Frontiers in Offshore Geotechnics: ISFOG 2005 Gourvenec & Cassidy (eds) 2005 Taylor & Francis Group, London, ISBN 0 415 39063 X

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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.

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.

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.

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).

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).

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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