Adhesion Factor for Rock Soketed Piles

A new socket roughness factor for prediction ofrock socket shaft resistance

J.P. Seidel and B. Collingwood

Abstract: Prediction of rock socket shaft resistance is a complex problem. Conventional methods for predicting thepeak shaft resistance are typically empirically related to unconfined compressive strength through the results of pileload tests. It is shown by reference to international pile socket databases that the degree of confidence which can beapplied to these empirical methods is relatively low. Research at Monash University has been directed at understandingand then modelling the complex mechanisms of shear transfer at the interface between the socketed piles and the sur-rounding rock. Important factors that affect the strength of pile sockets have been identified in laboratory and numeri-cal studies. With a knowledge of the effect of these factors, the reasons for the large scatter around traditionalempirical correlations can be deduced. A computer program called ROCKET has been developed which encompassesall aspects of the Monash University rock socket research. This program has been used to develop design charts forrock-socketed piles based on unconfined compressive strength and a nondimensional factor which has been designatedthe shaft resistance coefficient (SRC). Implementation of the SRC method in design requires an estimate of the likelysocket roughness to be made. Very few researchers or practitioners have measured socket roughness, so there is littleavailable guidance in selection of appropriate values. Although many socket load tests are described in the technical lit-erature, the physical parameter which is regularly missing is the socket roughness. With a knowledge of the shaft resis-tance, and an estimate of all other relevant parameters, the authors have been able to back-calculate the apparent socketroughness using the SRC method. Based on the back-calculated roughness data, socket roughness guidelines for use inanalysis and design of rock sockets have been proposed. Using these roughness guidelines, it is shown that the SRCmethod is able to predict the scatter observed in previously published international load test databases.

Key words: rock socket, drilled shaft, shaft resistance, roughness, shaft resistance coefficient.

Résumé: La prédiction de la résistance du fût encastré dans le roc est un problème complexe. Les méthodesconventionnelles pour prédire la résistance de pic du fût sont typiquement reliées empiriquement à la résistance encompression simple par l’intermédiaire des résultats d’essais de chargement sur pieu. Il est démontré en se référant auxbases de données internationales de pieux encastrés que le degré de confiance que l’on peut accorder à ces méthodesempiriques est relativement faible. La recherche au Monash University a été dirigée vers la compréhension et ensuite lamodélisation des mécanismes complexes du transfert de cisaillement à l’interface entre les pieux encastrés et le rocenvironnant. Les facteurs importants qui affectent la résistance des pieux encastrés ont été identifiés en laboratoire etpar des études numériques. Avec une connaissance de l’effet de ces facteurs, les raisons pour cette grande dispersiondans les corrélations empiriques traditionnelles peuvent être déduites. Un programme d’ordinateur appelé ROCKET aété développé comprenant tous les aspects de la recherche de Monash sur l’encastrement dans le roc. Ce programme aété utilisé pour développer des abaques de calcul pour les pieux encastrés basées sur la résistance en compression sim-ple et sur un facteur non dimensionnel qui a été appelé le coefficient de résistance du fût, SRC. La mise en applicationde la méthode SRC dans la conception requiert une estimation de la rugosité probable de l’encastrement à réaliser. Trèspeu de chercheurs ou de praticiens ont mesuré la rugosité de l’encastrement, de sorte qu’il y a peu de règles deconduite disponibles pour la sélection des valeurs appropriées. Quoique plusieurs essais de chargement d’encastrementsont décrits dans la littérature technique, le paramètre physique qui est régulièrement manquant est la rugosité del’encastrement. Avec la connaissance de la résistance du fût et une estimation des autres paramètres pertinents, lesauteurs ont pu calculer à rebours la rugosité apparente de l’encastrement en utilisant la méthode SRC. Basées sur lesdonnées de rugosité calculées à rebours, des règles pour la rugosité de l’encastrement ont été proposées pour l’analyseet la conception des encastrements dans le roc. En utilisant ces règles de rugosité, on montre que la méthode SRC peutprédire la dispersion observée dans les bases de données internationales des essais de chargement publiées.

Mots clés: encastrement dans le roc, puits foré, résistance du fût, rugosité, coefficient de résistance du fût.

[Traduit par la Rédaction] Seidel and Collingwood 153

1. Introduction

The use of large-diameter socketed piles to carry high andconcentrated loads is widespread internationally. The designof such piles socketed into rock is traditionally based on lo-cal knowledge derived from observation of full-scale static

Can. Geotech. J.38: 138–153 (2001) © 2001 NRC Canada

138

DOI: 10.1139/cgj-38-1-138

Received April 29, 1999. Accepted August 17, 2000.Published on the NRC Research Press Web site onFebruary 20, 2001.

J.P. Seidel and B. Collingwood.Department of CivilEngineering, Monash University, Melbourne, Australia.

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load tests, empirical factors related to the unconfined com-pressive strength of intact rock, or conservative city or stateordinances (Seidel and Haberfield 1994). However, it is atruism, confirmed by Osterberg (1998) on the basis of nu-merous static load tests on rock sockets, that the design ofthis type of pile is generally overconservative, by as much asan order of magnitude. Rock-socketed piles may be designedto carry their load by shaft resistance only, by base resis-tance only, or by both shaft and base resistances. There aresignificant advantages in the design of piles which carrytheir load by both shaft and base resistances. However, utili-sation of the base resistance component requires a construc-tion and inspection technique which guarantees thecleanliness of the pile base. This may be difficult and expen-sive to achieve, particularly for sockets in weak rock, deepsockets in general, or sockets which cannot be readily orsafely inspected. In addition, because shaft resistance is gen-erally mobilised at significantly smaller displacements thanbase resistance, piles typically carry most of their workingload in shaft resistance. As a consequence, there is a particu-lar design interest in shaft resistance. This paper will focusonly on the shaft resistance component of pile socket capac-ity.

1.1. The empirical basis of shaft resistance designEmpirical correlations between uniaxial compressive

strength of weak rock and unit shaft resistance of socketedpiles measured in load tests have been proposed by many re-searchers. The form of these empirical correlations can begeneralized as

[1] fsu = α quβ

where

fsu is the ultimate socket shaft resistance;qu is the uniaxial compressive strength of theweaker material (rock or concrete); andα andβ are factors determined empirically fromload tests.

The empirical factors proposed by a number of research-ers have been summarised by O’Neill et al. (1995) and areshown in Table 1.

Most of these empirical relationships were developed forspecific and limited data sets, which may have correlatedwell with the proposed equations. However, O’Neill et al.(1995) compared the nine empirical shaft resistance designmethods listed in Table 1 with an international database of137 pile load tests in intermediate-strength rock. O’Neill etal. concluded that none of the methods could be considereda satisfactory predictor for the database.

Two other significant database studies on the shaft resis-tance of piles socketed into rock have been conducted byRowe and Armitage (1984) and Kulhawy and Phoon (1993)and will be summarised hereafter. These studies includedpile sockets drilled with different equipment at many sitesand in a range of rock types.

1.2. Significant database studies of shaft resistanceRowe and Armitage (1984) undertook a comprehensive

review of correlations between strength,qu, and the adhesion

factor,α. For the purpose of clarity in this paper, the adhe-sion factor,αq, is defined as follows

[2] αqf

q= su

u

Equations [1] and [2] can then be combined and rewritten as

[3] αq = α quβ – 1

Rowe and Armitage (1984) separated their data into thosetests with roughness classes R1–R3 and tests on sockets withroughness R4, as defined in Table 2 (after Pells et al. 1980).The data included sockets loaded both in tension and com-pression. Figure 1 shows the data of Rowe and Armitage forclass R1 to R3 roughness for sockets of all diameters. Theyalso plotted data for sockets with class R4 roughness and forsockets greater than 350 mm in diameter, which was chosenas an arbitrary limit separating small and large sockets.Rowe and Armitage (1987) do not distinguish between theavailable side shear resistance of small- and large-diametersockets.

It is evident from Fig. 1 that there is wide scatter in thecomputed adhesion factors. Reasonable upper- and lower-bound limits suggest a possible factor of 5 variation inαq forany value ofqu. Some of this difference may be attributableto the database including both sockets in tension and com-pression. Nevertheless, Rowe and Armitage (1984) superim-posed the empirical relationships of Williams et al. (1980)and Horvath (1982) on the data and undertook a linear re-gression to determine a best-fit correlation for R1 to R3roughness (all sockets) as follows:

[4] αq = 0.4qu–0.43

© 2001 NRC Canada

Seidel and Collingwood 139

Design method α βHorvath and Kenney 1979 0.21 0.50Carter and Kulhawy 1988 0.20 0.50Williams et al. 1980 0.44 0.36Rowe and Armitage 1984 0.40 0.57Rosenberg and Journeaux 1976 0.34 0.51Reynolds and Kaderbeck 1980 0.30 1.00Gupton and Logan 1984 0.20 1.00Reese and O’Neill 1988 0.15 1.00Toh et al. 1989 0.25 1.00

Table 1. Empirical factors for shaft resistance design.

Roughnessclass Description

R1 Straight, smooth-sided socket; grooves orindentations less than 1 mm deep

R2 Grooves 1–4 mm deep, >2 mm wide, spacing 50–200 mm

R3 Grooves 4–10 mm deep, >5 mm wide, spacing50–200 mm

R4 Grooves or undulations >10 mm deep, >10 mmwide, spacing 50–200 mm

Table 2. Shaft roughness classifications (after Pells et al. 1980).



The database for R4 roughness was very limited, but the in-terpreted adhesions were generally higher than those for R1or R3 roughness. The following correlation was proposed byRowe and Armitage (1984) for R4 roughness (all sockets):

[5] αq = 0.55qu–0.389

Kulhawy and Phoon (1993) evaluated the unit shaft resis-tance for 127 load tests in soil and 114 load tests in rockcovering a very wide spectrum of geomaterial strengths.Their rock data included that of Rowe and Armitage (1984),supplemented with additional load test results. As their dataset included sockets in both soil and rock, they elected to de-fine their adhesion factor,α, in relation to undrained shearstrength,cu, rather than unconfined compressive strength,qu.This paper defines this adhesion factor asαc, i.e.,

[6] α αc qf

c= =su

u

2

The data of Kulhawy and Phoon are plotted as adhesion fac-tor, αc, versus normalized shear strength, defined as eithercu /pa or qu /2pa, wherepa is the atmospheric pressure (ap-proximated as 100 kPa).

Kulhawy and Phoon (1993) presented their data both forindividual pile tests and as site-averaged data. The latter pre-sentation is shown in Fig. 2. Despite being site-averaged, thedata still exhibit significant scatter, particularly for the sock-ets in rock. Nevertheless, significant trend lines were inter-

preted by Kulhawy and Phoon, and these are superimposedon the data. The authors explained the trend lines by notingthat sockets in soil are generally very smooth, whereas sock-ets in rock exhibit larger variations in roughness. On the ba-sis of the load test data, Kulhawy and Phoon proposed thefollowing general equations for sockets in soil and rock:

[7] α ψcqp

=

−u

a

0.5

2

Kulhawy and Phoon proposed the factorψ to be 0.5 for pilesin soil and to vary between 1.0 and 3.0 (average 2.0) for pileshafts in rock.

The site-averaged data suggest variations in interpretedadhesion factor for rock sockets of at least a factor of 3 andas much as 5. For the individual pile test data presented byKulhawy and Phoon (1993) (shown later in Fig. 13), varia-tions of up to an order of magnitude are observed, as in thestudy of Rowe and Armitage (1984).

It is evident from the studies of O’Neill et al. (1995),Rowe and Armitage (1984, 1987), and Kulhawy and Phoon(1983) that for any given rock strength, very large variationsin adhesion factor are possible. Design based entirely on em-pirical correlations with rock strength should therefore bevery conservative unless site-specific correlations are devel-oped which validate a more optimistic approach.

© 2001 NRC Canada

140 Can. Geotech. J. Vol. 38, 2001

Fig. 1. Shaft resistance correlations for roughness classes R1–R3 of Pells et al. (1980) (after Rowe and Armitage 1984).



The wide scatter of adhesion values observed in correla-tions with unconfined compressive strength of rock suggeststhat there are other factors which significantly influence theshaft resistance achieved. If design is based on rock strengthalone, without any opportunity to take these other factorsinto account, then a conservative design approach must betaken. Any other approach would risk an unsafe design. Bycontrast, if the design approach incorporates these other fac-tors, a less conservative and hence more cost efficient designshould result.

1.3. Socket roughnessOne of the physical factors which has a significant influ-

ence on shaft resistance is socket roughness. The importanceof socket roughness to shaft resistance has been well recog-nised by a number of researchers (e.g., Pells et al. 1980;Rowe and Armitage 1984; Johnston 1977; Horvath andKenney 1979; Williams 1980; Johnston and Lam 1989). Inall three database studies discussed, the effect of socketroughness on shaft resistance has been noted by the authors.

The roughness classes of Pells et al. (1980) shown in Ta-ble 2 were based on observation of sockets drilled using var-ious techniques in Sydney sandstone. Although subjective,this classification system has proven useful in practice forbroadly categorising socket conditions in the field. However,it cannot adequately characterise the full range of roughnesstypes which may be prevalent. Therefore, the roughnessclasses of Pells et al. are unlikely to form the basis of a uni-versally satisfactory system of socket categorisation for de-sign purposes. Nevertheless, it is noted that they do form thebasis for current practice in Sydney, Australia, and are incor-porated into the design method by Rowe and Armitage(1987).

Significant research into the influence of socket roughnesswas reported by Williams (1980) and Johnston and Lam(1989). Williams recorded socket roughness profiles and de-

veloped statistical parameters for their description, andJohnston and Lam used interface roughness as a key param-eter affecting normal stress in their constant normal stiffnessdirect shear tests. The work of Johnston and Lam underliesthe fundamental approach used in the authors’ research.

The research of Horvath and Kenney (1979) and Horvathet al. (1983) into the effect of socket grooving on the shaftresistance in Queenston shale was particularly significant,since it led to a proposed method to quantitatively incorpo-rate socket roughness into socket design. On the basis of thiswork, Horvath et al. proposed a roughness factor, RF, whichwas determined as a function of socket length,Ls, socket ra-dius, rs, mean roughness height,rh, and the traversed lengthof the socket,Lt, as follows:

[8] RF h

s

t

s

=∆r

r

L

L

In addition, they proposed an empirical equation for shaft re-sistance based on socket roughness:

[9]qs

cw

0.450.8(RF)σ

=

where qs is the shaft resistance, andσcw is the unconfinedcompressive strength of the rock or the concrete shaft,whichever is smaller.

The two quotients in eq. [8] which are multiplied to deter-mine the roughness factor are both measures of roughness intheir own right. The first quotient is the roughness of thesocket wall normalized by the socket radius. The secondquotient is the basis for determination of another roughnessparameter, the fractal dimension, by the so-called compassstepping method (Mandelbrot 1977). Horvath et al. (1983)possibly introduced both parts of the roughness factor to

© 2001 NRC Canada


Fig. 2. Adhesion factor versus normalized shear strength (after Kulhawy and Phoon 1993).

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account for the difference in socket groove shapes, whichwas a particular focus of their research.

Despite the efforts of researchers such as Pells et al.(1980), Horvath and Kenney (1979), Horvath et al. (1983),and Rowe and Armitage (1984, 1987) to incorporate socketroughness into design, the majority of socket design is stilldone in the absence of any consideration of this factor. Thisis possibly for two reasons: (i) the incorporation of socketroughness is, of itself, insufficient to significantly improvethe prediction of shaft resistance; and (ii ) the reliable mea-surement of socket roughness is not necessarily trivial, andhence is not undertaken in routine design.

2. The factors influencing rock socketbehaviour

A large fundamental research program into the behaviourof rock-socketed piles has been conducted at Monash Uni-versity for many years. This program has been based on ob-servation of large-scale direct shear tests, which simulate theconcrete–rock interface. These laboratory tests have led tothe development of analytical techniques which simulate theobserved interface behaviour. Some of the important pro-cesses simultaneously occurring at the interface which aremodelled include sliding on irregular surfaces, progressiveshearing of overstressed asperities, elastic redistribution ofstresses, and the shear behaviour of failed asperities. The an-alytical techniques have been modified to account for thedifferences in boundary conditions between shear box testsand rock sockets (Seidel 1993; Seidel and Haberfield 1994,1995b).

The research results have been incorporated in a computersoftware program called ROCKET for design of rock-socketed piles in compression or tension. This program hasbeen validated against full-scale socket load tests. UsingROCKET, it is possible to estimate the complete pile-topload–displacement behaviour of a pile socketed into singleor multilayered rock strata. Calibration of the model is notrequired, as the approach is theoretically, not empiricallybased.

It is common practice in the design of piles in soil to re-duce the computed shaft capacity by between 20 and 50%for tension loading. Although ROCKET does not differenti-ate between compression and tension loading, the engineermay wish to impose such a reduction factor on the computedresults. For short sockets in jointed rock, failure modes otherthan shear at the pile–rock interface may be more criticaland also need to be investigated.

Research at Monash University has confirmed the findingsof others which show that pile shaft resistance is influencedby the following parameters: (i) rock strength (drained intactand residual strength parameters are generally used),(ii ) socket roughness, (iii ) rock mass modulus (and Poisson’sratio), (iv) socket diameter, (v) initial normal stress between

concrete and rock prior to loading; and (vi) constructionpractices. These parameters influence the shaft resistance ofa rock-socketed pile and should therefore be taken into ac-count in the pile design process. The interaction of these fac-tors in determining the performance of socketed piles hasbeen previously recognized (e.g., Rowe and Armitage 1984);however, the complexity of this interaction has been difficultto implement reliably using empirical methods.

3. Elements of a new shaft resistancefactor

In the preliminary stages of rock-socketed pile design, itis rarely necessary to predict a full load–displacement pileresponse. Estimation of ultimate pile capacity is usually suf-ficient at this stage. The authors have developed simplecharts based on a nondimensional parameter known as theshaft resistance coefficient (SRC). The SRC, which is de-fined in section 4, accounts for the most critical factors in-fluencing rock socket shaft resistance. It is incorporated intoa new method of estimating ultimate shaft resistance whichoffers an alternative to empirical formulae. The SRC ap-proach is based on a parametric study using the ROCKETcomputer program. The elements which make up the SRCare outlined in the following sections.

3.1. The Monash socket roughness modelThe Monash University approach to predicting rock-

socket behaviour is based on idealizing rough rock surfacesas a series of interconnected chords of a constant length(Seidel and Haberfield 1995a). Consider a joint profile ofunit length. The profile can be characterised byN line seg-ments or chords of a constant length,la, as shown Fig. 3.The slope of each chord relative to the mean orientation ofthe profile can be determined and a frequency distribution ofchord angles produced.

It is assumed that the distribution of chord angles,θ, isGaussian with a mean,µθ, and standard deviation,sθ. If theprofile is oriented such that the line joining the two endpoints is horizontal, the mean,µθ, will equal zero. The stan-dard deviation of chord angles,sθ, is then a statistical mea-sure of roughness at the scale dictated by the chosen chordlength,la. The asperity heights, ha, will vary with a distribu-tion which can be approximated as Gaussian for reasonablesocket roughnesses (Seidel 1993).

Referring to the geometry of a single chord shown inFig. 4, the standard deviation of asperity height,sh, is givenby

[10] sh = la sin(sθ)

Consequently, the height and angle statistics are directly re-lated and cannot be considered independent variables, as hasbeen assumed previously by some researchers. Collingwood(2000) has shown by detailed analysis of sockets for which

© 2001 NRC Canada


Fig. 3. Roughness profile idealized as a series of interconnected chords of equal length.



accurate roughness profiles are available that the assumptionof a Gaussian roughness distribution is reasonable for nor-mally drilled sockets and some roughened sockets but inap-propriate for most sockets with distinctive grooving.

As the distribution of asperity angles is assumedGaussian, the mean absolute asperity angle may be calcu-lated from the standard deviation of asperity angles as

[11] θπ θ= 2

s

Then by once again considering the relationship between as-perity angle and asperity height, as illustrated in Fig. 4, themean of absolute asperity heights, ha, can also be calculatedas

[12] h l ra a= =sin( )θ ∆

The mean absolute asperity height represents the mean sca-lar height of all asperities. For simplicity, the mean absoluteasperity height is hereafter referred to as the mean roughnessheight and is denoted by the symbol∆r.

By contrast, the mean roughness height used by Horvathet al. (1983) is defined as the mean of the “distances fromthe socket profiles to the surface of the largest imaginarycylinder which would fit into the socket.” It should be notedthat, as illustrated in Fig. 5, this is fundamentally differentfrom the Monash University definition of mean roughnessheight, and the two are not interchangeable.

The Monash University roughness model has also beenextended using the concepts of fractal geometry to relateroughness statistics at different scales (Seidel and Haberfield1995a). However, such aspects of the model are beyond thescope of this paper.

3.2. Roughness and the constant normal surfaceboundary condition

The following analysis is based on the assumption that thepreferred mechanism for failure at the concrete–rock inter-face is initially by slip rather than shear through the intactrock or concrete. In cases where asperity angles are verylarge (e.g., grooved sockets) or where direct bonding acrossthe interface is dominant, this assumption may not be valid.However, direct bonding can often be compromised bysmearing of the socket wall, and in most cases it is believedthat the following analysis will be valid.

The beneficial effect of socket roughness is a combinedconsequence of the dilational nature of a rough concrete–

rock joint and the constant normal stiffness (CNS) boundarycondition which governs the normal stress at the concrete–rock interface. Figure 6 shows a rock socket in cross section.The pile is shown schematically to have a rough interface,which in its unloaded state is in intimate contact with therock against which it was cast. Loading of the pile will ini-tially result in elastic movements of the mated pile–rock sys-tem, and no relative movement at the concrete–rockinterface.

At a critical axial load, the pile will undergo slip relativeto the rock. Due to the rough socket surface, compatibilityrequires that this slip be accompanied by dilation at the in-terface. This is resisted by the surrounding rock by increas-ing the normal stress at the interface. The dilation of thesocket interface can be approximated as an expanding cylin-der in an elastic space, from which a relationship betweenthe increase in normal interface stress and dilation can befound. This so-called constant normal stiffness,K, was de-fined by Johnston and Lam (1989) as a function of rockmass modulus,Em, Poisson’s ratio,ν, and pile radius,rs:

[13] KE

v r=

+m

s( )1

Clearly, greater socket roughness will result in larger dila-tion for any given pile settlement once sliding at the pile–rock interface has commenced. The CNS boundary condi-tion produces an increase in stress normal to the interfaceand a corresponding increase in the frictional resistance be-tween pile and rock. The change in normal stress,∆σn, is re-lated to the dilation of the concrete–rock interface,∆rs, asfollows:

[14] ∆ ∆σn s= K r

© 2001 NRC Canada


Fig. 4. Geometry of a single asperity. Fig. 5. Comparison of Monash University and Horvath roughnessdefinitions.



It should be noted that the stiffness,K, is inversely propor-tional to the pile radius,rs.

Therefore, for a given socket roughness, the beneficial ef-fect of the normal stress increase resulting from dilation isinversely proportional to the socket radius.

Consequently, the shaft resistance available for a pilesocket will be a function not of roughness alone, but ofroughness normalized against pile radius (or diameter). Thisis reflected in the Horvath roughness factor which is normal-ized against pile radius.

3.3. Rock mass elastic parametersAs noted in the previous section, socket roughness is re-

sponsible for causing socket dilation after slip has occurredat the pile–socket interface. The increase in normal stress atthe pile–socket interface is a linear function of the constantnormal stiffness,K, as shown in eq. [14]. Equation [13]shows thatK is a linear function of the rock mass modulus,Em, and is inversely related to (1 +ν), whereν is the Pois-son’s ratio of the surrounding rock.

The rock mass elastic parameters are not only responsiblefor deflection predictions, but also directly influence theavailable shaft resistance. Indeed, this was recognised byWilliams et al. (1980), who proposed a reduction factor toaccount for the reduction in rock mass modulus caused byfrequent discontinuities. Any method of shaft resistance esti-mation should therefore incorporate the rock mass modulusand Poisson’s ratio.

3.4. Rock strengthTo generate a complete load–settlement prediction for a

rock socket using ROCKET, both intact and residual rockstrength parameters are required. However, where only thepeak shaft resistance or adhesion factor is required, it maybe sufficient to characterise rock strength by the intactstrength alone. The unconfined compressive strength,qu, isthe most commonly available measure of rock strength andis incorporated in the proposed shaft resistance coefficientfor this reason.

3.5. Initial normal stressA normal stress is imposed on the sidewall of a rock

socket by the head of wet concrete as it is placed. Researchby Bernal and Reese (1983), Clear and Harrison (1985), andLings et al. (1994) indicates that, for sockets varying indepth from 5 to 30 m, a variation in normal stress from 50 to500 kPa could be anticipated. Only in the case of expansiveconcretes could substantially larger normal stresses be ex-pected. It is not possible to conveniently incorporate this“initial normal stress” in the proposed coefficient. However,it is noted that parametric studies using ROCKET haveshown that for most piles and anchors, the peak shaft resis-tance is not particularly sensitive to such variations in initialnormal stress.

3.6. Construction effectsResearch is currently being undertaken by the authors into

the effects of construction practices on pile socket shaft re-sistance. This research is expected to provide guidance ontypical values of socket roughness (as a function of drillingtools and rock type or strength) and on the effect of drillingfluids, smear, and remoulded rock on the available shaft re-sistance. The socket roughness recommendations will be in-corporated into the roughness component of the proposedcoefficient. The effect of drilling fluids, smear, andremoulding will be incorporated into a separate constructionmethod reduction factor,ηc. Indicative values forηc basedon the recommendations of Williams and Pells (1981),Holden (1984), O’Neill and Hassan (1994), Hassan andO’Neill (1997), and Cheng (1997) are shown in Table 3. Se-lection of a construction method reduction factor for a par-ticular project should be based on an understanding ofprevailing ground conditions, construction techniques, andthe level of supervision and quality assurance during con-struction. Guidelines for selection of appropriate construc-tion method reduction factors are currently being developed.

It will be shown that the construction method reductionfactor is applied to the SRC and will not always necessarily

© 2001 NRC Canada


Fig. 6. Pile rock socket idealization (after Johnston and Lam 1989).



have a proportional influence on the predicted shaft resis-tance.

4. The shaft resistance coefficient

The shaft resistance coefficient (SRC) is a nondimensionalparameter which incorporates all the important factors influ-encing shaft resistance. The formulation of the SRC is pro-posed as follows:

[15] SRC cs

=+

η nv

rd1∆

where

∆r is the mean roughness height (either assesseddirectly by estimation or measurement, orcomputed as the product of asperity length,la,and the sine of the mean asperity angle,θ );ds is the socket diameter;ηc is the construction method reduction factorand will be assumed as 1 for all further analysesin this paper (also see Table 3); andn is the ratio of rock mass modulus to theunconfined compressive strength of the rock(Em/qu), known as the modular ratio.

In a study of the deformation of shallow footings on rock,Hobbs (1974) suggested rock mass modular ratios variedfrom 50 to 200 and averaged 100 for many different soilsand rocks varying from normally consolidated clays, weath-ered and unweathered argillaceous rocks, and arenaceoussedimentary rocks, and covering a wide range of compres-sive strengths.

The similarities of the roughness component of the SRCto the roughness factor (RF, see eq. [8]) proposed byHorvath et al. (1983) are noted. The SRC factor, however,also incorporates other significant parameters that influenceshaft resistance, namely rock mass modulus and Poisson’sratio and intact rock strength. Of the list of influencing pa-rameters given in section 2, only the initial hydrostatic con-crete stress is not incorporated. However, as previouslynoted, this parameter only has a second-order influence onshaft resistance.

The significance of the SRC is demonstrated by referenceto the following two sets of parametric variations shown inFigs. 7 and 8.

Figure 7 shows the shear stress – displacement responsespredicted by ROCKET for an assumed 900 mm diameter

pile socketed into rock with an unconfined compressivestrength of 5.0 MPa and a modular ratio of 100. A meanroughness height of 6.56 mm has been assumed, giving

[16] SRC100

1 0.256.56900

1.0 0.583=+

=

For each of the analyses in ROCKET, however, the chordlength and corresponding asperity angle have been adjustedto maintain the roughness height of 6.56 mm, as given in Ta-ble 4.

All sockets, despite the varying roughness, have the sameSRC of 0.583 and develop a peak shear stress at the inter-face of approximately 760 kPa. This analysis suggests thatroughness height, rather than roughness angle, influencesavailable shaft resistance. Nevertheless, increasing the angleof the roughness significantly increases the stiffness of thesocket response. Evidently, if the socket has distinct grooves,the failure mechanism at the socket wall may be quite differ-ent to that assumed in this model. Further work is requiredto extend the Monash University approach to sockets withdistinct grooves.

Figure 8 shows the shear stress – displacement responsesfor 450 and 900 mm diameter piles socketed into rock withan unconfined compressive strength of 20 MPa and assumedmodular ratios of between 50 and 200. The mean roughnessangle has in this case been held constant at 5°; however, as-perity lengths have been adjusted accordingly fromla =20 mm to la = 80 mm depending on the particular diameterand modular ratio. For all sockets, the SRC is 0.311, and thepeak interface shear stress is approximately 2500 kPa.

These two analyses demonstrate that for any given SRCand uniaxial compressive strength (UCS) value, the shearstrength of a socket with any combination ofEm, ν, qu, ∆r,and ds will be constant (within normal engineering toler-ances).

© 2001 NRC Canada


Construction method ηc

Construction without drilling fluidBest practice construction and high level of construction control (e.g., socket sidewalls free of smear and remoulded rock) 1.0Poor construction practice or low-quality construction control (e.g., smear or remoulded rock present on socket sidewalls) 0.3–0.9Construction under bentonite slurryBest practice construction and high level of construction control 0.7–0.9Poor construction practice or low level of construction control 0.3–0.6Construction under polymer slurryBest practice construction and high level of construction control 0.9–1.0Poor construction practice or low level of construction control 0.8

Table 3. Indicative construction method reduction factorsηc.

Mean asperity angle,θ (°)

Chord length,la (mm)

5 75.37.5 50.310 37.812.5 30.315 25.3

Table 4. Chord lengths and mean asperity anglesused in ROCKET analysis for Fig. 7.



4.1. Shaft resistance design chartThe SRC has been incorporated in a shaft resistance chart

(Fig. 9) which allows preliminary estimation of peak shaftresistance for rock sockets in tension or compression over awide range of rock strengths. This is based on the results of

a parametric study using ROCKET. To develop this chart,intact rock strength parameters were related to unconfinedcompressive strength using the Hoek-Brown rock failure cri-terion (Hoek and Brown 1980). Mohr-Coulomb strength pa-rameters adopted in the analyses were determined after the

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Fig. 7. Peak shear resistance for shafts with varying roughness but constant shaft resistance coefficient (SRC) and uniaxial compressivestrength (UCS).

Fig. 8. Peak shear resistance for shafts with varying diameter, asperity length, and modular ratio but constant SRC.



method of Hoek (1990) using only the unconfined compres-sive strength of the rock and appropriate values of the pa-rameterss and m.

Figure 9 shows the predicted variation in adhesion factor,αq, with rock strength for SRC values ranging from 0.10 to2.1. This plot indicates a significant range of possible shaft

resistance for any given rock strength, dependent on the fac-tors that make up the SRC value.

In Fig. 10, the adhesion factor,αq, is plotted against SRCfor constant values of UCS. The data for all uniaxial com-pressive strengths greater than or equal to 3.0 MPa can beapproximated by a single line of best fit. As rock strength

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Fig. 9. Effect of SRC on socket adhesion factor.

Fig. 10. Socket adhesion factor versus SRC.



decreases from 3.0 MPa, the adhesion factor for any givenvalue of SRC increases. Figure 10 also shows a comparisonbetween the SRC design data and the roughness factor corre-lation developed by Horvath et al. (1983) which is given ineq. [9]. For this comparison, an approximate relationship be-tween the roughness factor and the SRC was evaluatedbased on measured roughness profiles taken from a numberof the rock sockets of Horvath et al. A modular ratio,n, of100 and a Poisson’s ratio of 0.25 were adopted. Adhesionfactors predicted by the SRC method for UCS greater than3.0 MPa follow a general trend similar to that of the rough-ness factor correlation.

It will be shown in subsequent sections that the adhesionfactors predicted using suitable input parameters with theSRC design charts are in good general agreement with therange of socket load tests observed in practice. The majorbenefit of the SRC is to allow the design engineer to accountfor the parameters which influence shaft resistance and toincorporate these in a realistic, rather than unnecessarilyconservative design.

It is anticipated that the SRC approach can be used in anyone of the following ways: (i) for preliminary design, inwhich only the peak shear resistance is required and sensi-tivity analyses can be conducted to assess the effect of dif-ferent design decisions or assumptions; (ii ) for strengthdesign of pile sockets in which base resistance is neglecteddue to concerns about base cleanliness; and (iii ) combinedwith an existing pile socket design method such as that ofWilliams et al. (1980) or Rowe and Armitage (1987). Theshaft adhesion determined using the SRC approach can besubstituted for the peak shaft resistance values otherwiseused in these methods.

5. Estimation of socket roughness

Application of the SRC method in preliminary design re-quires estimation of likely socket roughness height. Little at-tention has been given to socket roughness in most studiesof rock-socketed piles and case study reports of socket loadtests. Consequently, the available quantitative data on socketroughness are extremely limited.

5.1. Socket roughness dataWilliams and Pells (1981) carried out a study of bored

pile behaviour in low- to moderate-strength sandstone,mudstone, and shale. They reported that in the higherstrength rocks, the slower drilling rate necessary typicallyproduced a smooth socket wall. By contrast, in the softerrocks, in which the drilling rate increased and where jointingis often more frequent, sockets were generally rougher.Kulhawy and Phoon (1993) similarly reported that socketsdrilled in hard rock as well as in soils are generally quitesmooth, whereas roughness in sockets of intermediate-strength rock is more pronounced and variable.

A small number of studies have produced actual rough-ness profiles which enable quantitative analysis. Detailedstudies have been carried out into sockets in Melbournemudstone (Williams 1980; Holden 1984; Kodikara et al.1992; Baycan 1996). The results confirm that roughness inthis low- to medium-strength argillaceous rock can vary con-siderably and appears to be influenced by rock discontinu-

ities, drilling technique, and rate of advance. Roughness pro-files in medium-strength shale were also recorded byHorvath et al. (1983), but most of their sockets were artifi-cially roughened by grooving. Other measurements havebeen reported in clay shale, argillite, and sandstone byO’Neill and Hassan (1994) and O’Neill et al. (1995).

On the basis of the observations by Kulhawy and Phoon(1993), and roughness recommendations by Pells et al.(1980) and Kodikara et al. (1992), Seidel et al. (1996) con-cluded that at either end of the spectrum of geomaterialstrength, sockets generally exhibit minimal roughness,whereas in the intermediate portion of the spectrum socketroughness can be highly significant. They proposed the up-per- and lower-bound mean roughness heights which areshown numerically in Table 5 and graphically in Fig. 11.

The roughness bounds given in Table 5 were based onlimited quantitative data. Subsequent research at MonashUniversity has aimed to develop more substantive roughnessguidelines for use in design.

The authors have developed a broadly applicable rough-ness measurement tool. The Monash University socketprofiler, known as the Socket-Pro, is remotely operable andcan accurately record the sidewall roughness of sockets atdepths of up to 60 m (Collingwood et al. 1999). This equip-ment is being used in field investigations of socket rough-ness within Australia and overseas. In addition, historicalload test data have been reanalysed to produce a more com-prehensive socket roughness database. The latter study is de-scribed in subsequent sections.

5.2. Back-calculated socket roughnessAs previously discussed, few of the many load test results

published include direct information on socket roughness.Nevertheless, given a reported or computed socket adhesionfactor, αq or αc, and values or estimates of the parametersEm, ν, qu, andds, it is possible to infer the SRC and hencethe socket roughness height∆r from the following equation:

[17] ∆rv d

n= +( )1 SRC s

cη

Thus, a quantitative assessment of the socket roughness canbe inferred from existing load test results, for which socketroughness observations were not originally recorded.

In the case of a pile for which the concrete–rock interfaceis clean and unbonded (ηc = 1), evaluation of∆r by the SRC

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qu (MPa) hmin (mm) hmax (mm)

0.5 1.7 3.51 2.6 7.93 5.3 16.25 3.5 13.410 2.2 6.630 1.3 3.550 1.1 2.6100 0.9 2.2

Table 5. Proposed upper- and lower-bound meansocket roughness heightshmax and hmin (Seidel et al.1996).



method should provide a reasonable estimate of the magni-tude of socket roughness.

However, if the shaft resistance was adversely influencedby construction procedures,∆r would be underestimated ifηc was assumed to be 1. In this case the inferred roughnesscould be considered an effective roughness height,∆re. If anappropriate value ofηc were adopted, a true estimate ofroughness height∆r could be inferred.

6. Socket roughness database

As part of research into the effect of construction prac-tices on the capacity of rock-socketed piles at Monash Uni-versity, a load test database has been compiled. Unlikedatabases previously published by Williams and Pells(1981), Rowe and Armitage (1984), and Kulhawy and Phoon(1993) which are primarily concerned with shaft resistanceas a function of rock strength, the Monash University studyaims to consider the full range of parameters that affect shaftresistance. The database contains all available details of rockproperties, construction techniques, socket roughness (wheremeasured or observed), and cleanliness and load test resultsfor 162 records of load tests carried out worldwide. Not sur-prisingly, many of these have been included in previousstudies. Piles constructed in a variety of rock types are rep-resented, including shale, mudstone, sandstone, chalk, lime-stone, and schist. The database includes nine socketsconstructed under bentonite and 15 roughened sockets, butthe latter are not included in this study. These very importantconstruction practices have been the subject of further re-search at Monash University and will be addressed in subse-quent publications.

The development of the SRC design method has allowedthe reanalysis of these load tests, considering all the relevantparameters. Using the method detailed in section 5.2, the ef-fective roughness height apparent in each socket was back-calculated, and a database of inferred socket roughness hasbeen compiled.

6.1. Socket roughness versus rock strengthFigure 11 shows effective roughness heights back-

calculated from 133 load tests on rock-socketed piles androck anchors. Sockets of greater than 450 mm diameter havebeen categorised as piles, and sockets of smaller diameterare shown as rock anchors. It is important to note that thedata for rock anchors are not exclusive to this database.Most of the rock anchor data are derived from load tests thathave been included in previous database studies as rock-socketed piles.

Data points shown as triangles in Fig. 11 represent loadtests in which failure was not achieved. The effective rough-ness height in these sockets is therefore greater than or equalto the value plotted.

The roughness bounds proposed by Seidel et al. (1996)and given in Table 5 are shown in Fig. 11 as broken lines.Although many data points lie outside these bounds, they arein good agreement with the general distribution of data.

Revised upper- and lower-bound socket roughness guide-lines are proposed and shown as solid lines in Fig. 11. Theseare based on the data for pile sockets only. Although thedata for rock anchors follow the same general trend as thatfor piles, they appear to have a greater tendency to producevery smooth sockets. This is presumably due to the limitinginfluence of smaller diameter boreholes on roughness

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Fig. 11. Back-calculated effective roughness height for rock sockets (D ≥ 450 mm) and rock anchors (D < 450 mm).



production, and the type of equipment and drilling methodsused to construct anchors.

A number of data points lie well above the new upper-bound roughness envelope. In many of these cases, little de-tail is reported in relation to construction techniques and ge-ology. The most extreme outlier shown in Fig. 11 representsa socket in extensively jointed Silurian siltstone, which isdescribed in detail by Williams and Ervin (1980). The pre-vailing joint frequency of 10–100 joints per metre causedsignificant overbreak which was noted to have produced anextremely rough socket. For this socket, the parametersαq,Em, qu, and ds were carefully evaluated by Williams andErvin. The extremely high back-calculated mean roughnessheight obtained for this socket during this study demon-strates the ability of the SRC approach to isolate the contri-bution of a particular parameter to shaft response.

As previously mentioned, the roughness data shown inFig. 11 have been back-calculated using a constructionmethod reduction factor,ηc, of 1.0. Although sockets con-structed under bentonite have been eliminated from thisstudy, it was not possible to identify sockets which were af-fected by remoulded rock or geomaterial smear on thesocket sidewalls. Field observations suggest that smear iscommon in sockets drilled in low-strength argillaceous ma-terials and has been observed in some arenaceous forma-tions. It has been shown to have a detrimental effect on pileperformance (Pells et al. 1980; O’Neill and Hassan 1994;Baycan 1996). At present, however, the conditions whichlead to the production of smear are not more than generallyunderstood.

Data points representing two sockets in which smear wasobserved and was allowed to remain are shown in Fig. 11.

Both sockets exhibit effective roughness height which iswell below average for their UCS. It is reasonable to assumethat the results of a number of other load tests plotted, par-ticularly in rock of less than 10 MPa, have been similarly af-fected. Consequently, the lower-bound roughness curve inFig. 11 may reflect the performance of smeared sockets,rather than a representing a true lower bound to socketroughness levels.

It is the aim of the current research program at MonashUniversity to provide more detailed guidance to designers onappropriate socket roughness on the basis of constructionmethods and rock properties. Laser-based socket profilingequipment has been developed and is currently being used ina program of roughness measurement in the field. Future ex-pansion of the socket roughness database, based on actualmeasurements of socket roughness, is expected to allowidentification of the parameters which influence socketroughness and the development of more detailed guidelines.

6.2. Comparison with existing rock socket databasesOn the basis of the proposed upper- and lower-bound

roughness limits, upper- and lower-bound values of SRC canbe defined for the spectrum of rock strengths. In developingthese SRC limits, the following socket dimensions and pa-rameters have been adopted: (i) diameter 450–1500 mm,(ii ) modular ratio 50–200, (iii ) Poisson’s ratio 0.25, and(iv) construction method reduction factor 0.75–1.0 The up-per- and lower-bound SRC limits are shown graphically inFig. 12. Extreme upper and lower limits are shown based onbest- and worst-case combinations of the above parameters.Figure 12 also shows “effective” upper and lower SRC lim-its. These represent the 98% confidence limits for SRC

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Fig. 12. Upper- and lower-bound SRC limits for typical pile sockets.



values within the extreme upper and lower limits, based onan assumed normal distribution of all SRC values.

Using both the extreme and effective SRC limits and thedesign chart reproduced in Fig. 9, the variation of maximumand minimum shaft adhesion factor,αq, with UCS can becomputed. Figure 13 shows the expected range of socket ad-hesion factors for typical pile sockets. The individual piletest data used by Kulhawy and Phoon (1993) are also shownin Fig. 13, taking due account for the different definitions ofαq andαc. Note that Fig. 9 includes curves for SRC values ofup to 2.1. Where the upper limits of SRC are greater than2.1, the upper limits on the adhesion factor have been pre-dicted using ROCKET.

It is clear from Fig. 13 that the variations in SRC whichresult from typical values of socket roughness, pile diameter,modular ratio, and construction effects simulate the range ofsocket adhesion factors measured in practice.

7. Summary and conclusions

Current design practice for predicting the peak shear re-sistance of socketed piles is often based on empirical meth-ods which only take rock strength into account. Thesemethods may be reliable if site-specific correlations are de-veloped. Even so, their reliability may be questionable, be-cause they may not account for important variables that mayvary across a site such as pile diameter or rock jointing.

None of the empirical formulations based on rock strengthalone can satisfactorily estimate peak shear resistance overthe full spectrum of rock types and rock strengths becausethey exclude many variables that affect the shaft resistanceof rock sockets.

The design method proposed by Rowe and Armitage(1987) recommends that peak shear resistance is roughness

dependent. They propose a larger peak shear strength forclass R4 roughness sockets than for class R1–R3 sockets.Horvath et al. (1983) propose that the shaft resistance is afunction of the roughness factor, RF, raised to the power0.4. The derivation of RF has been discussed earlier. Socketroughness is an important factor governing peak shaft resis-tance; however, previous empirical methods which have in-corporated roughness as a factor have not enjoyed wide use.They have also excluded other factors that affect shaft resis-tance.

Research which has led to the development of amicromechanical simulation approach for pile socket behav-iour has confirmed that pile shaft resistance is a function ofthe following parameters: rock strength (drained intact andresidual strength parameters are used), socket roughness,rock mass modulus (and Poisson’s ratio), socket diameter,initial normal stress between concrete and rock prior to load-ing, and construction practices. These factors (with the ex-ception of the initial normal stress) have been incorporatedinto a nondimensional parameter called the shaft resistancecoefficient (SRC). Using the computer program ROCKET,design charts have been developed which relate socket adhe-sion factor to SRC and rock strength. These design chartsare in good agreement with international databases on pileshaft behaviour.

Design methods which estimate peak shaft resistancebased on rock strength alone predict a unique shaft resis-tance corresponding to any given rock strength. The methodby Rowe and Armitage (1987) allows two discrete values foreach rock strength, with a factor of 1.3 difference. Themethod of Horvath and Kenney (1979) and Horvath et al.(1983) allows a range of shaft resistances based on the mea-sured RF. For the range of RF values indicated by Horvathand Kenney and Horvath et al. for field sockets in their

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Fig. 13. Variation of predicted adhesion factors compared with data of Kulhawy and Phoon (1993).



studies (0.035–0.095), the predicted peak shaft resistanceswould vary by a factor of 1.6, based on the power law pro-posed. By contrast, empirical evidence from the large data-bases of socket tests is that peak shaft resistances vary by afactor of approximately 5 for any given rock strength. It hasbeen shown that the SRC method predicts a similar range ofpossible shaft resistances, based on realistic upper- andlower-bound input parameters.

The SRC provides designers with an opportunity to ex-plicitly take into account the parameters which most signifi-cantly influence peak shaft resistance. Of course, there is acorresponding responsibility to determine the appropriate in-put parameters. The SRC can be used directly in the prelimi-nary design stage as a tool which allows the sensitivity ofshaft adhesion to influencing factors to be determined. Alter-natively, it can be used directly in a socket capacity analysisbased on shaft resistance alone. The adhesion factor esti-mated using SRC can also be incorporated into other designmethods such as those by Williams et al. (1980) or Roweand Armitage (1987).

To apply SRC in design, a prediction of borehole rough-ness characteristics must be made. Roughness is primarilyinfluenced by rock strength and discontinuities, and the drill-ing technique used. The present understanding of boreholeroughness is insufficient to ensure accurate predictions canbe made on a site-specific basis. However, upper- and lower-bound limits for general site conditions and constructionmethods have been identified. These limits are consistentwith the quantitative data which are currently available. De-tailed measurements are being made by the authors as partof an ongoing research program. Designers are encouragedto measure socket roughness during socket constructionwherever possible.

The SRC approach has also been used to back-calculatesocket roughness for a database of 138 pile load tests re-ported in the literature. The inferred socket roughnesses arein good general agreement with the earlier recommendationsof Seidel et al. (1996), based on earlier work of Pells et al.(1980), Kodikara et al. (1992), and Kulhawy and Phoon(1993).

Further research is being undertaken by the authors toquantify the effects of construction practices on the shaft re-sistance of piles socketed into rock. More detailed guidanceon the effect of drilling slurries, geomaterial smear, bonding,and drill type will follow.

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Adhesion Factor for Rock Soketed Piles

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