A Abel Henriques

Ana C M Teixeira

António Gomes Correia

Yusuke Honjo

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Semana de Engenharia 2010 
Guimarães, 11 a 15 de Outubro 
 
 
 
RELIABILITY ANALYSIS OF A PILE FOUNDATION AND 
CONTRIBUTION OF THE UNCERTAINTIES INVOLVED 
 
Ana C. M. Teixeiraa, António Gomes Correiaa, A. Abel Henriquesb, Yusuke Honjoc 
aCTAC / cDep. Civil Engineering/ U. Minho, b cDep. Civil Engineering/ FEUP, cDep. Civil Engineering / Gifu University 
E-mail: AnaCMTeixeira@civil.uminho.pt 
 
 
KEYWORDS 
pile, axial load, reliability, uncertainties, influence of the 
uncertainties, model, soil, SPT 
 
EXTENDED ABSTRACT 
The work present in this paper was developed under the 
PhD thesis entitled “Reliability and Cost Models of Pile 
Foundations”. The main goals of this study are: (1) to 
give technical and scientific bases about the use of 
reliability analysis in pile design, (2) compare levels of 
safety obtained by the traditional design methods, the 
Eurocode method (using partial factors) and the 
reliability based design method, (3) determine partial 
factors and give some recommendations for Portuguese 
Annex of Eurocode and also (4) obtain costs linear 
functions with statistics base that will assist to determine 
which costs are associated to a certain level of safety. 
Thus, in this paper is integrated in topic (1) where one 
way that geotechnical uncertainties can be treated in a 
simple way is shown. 
All civil engineers are aware of the uncertainties in the 
design and their importance. But in some areas, as in 
geotechnics, the uncertainties are mostly unknown or 
really difficult to measure. That is why, unlike in 
structural design, the traditional way that geotechni al 
engineers have to introduce the uncertainties on the 
design is using a high global safety factor (based on past 
experience). But, of course, this way of treating the 
uncertainties does not give a rational base to understand 
their influence on the design. That being said this paper 
show one way that geotechnical uncertainties can be 
treated in a simple way. The methodology used aims to 
eliminate the possible confusions and difficulties that 
traditional reliability methodologies used in structures 
can cause to geotechnical designers in practice. A series 
of calculations of the probability of failure for a single 
pile foundation with axial load were done, in order to 
investigate the influence of each uncertainty source. It 
was found, as expected, that the most important 
uncertainty comes from model error, not from the soil.  
The methodology used for the reliability analyses in this 
paper, differs from the typical employed in structural 
analysis, and was proposed by Honjo (2010) – see 
Figure 1. Here, the “Geotechnical Design Tools” andthe 
“Risk Assessment Tools” are separated as much as 
possible, allowing a better understanding of the different 
steps and responses obtained. Also the assessment of the 
risk is done by the simplest method, Monte Carlos 
simulations.  
 
Figure 1: Diagram of the methodology used in the 
reliability analysis (adapted from Honjo, 2010) 
 
The methodology will be applied to a pile from the 
FEUP (Faculdade de Engenharia da Universidade do 
Porto) experimental site. The pile was bored in residual 
soil and has 0.6 meters of diameter, 4 SPT tests of he 
area are available and different lengths are analysed. 
The measurement error was not considered in this study. 
In the first step, when determining the trends (e.g. SPT), 
the spatial variability and statistical estimation error are 
considered together. After, one needs to gather the 
uncertainties for other necessary parameters (basic 
variables), like loads, by statistical analysis or 
bibliography (for e.g. Phoon 2008) – see Table 1. The 
values of the loads were considered as Gk=Qk=463 kN. 
Then, the performance function (M = Resistance – 
Loads) is determined. This is a simple case since an 
empirical method based on SPT N values, SHB (2001), 
is used to determine the resistances (side Rf and tip Rt): 
 
M = (Rf + Rt) – (G + Q) 
    M = (δf × F + δt ×Qt) – (δg × Gk + δq × Qk)          (1) 
 
The model uncertainty (factors δf and δt, error when 
transforming the test parameters or soil parameters into 
the resistance) was obtained in Okahara et al. 1991– see 
Table 1. Finally, Monte Carlo Simulations are 
performed and the probability of failure and reliability 
indexes (β) are determined. The results are shown in 
Figure 2 and 3 (All uncertainties – continuous line). The 
value of the reliability index obtained for the actual 
length of the pile (6 meters – β=1.88) is lower than the 
recommended for this type of structures. According to 
the bibliography, the values of β should be between 3 
 
Semana de Engenharia 2010 
Guimarães, 11 a 15 de Outubro 
 
 
 
and 4 (CEN 2002). This can be justified by the factthat 
this is an experimental pile, so the consequences of 
failure are low. For a target β=3 the length of the pile 
should be around 8.5 meters. 
 
Table 1: Uncertainties for the application example 
variable Mean SD Distribution Reference 
NSPT 
10.3 + 
1.9z 4.6 Normal - 
Gk factor 
(δg) 
1.0 0.10 Normal 
Holicky et 
al. 2007 
Qk factor 
(δq) 
0.6 0.21 Gumbel 
Holicky et 
al. 2007 
F factor 
(δf) 
1.07 
0.49
2 
LogNormal 
Okahara et 
al. 1991 
Qt factor 
(δt) 
1.12 
0.70
6 
LogNormal 
Okahara et 
al. 1991 
 
MAIN RESULTS AND CONCLUSIONS 
For analysing the uncertainties the calculation above 
was repeated, but removing the: 
1. uncertainties in the side resistance (δf, Nside), 
2. uncertainties in the tip resistance (δt, Ntip), 
3. soil uncertainty (Nside, Ntip), 
4. and model uncertainty (δf, δt). 
 
The following results were obtained: 
 
0
2
4
6
8
10
12
1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00
D
ep
th
 (m
)
All uncertainties
Removing 1 (tip)
Removing 2 (side)
Removing 3 (soil)
Removing 4 (model)
 
Figure 2: Probability of failure (lognormal scale) 
 
0
2
4
6
8
10
12
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50
D
ep
th
 (m
)
All uncertainties
Removing 1 (tip)
Removing 2 (side)
Removing 3 (soil)
Removing 4 (model)
 
Figure 3: Reliability index 
 
From the 2 graphs above, one can realize that the pile 
length of 8.5 meters determined for β=3 (considering all 
uncertainties) drops down to around 6 meters when 
removing uncertainties 1 or 2 (side or tip) and to 5 
meters when removing uncertainty 4 (model). The 
methodology proposed by Honjo (2010) helps the 
geotechnical engineer to do a full reliability analysis 
without losing the intuitive understanding of the 
problem, important to make decisions during the design 
process. Five analyses were carried out for a single pile, 
with all uncertainties, and removing, at each time th
side, tip, soil and model uncertainties. The results show 
that the contribution of the side and tip uncertainties, in 
this case, is the same, the side resistance is dominant 
(Rf/Rt around 2) but the uncertainties on the tip are 
bigger. Concerning to the soil and model uncertainties, it 
is shown, as expected, that the model error is much more 
important in the reliability of the pile. When removing 
the uncertainties of the soil, one can see that the results 
are almost the same as the ones obtained when 
considering all uncertainties. This way, for code 
calibration and recommendation for reliability design 
one can take into account this conclusion. 
 
REFERENCES 
CEN (European Committee for Standardization). 2002. 
“Eurocode: Basis of Structural Design”. EN 1990. 
Holicky, M.; Markova, J. and Gulvanessian, H. 2007. “Code 
Calibration Allowing for Reliability Differentiation and 
Production Quality”. Application of Statistics and 
Probability in Civil Engineering: Proceedings of the 10th 
International Conference. Kanda, Takada and Furuat. 
Honjo, Y.; Hara, T. and Kieu Le, T. C. 2010. “Level III 
Reliability Based Design of Examples set by ETC10”. 
Proceedings of 17 SEAGC, Taiwan. 
Okahara, M.; Takagi, S.; Nakatani, S. and Kimura, Y. 1991. 
“A study on bearing capacity of a single pile and design 
method of cylinder shaped foundations”, Technical 
Memorandum of PWRL, 2919. 
Phoon, K.-K. 2008. “Reliability-Based Design in 
Geotechnical Engineering: Computations and 
Applications”. (K.-K. Phoon, Ed.) Routledge. 
SHB. 2001. “Specifications for highway bridges”, J.R.A. 
 
AKNOWLWDGEMENTS 
The authors wish to thank to Portuguese Foundation for 
Science and Technology (FCT) the support given 
through the doctoral grant SFRH/BD/45689/2008. 
 
AUTHOR BIOGRAPHIES 
ANA C. M. TEIXEIRA was born in 
Portugal and went to the University of 
Minho (UM), where she studied civil 
engineering from 2003 to 2008. Now she 
is on the 2nd year of PhD. E-mail: 
AnaCMTeixeira@civil.uminho.pt 
 
ANTÓNIO GOMES CORREIA  is Professor at UM. 
He is supervisor of the PhD thesis.  
E-mail: agc@civil.uminho.pt 
 
A. ABEL HENRIQUES  is Professor at FEUP. He is 
Co-supervisor of the PhD thesis. E-mail: arh@fe.up.pt 
 
YUSUKE HONJO  is Professor at Gifu University. He 
is Supervisor of the 6 months training of Ana Teixeira in 
Japan . E-mail: aarh@fe.up.pt 


RELIABILITY ANALYSIS OF A PILE FOUNDATION AND CONTRIBUTION OF THE UNCERTAINTIES INVOLVED

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RELIABILITY ANALYSIS OF A PILE FOUNDATION AND CONTRIBUTION OF THE UNCERTAINTIES INVOLVED

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