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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2018, Vol. 12 Issue (4) : 594-608     https://doi.org/10.1007/s11709-017-0446-2
RESEARCH ARTICLE
ANN-based empirical modelling of pile behaviour under static compressive loading
Abdussamad ISMAIL()
Department of Civil Engineering, Bayero University, Kano, Nigeria
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Abstract

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.
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http://journal.hep.com.cn/fsce/EN/10.1007/s11709-017-0446-2
http://journal.hep.com.cn/fsce/EN/Y2018/V12/I4/594
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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
Training
algorithm
No. of
nodes
R-RMSE
(training)
Id
(training)
R-RMSE
(testing)
Id
(testing)
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
BP PSO BP-PSO (I) BP-PSO (II)
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)
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