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Randolph,M. F., Dolwin, J. & Beck, R. (1994). Gebtechnique44, No. 3, 427-448Design of driven piles in sandM. F. RANDOLPH,*J. DOLWINtEstimation of the axial capacity of piles driven intosand involves considerable uncertainty, and designrules are generally not consistent with the physicalprocesses involved. This Paper reviews currentunderstanding of the factors that determine theaxial capacity of piles driven into sand, and outlines a new framework for design which takesaccount of the physical processes, is consistent withthe existing database of load test results, and issufficiently flexible to permit refinement as newdata become available. It allows for the effects ofconfining stress on the frictional and compressibility characteristics of sand, and hence on endInkeepingwithfieldbearingcapacity.observations, shaft friction is assumed to degradewith driving of the pile past a particular location,from an initial maximum value linked to the h is compared with field data, and effectsof factors such as the direction of loading are discussed.and R. BECKfL’estimation de la r&stance axiale de pieux battusdans du sable prbente une grande incertitude et leslois de conception ne sont gtn(?ralement pas enaccord avec les processus physiques impliqu6s.L’article passe en revue les connaissances usuellespermettant de dbterminer la r&stance axiale depieux battus dans du sable et prbsente une nouvellemCthode de conception qui int&re les processusphysiques, est en accord avec les bases de donnCesd’essais de chargement disponibles et est s&Samment flexible pour permettre leur mise i jourlorsque de nouvelles don&es sont disponibles. Elletient Cgalement compte de I’influence de la contrainte de confinement sur les caractkristiques defrottement et de compressibiliti: du sable et donesur la rbistance A la pointe. Lorsque le pieu dCpasse au tours du battage une position particulihre,le frottement lateral est supposC, pour rester enaccord avec les observations in-situ, diminuerdepuis une valeur maximale initiale fonction de larCsistance i la pointe locale. Les rCsultats obtenusg I’aide de cette approche sont cornpa& aux don&es in-situ et l’influence de certains facteurs, telsque la direction de chargement ou la vitesse de diplacement du pieu, est (?tudibe.KEYWORDS: bearing capacity; design; failure; piles;sands; silts.vicinity of the pile tip and the lowest values nearthe ground surface.Over the past decade, there has been intensedebate over the appropriatenessof current designmethods for driven piles in sand. General concerns have been expressedover the detail ofrecommendeddesign parameters,and also inrespect of the conceptual models implied by thedesign methods.In particular,there has beenwidespreaddiscussionof the use of limitingvalues of shaft friction and end-bearing, the treatment of partial displacementpiles, and potentialdifferences in tensile and compressive shaft capacity.There is a need for new, high-quality field dataon pile drivability and axial capacity in sand, particularly from piles of field scale, in order to helpresolve some of these uncertainties.However,there is also a need for elucidation of the basicmechanismsthat affect pile capacity, and alephysical models.INTRODUCTIONThe axial capacity of piles driven into sand isarguably the area of greatest uncertainty in foundation design. Design guidelines such as thosepublished by the American PetroleumInstitute(API, 1984, 1991) are generally not consistentwith the physical processes that dictate actual pilecapacity. For example, the experimentalobservation of a gradual reduction in the rate of increaseof pile capacity with embedment depth is allowedfor by imposing limiting values of end-bearingand shaft friction beyond some critical depth.However, detailed profiles of shaft friction tend toshow the opposite, with maximum values in theManuscript received 25 February 1993; revised manuscript accepted 7 December 1993.Discussion on this Paper closes 1 December 1994; forfurther details see p. ii.* University of Western Australia.t Wholohan Grill and Partners. Amoco ProductionCompany.427

428RANDOLPH. DOLWIN AND BECKThis Paper reviews the physical processes atwork during pile installation,and proposesaframeworkfor a new design approach.At thisstage, quantificationof some aspects of the newdesign approachis preliminary,and significantresearch effort over the next few years will beneeded to refine the approach. The principal aimhas been to provide a methodologythat has asound physical basis and the potential to takedue account of features such as absolute stresslevel, penetrationratio, degree of plugging, andtensile or compressive loading.The present work does not consider the effectsof cyclic loading on pile capacity. However, theform of the methodologyis such that it would bestraightforwardto introduceadditionalparameters to address changes in radial effective stressacting on the pile shaft under the action of cyclicloading, particularly the reduction in local effective stresses due to densificationof the soilaroundthe pile. Similarly,while the designapproach has been developed for silica sands, themethodologyhas the scope to deal with soils ofother mineralogy and also provides a consistentapproachfor soils of differing compressibility.This offers the designer the ability to accountgradually for the silt content within each sandstratum,avoiding the quantum jump betweenalternative design choices of silt or sand. Furthermore, the approach may be extended at a laterdate to providea unified design frameworkapplicable to both silica material and much morecompressible calcareous soils.Current design methods and the experimentalbasis for alternative approachesare reviewed inthis Paper. Particularattentionis paid to thedebate over the existence of limiting values ofend-bearing and shaft friction, and how values ofkey parameters are assumed to be affected by thetype and relative density of the soil. Conceptualmodels of the physical processes involved duringpile installationare drawn together, and the newdesign framework,based on those processes, isdescribed. Preliminary quantitativeassessment ofthe new approachis then presented,using thelimited database of reasonable-qualitypile loadtests that are currently available. The principalareas of uncertainty are highlighted and researchgoals are suggested that will lead to improvementin the proposed design model.REVIEWOF CURRENTDESIGNMETHODSMethods for estimating the capacity of drivenpiles in sand can be divided into two broad categories, based on fundamental parameters (frictionangle, density and stiffness) or on the results of insitu tests. In the latter approach,the mostcommon tests are the cone penetrationresistanceqc and the standard penetrationtest (SPT) blowcount N. In this Paper design rules based on insitu tests are expressed in terms of an appropriately average cone resistance, on the understanding that design rules of a similar nature areavailable in the literature for other forms of insitu test. Perhaps the most widely used designmethod based on intrinsic soil properties is thatcontained in the API guidelines for the construction of fixed offshore platforms.The currentguidelines were introducedin the 15th edition(API, 1984) and have remained largely unchangedin the most recent edition (API, 1991). Thatmethod is used as a backgroundfor the discussion of alternative approaches.The ultimate end-bearing resistance of a pile isgenerally expressed asqb N 4 a’vorqb k,qc(1)where N, is a bearing capacity factor, 0”’ is the insitu effective overburden stress and k, is the factorrelating pile end-bearing to the cone resistance qc.Typical values of N, range from 8-12 for loosesand to over 40 for very dense sand (e.g. API,1991). Similar values for k, lie in the range 040.6 (Bustamante & Gianeselli, 1982; Kraft, 1990).In the API guidelines, limiting values are put onthe absolute value of end-bearingresistance, correspondingto an overburdenstress of about240 kPa (a depth of 20-25 m in saturated soil).For shaft friction, the correspondingapproachisr, K tan 6 uV‘ or q,/u(2)where K is an earth pressure coefficient relatingthe normal effective stress acting around the pileat failure to the in situ effective overburden stress,tan 6 is the coefficient of friction between pile andsoil and a is a coeflicient that varies in the range60-120 (Bustamante& Gianeselli, 1982). In theAPI guidelines, the value of K is taken as 0.8 fora partial displacementpile and 1 for a full displacementpile, irrespectiveof the directionofloading(tensileor compressive).In bothapproaches,limitingvalues of shaft frictionranging from 40kPa(loose) to 12OkPa (verydense) are specified. In the API guidelines, thelimiting value of shaft friction for each category ofsoil is reached at an effective overburden stress ofabout 220 kPa. In design, it is common to adoptuniformvalues of the empiricallyevaluatedparametersK and a over the full depth of sandpenetratedby the pile. However, in reality theseparameters will vary along the pile shaft, and theproposeddesign approachwill considerlocalvalues of such parameters.The assumption in the API guidelines of limiting values of end-bearing and shaft friction being

DRIVENPILESreached at an absolute stress level (or depth),independentlyof pile diameter, contrasts with recommendationsby Visit (1967, 1970) where thecritical depth is expressed in terms of the pilediameter d and varies from 10d for loose/mediumsand up to 20d for dense sand (see Poulos &Davis, 1980). Such contradictionsare a directresult of the limited database of pile load tests,where lack of detail in the soil data, and naturalvariability, prevent conclusive interpretations.Inaddition, most of the piles consideredfall in arather narrow range of diameter and penetration,which precludes definitive assessment of the relative importanceof effective stress level, absolutepile length or normalized length L/d.It should be emphasizedthat in the APIapproach, for a given soil type, the distributionofshaft friction is assumed to be identical, regardlessof the diameter or penetrationof the pile. Thus,at depths less than the critical depth at which thelimiting value of shaft friction is reached, the pileshaft capacity would increase with the square ofthe embedment.Below the critical depth, therewould be a linear increase in shaft capacity.End-bearing resistanceThe assumptionthat end-bearingresistanceincreases linearly with depth up to some limitingvalue is an idealizationthat has little supportnowadays and is difficult to explain in physicalterms. A more widely held view is that, for ahomogeneoussanddeposit,the end-bearingresistance continues to increase with increasingdepth, but at a gradually decreasingrate. Thegradual reduction in the rate of increase of endbearing resistance with increasing stress level canbe attributed to two effects.(a) As the mean stress in the failure regionincreases (with depth), the friction angle of the.a,’ MPa10;\qb’ MPa10I429IN SANDsoil will decrease (Bolton, 1986). Thus thebearing capacity factor N, in equation(1)should be reduced as the overburdenstressincreases. This effect has been quantified byRandolph (1985) and Fleming, Weltman, Randolph & Elson (1992), and the resulting designcharts are presented in Fig. 1, where 4,” is the(effective) critical state friction angle and I, isthe relative density, of the soil.(b) The failure beneath the pile tip is a confinedfailure (with no rupture extending to a freesurface), which entails the end-bearingresistance being affected by the stiffness of the soilin additionto its strength.Essentially,thebearing capacity factor Nq is an increasingfunction of the rigidity index I, (ratio ofstiffness to strength). Since the stiffness of noncohesive soil increases with the mean stresslevel to some power less than unity (typicallyabout 0.5), the rigidity index will reduce withdepth, resulting in a decrease of N, withdepth. Kulhawy(1984) has addressedthisaspect of end-bearing resistance.In order to combine the effects of mean stresslevel on friction angle and rigidity index, it isnecessary to develop a semi-analyticalmodel ofdeepbearingfailure.The mostpromisingapproach appears to be through an analogy withspherical cavity expansionthat has been usedwidely (e.g. V&sic, 1975). The use of cavity expansion limit pressures to estimate end-bearing resistance is developed in more detail below.Shaft frictionWhile the interface friction angle 6 between pileand soil can be measured with reasonable accuracy (Kishida & Uesugi, 1987; Jardine, Everton& Lehane, 1992), there is considerableuncertainty and debate over the appropriatechoice of9 MPa1050”(b)(a)(C)Fig. 1. Design chart for end-bearing capacity (after Fleming et al., 1992): (a) q5., 27O; (b) q5., 30’; (c) 4,, 33”

430RANDOLPH,DOLWINAND BECKSkin frlctim0.110I20I40RelativeI60density: %I60ton/f?,100Fig. 2. Variation of stress ratio K with relative density(after Kraft, 1990)50the horizontal stress coefficient K and the extentto which limiting values of shaft friction shouldbe imposed. Kraft (1990) has presented an alternative approach for estimating K, based purelyon relative density of the soil (but independentofgrain size) and effective area ratio of the pile (fullor partial displacement).The suggested variationof K, shown in Fig. 2, is based on field test data,assuming interface friction angles of 6 0.7 ,,,for silica sands and 6 0.64,,,,, for calcareoussands, where c ,,,., is the peak (effective) frictionangle for the soil. (These values of 6 adopted byKraft are not necessarily consistent with laboratory data such as those presented by Kishida &Uesugi (1987) and Jardine et al. (1992), and will inany case vary with the relative roughness of thepile shaft.)For most soils, Kraft’s approach leads to lowervalues of shaft friction than the API guidelines.However, he recommendsthat no limiting valueof shaft friction should be imposed, with theresult that his approachgenerates lower shaftcapacities for short piles but higher shaft capacities for long piles. This contrasts with the conclusions of Hossain & Briaud (1991) that the APImethod tends to be conservativefor short piles,but overestimatesthe capacity of long piles, withthe crossover being at about 40 pile diameters.Overall, the profiles of shaft friction derived fromKraft’s approach are not in keeping with experimental evidence that shows average shaft frictionvalues that appear to approach a limit at largedepths.Kulhawy (1984) has argued that the experimental observationof limiting shaft friction arisesfrom a combinationof decreasing friction anglewith depth (or stress level) and decreasingKvalues with depth, due to the natural tendency forthe in situ stress ratio K, to decrease with depth.The effect of a decreasing friction angle with anincreasing stress level has been accounted for inthe approach proposed by Fleming et al. (1992).Fig. 3. Distribution(after Vesic, 1970)of shaft frictionalongpile shaftsThey suggest taking K as a constant proportionof N, (K O.O2N,), together with an interfacefriction angle of 4,,, which leads to ratios of shaftfriction to end-bearing ofT% O.O2q, tan c ,,(3)While this approach leads to ratios in keepingwith field measurements(e.g. Vesic, 1970) theshaft capacities of long piles are generally overestimated.An important effect that has been ignored in allthe approachesconsideredso far is the wellestablishedobservationthat the local shaft friction at any level varies with pile penetration. Thishas been reported by V&sic (1970) (see Fig. 3),Hanna & Tan (1973), Lehane, Jardine, Bond &Frank(1993) and manyotherresearchers.Heerema (1980) has emphasizedthe importanceof the effect, which he refers to as friction fatigue,in pile drivability studies.A recent design approach that allows for degradation of friction due to the length of pileinstalled is that of Toolan, Lings & Mirza (1990)who describe two approaches,both of whichallow for friction degradation,but in differentways. The two methods are outlined as follows.(a) Based on the experimentalobservationthatthe average shaft friction reaches a limitingvalue at quiteshallowpenetrations,anempiricalcorrelationof average measuredshaft friction with relative density is proposed,as detailed in Table 1. The actual distributionof shaft friction is assumed to be triangular,with the value at the pile tip being twice theaverage value. For soils of intermediaterelative densities to those shown, a linear interpolationis used. The assumptionof atriangulardistributionof shaftfriction

DRIVENTable 1.Design approach for average shaft friction (Toolan et al., 1990)Soil descriptionShaft friction: kPaRelativedensityOpen-ended pilesTipAverageLooseMedium denseDenseVery dense25122450159020408040801600;0;40;6Closed-ended pilesAverageTip1525501005010020030The approach proposed by Toolan et al. (1990)essentially provides an upper and lower bound tothe ratio B t&r”‘, with a sharp jump from theupper value (in the lower 10m of the pile) to thelower value over the remainder of the pile shaft.The sudden reduction in fi is clearly an idealization, and the fixed lower limit of /? 0.24 doesnot model the gradual effect of friction degradation observed in the field. However, it representsa reasonable attempt at a design approach thatdifferentiatesbetween high friction near the piletip and reduced, degraded,shaft friction overmuch of the length of the pile.broadly fits the data of V&sic (1970) shown inFig. 3, and leads to gradual reduction of shaftfriction at any given level as the pile penetration is increased. Thus, effects of friction degradationare accountedfor, at least in asimplistic way.(b) The alternativeapproachof Toolan et al.(1990) adopts a fixed ratio of /? z,/Q,,‘, whichis a function of relative density and pile penetration and applies over the bottom 10m ofthe pile. The proposed correlation is shown inFig. 4 for full displacementpiles, with valuesfor unpluggedopen-endedpiles being 20%lower. For piles that are embeddedbeyondlOm, the shaft friction down to 10m abovethe pile tip is calculated using a value of /?that is the lower of 0.24 and the value fromFig. 4. The value of /I 0.24 reflects degradedfriction due to two-way plastic slip duringinstallation.“i431PILES IN SANDPROPOSEDMETHODSFRAMEWORKFOR NEW DESIGNA new framework for calculating pile capacityin sand is now presented. At this stage, some ofthe quantitativedetails of the Open-endedxHi60%1 70%/ConcreteH-sectm:yO%/RelativedensityFig. 4. Proposed j3 values over bottom 10 m of pile (after Toolan ef al., 1990)

432RANDOLPH,method require further research. Preliminarygestions are given for key parameters.DOLWINsug-AND BECKrelationship between end-bearingthe limit pressure plimisqb piim(l tan 4’ tan c()End-bearing capacityAlthough it is convenient to express the endbearing capacity of a pile in terms of a bearingcapacity factor multiplied by the in situ verticaleffective stress, as in equation (I), the bearingcapacity factor will be a function of both thestrength(or frictionalangle) and the rigidityindex (G/p’, where G is the shear modulus and p‘the mean effective stress) of the material. Thesequantities vary differently with the absolute effective stress level. In addition, the relative magnitude of the in situ horizontal and vertical stresseswill affect the bearing capacity factor (Houlsby &Hitchman, 1988).In principle, these effects can be quantifiedthroughdetailednumericalanalysis using anappropriatesoil model. However, there is no generallyacceptedmodelfor the stress-strainresponse of granular material over the enormousstrain levels relevant to bearing failure, and thecomputationaleffort to conduct a full parametricstudy would be daunting. An alternative is to usethe analogy between spherical cavity expansionand bearing failure (Gibson, 1950), as

published by the American Petroleum Institute (API, 1984, 1991) are generally not consistent with the physical processes that dictate actual pile capacity. For example, the experimental observa- tion of a gradual reduction in the rate of increase of pile capacity with embedment depth is allowed for by imposing limiting values of end-bearing and shaft friction beyond some critical depth .

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