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Frontiers in Offshore Geotechnics: ISFOG 2005 Gourvenec &
Cassidy (eds) 2005 Taylor & Francis Group, London, ISBN 0 415
39063 X
815
1 INTRODUCTION
1.1 Buckling as a mode of failure
Buckling instability is one of the more destructiveforms of pile
failure. It is sudden and is the cause of failure of many, if not
most structures. The import-ance of buckling instability in
structural design cannot be underestimated. McRobie (2002) in
hisintroductory lecture on buckling to undergradu-ates states; If
you ever intend to design a structure, do not even think of
skipping these (buckling) lec-tures. This form of failure mechanism
dominates the design of slender members carrying substantialaxial
loads. Piles are slender members normally used to transfer the
axial load of the superstructure to the deep bearing strata. Bond
(1989) collated embed-ded lengths and diameters of piles used in
practice.The study shows that the length to diameter ratio of piles
ranges between 25 and 100. These can beconsidered as slender
columns, in the absence of soilsupport.
Buckling of piles is currently considered in piledesign under
the following headings:
1 Partially exposed piles, as in jetties or offshoreplatforms
where part of the pile is in water or air.
2 Piles in very soft soil (clay).3 During pile installation by
driving.
1.2 Limit State of Collapse and Limit State ofServiceability
The failure of piled foundations can be classified intotwo
groups:
(a) Structural failure of the pile whereby the loadcarrying
capacity of the foundation drops, see forexample Figure 1. The
figure shows plastic hingesformed in the piles during the 1964
Niigata earth-quake. The fundamental failure mechanisms that
Buckling considerations in pile design
S. Bhattacharya, T.M. Carrington & T.R. AldridgeFugro
Limited, United Kingdom
ABSTRACT: Buckling instability is one of the more destructive
forms of pile failure. Buckling of piles can be classified into two
groups; (a) Global buckling, where a part or full length deforms
longitudinally as in Eulers buckling of unsupported struts; (b)
Local buckling where the cross-section of the pile deforms and the
damage is localised. Global buckling is currently considered in
design where piles are partially exposed or driven in extremely
soft soil or during installation under driving stresses. Recent
studies have shown that fully embedded end-bearing piles passing
through saturated loose to medium dense sand can buckle if the
surrounding soil liquefies in an earthquake. There have been a
number of cases where offshorepiles have collapsed during driving
due to progressive closure of the internal dimensions the
initiat-ing mechanism being local buckling. This paper summarizes
the different cases where buckling should be considered in pile
design. Mechanisms of collapse of offshore piles by local buckling
are discussed in a companion paper.
Figure 1. Structural failure of piles by forming plastichinges
Hamada (1992). A piled foundation that collapsedduring the 1964
Niigata earthquake.
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can cause plastic hinge formation in a pile are shearfailure,
bending failure and buckling failure. Theabove three forms of
failure are often known asLIMIT STATE OF COLLAPSE. It must be
men-tioned that each of these types of failure can causea complete
collapse of the foundations.
(b) Failure by excessive settlement. Often the settle-ment of
piled foundations exceeds the acceptablelimits of the structure,
which is essentially SER-VICEABILITY LIMIT STATE. In this type of
fail-ure, the piles may not fail structurally.
This paper deals with the buckling aspect of LimitState of
Collapse.
1.3 Structural design of piles
Structurally most piles are designed against bendingfailure due
to lateral loads. The semi-empirical P-yconcept is normally used to
design the piles. However,this approach cannot be applied if
buckling under axialloading is a possibility for the member under
consid-eration. These considerations would lead to the factthat, if
part of the pile loses lateral support during itsdesign period, the
pile should be treated as unsup-ported column. The structural
design of the pile in theunsupported zone should be designed as a
columncarrying lateral loads.
A recent investigation, Bhattacharya et al. (2004),has revealed
that fully embedded end bearing pilespassing through loose to
medium dense sand canbuckle under the axial load alone if the
surrounding soilliquefies in an earthquake. Buckling of fully
embeddedpiles in extremely soft clay is known, but should also
beconsidered in loose to medium dense sand in liquefi-able areas.
This approach should be applied equally toearthquake or wave
induced liquefiable soils.
1.4 Purpose of this paper
This paper aims to list the cases where bucklingshould be
considered in design. Buckling of piles hasbeen subdivided into two
groups:
(a) Local buckling, where the transverse section ofthe pile
deforms. In practice, this is often observedat the pile tip.
(b) Global buckling, like Eulers buckling of an unsup-ported
strut, where the longitudinal section of thepile deforms.
Checking against local buckling is crucial for thinwalled
sections and is an important consideration dur-ing the installation
of piles, particularly when drivinginto extremely hard soil or
rock. A companion paper,Aldridge et al. (2005) in this symposium
deals with piletip damage. Therefore, this paper does not address
localbuckling. The codes of practice for pile design are
reviewed with respect to the current understanding. A simplified
design graph is recommended to avoidglobal buckling of piles in
liquefiable soils.
2 REVIEW OF CODES OF PRACTICE FORPILE DESIGN
This section of the paper reviews the design guide-lines against
buckling of piles in some of the mostused codes of practice.
2.1 Eurocode 7 and Part 5 of Eurocode 8
Eurocode 7 (1997) suggests that:Slender piles passing through
water or thick depositsof very weak soil need to be checked against
buckling.This check is not normally necessary when piles
arecompletely embedded in the ground unless the char-acteristic
undrained shear strength is less than 15 kPa.
For design of piles in seismic areas, Eurocode 8advises
designers to design against bending due to iner-tia and kinematic
forces arising from the deformationof the surrounding soil. It
says:Piles shall be designed to remain elastic. When thisis not
feasible, the sections of the potential plastichinging must be
designed according to the rules ofPart 13 of Eurocode 8.
Eurocode 8 (Part 5) also says:Potential plastic hinging shall be
assumed for:a region of 2d from the pile capa region of 2d from any
interface between two layers with markedly different shear
stiffness (ratio ofshear moduli 6)where d denotes the pile
diameter. Such region shallbe ductile, using proper confining
reinforcements.
2.2 American Petroleum Institute (API)
Clause 3.3.1.b of API (2000) recommends the following:Column
buckling tendencies should be consideredfor piling below the
mudline. Overall column buck-ling is normally not a problem in pile
design, becauseeven soft soils help to inhibit overall column
buckling.However, when laterally loaded pilings are subject
tosignificant axial loads, the load deflection (P-)effect should be
considered in stress computations. Aneffective method of analysis
is to model the pile as abeam column on an elastic foundation.
Clause 6.10.2 of API (2000) states:General column buckling of
the portion below the
mudline need not be considered unless the pile isbelieved to be
laterally unsupported because ofextremely low soil shear strengths,
large computedlateral deflections, or for some other reason.
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API (2000) considers stresses in a pile during driv-ing. The
code advises designers to have a minimumpile wall thickness to
avoid local buckling. The rec-ommendations are:For piles that are
to be installed by driving wheresustained hard driving is
anticipated, the minimumpiling wall thickness used should not be
less than
(1)
wheret wall thickness in mm,D diameter, in mm.
2.3 Japanese Road Association code(JRA 1996)
The guidelines for designing piles in liquefiable soilsare shown
in Figure 2. The code advises practicingengineers to design piles
against bending failure dueto lateral loads arising out of inertia
or slope move-ment (lateral spreading). The code discourages
theadditions of effects due to inertia and lateral spread-ing. To
check against the bending failure due to lateralspreading, the code
recommends that the non-liquefiedcrust above the liquefied soil
exerts passive pressure(qNL in Fig. 2) and the liquefied soil
offers 30% of thetotal overburden pressure (qL in Fig. 2).
Eurocode 8 (1998), JRA (1996) focus on bendingstrength and omit
considerations of the bending stiff-ness necessary to avoid
buckling in the event of soilliquefaction. API (2000) code does
consider columnbuckling, but only for soils having low shear
strength,i.e. soft clay. The following sections point out that
buck-ling needs to be considered even for fully-embeddedpiles
passing through loose to medium dense sandwhere there may liquefy
for any reason.
3 WHERE BUCKLING IS IMPORTANT
3.1 Pile as a beam-column
A pile can be best described as a beam-column i.e. acolumn
section carrying lateral loads. A general equa-tion can be
described following Heelis et al. (2004).
(2)
whereEI Flexural rigidity of the pile;P0 External axial
compressive force applied at
the top of the pile i.e. x 0f(x) is the friction per unit
lengthk(x) is the modulus of subgrade reaction.The above equation
suggests that if part of the soil
surrounding the pile loses its effective stress, thenf(x) 0 and
k(x) will be near zero, and the equationreduces to Eulers buckling
equation. The theoreticalbuckling load can be estimated by equation
3.
(3)
where Leff Effective length of the pile in the unsup-ported
zone. This depends of the boundary conditionof the pile below and
above the support loss zone, seeBhattacharya et al. (2004).
3.2 Role of lateral load in buckling
Rankine (1866) recognized that the failure load ofstructural
columns predicted by equation 3 is morethan the actual failure load
(PF) i.e. equation 3 isunconservative. This is because buckling is
very sen-sitive to imperfections and lateral loads. The
collapsealso involves an interaction between elastic and plas-tic
modes of failure. Lateral loads and geometricalimperfections both
lead to the creation of bendingmoments in addition to axial loads.
Bending momentshave to be accompanied by stress resultants that
dimin-ish the cross-sectional area available for carrying theaxial
load, so the failure load PF is less than the plasticsquash load
(PP) given by A. y (A area of the pilesection, y is the yield
stress of the material). Equally,the growth of zones of plastic
bending reduces theeffective elastic modulus of the section,
therebyreducing the critical load for buckling, so that PF
Pcr.Furthermore these processes feed on each other, asexplained in
Horne & Merchant (1965). As the elasticcritical load is
approached, all bending effects aremagnified. If lateral loads in
the absence of axial loadwould create a maximum lateral
displacement 0 in the
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Figure 2. Japanese Roadways Association (JRA) code.
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critical mode-shape of buckling, then the displacement under the
same lateral loads but with a co-existingaxial load P is given
by:
(4)
The same magnification factor applies to any initialout-of-line
straightness of the pile in the mode shapeof potential buckling.
Correspondingly, all curvaturesare similarly magnified and so are
the bending strainsinduced in the column by its lateral loads or
eccen-tricities. The progression towards plastic bending fail-ure
is accelerated as axial loads approach the elasticcritical load
(Pcr). Not only do axial loads induce extrabending moments (P-
effects), but the full plasticbending resistance cannot be
mobilized due to thefact that part of the pile section is required
to carrythe axial loads. Equation 4 indicates that for a
columncarrying an axial load of half its Euler load, that lat-eral
displacements and therefore bending momentswould be 1/(1 0.5) or
100% bigger than those cal-culated ignoring axial load effects.
This is importantif significant lateral loads must also be
carried.
3.3 List of cases where buckling is important
The cases where buckling needs special attention arelisted
below:
1 During installation by driving. The stability ofslender piles
during driving has been dealt with byBurgess (1976). This is also a
design considerationin offshore installations, see Figures 3 and 4.
Figure3 shows a typical offshore installation and Figure 4shows the
pile stick up. Once the pile is in the sleeve,it is important to
check the buckling potential underthe action of the lateral forces
due to the waveloading and the hammer weight.
2 Initial imperfection or lack of straightness. Figure 5shows a
pile attached to a towing bollard in an off-shore pile
installation. This creates an initial eccen-tric moment.
3 Loss of lateral support due to liquefaction or scour.Recent
investigation has shown that fully embed-ded end bearing piles
passing through saturated,loose to medium dense sand can buckle
under theaxial load alone if the surrounding soil liquefies inan
earthquake. The stress in the pile section willinitially be within
the elastic range, and the bucklinglength will be the entire length
of the pile in liquefiedsoil. Figure 6 shows a failure of a fully
embeddedpile by buckling in a centrifuge test.
4 Partially exposed pile. This is often encountered injetties or
offshore platforms.
5 Piles in extremely soft clay. Buckling of slendersteel piles
in soft, quick clay in Trondheim (Norway)has been reported by
Brantzaeg & Elvegaten (1957).
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Figure 3. A typical offshore pile installation.
Figure 4. Pile stick up.
Figure 5. Attachments at the bottom of the pile.
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6 Buckling of pile due to dredging operation in amarine harbour.
It has been reported by Sovinc(1981) that a piled marine harbour
was seriouslydamaged during a dredging operation due to
soilmovement.
7 Local buckling at the sleeve during driving.8 Local tips
buckling due to faulty shoe design.
4 SIMPLIFIED APPROACH TO AVOIDGLOBAL BUCKLING OF PILES
As mentioned earlier, the part of the pile in liquefiablesoil
should be treated as an unsupported column. A pilenot only has
axial stress but also may have bendingstresses in two axes due to
the lateral loads. The pilerepresents a most general form of a
beam-column
(column carrying lateral loads) element with bi-axialbending. If
the section of the pile is a long column,analysis would become
extremely complex and anexplicit closed-form solution does not
exist. The solu-tion of such a problem demands an understanding
ofthe way in which the various structural actions inter-act with
each other i.e. how the axial load influencesthe amplification of
lateral deflection produced by thelateral loads. In the simplest
cases i.e. when the sec-tion is a short column, the superposition
principlecan be applied i.e. direct summation of the loadeffects.
In other cases, careful consideration of thecomplicated
interactions needs to be made.Designing such a type of member needs
a three-dimensional interaction diagram where the axes are:Axial
(P), major-axis moment (Mx) and minor-axismoment (My). The analysis
becomes far more com-plicated in presence of dynamic loads. The
abovecomplicated non-linear process can be avoided bydesigning the
section of the pile as a short columni.e. for concrete section
length to least lateral dimen-sion less than 15 (British Code 8110)
or a slendernessratio (effective length to minimum radius of
gyration)less than 50.
Figure 8 shows the study of 14 reported case histor-ies of pile
foundation during earthquakes, afterBhattacharya (2003) and
Bhattacharya et al. (2004).The case histories were from four
different earth-quakes. Six of the piled foundations survived
whileothers suffered severe damage. Essentially, it isassumed that
the pile is unsupported in the liquefiablezone. For each of the
case histories, the Leff of the pilein the liquefiable region is
plotted against the min-imum radius of gyration (rmin) of the pile.
rmin is intro-duced to represent piles of any shape (square,
tubular,circular) and is given by I/A where I is the secondmoment
of area; and A is the cross sectional area ofthe pile section. For
a solid circular section, rmin is
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Figure 6. Buckling of a fully embedded pile in a centrifugetest,
after Bhattacharya (2003).
Figure 7. Failure of Adriatic harbour during dredging operation,
Sovinc (1981).
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0.25 times the diameter of the pile and for a hollowcircular
section rmin is 0.35 times the outside diameterof the pile. Leff is
dependent on the thickness of theliquefiable zone, depth of
embedment and the fixityat the pile head. In the figure, a line
representing aslenderness ratio of 50 could differentiate the
goodperformance piles from the poor performance. It isworthwhile to
note that slenderness and buckling dif-ferentiated between the good
and poor performanceirrespective of whether the ground surface was
slopedor not. Thus the study shows that piles should bedesigned as
short columns, i.e. large diameter pilesare better.
Figure 9 shows a typical graph showing the min-imum diameter of
pile necessary to avoid global buck-ling depending on the thickness
of the liquefiablesoils following Bhattacharya & Tokimatsu
(2004). Ifthe diameter of a pile is chosen based on Figure 9,then
non-linear P- analysis can be avoided and thelateral load
amplification effects, explained in section3.2 are minimal.
Essentially, the section of the pile is
kept as short column i.e. for concrete section length to least
lateral dimension less than 15 or a slen-derness ratio (effective
length to minimum radius ofgyration) less than 50.
The main assumptions in developing the designchart are:
1 The piles are either solid concrete section having E(Youngs
Modulus) of 22.5 GPa or steel tubularsection having E of 210
GPa.
2 The piles are not in a single row and at least in2 2-matrix
form this ensures that the pile headsare restrained against
rotation but free to translate.
3 The thickness of the steel pile is based on equation (1).
5 CONCLUSIONS
Buckling of pile can be classified into two groups:global
buckling and local buckling. In global buck-ling, the pile deforms
longitudinally leading to lateralinstability of the entire
structure. On the other hand inlocal buckling, the cross section of
the pile deformsleading to a localized damage. In either case, the
loadcarrying capacity of the pile reduces drastically andmay lead
to complete collapse of the foundation. Eightcases have been listed
where buckling is a design con-sideration.
Global buckling should be considered for fullyembedded
end-bearing piles passing through loose tomedium dense where they
may liquefy for any reason.This can be avoided by reducing the
slenderness ratioof the pile in the likely-to-be-unsupported zone.
Asimplified approach to avoid buckling under such situ-ations has
been described.
REFERENCES
Aldridge, T.R, Carrington, T.M and Kee, N.R. 2005.Propagation of
pile tip damage during installation,Proceedings of ISFOG 2005,
Australia.
API 2000. Recommended practice for Planning, Designingand
Constructing Fixed Offshore Platforms WorkingStress Design.
American Petroleum Institute.
Bhattacharya, S. 2003. Pile instability during
earthquakeliquefaction, PhD Thesis; University of Cambridge
(U.K).
Bhattacharya, S., Madabhushi, S.P.G and Bolton, M.D.2004. An
alternative mechanism of pile failure in liquefi-able deposits
during earthquakes, Geotechnique 54, No 3, pp 203213.
Bhattacharya and Tokimatsu 2004. Essential criteria for designof
piled foundations in seismically liquefiable areas,Proceedings of
the 39th Japan National Conference onGeotechnical Engineering,
Niigata, 7th to 9th July 2004.
Bond, A.J. 1989. Behavior of displacement piles in
over-consolidated clays, PhD Thesis, Imperial College (U.K).
820
Minimum dia of pile from buckling consideration
00.250.5
0.751
1.251.5
1.752
2.25
4 6 8 10 12 14 16 18 20Thickness of liquefiable layer (m)
Dia
met
er o
f pile
(m) Concrete pile
Steel tubular pile
Figure 9. Minimum diameter to avoid buckling of
piles,Bhattacharya and Tokimatsu (2004).
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 10 20 30 40 50Effective length (Leff) m
(r min) m
Goodperformance
Poorperformance
Figure 8. Study of 15 case histories, Bhattacharya et
al.(2004).
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Brandtzaeg, A. and Elvegaten, E.H. 1957. Buckling tests
ofslender steel piles in soft, quick clay, Proceedings of the4th
International Conference on Soil Mechanics andFoundation
Engineering (ICSMFE), London, 12th to24th August 1957. Volume II,
pp 1923.
Eurocode 7 1997. Geotechnical design, Brussels,
EuropeanCommittee for Standardization.
Eurocode 8 (Part 5) 1998. Design provisions for
earthquakeresistance of structures-foundations, retaining
structuresand geotechnical aspects, European Committee for
stand-ardization, Brussels.
Hamada 1992. Large ground deformations and their effectson
lifelines: 1964 Niigata earthquake, Technical reportNCEER-92-0001,
Volume 1.
Heelis, M.E., Pavlovic, M.N. and West, R.P. 2004. The
ana-lytical prediction of the buckling loads of fully and
par-tially embedded piles, Geotechnique 54, No 6, pp 363373.
McRobie, A. 2002. Buckling and stability, Undergraduatelecture
notes; University of Cambridge (U.K).
Rankine, W.J.M. 1866. Useful rules and tables, London.Sovinc, I.
1981. Buckling of piles with initial curvature,
Proc of the International Conference on soil mechanicsand
foundation engineering, Volume 8, pp 851855.
JRA 1996. Japanese Road Association, Specification forHighway
Bridges, Part 5, Seismic Design.
Rankine, W.J.M. 1866. Useful rules and tables, London.Horne, M.R
and Merchant, W. 1965. The Stability of Frames,
Pergamon.
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