Heave induced piletension: a simple one-dimensional analysisby Michael P O'Reilly, BEng, LLB, PhD,CEng, MICE, ACIArb, University ofNottingham, and Abir Al-Tabbaa, BSc,MPhil, PhD, Ove Arup &Partners.

IntroductionPiles are often constructed in soil whichsubsequently heaves as a result ofverticalstress reduction, for example bybasement excavation or risinggroundwater level. A simple procedure

'scribedfor calculating the magnitudee ureis

of the tension forces induced into suchpiles and hence the required capacity oftension reinforcement. While the generalprinciples of heave induced tension are

iwidely understood by practisinen 'ineers, the authors are not aware of

iiig

any previous publication which hasproposed a one-dimensional soil-pileinteraction solution as outlined in thisin 'ote.This method is able to account for soilstiffness (including non-linear stiffness if

Notationce undrained shear strengthD pile diameterE', effective vertical stiffness ofsoil under conditionsofzero hiteral deformationL pile lengthP tensile load in pileP the maximum value of P

val' e ective stresstt value of tensile change in vertical effecti

smally applied load to pile head or pile toeS pile spacingT, Time Factor (consolidation theory)z depth below pile head levelLTP limiting tension proffieATP actual tension proffleMFE maximum force envelopea adhesion factord tl„psoil and pile vertical displacement relative to theneutral pointr shear stress along the pile-soil interface

soil-pile interface shear strength

28 by area of the pile cross-sectional area.

GROUND ENGINEERING . JUNE 1990

aPPropriate), pile stiffness, pile spacmg,iction properties of the soil-pile

mterface and time-related effects (e therate of swelling). The routine describeduses simple assumptions and may easil

programmed. However, it is not soy

complicated that it cannot be carried outby hand.

This note concentrates specifically on thecase of straight-shafted bored pilesconstructed in soil subjected to heavepressures before the imposition ofexternally applied loads from buildings orother sources. Building loads usuall yinduce compressive stresses into the pileand hence the critical case for tension willgeneraQy occur before the pileexperiences such loading. A short note onthe extension of the method outlined hereto the analysis of cases involvingexternally applied loads appears at theend of this technical note.

Basic principles of heaveinduced tensionConsider a pile installed in swellingground. The soil adjacent to the upper partof the pile moves upwards relative to theshaft, thereby exerting an upward forceon the pile. Since the pile remains inequilibrium there must be a downwardresulting force ofequal magnitude on thepile which must derive from the upwardmovement of the pile relative to the soiladjacent to the lower part of the pile. Theform of shear stress distribution along thepile shaft is thus as shown in Figures 1 (a)and 1 (h) with a maximum absolute valueof shear stress at any level equivalent tothe pile-soil interface strength. Summinliiinuiigup the interface strengths (expressed in

terms of force per unit length ofpile) alongthe pile from the top produces acumulative capacity line as shown inFigure 1(c);that is to say, a hne whosevalue at any elevation represents the shaftcapacity of the pile above that elevation. Asimilar exercise may be performedsumming up the strengths from thebottom. Combining the two cumulativecapacity lines gives the limiting tensionprofile (LTP) as shown in Figure 1(c)(Collins, 1953).This LTP represents themaximum theoretical tension force profilein the pile consistent with the assumedstrength profile and the equilibriumrequirement (assuming no externalloading). Also shown in Figure 1(c)is theactual tension profile (ATP) for atypicalsituation, which must in every case lie onor within the LTP.

The point at which the maximum tensionf'norce occurs may be consideredeutral point'Bozozuk, 1972)and

as a

corresponds to the plane ofzero shearstrain in Figure 1(a)and ofzero shearstress in Figme 1 (h). At this elevation

ththere is no relative displaceme t betw

e pile and the soil. The relativedis

's awaydisplacement increases at point

om the neutral point. The reason that the

f'TP is not coincident with the LTP 'his at a

tuute displacement between the il dhe pile is required for the full interface

shear strength to be mobilised, andconsequently in the vicinity of the neutralpoint where the relative soil-piledisplacements tend to be small, thetension force on the ATP is less than thaton the LTP.

It is possible to define two upper-boundcriteria for the maximum tensile force on

Sheer Stress0 +vs T Tsiieloil toad

Initiallyho/frontal planes

0+ve shear strain

-EI —————taro sheer strain(neutral point)

-ve shear stron

0—---'T"---------Pile

pgs-soaaterfacestrength

I

\i'I

ess 'tn

sve i'i

o

/tive shaft

ty summed04 of pihl

//

//

//

//

Cumulative shaf t/ cspacit summed

from p head

a) Prie in heaving ground h) Shear stresses acting onpde shaft durmg heave

cl Tension loads induced into pile

Fig1. Theshearstressand tensioground.

ension load profdes for a piie constructedin heaving

mex j f'mex dzc

/ 2 0

Meximum forcenvelope IMFEI

Fig 3.Vniformgrid ofpilesshowing yamused for analysia

0 0

0 0

0 0

0 0

0 0 0 0

A0 ,'0 ' 0

z - y faround prism used

0 0 0 0 for analysis

0 0 0 0

Fig2. Mazdmum force envelope.

the ATP, P, induced into a pile inswelling ground. These are:i) P must he less than or equalto half

the total shaft capacity (to maintainequilibrium in the absence ofexternalloading), ie:

P ~ I/2[mD r dz]

ii) P must be less than or equal to theforce which causes the tension. If, forinstance, an extensive square grid ofpiles with spacing S is subjected touniform surface unloading pressure q(without change in the groundwaterregime) the force which generates theheave associated with any given pile isq.S'.Thus:

P ~qSCombining these two inequalities definesa maximum force envelope (MFE) asshown in Fiyuze 2.For all values of Sthetension P at all points along a pile will beless than or equal to the value on the MFE.For widely spaced piles criterion (i)dominates while for closely spaced pilescriterion (ii) dominates.

The method of analysisThe analysis described here provides amethod for calculating the tension forceprofile along a pile in heaving ground. It isan interactive one-dimensional soil-pileanalysis which takes into account not onlythe infiuence of the soil on the pile hut alsothe influence of the pile on the soil. Itinvolves estimating, in the first instance, atensile load profile in the pile which is inequilibrium. This estimate is then checkedfor shear stress-displacementcompatibility along the pile-soil interface.If the estimate fails to produce acompatible solution, a revised estimate isadopted and the procedure is repeated,iterating until the unique solution for thetensile load profile (ATP) is obtainedwhich is both in equilibrium and satisfiescompatibility. The following steps areused in the analysis:

i) Calculate the applied profile of changein tensile effective stress q.

Changes in ground level, suzface loadingand water regime during construction and

events occuring after construction willaffect the effective stress profile. For thepurposes of this analysis it is necessary todetermine the profile ofchanges ineffective tensile stress (denoted q) since itis these which cause heave. In fine-grained soils the change in effective stresswill he time-dependent. Simpleconsolidation calculations enable theprofile at a number of times to becalculated so that the heave-induced piletension can be determined as a function oftime.

In this note two distinct profiles of changein effective stress are identified. The first,denoted q, and which is considered herein step (i) refers to changes in effectivestress assuming no influence from thepiles. It is described as the applied profileof change in tensile effective stress. Thesecond profile, discussed in step (iv)below, is the resultant of the appliedprofile of changes in tensile stress and thecompressive stress induced into theground as a result of the constrainingeffect of the piles on the swelling soil.

ii) Estimate the tension force profile (ATP)in the pile.

A fizst estimate of the ATP may beobtained by choosing a profile somewhatlower than the LTP (see Figure I c)andwith P less than the MFE value (seeFigure 2).

iii) Divide the pQe and soil into layers.

For the purpose of performing thecalculations divide the system into anumber of layers. The greater the numberof layers, the more accurate the solution.Assign to each layer the calculated valuesofchange in tensile stress (q), assumedsoil stiffness (E'„),pile stiffness and soil-pile interface strength (r~.iv) Calculate the influence ofpile tensionon the effective stress changes in thegrouiid.

As noted above, piles tend to constrain theswelling soiL Consider the plan view of abasement with a regular grid of piles withspacing Sas showninFigure3. For thepurpose ofanalysing piles in the interior ofthe piled region a representative pile maybe extracted together with its associatedsoil 'prism'f area S~.Symmetryconsiderations indicate that no shearstresses act on the face of the prism so thatit can be treated simply as a constantsection free standing column of soil with apile at its core. Piles towards the edge of a

group will have equivalent values of Stending towards infinity, as will singlepiles.

For every unit of load induced into the pileby the soil, the pile must induce anequivalent magnitude of force back intothe soil. One simple way ofconverting thisrefiected force into a stress is to divide itdirectly bythe prism area S'.This p~a conservative solution in the sense thatthe compressive component adjacent tothe pile is underestimated using thistechnique. Using this method, it can beseen that an additional component ofcompressive stress ofmagnitude P/S isinduced at each level where P is theassumed pile tension at that level.Subtracting the compressive stresscomponent from the change in appliedeffective stress profile (see (i)above)(tensile changes being taken as positive)gives a resultant profile of change ineffective stress, (q—P/Sl).

v) Calculate the vertical displacement ofthe pile and the soil.

Given a tension force profile in the pile(see (ii) above) and a change in effectivestress profile in the soQ (see (Jv) above)the vertical strain and defozmations ofeach layer of the pile and the soil can hecomputed from the assumed stiffnesses.By summing up these deformations, aprofile of the vertical pile and soildisplacements, r)p and b„can hecalculated.

At the neutral point there is zero relativedisplacement between the soil and thepile; immediately above this point the soilis moving upwards relative to the pile, andimmediately below this point the soil ismoving downwards relative to the pile. Bysetting the vertical displacement ofbothpile and soQ to zero at the neutral point, therelative soil-pile shear displacements (r),—r)p) along the entire length of the pilecan be calculated as shown in Figure 4.

vi) Assume an interface shear stress-displacement relationship and test forcompatibility.

Figure 8shows a possible interface shearstress-displacement relationship. Fielddata which has been back-calculatedfrom pile tests may be found in theliterature for a variety of soil and pile typesand arrangements (eg see a number of thecontributions in Van Impe (Ed) 1988).Forthe purpose of the examples given in thisnote the relationship shown in Figure 8will be used, as this seems to the authors to 29

GROUND ENGINEERING JUNE . 1990

Downward Displacement 0 Upward'isplacement

SZPile head bp

Keg

Bp Pile dis

Soil dissoil-acement

'isplecements meto the neutral po

30

Qlnstrative calculationsIn order to illustrate the approach outlinedin this note two studies are presented.Example one shows the inQuence of timeon the tension forces generated in a pile. Italso 6lustrates the point that even whenclay strata are not the predominant soiltype, the tensile forces induced may stillexceed the pile strength. In Example two aseries of design charts are produced for aparticular stratigraphy (typical of LondonClay). These illustrate the influence ofpilelength, diameter and spacing and soilstiffness on the calculated values of P

In these calculations, concrete and steelstiffnesses are assumed to be 20GPa and210GPa respectively. Creep effects areneglected and the pile is assumed to bereinforced full-length. It is assumed in thesections below that the pile retains anuncracked stiffness but experiences ahairline crack at the elevation of maximumtensile force in the pile so that the steel has

1.0D

fr

e c 0.8

e3' 0.2e 't

sf 2 3 4 8 8 7 8

mm of soil-pile displacement

Fig 5.Possible idealfsed interface shearsfxeas~placement xelatfonsbfp.

GROUND ENGINEERING JUNE 1990

be fairly typical of reported results. Usingthis shear stress-displacementrelationship and the relative sheardisPlacement (f), —f)p) curve ofFigmre 4enables an interface shear stress profile tobe computed which can be integrated togive a calculated ATP. This calculatedprofile can now be compared with theATP 6rst estimated (see step (ii)).Anydiscrepancy indicates a failure to estimatethe profile on the first occasion withsufficient accuracy.

vii) Repeat the process iterating until aconsistent solution is produced.

Adopt a compromise ATP between thefirst estimate and the calculated pro61esas a'revised estimate pro61e'nd repeatthe process, iterating until a solution forthe ATP is obtained which is both inequilibrium and satis6es stress-displacement compatibility.

Fig4. Vartfcaldfsplacementsexpe2iencedbysoil and piledtrrfngbeave.

Pile toe

to carry all the tension load. The shearstress-displacement relationship usedthroughout is that shown in Figure 5.It isassumed for the sake of simplicity that thevertical stress-strain response of the soil islinear. In addition it is assumed that evenunder long-term drained conditions thesoil-pile interface strength for clay is someproportion, a, of the undrained shearstrength c„.The value of a used here is0.8;this would normally be consideredhigh for pile design but in this case ofpiletension a conservative solution requires ahigh value. The two examples givenbelow were solved by computer, usinglayers 0.13m and 0.25m thick respectively.The acceptance criterion for the solutionwas that the input (equilibrium) and output(compatibility) values of tension forcesshould he within 5% ofeach other forevery soil/pile layer.

i) Example one:A single reinforced concrete pile 0.9m indiameter, 20m long with 0.75%longitudinal steel is constructed in theidealised ground profile shown in Figmts6(a) a layered sand-clay-sand. Initiallythe ground is subjected to a surcharge of100kPa which is removed after the pile isbuilt. The vertical effective soil stiffness,E'„,and maximum soil-pile interface shearstress, r, for the granular material areassumed to be E'„=(50+20z)MPa and

= (25+ 10z)kPa, where z is the depthbelow the pile head. The shear strength ofthe clay stratum is assumed to beapproximately constant at c„=120kPa,with stiffness E'„=60MPa.

The long-term change in tensile effectivestress ofall layers is q= 100kPa. Thisoccurs very rapidly in the granularmaterial. For the clay, Terzaghi's one-dimensional consolidation theory (egTerzaghi and Peck 1951)is used tocalculate the effective stress changes withtime, assuming a free water supply at thetop and bottom of the layer.

The computed actual tension profile for anumber of time factors for the clay layer,T„=0.1to infinity are shown in Figure6fb). Also indicated is the LTP and the

maximum permissible tension assuming asteel yield strength of 0.35kN/mm'. Fromthese computations it seems that for timesup to T„=0.12,0.75% steel is suf6cient tocarry the load. After this, externalcompressive loads (eg building loads atthe pile head) will be required to keep themagnitude of the tension forces in the pilebelow the reinforcement strength. For asoil with a vertical coefficient ofconsolidation of 5m2/yr, T„=0.12corresponds to a time ofapproximatelythree months for the clay thickness shown,assuming that only vertical drainage

One matter of some significance which isobserved in Figmre 6 is that the elevationof the neutral point rises slightly with time.The physical implication of this is that astress-reversal occurs in the zonebetween the elevation of the neutral pointat T„=Oand its elevation at T„=infinity.This is because the soil in this zone initiallymoves upward relative to the pile, butends up moving downward relative to thepile. Whenever a non-linear interfacestress-displacement relationship is used,this may cause difficulty, as shown in

Ffgmts Z. This figure shows a non-linearrelationship and the stress-displacementhistory OAB experienced hy ahypothetical element on the pile-soilinterface. If the stress reversal is notaccounted for, the interface displacement(f), —6p) at B, f)tt, would suggest aninterface stress rh whereas in fact r2 is thecorrect value. In order to identify thestress correctly, portions OA and AB ofthe loading history must be consideredseparately and in sequence. Sincedifferent interface elements willexperience stress reversals at differenttimes, a rigorous solution requires atime-incremental solution procedure. Inthe present case (Example one), however,this problem did not arise since thestress-displacement relationship adoptedwas linear up to 2mm relativedisplacement; all points in the stressreversal zone were close to the neutralpoint and hence all relative displacementsin this zone were less than 2mm.

100kN/mt Suroharoe (removed)

1000Tension in pile (kN)

2000 3000 4000

Send

nt strendth Outedrsss of 0 35kN/mrna

0.0m dia pile ~Clay

0

0oooSr 10

S12

1~0

'Send

~) Idealised Sround profile hl Tension profits m pile at various time factors

Flg 6.Illustrativeexample numberone.

Consequently no error was caused byperforming a one-step computation.

ii) '%~~~pie two:Reinforced concrete piles with 1%longitudinal steel reinforcement areconstructed in clay with undrained shearstrength c„=(50+ Sz)kPa. The verticalstiffness E'„isassumed to be proportionalto c„.An extensive surface unloading ofmagnitude q is applied and it is assumedthat sufficient time has elapsed since theunloading for pore pressure equilibriumto occur and that as a result all layers ofsoil experience the same applied tensQechange in effective stress, namely q. Theanalyses assume a single-stage of loading.However, since the soil strains are in facttime-dependent with the rates of strain atany time being a function of depth, a smalldegree of stress reversal will occur in thegeneral case and hence the solutionsgiven may not be strictly rigorous, as wasdemonstrated above by reference toFlynre?. As for Example one, however,the error will be slight; its exact magnitudewill depend on the prevailing drainageconditions, which in this case have notbeen specified.

A series of design charts have beenproduced in Flynze 8showing thepredicted value of P for a range ofsituations. Two values ofunloading,q=50kPa and 100kPa are considered inFlgnres 8a and b respectively. Three pilelengths, L= 10m, 20m and 30m areconsidered in parts (i), (ii) and (iii)respectively ofFignzes Basad b.Theaxes adopted (P~ vs Sz/D) in thesecharts were chosen so that the MFE wasrepresented by a simple and uniquebi-linear relationship for ail pilediameters.

As an example of the use of the chartsconsider the case of 1.2m diameter piles,30m long set out on an extensive squaregrid of 8m installed in a basement whichexperiences about Sm soil removalwithout affecting the groundwater regime(ie q is about 100kPa). Consider a pile inthe interior of the piled area for whichS=8m, giving (S'/D) =53m. Assume that

E'„is500c„.From Figaro 8bfili) andinterpolating between E'„=200c„andE'„=800c„givesP~=3375kN/m orP =4050kN which Is equivalent to atensile stress in the steel of 0.358kN/mm'fthere is 1% reinforcement. The designermust consider whether this stress isexcessive, or if in view of the conservativeassumptions made (eg full dissipation ofpore pressures) it is acceptable.

A number of general features emergefrom these analyses. The following areexamples:

i) the importance of the MFE, whichbounds all the results, is apparent.ii) the assumed soil stiffness has a markedinfluence on P~.iii) closely spaced piles are stronglyinfluenced by the sloping portion of theMFE and are therefore very dependent onthe magnitude ofunloading q, while morewidely spaced piles are less dependentonq.

iv) for any given spacing parameter S'/Dthe value ofP~ is to a firstapproximation independent of the pilediameter especially for the 10m and 20mlong piles; hence the load in the pile isproportional to the diameter and thepercentage reinforcement required isinversely proportional to the pilediameter.

Comparison with field dataand an elastic solutionincorporating pile-soil slipField observations of heave-inducedtension are rare in the literature. One casehistory reported by Donaldson (1967)andanalysed by Poulos and Davies (1979)concerns a 230mm diameter, 9.15m longpile in expansive soil in dry southernAfrican conditions which was made toheave by inundating the area around thepile with water. Poulos and Davis assumedsoil stiffness and soil-pile interfacestrength profiles. They used an elasticanalysis with interface slip when theinterface strength was attained.

In order to compare the present method

with an elastic solution incorporatingsoil-pile slip, the soil properties assumedby Poulos and Davis (which may be foundin their hook) were input into the presentanalysis. Since they assumed that soilremote from the pile would heave 9mm, achange in tensile effective stress of12.5kPa was assumed on the rather czudebasis that this is the unloading whichcauses 9mm heave over the length of thepile with the stiffness profQe adopted. Inthe absence of data, the shear stress-displacement relationship shown inEVynze Swas used. The results of thecalculations performed by Poulos andDavis and the present authors arecompared with the field data in Figure 8.As can be seen, both sets of computationsgive a reasonable prediction.

Extension to casesinvolving externallyapplied loadIn practice (eg see Wright and Doe, 1989)it will often be necessary to determine thetension induced into a pile which isinstalled in swelling ground but which isalso subjected to externally appliedloading at the head (eg from buildings) orat the toe (base hearing or the anchoringeffect of an undezream). The methoddescribed herein may readily beextended to cover such situations as isshown in Flynze 10.The application of avertical load Q at the pile head or pile toe(positive when directed towards the pQe)causes the LTP to shift as indicated inFiynze 10in order to maintainequilibrium, and the upper-boundcriterion for P based on equQibriumbecomes:

L

P Va[( AD r .dz) —Q]10

Soa ~ pile dlsplsssmsnt

Fig?.Stmssreversal aad the problem ofshearstress determlaatioa for the caseof anon-linear interface shear stress-dfsplacemant ralattanahjp.

GROUND ENGINEERING JUNE 1990

Pmax

D

2000

1000—

(j) L = lpm

(kN/ml

020 40

MFE

Ev = 800 cuEv = 200 cu

10060 .80S /D (ml

D Pmax/D at(m)

(kN/m)

06, 1 2 I865)06, 12 I/00)

120

Pmax

D(k N/ml

2000

(j) L = tpm

20 40

MFE

E„ = 800 cuEv = 200 cu

60 80 100S'/D (m)

D(ml o E

2X

O.E. 1 2 (810)0.6 1.2 (490)

120

3000—(jj) L = 20m

2000—

Pmax

D(kN/m)

1000

3000-

06 l2480)

1.2 (2125) 2000—0 6 '1935)

D1kN/m)

1000

(jj) L = 20m

1.2 (2240)0.6 (2225)

1 2 (1480)0.6 (1410)

20 40 60 80 100 120

S /D (ml

20 40 60 80 100 120S /D Im)

5000

4000—

3000

Pmax

D(k N/m)

2000

1000

(Ill) L = 30m 2 4 I4645)(4640)

0.6 (4630)(4530)

2.4 (3780)1 2 (3705)0.6 (3460)

0.3 (2970)

5000 I-

4000

3000Pmax

D

(k N/m)

2000

1000

(jjj) L = 30m

(4235)(4215)(4160)

(4015)

2 4 (2890)1.2 (2710)0.6 (2360)

0.3 (1820)

020 40 60

St/D Im)

b) Case of q = 100 kPa

80 100 120 20 40

a) Case of q = 50 kPa

60 80 100 120Ss/D (m)

um tension forces axpenenced by piles.

Concluding noteA simple method for determining thetension force induced into a pile inswelling ground has been presented. Thismethod produces results which appear tobe consistent with the theoreticalmaximum force envelope (MFE) andwhich compare well with Poulos andDavis's elastic solution and with field data.Examples one and two indicate theusefulness of the present technique notonly in terms of its ability to providesolutions to real engineering problems butalso in its ability to allow parametricstudies to be performed which help the

QI//cX'i

'i

Q

Fig S.1HustratiTPe example number 2. Maxim

The full solution for the ATP is achievedwhen equilibrium and shaft stress-displacement compatibQity are bothattained. Caution must be exercised,however, in relation to the compatibilityrequirement. Since the elevation of theneutral point may change significantlywhen external loads are applied (as isreadily observed in Figure l if) it isimportant to consider each stage ofloading or unloading in chronologicalsequence with proper allowances forconsolidation effects and the possibility ofinterface stress reversal effects asdescribed above with reference toFigure?.

~

designer understand the problem ofheaveinducedtension.

k(8 Tension

20 40 60 60 100

4I

4/

DC0cs

4I

w4I

eE

10

Pile

'ompression p Tension Compression p Tension Compression 0 Tension

~ Measured IDonaldson 1967)

Poulos and Davis

Present method

a) Pile without external losdinp b) Pile with vertical downward loadat pile head

c) Pile with vertical downward load st pile base(eg from underream anchorage)

32 Fig lO. Limiting tension proBiesfor piles with and without externally applied loads.GROUND ENGINEERING JUNE 1990

Fig 9.Compamton with Beld data and anelasticsolution with pile-soilinterfaceslip.

I'uiPment RevieftJ

AcknowledgementThe authors wish to thankDr JA Lord,Dr JW Pappin and Mr JMMitchell for their advice andencouragement. The use ofOve Arup &

Partners'omputing

facilities isgratefully acknowledged.

ReferencesBozozuk, M (1972).Dovrndragmeasurements on a 160ft floating pipetest pile in Marine clay. Canadian Geot J,Vol 9, No 2, pp 127-136.Collin, LE (1953).A preliminary theoryfor the design of undeneamed piles.Trans Southern African Institution ofCivil Engineers, Vol 3, No 11.Donaldson, GW (1967),Themeasurement of stresses in anchorpiles. Proc 4th Regional Conf for Africaon Soil Mech and Foundation Eng, Vol I,pp 253-256.Poulos, HG &Davis, EH(1979).Pilefoundation analysis and design. JohnWiley, London.Terzaghi, K &Peck, RB (1951).Soilmechanics in engineering practice. JohnWiley, London.Van Imps, WF (Editor) (1988).Deepfoundations on bored and auger piles.Balkema.Wright, RH &Doe, G (1989).Little Britainproject: construction of basement. ProcInt Conf on piling and deep foundations,London, Eds Burland JBand Mitchell JM,Vol I, pp 221-230.

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