Adhesion Factor for Rock Soketed Piles

138

A new socket roughness factor for prediction of rock socket shaft resistance J.P. Seidel and B. Collingwood

Abstract: Prediction of rock socket shaft resistance is a complex problem. Conventional methods for predicting the Abstract: peak shaft resistance are typically empirically related to unconfined compressive strength through the results of pile load tests. It is shown by reference to international pile socket databases that the degree of confidence which can be applied to these empirical methods is relatively low. Research at Monash University has been directed at understanding and then modelling the complex mechanisms of shear transfer at the interface between the socketed piles and the surrounding rock. Important factors that affect the strength of pile sockets have been identified in laboratory and numerical studies. With a knowledge of the effect of these factors, the reasons for the large scatter around traditional empirical correlations can be deduced. A computer program called ROCKET has been developed which encompasses all aspects of the Monash University rock socket research. This program has been used to develop design charts for rock-socketed piles based on unconfined compressive strength and a nondimensional factor which has been designated the shaft resistance coefficient (SRC). Implementation of the SRC method in design requires an estimate of the likely socket roughness to be made. Very few researchers or practitioners have measured socket roughness, so there is little available guidance in selection of appropriate values. Although many socket load tests are described in the technical literature, the physical parameter which is regularly missing is the socket roughness. With a knowledge of the shaft resistance, and an estimate of all other relevant parameters, the authors have been able to back-calculate the apparent socket roughness using the SRC method. Based on the back-calculated roughness data, socket roughness guidelines for use in analysis and design of rock sockets have been proposed. Using these roughness guidelines, it is shown that the SRC method 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 méthodes conventionnelles pour prédire la résistance de pic du fût sont typiquement reliées empiriquement à la résistance en compression simple par l’intermédiaire des résultats d’essais de chargement sur pieu. Il est démontré en se référant aux bases de données internationales de pieux encastrés que le degré de confiance que l’on peut accorder à ces méthodes empiriques est relativement faible. La recherche au Monash University a été dirigée vers la compréhension et ensuite la modélisation des mécanismes complexes du transfert de cisaillement à l’interface entre les pieux encastrés et le roc environnant. Les facteurs importants qui affectent la résistance des pieux encastrés ont été identifiés en laboratoire et par des études numériques. Avec une connaissance de l’effet de ces facteurs, les raisons pour cette grande dispersion dans les corrélations empiriques traditionnelles peuvent être déduites. Un programme d’ordinateur appelé ROCKET a été développé comprenant tous les aspects de la recherche de Monash sur l’encastrement dans le roc. Ce programme a été utilisé pour développer des abaques de calcul pour les pieux encastrés basées sur la résistance en compression simple et sur un facteur non dimensionnel qui a été appelé le coefficient de résistance du fût, SRC. La mise en application de la méthode SRC dans la conception requiert une estimation de la rugosité probable de l’encastrement à réaliser. Très peu de chercheurs ou de praticiens ont mesuré la rugosité de l’encastrement, de sorte qu’il y a peu de règles de conduite disponibles pour la sélection des valeurs appropriées. Quoique plusieurs essais de chargement d’encastrement sont décrits dans la littérature technique, le paramètre physique qui est régulièrement manquant est la rugosité de l’encastrement. Avec la connaissance de la résistance du fût et une estimation des autres paramètres pertinents, les auteurs ont pu calculer à rebours la rugosité apparente de l’encastrement en utilisant la méthode SRC. Basées sur les données de rugosité calculées à rebours, des règles pour la rugosité de l’encastrement ont été proposées pour l’analyse et la conception des encastrements dans le roc. En utilisant ces règles de rugosité, on montre que la méthode SRC peut prédire 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

Received April 29, 1999. Accepted August 17, 2000. Published on the NRC Research Press Web site on February 20, 2001. J.P. Seidel and B. Collingwood. Department of Civil Engineering, Monash University, Melbourne, Australia. Can. Geotech. J. 38: 138–153 138–153 (2001)

153

1. Introduction The use of large-diameter socketed piles to carry high and concentrated loads is widespread internationally. The design of such piles socketed into rock is traditionally based on local knowledge derived from observation of full-scale static

DOI: 10.1139/cgj-38-1-138

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load tests, empirical factors related to the unconfined com pressive strength of intact rock, or conservative city or state ordinances (Seidel and Haberfield 1994). However, it is a truism, confirmed by Osterberg (1998) on the basis of numerous static load tests on rock sockets, that the design of this type of pile is generally overconservative, by as much as an order of magnitude. Rock-socketed piles may be designed to carry their load by shaft resistance only, by base resistance only, or by both shaft and base resistances. There are significant advantages in the design of piles which carry their load by both shaft and base resistances. However, utilisation of the base resistance component requires a construc tion and inspection technique which guarantees the cleanliness of the pile base. This may be difficult and expensive to achieve, particularly for sockets in weak rock, deep sockets in general, or sockets which cannot be readily or safely inspected. In addition, because shaft resistance is gen erally mobilised at significantly smaller displacements than base resistance, piles typically carry most of their working load in shaft resistance. As a consequence, there is a particular design interest in shaft resistance. This paper will focus only on the shaft resistance component of pile socket capacity.

Table 1. Empirical factors for shaft resistance design.

1.1. The empirical basis of shaft resistance design Empirical correlations between uniaxial compressive strength of weak rock and unit shaft resistance of socketed piles measured in load tests have been proposed by many researchers. The form of these empirical correlations can be generalized as

R4

[1]

f su =

α quβ

Design method

α

β

Horvath and Kenney 1979 Carter and Kulhawy 1988 Williams et al. 1980 Rowe and Armitage 1984 Rosenberg and Journeaux 1976 Reynolds and Kaderbeck 1980 Gupton and Logan 1984 Reese and O’Neill 1988 Toh et al. 1989

0.21 0.20 0.44 0.40 0.34 0.30 0.20 0.15 0.25

0.50 0.50 0.36 0.57 0.51 1.00 1.00 1.00 1.00

Table 2. Shaft roughness classifications (after Pells et al. 1980). Roughness class R1

f su is the ultimate socket shaft resistance; q u is the uniaxial compressive strength of the weaker material (rock or concrete); and α and β are factors determined empirically from load tests.

The empirical factors proposed by a number of researchers have been summarised by O’Neill et al. (1995) and are shown in Table 1. Most of these empirical relationships were developed for specific and limited data sets, which may have correlated well with the proposed equations. However, O’Neill et al. (1995) compared the nine empirical shaft resistance design methods listed in Table 1 with an international database of 137 pile load tests in intermediate-strength rock. O’Neill et al. concluded that none of the methods could be considered a satisfactory predictor for the database. Two other significant database studies on the shaft resistance of piles socketed into rock have been conducted by Rowe and Armitage (1984) and Kulhawy and Phoon (1993) and will be summarised hereafter. These studies included pile sockets drilled with different equipment at many sites and in a range of rock types.

1.2. Significant database studies of shaft resistance Rowe and Armitage (1984) undertook a comprehensive review of correlations between strength, qu, and the adhesion

Straight, smooth-sided socket; grooves or indentations less than 1 mm deep Grooves 1–4 mm deep, >2 mm wide, spacing 50– 200 mm Grooves 4–10 mm deep, >5 mm wide, spacing 50–200 mm Grooves or undulations >10 mm deep, >10 mm wide, spacing 50–200 mm

R2 R3

factor, α. For the purpose of clarity in this paper, the adhesion factor, αq, is defined as follows [2]

where

Description

αq =

f su qu

Equations [1] and [2] can then be combined and rewritten as [3]

αq

=

α quβ – 1

Rowe and Armitage (1984) separated their data into those tests with roughness classes R1–R3 and tests on sockets with roughness R4, as defined in Table 2 (after Pells et al. 1980). The data included sockets loaded both in tension and compression. Figure 1 shows the data of Rowe and Armitage for class R1 to R3 roughness for sockets of all diameters. They also plotted data for sockets with class R4 roughness and for sockets greater than 350 mm in diameter, which was chosen as an arbitrary limit separating small and large sockets. Rowe and Armitage (1987) do not distinguish between the available side shear resistance of small- and large-diameter sockets. It is evident from Fig. 1 that there is wide scatter in the computed adhesion factors. Reasonable upper- and lowerbound limits suggest a possible factor of 5 variation in αq for any value of qu. Some of this difference may be attributable to the database including both sockets in tension and compression. Nevertheless, Rowe and Armitage (1984) superimposed the empirical relationships of Williams et al. (1980) and Horvath (1982) on the data and undertook a linear regression to determine a best-fit correlation for R1 to R3 roughness (all sockets) as follows: [4]

αq

= 0.4q u–0.43 © 2001 NRC Canada

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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 database for R4 roughness was very limited, but the interpreted adhesions were generally higher than those for R1 or R3 roughness. The following correlation was proposed by Rowe and Armitage (1984) for R4 roughness (all sockets): [5]

αq

= 0.55q u –0.389

Kulhawy and Phoon (1993) evaluated the unit shaft resistance for 127 load tests in soil and 114 load tests in rock covering 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 data set included sockets in both soil and rock, they elected to define their adhesion factor, α, in relation to undrained shear strength, cu, rather than unconfined compressive strength, qu. This paper defines this adhesion factor as αc, i.e., [6]

αc =

f su cu

= 2α q

The data of Kulhawy and Phoon are plotted as adhesion factor, αc, versus normalized shear strength, defined as either cu / pa or qu /2 pa, where pa is the atmospheric pressure (approximated as 100 kPa). Kulhawy and Phoon (1993) presented their data both for individual pile tests and as site-averaged data. The latter presentation is shown in Fig. 2. Despite being site-averaged, the data still exhibit significant scatter, particularly for the sockets in rock. Nevertheless, significant trend lines were inter-

preted by Kulhawy and Phoon, and these are superimposed on the data. The authors explained the trend lines by noting that sockets in soil are generally very smooth, whereas sockets in rock exhibit larger variations in roughness. On the basis of the load test data, Kulhawy and Phoon proposed the following general equations for sockets in soil and rock: − 0.5

[7]

  α c = ψ  q u   2 pa 

Kulhawy and Phoon proposed the factor ψ to be 0.5 for piles in soil and to vary between 1.0 and 3.0 (average 2.0) for pile shafts in rock. The site-averaged data suggest variations in interpreted adhesion factor for rock sockets of at least a factor of 3 and as much as 5. For the individual pile test data presented by Kulhawy and Phoon (1993) (shown later in Fig. 13), variations of up to an order of magnitude are observed, as in the study 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 variations in adhesion factor are possible. Design based entirely on empirical correlations with rock strength should therefore be very conservative unless site-specific correlations are developed which validate a more optimistic approach. © 2001 NRC Canada


141

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

The wide scatter of adhesion values observed in correlations with unconfined compressive strength of rock suggests that there are other factors which significantly influence the shaft resistance achieved. If design is based on rock strength alone, without any opportunity to take these other factors into account, then a conservative design approach must be taken. Any other approach would risk an unsafe design. By contrast, if the design approach incorporates these other factors, a less conservative and hence more cost efficient design should result.

1.3. Socket roughness One of the physical factors which has a significant influence on shaft resistance is socket roughness. The importance of socket roughness to shaft resistance has been well recognised by a number of researchers (e.g., Pells et al. 1980; Rowe and Armitage 1984; Johnston 1977; Horvath and Kenney 1979; Williams 1980; Johnston and Lam 1989). In all three database studies discussed, the effect of socket roughness on shaft resistance has been noted by the authors. The roughness classes of Pells et al. (1980) shown in Table 2 were based on observation of sockets drilled using various techniques in Sydney sandstone. Although subjective, this classification system has proven useful in practice for broadly categorising socket conditions in the field. However, it cannot adequately characterise the full range of roughness types which may be prevalent. Therefore, the roughness classes of Pells et al. are unlikely to form the basis of a universally satisfactory system of socket categorisation for design purposes. Nevertheless, it is noted that they do form the basis for current practice in Sydney, Australia, and are incorporated into the design method by Rowe and Armitage (1987). Significant research into the influence of socket roughness was reported by Williams (1980) and Johnston and Lam (1989). Williams recorded socket roughness profiles and de-

veloped statistical parameters for their description, and Johnston and Lam used interface roughness as a key parameter affecting normal stress in their constant normal stiffness direct shear tests. The work of Johnston and Lam underlies the fundamental approach used in the authors’ research. The research of Horvath and Kenney (1979) and Horvath et al. (1983) into the effect of socket grooving on the shaft resistance in Queenston shale was particularly significant, since it led to a proposed method to quantitatively incorporate socket roughness into socket design. On the basis of this work, Horvath et al. proposed a roughness factor, RF, which was determined as a function of socket length, Ls, socket radius, r s, mean roughness height, r h, and the traversed length of the socket, Lt, as follows: [8]

RF

=

∆ r h L t r s L s

In addition, they proposed an empirical equation for shaft resistance based on socket roughness: [9]

qs

σ cw

=

0.8(RF) 0.45

where qs is the shaft resistance, and σcw is the unconfined compressive strength of the rock or the concrete shaft, whichever is smaller. The two quotients in eq. [8] which are multiplied to determine the roughness factor are both measures of roughness in their own right. The first quotient is the roughness of the socket wall normalized by the socket radius. The second quotient is the basis for determination of another roughness parameter, the fractal dimension, by the so-called compass stepping method (Mandelbrot 1977). Horvath et al. (1983) possibly introduced both parts of the roughness factor to © 2001 NRC Canada

142


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

account for the difference in socket groove shapes, which was 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 socket roughness into design, the majority of socket design is still done in the absence of any consideration of this factor. This is possibly for two reasons: ( i) the incorporation of socket roughness is, of itself, insufficient to significantly improve the prediction of shaft resistance; and ( ii) the reliable measurement of socket roughness is not necessarily trivial, and hence is not undertaken in routine design.

2. The factors influencing rock socket behaviour A large fundamental research program into the behaviour of rock-socketed piles has been conducted at Monash University for many years. This program has been based on observation of large-scale direct shear tests, which simulate the concrete–rock interface. These laboratory tests have led to the development of analytical techniques which simulate the observed interface behaviour. Some of the important processes simultaneously occurring at the interface which are modelled include sliding on irregular surfaces, progressive shearing of overstressed asperities, elastic redistribution of stresses, and the shear behaviour of failed asperities. The analytical techniques have been modified to account for the differences in boundary conditions between shear box tests and rock sockets (Seidel 1993; Seidel and Haberfield 1994, 1995b). The research results have been incorporated in a computer software program called ROCKET for design of rocksocketed piles in compression or tension. This program has been validated against full-scale socket load tests. Using ROCKET, it is possible to estimate the complete pile-top load–displacement behaviour of a pile socketed into single or multilayered rock strata. Calibration of the model is not required, as the approach is theoretically, not empirically based. It is common practice in the design of piles in soil to reduce the computed shaft capacity by between 20 and 50% for tension loading. Although ROCKET does not differentiate between compression and tension loading, the engineer may wish to impose such a reduction factor on the computed results. For short sockets in jointed rock, failure modes other than shear at the pile–rock interface may be more critical and also need to be investigated. Research at Monash University has confirmed the findings of others which show that pile shaft resistance is influenced by the following parameters: ( i) rock strength (drained intact and residual strength parameters are generally used), (ii) socket roughness, (iii) rock mass modulus (and Poisson’s ratio), (iv) socket diameter, ( v) initial normal stress between

concrete and rock prior to loading; and ( vi) construction practices. These parameters influence the shaft resistance of a rock-socketed pile and should therefore be taken into account in the pile design process. The interaction of these factors in determining the performance of socketed piles has been previously recognized (e.g., Rowe and Armitage 1984); however, the complexity of this interaction has been difficult to implement reliably using empirical methods.

3. Elements of a new shaft resistance factor In the preliminary stages of rock-socketed pile design, it is rarely necessary to predict a full load–displacement pile response. Estimation of ultimate pile capacity is usually sufficient at this stage. The authors have developed simple charts based on a nondimensional parameter known as the shaft resistance coefficient (SRC). The SRC, which is defined in section 4, accounts for the most critical factors influencing rock socket shaft resistance. It is incorporated into a new method of estimating ultimate shaft resistance which offers an alternative to empirical formulae. The SRC approach is based on a parametric study using the ROCKET computer program. The elements which make up the SRC are outlined in the following sections.

3.1. The Monash socket roughness model The Monash University approach to predicting rocksocket behaviour is based on idealizing rough rock surfaces as a series of interconnected chords of a constant length (Seidel and Haberfield 1995 a). Consider a joint profile of unit length. The profile can be characterised by N line segments or chords of a constant length, la, as shown Fig. 3. The slope of each chord relative to the mean orientation of the profile can be determined and a frequency distribution of chord angles produced. It is assumed that the distribution of chord angles, θ, is Gaussian with a mean, µθ, and standard deviation, sθ. If the profile is oriented such that the line joining the two end points is horizontal, the mean, µθ, will equal zero. The standard deviation of chord angles, sθ, is then a statistical measure of roughness at the scale dictated by the chosen chord length, la. The asperity heights, ha, will vary with a distribution which can be approximated as Gaussian for reasonable socket roughnesses (Seidel 1993). Referring to the geometry of a single chord shown in Fig. 4, the standard deviation of asperity height, sh, is given by [10]

sh = la sin( sθ)

Consequently, the height and angle statistics are directly related and cannot be considered independent variables, as has been assumed previously by some researchers. Collingwood (2000) has shown by detailed analysis of sockets for which © 2001 NRC Canada

Seidel and Collingwood Fig. 4. Geometry of a single asperity.

143 Fig. 5. Comparison of Monash University and Horvath roughness definitions.

accurate roughness profiles are available that the assumption of a Gaussian roughness distribution is reasonable for normally drilled sockets and some roughened sockets but inappropriate for most sockets with distinctive grooving. As the distribution of asperity angles is assumed Gaussian, the mean absolute asperity angle may be calculated from the standard deviation of asperity angles as [11]

θ =

2

π

sθ

Then by once again considering the relationship between asperity angle and asperity height, as illustrated in Fig. 4, the mean of absolute asperity heights, ha, can also be calculated as [12]

ha

= l a sin ( θ ) = ∆r

The mean absolute asperity height represents the mean scalar height of all asperities. For simplicity, the mean absolute asperity height is hereafter referred to as the mean roughness height and is denoted by the symbol ∆r . By contrast, the mean roughness height used by Horvath et al. (1983) is defined as the mean of the “distances from the socket profiles to the surface of the largest imaginary cylinder which would fit into the socket.” It should be noted that, as illustrated in Fig. 5, this is fundamentally different from the Monash University definition of mean roughness height, and the two are not interchangeable. The Monash University roughness model has also been extended using the concepts of fractal geometry to relate roughness statistics at different scales (Seidel and Haberfield 1995a). However, such aspects of the model are beyond the scope of this paper.

3.2. Roughness and the constant normal surface boundary condition The following analysis is based on the assumption that the preferred mechanism for failure at the concrete–rock interface is initially by slip rather than shear through the intact rock or concrete. In cases where asperity angles are very large (e.g., grooved sockets) or where direct bonding across the interface is dominant, this assumption may not be valid. However, direct bonding can often be compromised by smearing of the socket wall, and in most cases it is believed that the following analysis will be valid. The beneficial effect of socket roughness is a combined consequence of the dilational nature of a rough concrete–

rock joint and the constant normal stiffness (CNS) boundary condition 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 the rock against which it was cast. Loading of the pile will initially result in elastic movements of the mated pile–rock system, and no relative movement at the concrete–rock interface. At a critical axial load, the pile will undergo slip relative to the rock. Due to the rough socket surface, compatibility requires that this slip be accompanied by dilation at the interface. This is resisted by the surrounding rock by increasing the normal stress at the interface. The dilation of the socket interface can be approximated as an expanding cylinder in an elastic space, from which a relationship between the increase in normal interface stress and dilation can be found. This so-called constant normal stiffness, K , was defined by Johnston and Lam (1989) as a function of rock mass modulus, E m, Poisson’s ratio, ν, and pile radius, r s: [13]

K =

E m

(1 + v) r s

Clearly, greater socket roughness will result in larger dilation for any given pile settlement once sliding at the pile– rock interface has commenced. The CNS boundary condition produces an increase in stress normal to the interface and a corresponding increase in the frictional resistance between pile and rock. The change in normal stress, ∆σn, is related to the dilation of the concrete–rock interface, ∆r s, as follows: [14]

∆σ n =

K ∆ r s © 2001 NRC Canada

144


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

It should be noted that the stiffness, K , is inversely proportional to the pile radius, r s. Therefore, for a given socket roughness, the beneficial effect of the normal stress increase resulting from dilation is inversely proportional to the socket radius. Consequently, the shaft resistance available for a pile socket will be a function not of roughness alone, but of roughness normalized against pile radius (or diameter). This is reflected in the Horvath roughness factor which is normalized against pile radius.

3.3. Rock mass elastic parameters As noted in the previous section, socket roughness is responsible for causing socket dilation after slip has occurred at the pile–socket interface. The increase in normal stress at the pile–socket interface is a linear function of the constant normal stiffness, K , as shown in eq. [14]. Equation [13] shows that K is a linear function of the rock mass modulus, E m, and is inversely related to (1 + ν), where ν is the Poisson’s ratio of the surrounding rock. The rock mass elastic parameters are not only responsible for deflection predictions, but also directly influence the available shaft resistance. Indeed, this was recognised by Williams et al. (1980), who proposed a reduction factor to account for the reduction in rock mass modulus caused by frequent discontinuities. Any method of shaft resistance estimation should therefore incorporate the rock mass modulus and Poisson’s ratio. 3.4. Rock strength To generate a complete load–settlement prediction for a rock socket using ROCKET, both intact and residual rock strength parameters are required. However, where only the peak shaft resistance or adhesion factor is required, it may be sufficient to characterise rock strength by the intact strength alone. The unconfined compressive strength, qu, is the most commonly available measure of rock strength and is incorporated in the proposed shaft resistance coefficient for this reason.

3.5. Initial normal stress A normal stress is imposed on the sidewall of a rock socket by the head of wet concrete as it is placed. Research by Bernal and Reese (1983), Clear and Harrison (1985), and Lings et al. (1994) indicates that, for sockets varying in depth from 5 to 30 m, a variation in normal stress from 50 to 500 kPa could be anticipated. Only in the case of expansive concretes could substantially larger normal stresses be expected. It is not possible to conveniently incorporate this “initial normal stress” in the proposed coefficient. However, it is noted that parametric studies using ROCKET have shown that for most piles and anchors, the peak shaft resistance is not particularly sensitive to such variations in initial normal stress. 3.6. Construction effects Research is currently being undertaken by the authors into the effects of construction practices on pile socket shaft resistance. This research is expected to provide guidance on typical values of socket roughness (as a function of drilling tools and rock type or strength) and on the effect of drilling fluids, smear, and remoulded rock on the available shaft resistance. The socket roughness recommendations will be incorporated into the roughness component of the proposed coefficient. The effect of drilling fluids, smear, and remoulding will be incorporated into a separate construction method reduction factor, ηc. Indicative values for ηc based on the recommendations of Williams and Pells (1981), Holden (1984), O’Neill and Hassan (1994), Hassan and O’Neill (1997), and Cheng (1997) are shown in Table 3. Selection of a construction method reduction factor for a particular project should be based on an understanding of prevailing ground conditions, construction techniques, and the level of supervision and quality assurance during construction. Guidelines for selection of appropriate construction method reduction factors are currently being developed. It will be shown that the construction method reduction factor is applied to the SRC and will not always necessarily © 2001 NRC Canada


145

Table 3. Indicative construction method reduction factors

ηc. ηc

Construction method Construction without drilling fluid Best practice construction and high level of construction control (e.g., socket sidewalls free of smear and remoulded rock) Poor construction practice or low-quality construction control (e.g., smear or remoulded rock present on socket sidewalls) Construction under bentonite slurry Best practice construction and high level of construction control Poor construction practice or low level of construction control Construction under polymer slurry Best practice construction and high level of construction control Poor construction practice or low level of construction control

1.0 0.3–0.9 0.7–0.9 0.3–0.6 0.9–1.0 0.8

have a proportional influence on the predicted shaft resistance.

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

4. The shaft resistance coefficient

Mean asperity angle, θ (°)

Chord length, la (mm)

5 7.5 10 12.5 15

75.3 50.3 37.8 30.3 25.3

The shaft resistance coefficient (SRC) is a nondimensional parameter which incorporates all the important factors influencing shaft resistance. The formulation of the SRC is proposed as follows: [15]

SRC

= ηc

n

∆r

1 + v d s

where

∆ r is the mean roughness height (either assessed directly by estimation or measurement, or computed as the product of asperity length, l a, and the sine of the mean asperity angle, θ ); d s is the socket diameter; ηc is the construction method reduction factor and will be assumed as 1 for all further analyses in this paper (also see Table 3); and n is the ratio of rock mass modulus to the unconfined compressive strength of the rock ( E m / q u), known as the modular ratio. In a study of the deformation of shallow footings on rock, Hobbs (1974) suggested rock mass modular ratios varied from 50 to 200 and averaged 100 for many different soils and rocks varying from normally consolidated clays, weathered and unweathered argillaceous rocks, and arenaceous sedimentary rocks, and covering a wide range of compressive strengths. The similarities of the roughness component of the SRC to the roughness factor (RF, see eq. [8]) proposed by Horvath et al. (1983) are noted. The SRC factor, however, also incorporates other significant parameters that influence shaft resistance, namely rock mass modulus and Poisson’s ratio and intact rock strength. Of the list of influencing parameters given in section 2, only the initial hydrostatic concrete stress is not incorporated. However, as previously noted, this parameter only has a second-order influence on shaft resistance. The significance of the SRC is demonstrated by reference to the following two sets of parametric variations shown in Figs. 7 and 8. Figure 7 shows the shear stress – displacement responses predicted by ROCKET for an assumed 900 mm diameter

pile socketed into rock with an unconfined compressive strength of 5.0 MPa and a modular ratio of 100. A mean roughness height of 6.56 mm has been assumed, giving [16]

SRC

=

100

6.56

1 + 0.25 900

1.0

= 0.583

For each of the analyses in ROCKET, however, the chord length and corresponding asperity angle have been adjusted to maintain the roughness height of 6.56 mm, as given in Table 4. All sockets, despite the varying roughness, have the same SRC of 0.583 and develop a peak shear stress at the interface of approximately 760 kPa. This analysis suggests that roughness height, rather than roughness angle, influences available shaft resistance. Nevertheless, increasing the angle of the roughness significantly increases the stiffness of the socket response. Evidently, if the socket has distinct grooves, the failure mechanism at the socket wall may be quite different to that assumed in this model. Further work is required to extend the Monash University approach to sockets with distinct grooves. Figure 8 shows the shear stress – displacement responses for 450 and 900 mm diameter piles socketed into rock with an unconfined compressive strength of 20 MPa and assumed modular ratios of between 50 and 200. The mean roughness angle has in this case been held constant at 5°; however, asperity lengths have been adjusted accordingly from la = 20 mm to la = 80 mm depending on the particular diameter and modular ratio. For all sockets, the SRC is 0.311, and the peak interface shear stress is approximately 2500 kPa. These two analyses demonstrate that for any given SRC and uniaxial compressive strength (UCS) value, the shear strength of a socket with any combination of E m, ν, qu, ∆r , and d s will be constant (within normal engineering tolerances). © 2001 NRC Canada

146


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

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

4.1. Shaft resistance design chart The SRC has been incorporated in a shaft resistance chart (Fig. 9) which allows preliminary estimation of peak shaft resistance for rock sockets in tension or compression over a wide 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 unconfined compressive strength using the Hoek-Brown rock failure criterion (Hoek and Brown 1980). Mohr-Coulomb strength pa rameters adopted in the analyses were determined after the © 2001 NRC Canada


147

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

Fig. 10. Socket adhesion factor versus SRC.

method of Hoek (1990) using only the unconfined compressive strength of the rock and appropriate values of the parameters s and m. Figure 9 shows the predicted variation in adhesion factor, αq, with rock strength for SRC values ranging from 0.10 to 2.1. This plot indicates a significant range of possible shaft

resistance for any given rock strength, dependent on the factors that make up the SRC value. In Fig. 10, the adhesion factor, αq, is plotted against SRC for constant values of UCS. The data for all uniaxial compressive strengths greater than or equal to 3.0 MPa can be approximated by a single line of best fit. As rock strength © 2001 NRC Canada

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decreases from 3.0 MPa, the adhesion factor for any given value of SRC increases. Figure 10 also shows a comparison between the SRC design data and the roughness factor correlation developed by Horvath et al. (1983) which is given in eq. [9]. For this comparison, an approximate relationship between the roughness factor and the SRC was evaluated based on measured roughness profiles taken from a number of the rock sockets of Horvath et al. A modular ratio, n, of 100 and a Poisson’s ratio of 0.25 were adopted. Adhesion factors predicted by the SRC method for UCS greater than 3.0 MPa follow a general trend similar to that of the roughness factor correlation. It will be shown in subsequent sections that the adhesion factors predicted using suitable input parameters with the SRC design charts are in good general agreement with the range of socket load tests observed in practice. The major benefit of the SRC is to allow the design engineer to account for the parameters which influence shaft resistance and to incorporate these in a realistic, rather than unnecessarily conservative design. It is anticipated that the SRC approach can be used in any one of the following ways: ( i) for preliminary design, in which only the peak shear resistance is required and sensitivity analyses can be conducted to assess the effect of different design decisions or assumptions; ( ii) for strength design of pile sockets in which base resistance is neglected due to concerns about base cleanliness; and ( iii) combined with an existing pile socket design method such as that of Williams et al. (1980) or Rowe and Armitage (1987). The shaft adhesion determined using the SRC approach can be substituted for the peak shaft resistance values otherwise used in these methods.

5. Estimation of socket roughness Application of the SRC method in preliminary design requires estimation of likely socket roughness height. Little attention has been given to socket roughness in most studies of rock-socketed piles and case study reports of socket load tests. Consequently, the available quantitative data on socket roughness are extremely limited.

5.1. Socket roughness data Williams 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 higher strength rocks, the slower drilling rate necessary typically produced a smooth socket wall. By contrast, in the softer rocks, in which the drilling rate increased and where jointing is often more frequent, sockets were generally rougher. Kulhawy and Phoon (1993) similarly reported that sockets drilled in hard rock as well as in soils are generally quite smooth, whereas roughness in sockets of intermediatestrength rock is more pronounced and variable. A small number of studies have produced actual roughness profiles which enable quantitative analysis. Detailed studies have been carried out into sockets in Melbourne mudstone (Williams 1980; Holden 1984; Kodikara et al. 1992; Baycan 1996). The results confirm that roughness in this low- to medium-strength argillaceous rock can vary considerably and appears to be influenced by rock discontinu-

Can. Geotech. J. Vol. 38, 2001 Table 5. Proposed upper- and lower-bound mean socket roughness heights hmax and hmin (Seidel et al. 1996). qu (MPa)

hmin (mm)

hmax (mm)

0.5 1 3 5 10 30 50 100

1.7 2.6 5.3 3.5 2.2 1.3 1.1 0.9

3.5 7.9 16.2 13.4 6.6 3.5 2.6 2.2

ities, drilling technique, and rate of advance. Roughness profiles in medium-strength shale were also recorded by Horvath et al. (1983), but most of their sockets were artificially roughened by grooving. Other measurements have been reported in clay shale, argillite, and sandstone by O’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) concluded that at either end of the spectrum of geomaterial strength, sockets generally exhibit minimal roughness, whereas in the intermediate portion of the spectrum socket roughness can be highly significant. They proposed the upper- and lower-bound mean roughness heights which are shown numerically in Table 5 and graphically in Fig. 11. The roughness bounds given in Table 5 were based on limited quantitative data. Subsequent research at Monash University has aimed to develop more substantive roughness guidelines for use in design. The authors have developed a broadly applicable roughness measurement tool. The Monash University socket profiler, known as the Socket-Pro, is remotely operable and can accurately record the sidewall roughness of sockets at depths of up to 60 m (Collingwood et al. 1999). This equipment is being used in field investigations of socket roughness within Australia and overseas. In addition, historical load test data have been reanalysed to produce a more comprehensive socket roughness database. The latter study is described in subsequent sections.

5.2. Back-calculated socket roughness As previously discussed, few of the many load test results published include direct information on socket roughness. Nevertheless, given a reported or computed socket adhesion factor, αq or αc, and values or estimates of the parameters E m, ν, qu, and d s, it is possible to infer the SRC and hence the socket roughness height ∆r from the following equation: [17]

∆r = (1 + v) SRC d s η cn

Thus, a quantitative assessment of the socket roughness can be inferred from existing load test results, for which socket roughness observations were not originally recorded. In the case of a pile for which the concrete–rock interface is clean and unbonded ( ηc = 1), evaluation of ∆ r by the SRC © 2001 NRC Canada


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Fig. 11. Back-calculated effective roughness height for rock sockets ( D

method should provide a reasonable estimate of the magnitude of socket roughness. However, if the shaft resistance was adversely influenced by construction procedures, ∆r would be underestimated if ηc was assumed to be 1. In this case the inferred roughness could be considered an effective roughness height, ∆r e. If an appropriate value of ηc were adopted, a true estimate of roughness height ∆r could be inferred.

6. Socket roughness database As part of research into the effect of construction practices on the capacity of rock-socketed piles at Monash University, a load test database has been compiled. Unlike databases previously published by Williams and Pells (1981), Rowe and Armitage (1984), and Kulhawy and Phoon (1993) which are primarily concerned with shaft resistance as a function of rock strength, the Monash University study aims to consider the full range of parameters that affect shaft resistance. The database contains all available details of rock properties, construction techniques, socket roughness (where measured or observed), and cleanliness and load test results for 162 records of load tests carried out worldwide. Not surprisingly, many of these have been included in previous studies. Piles constructed in a variety of rock types are represented, including shale, mudstone, sandstone, chalk, limestone, and schist. The database includes nine sockets constructed under bentonite and 15 roughened sockets, but the latter are not included in this study. These very important construction practices have been the subject of further research at Monash University and will be addressed in subsequent publications.

≥ 450 mm) and rock anchors ( D < 450 mm).

The development of the SRC design method has allowed the reanalysis of these load tests, considering all the relevant parameters. Using the method detailed in section 5.2, the effective roughness height apparent in each socket was backcalculated, and a database of inferred socket roughness has been compiled.

6.1. Socket roughness versus rock strength Figure 11 shows effective roughness heights backcalculated from 133 load tests on rock-socketed piles and rock anchors. Sockets of greater than 450 mm diameter have been categorised as piles, and sockets of smaller diameter are shown as rock anchors. It is important to note that the data for rock anchors are not exclusive to this database. Most of the rock anchor data are derived from load tests that have been included in previous database studies as rocksocketed piles. Data points shown as triangles in Fig. 11 represent load tests in which failure was not achieved. The effective roughness height in these sockets is therefore greater than or equal to 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 are in good agreement with the general distribution of data. Revised upper- and lower-bound socket roughness guidelines are proposed and shown as solid lines in Fig. 11. These are based on the data for pile sockets only. Although the data for rock anchors follow the same general trend as that for piles, they appear to have a greater tendency to produce very smooth sockets. This is presumably due to the limiting influence of smaller diameter boreholes on roughness © 2001 NRC Canada

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

production, and the type of equipment and drilling methods used to construct anchors. A number of data points lie well above the new upperbound roughness envelope. In many of these cases, little detail is reported in relation to construction techniques and geology. The most extreme outlier shown in Fig. 11 represents a socket in extensively jointed Silurian siltstone, which is described in detail by Williams and Ervin (1980). The pre vailing joint frequency of 10–100 joints per metre caused significant overbreak which was noted to have produced an extremely rough socket. For this socket, the parameters αq, E m, qu, and d s were carefully evaluated by Williams and Ervin. The extremely high back-calculated mean roughness height obtained for this socket during this study demonstrates the ability of the SRC approach to isolate the contribution of a particular parameter to shaft response. As previously mentioned, the roughness data shown in Fig. 11 have been back-calculated using a construction method reduction factor, ηc, of 1.0. Although sockets constructed under bentonite have been eliminated from this study, it was not possible to identify sockets which were affected by remoulded rock or geomaterial smear on the socket sidewalls. Field observations suggest that smear is common in sockets drilled in low-strength argillaceous materials and has been observed in some arenaceous formations. It has been shown to have a detrimental effect on pile performance (Pells et al. 1980; O’Neill and Hassan 1994; Baycan 1996). At present, however, the conditions which lead to the production of smear are not more than generally understood. Data points representing two sockets in which smear was observed and was allowed to remain are shown in Fig. 11.

Both sockets exhibit effective roughness height which is well below average for their UCS. It is reasonable to assume that the results of a number of other load tests plotted, particularly in rock of less than 10 MPa, have been similarly affected. Consequently, the lower-bound roughness curve in Fig. 11 may reflect the performance of smeared sockets, rather than a representing a true lower bound to socket roughness levels. It is the aim of the current research program at Monash University to provide more detailed guidance to designers on appropriate socket roughness on the basis of construction methods and rock properties. Laser-based socket profiling equipment has been developed and is currently being used in a program of roughness measurement in the field. Future expansion of the socket roughness database, based on actual measurements of socket roughness, is expected to allow identification of the parameters which influence socket roughness and the development of more detailed guidelines.

6.2. Comparison with existing rock socket databases On the basis of the proposed upper- and lower-bound roughness limits, upper- and lower-bound values of SRC can be defined for the spectrum of rock strengths. In developing these 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 upper- and lower-bound SRC limits are shown graphically in Fig. 12. Extreme upper and lower limits are shown based on best- and worst-case combinations of the above parameters. Figure 12 also shows “effective” upper and lower SRC limits. These represent the 98% confidence limits for SRC © 2001 NRC Canada


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

values within the extreme upper and lower limits, based on an assumed normal distribution of all SRC values. Using both the extreme and effective SRC limits and the design chart reproduced in Fig. 9, the variation of maximum and minimum shaft adhesion factor, αq, with UCS can be computed. Figure 13 shows the expected range of socket adhesion factors for typical pile sockets. The individual pile test data used by Kulhawy and Phoon (1993) are also shown in Fig. 13, taking due account for the different definitions of αq and αc. Note that Fig. 9 includes curves for SRC values of up to 2.1. Where the upper limits of SRC are greater than 2.1, the upper limits on the adhesion factor have been predicted using ROCKET. It is clear from Fig. 13 that the variations in SRC which result from typical values of socket roughness, pile diameter, modular ratio, and construction effects simulate the range of socket adhesion factors measured in practice.

7. Summary and conclusions Current design practice for predicting the peak shear resistance of socketed piles is often based on empirical methods which only take rock strength into account. These methods may be reliable if site-specific correlations are developed. Even so, their reliability may be questionable, because they may not account for important variables that may vary across a site such as pile diameter or rock jointing. None of the empirical formulations based on rock strength alone can satisfactorily estimate peak shear resistance over the full spectrum of rock types and rock strengths because they exclude many variables that affect the shaft resistance of 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 for class R4 roughness sockets than for class R1–R3 sockets. Horvath et al. (1983) propose that the shaft resistance is a function of the roughness factor, RF, raised to the power 0.4. The derivation of RF has been discussed earlier. Socket roughness is an important factor governing peak shaft resistance; however, previous empirical methods which have incorporated roughness as a factor have not enjoyed wide use. They have also excluded other factors that affect shaft resistance. Research which has led to the development of a micromechanical simulation approach for pile socket behaviour has confirmed that pile shaft resistance is a function of the following parameters: rock strength (drained intact and residual strength parameters are used), socket roughness, rock mass modulus (and Poisson’s ratio), socket diameter, initial normal stress between concrete and rock prior to loading, and construction practices. These factors (with the exception of the initial normal stress) have been incorporated into a nondimensional parameter called the shaft resistance coefficient (SRC). Using the computer program ROCKET, design charts have been developed which relate socket adhesion factor to SRC and rock strength. These design charts are in good agreement with international databases on pile shaft behaviour. Design methods which estimate peak shaft resistance based on rock strength alone predict a unique shaft resistance corresponding to any given rock strength. The method by Rowe and Armitage (1987) allows two discrete values for each rock strength, with a factor of 1.3 difference. The method of Horvath and Kenney (1979) and Horvath et al. (1983) allows a range of shaft resistances based on the measured RF. For the range of RF values indicated by Horvath and Kenney and Horvath et al. for field sockets in their © 2001 NRC Canada

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studies (0.035–0.095), the predicted peak shaft resistances would vary by a factor of 1.6, based on the power law proposed. By contrast, empirical evidence from the large databases of socket tests is that peak shaft resistances vary by a factor of approximately 5 for any given rock strength. It has been shown that the SRC method predicts a similar range of possible shaft resistances, based on realistic upper- and lower-bound input parameters. The SRC provides designers with an opportunity to explicitly take into account the parameters which most significantly influence peak shaft resistance. Of course, there is a corresponding responsibility to determine the appropriate input parameters. The SRC can be used directly in the preliminary design stage as a tool which allows the sensitivity of shaft adhesion to influencing factors to be determined. Alternatively, it can be used directly in a socket capacity analysis based on shaft resistance alone. The adhesion factor estimated using SRC can also be incorporated into other design methods such as those by Williams et al. (1980) or Rowe and Armitage (1987). To apply SRC in design, a prediction of borehole roughness characteristics must be made. Roughness is primarily influenced by rock strength and discontinuities, and the drilling technique used. The present understanding of borehole roughness is insufficient to ensure accurate predictions can be made on a site-specific basis. However, upper- and lowerbound limits for general site conditions and construction methods have been identified. These limits are consistent with the quantitative data which are currently available. Detailed measurements are being made by the authors as part of an ongoing research program. Designers are encouraged to measure socket roughness during socket construction wherever possible. The SRC approach has also been used to back-calculate socket roughness for a database of 138 pile load tests reported in the literature. The inferred socket roughnesses are in good general agreement with the earlier recommendations of 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 to quantify the effects of construction practices on the shaft re sistance of piles socketed into rock. More detailed guidance on the effect of drilling slurries, geomaterial smear, bonding, and drill type will follow.

References Baycan, S. 1996. Field performance of expansive anchors and piles in rock. Ph.D. dissertation, Department of Civil Engineering, Monash University, Melbourne, Australia. Bernal, J.B., and Reese, L.C. 1983. Study of the lateral pressure of fresh concrete as related to the design of drilled shafts. Research Report 308-1F, Center for Transportation Research, The University of Texas, Austin, Tex. Carter, J.P., and Kulhawy, F.H. 1988. Analysis and design of drilled shaft foundations socketed into rock. Electric Power Research Institute Report EL 5918, Cornell University, Ithaca, N.Y. Cheng, F.K.K. 1997. Laboratory study of bonding and wall smear in rock socketed piles. Ph.D. dissertation, Department of Civil Engineering, Monash University, Melbourne, Australia.

Can. Geotech. J. Vol. 38, 2001 Clear, C.A., and Harrison, T.A. 1985. Concrete pressure on formwork. Report 108, Construction Industry Research and Information Association, London. Collingwood, B. 2000. The effect of construction practices on the performance of rock socketed piles. Ph.D. dissertation, Department of Civil Engineering, Monash University, Melbourne, Australia. Collingwood, B., Seidel, J.P., and Haberfield, C.M. 1999. Laser based roughness measurement for design and verification of rock socketed piles. In Proceedings of the 8th ANZ Conference on Geomechanics, Institution of Engineers, 15–17 Feb. 1999, Hobart, pp. 375–382. Gupton, C., and Logan, T. 1984. Design guidelines for drilled shafts in weak rock in South Florida. Preprint, Annual Meeting of South Florida Branch of the American Society of Civil Engi neers, Miami, Fla. Hassan, K.M., and O’Neill, M.W. 1997. Side load-transfer mechanisms in drilled shafts in soft argillaceous rock. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 123(2): 145–152. Hobbs, N.B. 1974. Settlement of foundations on rock. General Report. In Proceedings of the British Geotechnical Society Conference on Settlement of Structures, Cambridge, pp. 498–529. Hoek, E. 1990. Estimating Mohr-Coulomb friction and cohesion values from the Hoek-Brown failure criterion. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 27(3): 227–229. Hoek, E., and Brown, E.T. 1980. Empirical strength criterion for rock masses. Journal of the Geotechnical Engineering Division, ASCE, 106: 1013–1035. Holden, J.C. 1984. Construction of bored piles in weathered rocks. Technical Report 69, Road Construction Authority of Victoria, Melbourne, Australia. Horvath, R.G. 1982. Behaviour of rock-socketed drilled pier foundations. Ph.D. Thesis, University of Toronto, Toronto, ON. Horvath, R.G., and Kenney, T.C. 1979. Shaft resistance of rocksocketed drilled piers. In Proceedings of the American Society of Civil Engineers Annual Convention, 25 Oct. 1979, Atlanta, Preprint 3698. Horvath, R.G., Kenney, T.C., and Kozicki, P. 1983. Methods for improving the performance of drilled piers in weak rock. Canadian Geotechnical Journal, 20: 758–772. Johnston, I.W. 1977. Rock-socketing down-under. Contract Journal, 279: 50–53. Johnston, I.W., and Lam, T.S.K. 1989. Shear behaviour of regular triangular concrete/rock joints—analysis. Journal of Geotechnical Engineering, ASCE, 115(5): 711–727. Kodikara, J.K., Johnston, I.W., and Haberfield, C.M. 1992. Analyt ical predictions for side resistance of piles in rock. In Proceedings of the 6th Australia – New Zealand Conference on Geomechanics, Christchurch, pp. 157–162. Kulhawy, F.H., and Phoon, K.K. 1993. Drilled shaft side resistance in clay soil to rock. In Proceedings of the Conference on Design and Performance of Deep Foundations: Piles and Piers in Soil and Soft Rock. American Society of Civil Engineers, Geotechnical Special Publication 38, pp. 172–183. Lings, M.L., Ng, C.W.W., and Nash, D.F.T. 1994. The lateral pressure of wet concrete in diaphragm wall panels cast under bentonite. Proceedings of the Institution of Civil Engineers, Geotechnical Engineering, 107: 163–172. Mandelbrot, B.B. 1977. Fractals: form, chance and dimension. W.H. Freeman and Co., San Francisco. O’Neill, M.W., and Hassan, K.M. 1994. Drilled shafts: effects of construction on performance and design criteria. In Proceedings © 2001 NRC Canada

Seidel and Collingwood of the International Conference on Design and Construction of Deep Foundations. Vol. 1. Federal Highways Administration, Washington, D.C., pp. 137–187. O’Neill, M.W., Townsend, F.C., Hassan, K.M., Buller, A., and Chan, P.S. 1995. Load transfer for drilled shafts in intermediate geomaterials. U.S. Department of Transportation, FHWA-RD95-172, Draft report. Osterberg, J. 1998. The Osterberg load test method for bored and driven piles the first ten years. In Proceedings of the 7th International Conference on Piling and Deep Foundations, 15–17 June, Vienna, pp. 1.28.1–1.28.11. Pells, P.J.N., Rowe, R.K., and Turner, R.M. 1980. An experimental investigation into side shear for socketed piles in sandstone. In Proceedings of the International Conference on Structural Foundations on Rock, Sydney, pp. 291–302. Reese, L.C., and O’Neill, M.W. 1988. Drilled shafts: construction procedures and design methods. Publication FHWA-HI-88-042, Federal Highway Administration, Washington, D.C. Reynolds, R.T., and Kaderbeck, T.J. 1980. Miami limestone foundation design and construction. Preprint 80-546, Annual Meeting of South Florida Branch of the American Society of Civil Engineers, Miami. Rosenberg, P., and Journeaux, N. 1976. Friction and end bearing tests on bedrock for high capacity socket design. Canadian Geotechnical Journal, 13(3): 324–333. Rowe, R.K., and Armitage, H.H. 1984. The design of piles socketed into weak rock. Report GEOT-11-84, University of Western Ontario, London, Ont. Rowe, R.K., and Armitage, H.H. 1987. A design method for drilled piers in soft rock. Canadian Geotechnical Journal, 24: 114–125. Seidel, J.P. 1993. The analysis and design of pile shafts in weak rock. Ph.D. dissertation, Department of Civil Engineering, Monash University, Melbourne, Australia. Seidel, J.P., and Haberfield, C.M. 1994. A new approach to the prediction of drilled pier performance in rock. In Proceedings of

153 the U.S. Federal Highways Administration International Conference on Design and Construction of Deep Foundations, December 1994, Orlando, Fla., pp. 556–570. Seidel, J.P., and Haberfield, C.M. 1995 a. Towards an understanding of joint roughness. International Journal of Rock Mechanics and Rock Engineering, 28(2): 69–92. Seidel, J.P., and Haberfield, C.M. 1995 b. The axial capacity of pile sockets in rocks and hard soils. Ground Engineering, 28(2): 33– 38. Seidel, J.P., Gu, X.F., and Haberfield, C.M. 1996. A new factor for improved prediction of the resistance of pile shafts in rock. In Geomechanics in a Changing World, Proceedings of the 7th ANZ Conference on Geomechanics, Adelaide, July, Institute of Engineers, Australia, pp. 693–697. Toh, C.T., Ooi, T.A., Chiu, H.K., Chee, S.K., and Ting, W.H. 1989. Design parameters for bored piles in weathered sedimentary formations. In Proceedings of the International Conference on Soil Mechanics and Foundation Engineering, Rio de Janeiro, pp. 1073–1078. Williams, A.F. 1980. The side resistance of piles socketed into weak rock. Ph.D. dissertation, Department of Civil Engineering, Monash University, Melbourne, Australia. Williams, A.F., and Ervin, M.C. 1980. The design and performance of cast-in-situ piles in extensively jointed Silurian mudstone. In Proceedings of the 3rd ANZ Conference on Geomechanics, 12– 16 May 1980, Wellington, pp. 115–121. Williams, A.F., and Pells, P.J.N. 1981. Side resistance rock sockets in sandstone, mudstone, and shale. Canadian Geotechnical Journal, 18: 502–513. Williams, A.F., Johnston, I.W., and Donald, I.B. 1980. The design of socketed piles in weak rock. In Proceedings of the International Conference on Structural Foundations on Rock. A.A. Balkema, Sydney, pp. 327–347.

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Adhesion Factor for Rock Soketed Piles

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