison of PUNN, Hyperbolic and t-z methods (Bored concrete circular pile, AB =0.4564 m2, L=15.4 m)
Fig.11  Performance comparison of PUNN, Hyperbolic and t-z methods (Driven H-steel pile (HP 310 × 79 / HP 12 × 53), L=20.11 m)
Fig.12  Performance comparison of PUNN, Hyperbolic and t-z methods (Driven pipe pile (concrete filled), AB = 0.0995 m 2, L=29.036 m)
Fig.13  Performance comparison of PUNN, Hyperbolic and t-z methods (Driven concrete square pile, AB = 9.29E-02 m2, L=21.51 m, soil type: SW, N shaft= 70, Nbase = 10)
Fig.14  Variation of settlement with SPT blowcounts (Various methods of installation in sand; L=11.0 m; D=0.60 m)
Fig.15  Variation of settlement with SPT blowcounts (Driven concrete pile; L=11.0 m; D=0.60 m)
Fig.16  Variation of settlement with SPT blowcounts (Bored concrete pile [Dry excavation]; L=11.0 m; D=0.60 m)
Fig.17  Variation of settlement with SPT blowcounts (Bored concrete pile [Wet excavation]; L=11.0 m; D=0.60 m)
Fig.18  Variation of settlement with SPT blowcounts (Various types of pile; L=11.0 m; D=0.60 m)
Fig.19  Variation of settlement with stiffness (Driven concrete pile;D=0.60m)
Fig.20  Variation of settlement with slenderness ratio (Driven concrete pile)
1 Poulos H G. Settlement of pile foundations. Numerical methods in Geotechnical Engineerng, McGraw-Hill, New York, 1977, 326–363
2 Desai C S. Deep foundations. Numerical methods in Geotechnical Engineerng. McGraw-Hill, New York, 1977, 235–271
3 Tomlinson M J. Pile Design and Construction Practice. Longman, 6th edition, 1995
4 Chin F K. Estimation of the ultimate load of piles from tests not carried to failure. In: Proc. 2nd SE Asian Conf. Soil Engrg, Singapore, 1970, 81–92
5 Fleming W. A new method of single pile settlement and analysis. Geotechnique, 1992, 42(3): 411–425
6 Poskitt T J. A new method for single pile settlement prediction and analysis. Geotechnique, 1993, 43(4): 615–619
7 Hamdia K M, Lahmer T, Nguyen-Thoi T, Rabczuk T. Predicting the fracture toughness of pncs: A stochastic approach based on ann and anfis. Computational Materials Science, 2015, 102: 304–313
8 Rafiq M Y, Bugmann G, Easterbrook D J. Neural network design for engineering applications. Computers & Structures, 2001, 79(17): 1541–1552
9 Ghaboussi J, Sidarta D E. New nested adaptive neural networks (nann) for constitutive modelling. Computers and Geotechnics, 1998, 22(1): 29–52
10 Lee T L, Jeng D S. Artificial neural networks for tide forecasting. Ocean Engineering, 2002, 29(9): 1003–1022
11 Kabiri-Samani A R, Aghaee-Tarazjani J, Borghei S M, Jeng D S. Application of neural networks and fuzzy logic models to long-shore sediment transport. Applied Soft Computing, 2011, 11(2): 2880–2887
12 Ismail A, Jeng D S, Zhang L L, Zhang J S. Predictions of bridge scour: Application of a feed-forward neural network with an adaptive activation function. Engineering Applications of Artificial Intelligence, 2013, 26(5-6): 1540–1549
13 Vu-Bac N, Lahmer T, Keitel H, Zhao J, Zhuang X, Rabczuk T. Stochastic predictions of bulk properties of amorphous polyethylene based on molecular dynamics simulations. Mechanics of Materials, 2014, 68: 70–84
14 Vu-Bac N, Lahmer T, Zhang Y, Zhuang X, Rabczuk T. Stochastic predictions of interfacial characteristic of polymeric nanocomposites (pncs). Composites. Part B, Engineering, 2014, 59: 80–95
15 Pooya Nejad F, Jaksa M B, Kakhi M, McCabe B A. Prediction of pile settlement using artificial neural networks based on standard penetration test data. Computers and Geotechnics, 2009, 36(7): 1125–1133
16 Ismail A, Jeng D S. Modelling load settlement behaviour of piles using high-order neural network (hon-pile model). Eng. Appl. of AI., 2011, 24(5): 813–821
17 Eberhart R C, Kennedy J. A new optimizer using particle swarm theory. Proceedings of the Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan, 1995, 39–43
18 Zhang J R, Zhang J, Lok T M, Lyu M R. A hybrid particle swarm optimizationback propagation algorithm for feedforward neural network training. Applied Mathematics and Computation, 2007, 185(2): 1026–1037
19 Clerc M, Kennedy J. The particle swarm-explosion, stability and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation, 2002, 6(1): 58–73
20 Fun M H, Hagan M T. Levenberg-marquardt training for modular networks. In IEEE International Conference on Neural Networks, 1996, 468–473
21 Yu J, Wang S, Xi L. Evolving artificial neural networks using an improved pso and dpso. Neurocomputing, 2008, 71(4-6): 1054–1060
22 Durbin R, Rumelhart R. Product units: A computationally powerful and biologically plausible extension to backpropagation networks. Neural Computation, 1989, 1(1): 133–142
23 Prevost J H, Popescu R. Constitutive relations for soil materials. Electronic Journal of Geotechnical Engineering, 1996, 1
24 Poulos H G, Davis E H. Pile foundation analysis and design. Wiley, New Jersey, 1980
25 Kulhawy F H, Mayne P W. Manual on estimating soil properties fro foundation design. Technical Report 2-38, Electric power Res. Inst. EL-6800; Palo Alto Carlifonia, 1990
26 Bowles J E. Foundation analysis and design. McGraw-Hill, New York, 1997
27 Fleming W G K, Weltman A J, Randolph M F, Elson W K. Piling Engineering. Taylor and Francis, Oxford, 2009
28 Swingler K. Applying neural networks: a practical guide. Academic Press, New York, 1996
29 Looney C G. Advances in feed-forward neural networks: demystifying knowledge acquiring black boxes. IEEE Transactions on Knowledge and Data Engineering, 1996, 8(2): 211–226
30 Nelson M, Illingworth W T. A practical guide to neural nets. Addisin-Wesley, Reading MA, 1990
31 Vu-Bac N, Silani M, Lahmer T, Zhuang X, Rabczuk T. A unified framework for stochastic predictions ofmechanical properties of polymeric nanocomposites. Computational Materials Science, 2015, 96: 520–535
32 Vu-Bac N, Lahmer T, Zhuang X, Nguyen-Thoi T, Rabczuk T. A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software, 2016, 100: 19–31
33 McVay M C, Towsend F C, Bloomquist D G, O’Brien M O, Caliendo J A. Numerical analysis of vertically loaded pile groups. Proceedings of the Foundation Engineering Congress, North Western University, Illinois, 1989, 675–690
34 Meyerhof G G. Bearing capacity and settlement of pile foundations. Journal of Geotechnical Engineering, 1976, GT3(102): 197–228
35 Skempton A W. Cast in situ bored piles in london clay. Geotechnique, 1959, 3(4): 153–173
36 Goh A T C. Back-propagation neural networks for modeling complex systems. Artificial Intelligence in Engineering, 1995, 9(9): 143–151
37 Rahman M S, Wang J, Deng W, Carter J P. A neural network model of the uplift capacity of suction caissons. Computers and Geotechnics, 2001, 28(4): 269–287
38 Reese L C, O’Neill M W. Drilled shafts: Construction and design. Technical Report HI-88-042, FHWA, 1988
39 Balakrishnan E G, Balasubramaniam A S, Phien-Wej N. Load deformation analysis of bored piles in residual weathered formation. Journal of Geotechnical and Geoenvironmental Engineering, 1999, 125(2): 122–131
Full text