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Load transfer of fibre-reinforced polymer (FRP) composite tapered piles in dense sand Mohammed Sakr, M. Hesham El Naggar, and Moncef Nehdi

Abstract: This paper describes an experimental study conducted using a large, laboratory-scale testing facility to test pile segments at different stress levels. The objectives of the study were twofold: to examine the load-transfer mechanism of tapered piles in compression, and to evaluate the effect of pile material on pile performance characteristics. The results of axial compressive loading tests on 26 pile load tests were presented using fibre-reinforced polymer (FRP) concrete composite tapered piles and steel piles. Two installation techniques were used, including conventional head driving and toe driving using a new technique. Piles were tested at different confining pressures to represent a pile segment at depths of 4.0 and 8.0 m. The load distribution along the pile shafts was measured and the results were compared with those from an analytical solution in terms of the taper coefficient Kt. The comparison showed reasonable agreement between Kt values established from the experiments and those obtained from the analytical solution. The measured toe resistance of tapered and cylindrical piles was compared with those from the analytical solution. A simple rational approach was proposed for the design of tapered piles. Key words: tapered piles, FRP, pile capacity, axial performance, centrifuge modeling, shaft resistance, toe resistance. Résumé : Cet article décrit une étude expérimentale réalisée au moyen d’un gros montage d’essai en laboratoire pour tester des segments de pieux à divers niveaux de contraintes. L’objectif de l’étude était double: examiner le mécanisme de transfert de charge de pieux coniques en compression et évaluer l’effet du matériau du pieu sur les caractéristiques de performance du pieu. Les résultats des essais de chargement axial en compression sur 26 pieux ont été présentés en utilisant des pieux coniques en béton composite FRP et des pieux en acier. Deux méthodes de mise en place ont été utilisées comprenant la méthode conventionnelle de fonçage à la tête et à la pointe en utilisant une nouvelle technique. Les pieux ont été testés à différentes pressions de confinement pour représenter un segment de pieu à des profondeurs de 4,0 et 8,0 m. La distribution de la charge le long du fût des pieux a été mesurée et les résultats ont été comparés avec une solution analytique en fonction du coefficient de conicité Kt. La comparaison a montré une concordance raisonnable entre les valeurs de Kt déterminées en partant des expériences et celles obtenues par la solution analytique. On a proposé une simple approche rationnelle pour le calcul des pieux coniques. Mots clés : pieux coniques, FRP, capacité des pieux, performance axiale, modélisation par centrifuge, résistance du fût, résistance à la pointe. [Traduit par la Rédaction]

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Introduction Many factors affect the development of skin friction and toe resistance of tapered piles. These include the taper angle, soil type, effective vertical stress, and pile–soil interface frictional resistance characteristics. Design rules for the evaluation of unit static shaft and toe resistance for tapered piles in dense sand are vague. For example, the Canadian foundation engineering manual (Canadian Geotechnical Society 1992) suggests that the increase in shaft resistance due to the pile taper could be taken into consideration by increasing the coReceived 3 February 2003. Accepted 22 July 2003. Published on the NRC Research Press Web site at http://cgj.nrc.ca on 14 January 2004. M. Sakr and M.H. El Naggar.1 Geotechnical Research Centre, Faculty of Engineering Science, University of Western Ontario, London, ON N6A 5B9, Canada. M. Nehdi. Department of Civil and Environmental Engineering, University of Western Ontario, London, ON N6A 5B9, Canada. 1

Corresponding author (e-mail: [email protected]).

Can. Geotech. J. 41: 70–88 (2004)

I:\cgj\Cgj4101\T03-067.vp January 8, 2004 9:58:59 AM

efficient of lateral earth pressure, Ks, by 30%–50%. This recommendation does not make any reference to or give any guidance as to the effect of the various factors that influence the performance of tapered piles. The performance of tapered piles can be investigated experimentally in the field or using models in which effective stress conditions are simulated using either centrifuge testing or large-scale model piles. Norlund (1963) investigated the effect of the taper on the compressive capacity of piles driven into cohesionless soil and reported a substantial increase of axial compressive capacity of tapered piles over straight-sided piles. Ladanyi and Guichaoua (1985) compared the response of tapered piles, straight-sided piles, and corrugated piles in permafrost soils. They concluded that tapered piles loaded in compression were the safest because they display strain-hardening behaviour, gaining strength continuously with increasing settlement. Zil’berberg and Sherstnev (1990) conducted field tests on tapered and cylindrical piles with the same average embedded radius driven into sandy soil. They reported a substantial increase in the axial compressive bearing capacity of tapered piles ranging from 200% to 250% when compared with the capacity of

doi: 10.1139/T03-067

© 2004 NRC Canada


Sakr et al.

cylindrical piles with the same average diameter and embedded length. Wei and El Naggar (1998) reported the results of an experimental study on tapered piles in a laboratory setup. They confirmed that the pile capacity increases with an increase in the taper angle and concluded that the taper effect was most efficient for the topmost 20 pile diameters of the pile length. Kodikara and Moore (1993) developed a model for the analysis of tapered piles wherein the soil resistance was modeled by two components. The first component is the friction and adhesion along the shaft, and the second component is due to the lateral soil reaction mobilized by the hole expansion resulting from the pile penetrating the ground. El Naggar and Sakr (2000) conducted an experimental study on tapered piles in loose sand using centrifuge testing. They compared the performance of tapered and straight-sided wall piles for both smooth (steel) and rough (concrete or wooden) pile surfaces and developed a simplified analytical model based on the experimental results to evaluate shaft friction of tapered piles in sand. Fibre-reinforced polymer (FRP) composite materials were introduced for deep foundation applications in the last decade. Composite piling has been used in practice in waterfront barriers, fender piles, and bearing piles for light structures (Iskander and Hassan 1998). Most composite piling products are made of fibreglass polymers or high-density polyethylene (HDPE) with fibreglass reinforcement and additives to improve their mechanical properties, durability, and ultraviolet (UV) protection. Their light weight, high specific strength, high durability, corrosion resistance, chemical and environmental resistance, and low maintenance cost are desired features for deep foundations. Combining the durability of FRP materials with the structurally superior performance of tapered piles may result in substantial benefits for the deep-foundation industry. This is the underlying motivation for the research reported herein.

Scope of the work The primary objectives of this study are to understand the performance characteristics of FRP composite tapered piles installed in dense sand and to develop a rational approach for their design. For this purpose, large-scale model pile testing using a pressure chamber has been undertaken at the University of Western Ontario to investigate the performance of FRP composite piles. Tapered and cylindrical piles were installed in dense sand and subjected to axial compressive loading. Thirteen soil samples were prepared to test a 1.2 m pile segment in the pressure chamber. Two installation methods were used in this study: conventional head driving, and a novel technique called toe driving suitable for FRP piles. Five piles were installed using toe driving and eight piles using head driving. Twenty-six axial compression load tests were conducted on piles at combinations of radial and vertical pressures of 30 and 60 kPa and 60 and 120 kPa to simulate a pile segment at depths of 4.0 and 8.0 m, respectively, in normally consolidated dry sand. Three tapered piles with different taper angles and two cylindrical piles were used in this study. Testing both tapered and cylindrical piles in the same experimental setup allowed for a direct comparison between the FRP composite tapered and cylindrical piles and

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between cylindrical FRP composites and steel piles. The test results are presented herein and an approach based on cavity expansion theory is validated for the design of tapered piles in dense sand.

Experimental arrangement A schematic elevation view of the pressure chamber used in this study to test an embedded pile segment 1.2 m in length at different confining pressures is shown in Fig. 1. The soil column is formed in a containment steel cylinder with 1.34 m inside diameter and height of 1.52 m. A 50.8 mm thick waffle-type neoprene energy absorber is placed at the base of the chamber to reduce the energy in waves reflected from the base during driving. The inner surface of the upper steel cover plate and the interior walls of the chamber are lined with a flexible boundary (rubber bladder). Boundary conditions in the pressure chamber are of prime importance to achieve experimental results representative of the in situ conditions. O’Neill and Raines (1991) stated that flexible boundary conditions would produce slightly lower pile capacity than would occur in a prototype for piles tested in dense sand, since the flexible lateral boundaries result in radial soil stresses that are lower than those which would exist with rigid boundaries. Also, since the pressure chamber has finite dimensions, its size should be designed so as to contain at least the plastic zone of the soil (i.e., the zone of permanent soil deformation) around the pile. Vipulanandan et al. (1989) conducted a series of impact driving tests in submerged dense sand using a pressure chamber. In their study, the model pile was 102 mm in diameter and penetrated into the soil column up to 2.03 m, and the pressure chamber had an inside diameter of 0.84 m and height of 2.56 m. Vipulanandan et al. suggested that a radial boundary of greater than seven pile radii and a vertical boundary of four pile radii from the pile toe to the steel base of the chamber would be appropriate to enclose the plastic zone around the pile and to capture the pile response during driving and subsequent testing. Sakr and El Naggar (2003) measured the settlement at the soil surface around the pile during load testing of model piles in loose sand using a geotechnical centrifuge facility. The centrifuge tube was 904 mm in inner diameter and 850 mm deep. The average pile diameter was 30 mm and was placed at a minimum distance of 224 mm from the tub steel wall. Sakr and El Naggar found that the settlement of the soil surface at a distance equal to eight pile radii from the pile is about 4% of the pile head settlement for tapered piles and about 2% of the pile head settlement for cylindrical piles. The low settlement ratio at eight pile radii suggests that the boundary at this distance would have a negligible effect on the results. In this study, an average pile diameter of 180 mm and a maximum pile penetration of 1.20 m were maintained. This ensured a distance of eight pile radii from the horizontal boundary and three pile radii from the pile toe. The pile installation setup consisted of a pressure chamber, pile driver, toe-driving device, model piles, instrumentation, and data-acquisition system. Three pilot pile installations were conducted to examine the effect of confining stresses during installation on the subsequent load testing at different © 2004 NRC Canada



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Can. Geotech. J. Vol. 41, 2004

Fig. 1. Schematic elevation of pressure chamber, tested pile, and hammer.

pressures. Two of the installations were conducted at radial and vertical confining pressures of 60 and 120 kPa, and the third pile installation was conducted at radial and vertical confining pressures of 60 and 30 kPa (coefficient of lateral earth pressure at rest K0 = 2) to examine the effect of changing radial stresses on the static resistance of tested piles. In the remaining tests, the vertical stress applied to the column of the soil was 60 kPa during driving and varied between 60 and 120 kPa during testing. The pressure applied to the radial air bladder was increased gradually until the reading of the total pressure cell near the pile reached 30 kPa and then was kept constant during driving and was varied between 30 and 60 kPa during subsequent load testing. A detailed description of the pressure chamber and experimental setup is given in Sakr et al. (2004). The soil used in the tests consisted of fine subrounded to rounded air-dried Fanshawe brick sand. It was classified as poorly graded sand, with particle sizes in the range 0.075– 2.00 mm, effective diameter D50 = 0.26 mm, and uniformity coefficient Cu = 2.14. The sand maximum unit weight was 17.72 kN/m3, and the minimum unit weight was 14.66 kN/m3. The maximum and minimum void ratios were emax = 0.794 and emin = 0.484, respectively. The soil samples were prepared using a raining technique using a sand spreader with a constant free-fall flow of 1.5 m. A relative density of about 90% with a standard deviation of 2.5% is obtained using this procedure, which ensures good homogeneity and reproducibility of the density within the sample volume. Model piles Five instrumented piles were used in the study. Four of

the piles were fabricated from FRP shell, and one pile was a cylindrical steel pile. Three of the FRP piles were tapered with different angles and the fourth was cylindrical. Tapered piles T1, T2, and T3 had taper angles α = 0.53°, 0.71°, and 1.13°, respectively. The geometrical properties of the piles are summarized in Table 1. The piles were provided with an interior annular shoe at the pile toe to facilitate the toedriving process and to allow for closing the pile toe during subsequent static pile load testing, as discussed in the sections to follow. Figure 2 shows the details of the pile toe and the load cell closure mounted at the pile toe. The cylindrical steel pile, SC, was an open-ended model made of cold-drawn steel tubing 168 mm in diameter and with a modulus of elasticity of 2.15 × 105 MPa and thickness of 6.35 mm. The cylindrical FRP pile, FC, is an off-theshelf pipe with an average diameter of 162.4 mm and a ply angle of 55°, and the material is denoted FRP I. The FRP tapered piles were fabricated using glass filament wound (GFW). Six layers of GFW were placed at ply angles of 0° (parallel to pile axis) and 90° (hoop layer). This material is denoted FRP II. The thickness of FRP shells and their geometry are presented in Table 1. The FRP tubes were filled with a self-consolidating concrete (SCC) developed by Nehdi et al. (2003). Table 2 summarizes the properties of FRP, the resin used for fabricating the piles, and the SCC. Pile instrumentation Piles were instrumented externally to facilitate measuring dynamic data during pile driving and the axial forces during subsequent axial load tests. The external instrumentation allowed for the strain gauges to be attached easily, quickly, and accurately and facilitated driving the piles using the toe© 2004 NRC Canada



Sakr et al.

73 Table 1. Geometry of model piles. Diameter (mm)

Thickness (mm)

Pile

dt

db

da

ts

tb

Length, l (mm)

SC ST T1 T2 T3

168.3 162.4 170.0 159.0 155.0

168.3 162.4 198.0 197.0 215.0

168.3 162.4 184.0 178.0 185.0

6.35 5.00 9.80 7.80 8.20

17.8 12.7 11.2 12.6 7.8

1524 1524 1524 1524 1520

FRP reinforcement direction

Taper angle, α (°)

na 55° 0° 0° 0°

0.00 0.00 0.53 0.71 1.13

Note: da, average diameter of the model pile shaft; db, model diameter at the pile head; dt, model diameter at the pile toe; na, not applicable; tb, annular shoe thickness; ts, thickness of the pile wall.

Table 2. Properties of pile materials. Property

GRC (glass fibre)

Resin

SCC

Density (Mg/m3) Compressive strength (MPa) Tensile strength (MPa) Flexural strength (MPa) Interlaminar shear strength (MPa) Modulus of elasticity (GPa)

1.65 380 440 480 38 17.0

1.18 120 70 110 — 3.0

2.42 58 (28-day) — — — —

Fig. 2. Details of pile toe and attached load cell: (a) steel pile; (b) fibre-reinforced pile (FRP) filled with self-consolidating concrete (SCC).

driving technique. For steel piles, the strain gauges and connecting wires were affixed in recessed square grooves 25.4 mm wide and 1.3 mm deep. For FRP piles, the external surface was made smooth and strain gauges were affixed to the top of the fibres. Surface protection was provided by applying three layers of a coating system. Seven strain gauge bridges were used to measure the axial stresses along the pile shaft. Four strain gauges (CEA-06125UW-120 manufactured by Micro-Measurements Group Inc., Raleigh, N.C.) were attached at each level, thus constituting a full bridge. The strain gauges were distributed over the length of the piles such that the first bridge was approximately 206 mm from the pile head above the sand surface to facilitate direct comparison of the load measured using a sensitive load cell placed on top of the pile and the full bridge strain gauge circuit. The remaining six bridges were distributed equally over the pile embedded length. Figure 3 shows the distribution of the strain gauges on piles and the strain gauge numbering. The strain gauges were calibrated by applying an incremental load up to 200 kN for cylindrical piles and 500 kN for tapered piles to the pile head using an MTS machine and measuring the output voltage. Excitations of 2.5 and 5.0 V were used for FRP and steel piles, respectively. The disparity between the load measured from the topmost bridge in the instrumented pile, G7, and the load cell reading was less than 6%. Two total earth pressure cells were placed at 0.6 m below the soil surface (mid-pile embedded length); one was used to measure the vertical stress and the other the radial stress in the vicinity of the pile during pile installation and subsequent static testing. Other instrumentation used included a load cell placed on top of the pile during static loading and two linear variable displacement transducers (LVDTs) located at the pile head to measure settlement during axial loading. Figures 4a and 4b show a schematic and an oblique © 2004 NRC Canada



74 Fig. 3. Strain gauge distribution and numbering on model piles. All dimensions in millimetres. tb, annular shoe thickness; ts, thickness of the pile wall.

view, respectively, of the loading setup. The axial compression test results are presented in the following sections.

Test procedure Thirteen pile installations were conducted, eight using head driving and five using the toe-driving technique. For each pile installation, the boundary stresses were applied for 2 h prior to starting the installation process to ensure that the initial stress condition was constant. A detailed description of the mechanism of toe driving is provided by Sakr et al. (2004). Each test involved the following steps: (i) preparing the soil sample to the desired relative density (90%) using the raining technique; (ii) increasing the pressure in the air bladder (confining stresses) gradually until the total earth pressure cells measure the desired stress level, and then maintaining this pressure; (iii) installing the pile (driving); (iv) uplift load testing; (v) redriving the piles to a position slightly deeper than their initial position; (vi) axial compression – uplift compression load testing at radial and vertical pressures of 30 and 60 kPa, respectively; and (vii) axial compression – uplift compression load testing at radial and vertical pressures of 60 and 120 kPa, respectively. Radial and vertical effective stresses of 30 and 60 kPa, respectively, were applied to the pressure chamber during the pile installation to simulate driving piles at a depth of 4.0 m for normally consolidated sand (K0 = 0.5). Piles were driven to a final penetration depth of 1.2 m using a 1 kN weight falling from 1.2 m at a rate of


6 blows/min. Immediately after driving, two uplift load tests were conducted up to a displacement of 0.15 pile diameters at radial and vertical pressures, respectively, of 30 and 60 kPa and 60 and 120 kPa. The pile was then redriven slightly deeper than its initial position. In the case of the toedriving installation, a toe closure mechanism was lowered to the pile toe immediately after redriving the pile, and the FRP pile was filled with SCC. After a curing time of 7 days for the SCC, a compressive axial load test was conducted to a maximum displacement of 0.20 pile diameters at radial and vertical pressures of 30 and 60 kPa, respectively, followed by uplift and compressive load tests. The combination of radial and vertical pressures of 30 and 60 kPa is referred to in the subsequent sections as low pressure and denoted LP. Another axial compression – uplift compression load test to a displacement of 0.20 pile diameters at radial and vertical pressures of 60 and 120 kPa, respectively (representing a pile segment at 8.0 m depth), was then conducted. The combination of radial and vertical pressures of 60 and 120 kPa is referred to in the subsequent sections as high pressure and denoted HP. In both the LP and HP tests, the applied pressures were such that the K0 was 0.5 to simulate normally consolidated dense sand. The loading setup during the compression phase consisted of an MTS hydraulic actuator placed on top of a swing bearing disk, which in turn was centred on top of the pile head. Stresses in the soil mass during pile driving Total stress pressure cells were used to measure both vertical and radial stresses during pile installation for different piles considered in this study. Figure 5a shows the vertical pressure developed at depth 600 mm from the surface of the sand, and Fig. 5b shows the radial pressure developed at a radial distance of 370 mm from the centreline of the pile. Figure 5 shows that there is a general trend for both vertical and radial stresses to increase to a maximum as the pile approaches the position of the pressure cell and then to decrease as the pile toe passes the pressure cell. Vertical stress at the end of the driving process decreased to values ranging from 60 to 54 kPa, which is close to the initial value before installation started (60 kPa). Figure 5b shows that the radial stresses increased for all piles as the pile toe advanced into the soil followed by a gradual decrease and reached values close to the initial stresses at the end of the driving process. The radial stresses during installation of tapered piles were higher than those of the cylindrical pile FC. The maximum observed values occurred at about 100 mm above the total earth pressure cell. Similar observations were made by Lehane et al. (1993) in their study on closed-ended piles installed in sand. Effect of applied confining pressure during driving on pile capacity Piles FC and T3 were driven at HP to quantify the effect of in situ stresses during driving on the axial behaviour of piles during the subsequent compression load testing. Figure 6 compares the load–settlement curves for piles driven at both HP and LP and shows that applying HP during driving results in only slightly stiffer response for all tests compared with the LP case. This means that using a combination of ra© 2004 NRC Canada



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Fig. 4. (a) Schematic elevation of axial compression loading setup. (b) Oblique view of testing setup.

Fig. 5. Effective stresses in sand column measured at the point noted in Fig. 1 (total earth pressure cells) during pile installation (piles FC, T1, T2, and T3): (a) vertical pressure; (b) radial pressure.

dial and vertical pressures of 30 and 60 kPa or 60 and 120 kPa during driving had only a minor effect on the pile performance for piles examined in this study. Therefore, the effect of varying confining stress on compressive pile capac-

ity is considered negligible (for the range of pressures used in this study). Thus the remaining installations were performed at LP to save time, effort, and cost associated with sample preparation and pile installation at HP. © 2004 NRC Canada



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Fig. 6. Effect of driving stresses on the axial capacity of piles in compression.

Effect of lateral confining pressure To study the effect of varying lateral confining pressure on the axial capacity of tested piles, pile FC was installed and tested at radial and vertical pressures of 60 and 30 kPa, respectively. The results of the axial compression load test for overconsolidated sand (K0 = 2.0) for pile FC were compared with the case when the pile was installed and tested at radial and vertical pressures of 30 and 60 kPa (K0 = 0.5, normally consolidated sand; Fig. 7). Figure 7 shows that the initial part of the load–displacement curve was approximately linear (up to a pile displacement ratio of ∆r = 0.025 for the normally consolidated sand (K0 = 0.5) and ∆r = 0.05 for the overconsolidated sand (K0 = 2.0)). At higher displacement levels, however, the pile tested at K0 = 2.0 continued to resist higher axial compressive loads than when it was tested at K0 = 0.5. For example, the axial compressive load was 131.5 kN for pile FC installed in overconsolidated soil (K0 = 2.0) at ∆r = 0.1 and 99.1 kN for the same pile installed in normally consolidated sand (K0 = 0.5). All compressive load tests conducted for pile FC in normally or overconsolidated sand reached plunging failure at ∆r ≈ 0.12. It appears that the pile performance is highly influenced by the radial pressure. Therefore, the applied radial and vertical pressures for all tests were such that K0 = 0.5 to capture the effect of pile taper independently from stress levels.

Test results The results of compressive load tests are presented in the form of load–settlement curves. These curves are used to determine the load capacity of the piles and the load distribution along the shaft using the strain gauge measurements along the pile shaft. Compression tests were conducted for piles installed using toe driving and head driving. Figure 8 shows the load–settlement curves for LP tests of the FRP cylindrical and tapered piles installed using head and toe driving. The pile displacement is given in terms of a displacement ratio, ∆r = (pile head displacement)/(average pile diameter). It is noted from Fig. 8 that piles SC and FC

had a similar response. The slight difference between the responses of piles SC and FC can be attributed to the difference in interface frictional angle, δ, for both steel–sand and FRP–sand. The tapered piles displayed a stiffer response than the cylindrical piles in all loading stages. A comparison of the response of cylindrical and tapered piles at ∆r > 0.1 showed that the cylindrical piles reached a plunging failure, whrease tapered piles sustained a continuous increase in the pile load with an increase in the settlement (no sign of plunging failure). When comparing Figs. 8a (head driving) and 8b (toe driving), it is found that piles installed using toe driving showed a stiffer response than piles installed using head driving. Figure 9 shows the load–settlement curves for HP pile load tests for head driving (Fig. 9a) and toe driving (Fig. 9b). As expected, HP load tests yielded a much stiffer response for both cylindrical and tapered piles than LP tests (Fig. 8). Similar to LP tests, the pile taper increased the pile capacity and stiffness, and piles installed using toe driving offered higher resistance than those installed using head driving. Pile capacity determination The axial pile capacity was defined as the load corresponding to a displacement equal to 10% of the pile diameter (Terzaghi 1942). Table 3 shows the pile capacity for all piles tested in compression. The effect of pile taper on its capacity can be evaluated in terms of capacity ratio, defined as the ratio between the capacity of the tapered and cylindrical piles installed and tested under the same conditions. Table 3 shows that the capacity ratios for piles T1, T2, and T3 installed using head driving at LP and tested at LP are 1.32, 1.45, and 1.74, respectively. As expected, the axial capacity of the pile increased as α increased. Table 3 shows that the axial capacity of all piles installed using toe driving is higher than the capacity of the piles installed using head driving. For piles T1, T2, and T3 tested at LP, the capacity ratios were 1.42, 1.57, and 1.82, respectively, for installation using toe driving and 1.32, 1.45, and © 2004 NRC Canada



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Fig. 7. Effect of lateral coefficient of earth pressure, K0, on the axial capacity of piles.

Fig. 8. Load–displacement curves for piles tested at low pressures and installed using (a) head driving, and (b) toe driving.

1.74, respectively, for installation using head driving. Similarly, for piles T1, T2, and T3 tested at HP, the capacity ratios were 1.48, 1.75, and 2.35, respectively, for installation

using head driving and 1.76, 2.08, and 2.56, respectively, for installation using toe driving. This may be attributed to the fact that toe driving densifies the soil in the vicinity of the © 2004 NRC Canada



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Fig. 9. Load–displacement curves for piles tested at high pressure and installed using (a) head driving, and (b) toe driving.

pile, since most of the hammer impact is transferred directly to the soil at the pile toe. It is also noted that the tapered piles tested at HP showed a substantial increase in their axial capacity compared with those tested at LP. The results are compared in Table 4 based on the surface coefficient, KS, which is defined as the ratio of the axial capacity per unit area of tapered FRP piles to the axial capacity per unit area of cylindrical FRP piles installed and tested under the same conditions, i.e., [1]

KS =

(Q c / pl ) tapered (Q c / pl ) cylindrical

where Qc is the axial pile capacity, p is the average pile perimeter, and l is the embedded pile length. It is evident from Table 4 that the tapered piles displayed higher axial capacities, as all KS values were higher than 1.0. It is also noted from Table 4 that KS increased with an increase in α. Furthermore, Table 4 shows that KS for a given pile installed using toe driving was higher than its value for the same pile

installed using head driving and that KS values for HP tests were higher than those for LP tests. The installation coefficient, KI, is introduced to capture the effect of driving technique on the axial compressive capacity of the pile. KI is defined as the ratio of axial capacity of a pile installed using toe driving to that of the same pile installed using head driving at the same testing pressure, i.e., [2]

KI =

(Q c ) toe (Q c ) head

Table 4 shows that KI varied between 1.03 and 1.23, with an average value of 1.16, meaning that toe driving is superior to head driving because it enhances the axial performance of piles in dense sand. Shaft resistance The axial capacity of a pile is the sum of its shaft resistance, Qs, and toe resistance, Qt, minus its self-weight. The self-weight of the pile is small and is usually neglected. The shaft resistance is given by © 2004 NRC Canada



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79 Table 3. Axial compressive capacities of tested piles under different pressures. Testing pressure (kPa)

Pile

Installation method

Radial

FC FC SC SC T1 T1 T2 T2 T3 T3 FC FC SC SC T1 T1 T2 T2 T3 T3

Head driving Toe driving Head driving Toe driving Head driving Toe driving Head driving Toe driving Head driving Toe driving Head driving Toe driving Head driving Toe driving Head driving Toe driving Head driving Toe driving Head driving Toe driving

30 30 30 30 30 30 30 30 30 30 60 60 60 60 60 60 60 60 60 60

Vertical

Compressive capacity, Qc (kN)

Capacity ratio

Shaft resistance, Qs (kN)

Toe resistance, Qt (kN)

Toe resistance ratio (%)

60 60 60 60 60 60 60 60 60 60 120 120 120 120 120 120 120 120 120 120

99.1 109.8 98.9 96.1 131.3 156.0 143.5 172.9 172.9 199.3 136.3 140.4 139.5 141.7 202.2 246.5 237.9 292.7 320.0 359.1

1.00 1.00 1.00 1.00 1.32 1.42 1.45 1.57 1.74 1.82 1.00 1.00 1.00 1.00 1.48 1.76 1.75 2.08 2.35 2.56

47.5 53.0 48.2 43.0 72.2 88.5 81.0 99.5 108.7 125.2 72.1 77.2 72.3 66.3 97.1 105.7 112.5 122.2 146.3 159.9

51.6 56.8 50.7 53.1 59.1 67.5 62.5 73.4 64.2 74.1 64.2 63.2 67.2 75.4 105.1 140.8 125.4 170.5 173.7 199.2

52.0 51.7 51.2 55.0 45.0 43.3 43.6 42.5 37.1 37.2 45.7 45.0 48.2 53.2 52.0 57.1 52.7 58.3 54.3 55.5

erage unit shaft friction is evaluated from the experimental results by dividing the load transferred to the soil between the pile head and toe by the surface area of the shaft, i.e.,

Table 4. Comparison of axial pile capacity. Testing pressure (kPa)

Pile

Installation method

Radial

FC T1 T2 T3 FC T1 T2 T3 FC T1 T2 T3 FC T1 T2 T3

Head driving Head driving Head driving Head driving Toe driving Toe driving Toe driving Toe driving Head driving Head driving Head driving Head driving Toe driving Toe driving Toe driving Toe driving

30 30 30 30 30 30 30 30 60 60 60 60 60 60 60 60

Vertical

Axial capacity, Qc (kN)

KS

60 60 60 60 60 60 60 60 120 120 120 120 120 120 120 120

99.1 131.3 143.5 172.9 109.8 156.0 172.9 199.3 136.3 202.2 237.9 320.0 140.4 246.5 292.7 359.1

1.00 1.19 1.35 1.59 1.00 1.42 1.64 1.84 1.00 1.33 1.63 2.13 1.00 1.58 1.95 2.33

[4] KI

1.11 1.19 1.20 1.15

1.03 1.22 1.23 1.12

l

[3]

Q s = ∫ q max p dz 0

where z is the depth below the ground surgace and qmax is the unit shaft resistance. The unit shaft resistance is the maximum shear stress on the pile shaft at a given depth when the failure (or ultimate) load is applied at the pile head. The av-

qs =

Q c − Qt pl

where qs is the value of average unit shaft friction; and Qc and Qt are the loads measured at the pile head and toe, respectively. Figures 10 and 11 show measured average unit shaft resistance, qs, normalized by the mean effective stress at the middle of the embedded pile depth, σ′, versus the displacement ratio, ∆r. Figure 10a shows qs/σ′ for piles installed using head driving at LP, and Fig. 10b shows qs/σ′ for the toe-driving case at LP. The following observations are evident: (1) As the taper angle increased from 0° to 1.13°, the skin friction increased substantially. This is because the pile taper plays an important role in displacing the surrounding soil radially and mobilizing additional confinement pressure, thus leading to higher skin friction and higher shaft resistance. (2) The skin friction for tapered piles continued to increase with an increase in the displacement level, even for ∆r > 0.1. For cylindrical piles, the ultimate skin friction was reached at ∆r slightly greater than 0.1, without any further increase at higher displacement levels. This means that tapered piles can offer higher axial capacity if larger displacement is allowed. It also means that tapered piles are safer in the sense that they do not go through plunging failure. (3) When comparing Figs. 10 and 11, it was noted that the normalized shaft resistance decreased as the confining © 2004 NRC Canada



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Fig. 10. Skin friction of piles tested at low pressures and installed using (a) head driving, and (b) toe driving.

pressure increased for both tapered and cylindrical piles. The decrease is more pronounced for the case of tapered piles. Two points can be made here. First, the beneficial effect of pile taper is more significant at lower confining pressure. Similar observations were made by Wei and El Naggar (1998) and El Naggar and Sakr (2000). Second, the unit shaft friction of cylindrical piles continues to increase with an increase in depth (confining pressure) but at a declining rate. Norlund (1963) attributed the higher frictional resistance of tapered piles driven into sand to soil compaction in the vicinity of the pile which increases the soil friction angle. Ladanyi and Guichaoua (1985) attributed the increased resistance of tapered piles to an increase in lateral confinement stresses in the ground which increases the shear resistance to pile penetration. Figure 12 shows the vertical and radial effective stresses during static compression loading for piles FC and T3 (α = 1.13°) tested at LP and HP. Figure 12a shows that the change in vertical and radial stresses in the soil due to the compression loading was small for pile FC tested at LP. For pile T3, however, the compression loading resulted in a substantial increase in the radial stresses but a small increase in the vertical stresses. For example, the ini-

tial radial stress at the beginning of loading was 27 kPa and increased to 71 kPa at the end of the compression loading test. The confining stress values at the beginning of compression load tests were slightly lower than the initial stress condition due to the installation process and subsequent uplift load testing. The change in confining stresses is considered to be minor, however, and has almost no effect on the analysis of the results. Figure 12b shows the vertical and radial pressure distribution for piles FC and T3 tested at HP. Again, the change in stresses within the soil is small for pile FC and large for pile T3. It should be noted that in this case the increase is much higher than in the LP case, especially for the vertical stresses. For example, the radial stress at the beginning of loading for pile T3 was 61 kPa and at the end of the compression loading test was 158 kPa. Meanwhile, the vertical stress increased from 120 to 159 kPa. This observation supports the hypothesis that the increase in shaft friction of tapered piles is a result, at least in part, of an increase in the radial pressure (Ladanyi and Guichaoua 1985). Effect of pile taper on shaft resistance El Naggar and Sakr (2000) evaluated the shaft resistance of tapered piles using the following expression: © 2004 NRC Canada



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Fig. 11. Skin friction of piles tested at high pressures and installed using (a) head driving, and (b) toe driving.

l

[5]

(Q s)tapered = ∫ Kt Ksσv′ tan(δ) p dz 0

where Kt is the taper coefficient, σv′ is the effective vertical stress at the mid-depth of the pile segment, and δ is the pile– soil interface friction angle. The taper coefficient, Kt, can be evaluated from the following expression: [6]

Kt = A +

B ∆r σv

where ∆r is the settlement ratio (∆r = 0.1), σv is the effective vertical stress at the mid depth of the pile, A and B depend on α, δ, Ks, and Es (elastic modulus of the ground) and are given by [7a]

A=

tan(α + δ) cot(δ) 1 + 2ζ tan(α) tan(α + δ)

[7b]

B=

4G tan(α) tan(α + δ) cot(δ) [1 + 2ζ tan(α) tan(α + δ)]Ks

where G is the shear modulus of the elastic ground at the middle of the embedded pile length at low strain level; and ζ = ln(r1/rm), in which rm is the average pile radius and r1 is a radius at which the shear stress becomes negligible and is taken to be equal to 2.5l(1 – ν), where l is the pile length and ν is Poisson’s ratio of the soil. The pile–soil interface friction angle, δ, was evaluated from interface shear box tests and found to be 27.5°, 32.3°, and 26.6° for the interfaces with the FRP I, FRP II, and steel piles, respectively. Pile installation using toe driving resulted in densifying the soil in the vicinity of the pile and increasing frictional resistance and interface friction angles. Backcalculation of interface friction angle for cylindrical piles indicated an increase of pile interface friction angle by about 2.5°. The average coefficient of lateral earth pressure, Ks, was evaluated from the results of the cylindrical pile test using eq. [3] with q max = Ksσv′ tan(δ). The average coefficients of lateral earth pressure, Ks, for piles tested at LP and HP were 2.0 and 1.7, respectively. Table 5 compares the measured shaft resistance values with the calculated values using eq. [5]. It is noted from Table 5 that the calculated shaft resistance agreed well with the © 2004 NRC Canada



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Fig. 12. Effective stresses in sand column measured at point noted in Fig. 1 for compression tests on cylindrical pile FC and tapered pile T3 for piles tested at (a) low testing pressure, and (b) high testing pressure.

Table 5. Comparison of measured and calculated shaft resistance of tested piles. Shaft resistance (kN)

Pile

Test

Installation method

Taper coefficient, Kt

FC FC T1 T1 T2 T2 T3 T3 FC FC T1 T1 T2 T2 T3 T3

LP LP LP LP LP LP LP LP HP HP HP HP HP HP HP HP

Head driving Toe driving Head driving Toe driving Head driving Toe driving Head driving Toe driving Head driving Toe driving Head driving Toe driving Head driving Toe driving Head driving Toe driving

1.00 1.00 1.46 1.47 1.61 1.64 2.04 2.05 1.00 1.00 1.36 1.39 1.49 1.52 2.00 2.00

Calculated, (Qs)c

Measured, (Qs)m

Prediction ratio, (Qs)m/(Qs)c

47.8 53.0 71.0 82.5 78.0 89.0 102.7 114.5 70.5 78.2 100.3 113.7 106.3 120.2 148.3 164.4

47.5 53.0 72.2 88.5 81.0 99.5 108.7 125.2 72.1 77.2 97.1 105.7 112.5 122.2 146.3 159.9

0.99 1.00 1.02 1.07 1.04 1.12 1.06 1.09 1.02 0.99 0.97 0.93 1.06 1.02 0.99 0.97

© 2004 NRC Canada



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Fig. 13. Skin friction for FRP cylindrical (FRP-C) and tapered piles tested at low pressures and installed using (a) head driving and (b) toe driving.

measured values. The taper coefficient and shaft friction decreased as the confining pressures increased. This can be attributed to the higher shear modulus at deeper depths, and therefore the relative increase in the radial stresses due to the taper effect is less pronounced. Skin friction The unit skin friction values of the pile shaft were calculated from the strain gauge readings at the failure loads. The difference between forces measured at any two stations of strain gauges along the pile shaft represented the total load transferred to the surrounding soil between the two sets. The unit skin friction between these two stations is obtained by dividing this difference by the corresponding surface area. It is worth mentioning that uplift pile load tests, conducted prior to the compression load tests, released most of the residual stresses developed during the driving process. Therefore, the effect of residual load is considered to be in-

significant, and the skin friction is calculated without correction for residual stresses. Figures 13 and 14 present the unit skin friction profile at the ultimate compressive load for all piles. The skin friction curves for cylindrical and tapered piles tested at LP are plotted in Fig. 13, and the results for the HP case are shown in Fig. 14. It can be noted from Figs. 13 and 14 that the unit skin friction values increased as the taper angle increased for different installation methods and testing pressures. The unit skin friction increased at a linear rate at the top portion of the tested piles. Near the pile toe, however, the skin friction is almost constant. Vesic (1970) and Lehane et al. (1993) showed that the highest values of β (where β = q s / σv′ ) occur near the pile toe. The distribution of shaft friction near the pile toe is intimately related to the end-bearing pressure generated by the toe. It is believed that a plastic zone developed near the pile toe and a constant, or almost constant, radial pressure was present, and thus there was no substantial in© 2004 NRC Canada



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Fig. 14. Skin friction for FRP cylindrical and tapered piles tested at high pressures and installed using (a) head driving and (b) toe driving.

crease in the skin friction near the pile toe. Moreover, for tapered piles the lower radial expansion at the pile toe is partially responsible for the lower skin friction near the pile toe. Toe resistance The load transmitted to the pile toe was evaluated from the readings of the load cell located at the pile toe (see Fig. 2). The toe bearing pressure normalized by the initial mean effective pressure at the pile toe for LP and HP is shown in Figs. 15 and 16, respectively. In general, the toe bearing pressure for the tapered piles is higher than that of the cylindrical pile. Figure 15 shows that the toe bearing pressure for pile FC reached a limit value at ∆r = 0.2 for piles tested at LP. For tapered piles, the toe bearing pressure continued to increase as the displacement level increased. The toe bearing pressure for piles installed using toe driving was slightly higher than that for piles installed using head driving. Toe bearing pressure for piles tested at HP (Fig. 16) showed behaviour similar to that for piles tested at LP, but the normalized toe bearing pressure values were higher than those for the case of LP, probably because they were affected by the pretest load history. The toe capacity of a pile is usually expressed in terms of

a bearing capacity factor, Nq, multiplied by the effective vertical overburden pressure, σv′. The values of Nq depicted in the Canadian foundation engineering manual (Canadian Geotechnical Society 1992) are broad, however, and do not reflect the densification around the pile due to the installation method or the effect of taper angle on the bearing capacity characteristics of the surrounding soil. Moreover, the relative magnitude of the in situ horizontal and vertical stresses will affect the bearing capacity factor (Houlsby and Hitchman 1988). A simplified and rational approach for predicting the end-bearing capacity based on the spherical cavity expansion solution and elasticity theory was suggested by Randolph et al. (1994). In this solution, a rigid cone of the soil is assumed beneath the pile toe. Outside the conical region there is a zone of soil, nominally under isotropic stress equal to the limit pressure that can be determined using spherical cavity expansion theory. According to this theory, the end-bearing pressure, qb, is determined from [8]

q b = plim (1 + tan φ′ tan θ)

where plim is the limit soil pressure, φ′ is the effective internal frictional resistance, and θ is the cone angle (equal to φ). For dense sand, the limit pressure values can be determined © 2004 NRC Canada



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Fig. 15. Normalized bearing pressure for piles tested at low pressures and installed using (a) head driving and (b) toe driving.

using the spherical cavity expansion theory suggested by Yu and Houlsby (1991), which accounts for the effect of dilation of sand. The limit pressure for dense sand is given by

[9]

plim

 1 + sin φ′   3R∞ po  1 − sin φ′   =  ′  2 + 1 + sin φ   1 − sin φ′  

where R∞ is the cavity pressure ratio (ratio of the initial cavity radius to the final cavity radius) and can be determined using series expansion (for more details see, Yu and Houlsby 1991), and po is the initial effective mean stress. The peak friction angle φ and dilation angles can be determined based on relative density ratios following Bolton (1986, 1987) as [10]

φ = φ′ + 1.5I r

where

[11a] I r = 5I d − 1

for

σo′ ≤ 150 kPa

[11b] I r = I d [5.4 − ln(σo′ / pa )] − 1

for

σo′ > 150 kPa

where Id is the relative density, Ir is the rigidity index, σo′ is the mean effective stress, and Pa is the atmospheric pressure. The shear modulus can be obtained from the following expression: [12]

 σ′ Go = S exp(c1I d )  o pa  pa

   

where S is the modulus number (S = 75 for soils with 15%– 30% of particles passing through a 0.2 mm sieve (the current experiment)), c1 = 0.7, and n = 0.5. Table 6 shows the measured and calculated toe resistances for cylindrical and tapered piles at settlement ratio ∆r = 0.1. It is noted from Table 6 that the toe resistance of tapered piles was higher than that of the cylindrical pile, and the toe resistance increased as the taper angle increased. The measured toe resistance for different piles was lower, in general, © 2004 NRC Canada



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Fig. 16. Normalized bearing pressure for piles tested at high pressures and installed using (a) head driving and (b) toe driving.

than the calculated toe resistance based on eq. [8]. This can be attributed to the flexible boundary conditions imposed near the pile toe and their effect in restricting the full mobilization of toe resistance. Another reason for this behaviour is the choice of a “failure” criterion based on a small settlement ratio of 0.1, which resulted in underestimating the potential end-bearing capacity. As shown in Figs. 15 and 16, at large pile settlement ratios (∆r = 0.2) the unit end-bearing capacity of tested piles reached values of about 1.3–1.5 of the values measured at displacement ratio ∆r = 0.1. The total calculated pile capacity is plotted against the measured pile capacity in Fig. 17. As expected, the predicted overall pile capacities were higher, in general, than the measured values. The overall average ratio of calculated to measured capacity for all piles was 1.15, with a standard deviation of 0.12. Therefore, the proposed design method is considered feasible.

Conclusions Axial load tests were conducted on closed-toe tapered and

cylindrical FRP concrete composite piles driven into dry, dense, siliceous sand enclosed in a large-scale pressure chamber. The applied pressure simulated toe penetrations into a sand layer at depths of 4.0 and 8.0 m. The following conclusions are drawn: (1) The performance of FRP–concrete composite piles was comparable to that of steel piles. (2) The performance of tapered FRP composite piles was superior to that of cylindrical FRP composite piles per unit of volume. The shaft resistance of tapered FRP composite piles increased substantially compared with that of cylindrical FRP piles as a result of increasing the radial pressures. Measurements of the radial stresses during testing showed a more substantial increase in radial pressure for tapered piles than for cylindrical piles. (3) Piles installed using toe driving showed better performance manifested in higher skin friction than piles installed using head driving. The improvement in the pile performance in the case of toe driving may be ascribed to an increase in the angle of internal friction of the soil © 2004 NRC Canada



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87 Table 6. Comparison of measured and calculated tip resistance of tested piles. Toe resistance (kN)

Pile

Test

Installation method

FC FC T1 T1 T2 T2 T3 T3 FC FC T1 T1 T2 T2 T3 T3

LP LP LP LP LP LP LP LP HP HP HP HP HP HP HP HP

Head driving Toe driving Head driving Toe driving Head driving Toe driving Head driving Toe driving Head driving Toe driving Head driving Toe driving Head driving Toe driving Head driving Toe driving

Peak friction angle, φ (°)

Cavity pressure ratio, R∞

Calculated, (Qt)c

Measured, (Qt)m

Prediction ratio, (Qt)m/(Qt)c

42.2 44.8 41.7 44.2 42.2 44.8 42.1 44.8 42.2 44.8 41.7 44.2 42.2 44.8 42.1 44.8

15.4 16.4 17.5 18.0 17.8 20.2 17.5 18.6 15.4 16.4 16.1 18.0 17.0 17.6 17.5 18.6

68.5 84.1 85.1 99.7 77.3 99.8 71.8 87.3 107.6 125.6 146.1 171.0 168.7 198.8 175.3 195.6

51.6 56.8 59.1 67.5 62.5 73.4 64.2 74.1 64.2 63.2 105.1 140.8 125.4 170.5 173.7 199.2

0.75 0.68 0.69 0.68 0.81 0.74 0.89 0.85 0.60 0.50 0.72 0.82 0.74 0.86 0.99 1.02

Fig. 17. Comparison of ultimate capacity of tested piles in compression.

as a result of direct impact on the soil during toe driving. (4) The experimental results compared well with the analytical solution for calculating the shaft friction of tapered piles based on the cylindrical cavity expansion theory.

Toe resistance for cylindrical and tapered FRP composite piles was evaluated based on the spherical cavity expansion theory and agreed reasonably well with experimental results. The overall calculated bearing capacity of tested piles was within 20% of the measured © 2004 NRC Canada



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bearing capacity. Predicting tapered FRP capacity based on the aforementioned approach proved to be efficient, at least for the range of pile and soil parameters considered in this study. These conclusions are based on limited data and experimental test setup. To draw a general recommendation, however, field testing on FRP composite piles needs to be conducted. The results of this investigation will provide a valuable tool for evaluating the performance of FRP tapered piles.

References Canadian Geotechnical Society. 1992. Canadian foundation engineering manual. BiTech Publications, Vancouver, B.C. Bolton, M.D. 1986. The strength and dilatancy of sands. Géotechnique, 36(2): 219–226. Bolton, M.D. 1987. Discussion on the strength and dilatancy of sands. Géotechnique, 37(1): 65–78. El Naggar, M.H., and Sakr, M. 2000. Evaluation of axial performance of tapered piles from centrifuge tests. Canadian Geotechnical Journal, 37: 1295–1308. Houlsby, G.T., and Hitchman, R. 1988. Calibration chamber tests of a cone penetrometer in sand. Géotechnique, 38(1): 39–44. Iskander, M.G., and Hassan, M. 1998. State of the practice review in FRP composite piling. Journal of Composites for Construction, ASCE, 2(3): 116–120. Kodikara, K.K., and Moore, I.D. 1993. Axial response of tapered piles in cohesive frictional ground. Journal of Geotechnical Engineering, ASCE, 119: 675–693. Ladanyi, B., and Guichaoua, A. 1985. Bearing capacity and settlement of shaped piles in permafrost. In Proceedings of the 11th International Conference on Soil Mechanics and Foundation Engineering, San Francisco, Calif., 12–16 Aug. 1985. Vol. 4. A.A. Balkema, Rotterdam, The Netherlands. pp. 1421–1427. Lehane, B.M., Jardine, R.J., Bond, A.J., and Frank, R. 1993. Mechanisms of shaft friction in sand from instrumented pile tests. Journal of Geotechnical Engineering, ASCE, 119(1): 19–35.

Can. Geotech. J. Vol. 41, 2004 Nehdi, M., El Chabib, H., and El Naggar, M.H. 2003. Development of cost-effective self-consolidating concrete for deep foundation applications. Concrete International, American Concrete Institute, 25(3): 49–57. Norlund, R.L. 1963. Bearing capacity of piles in cohesionless soils. Journal of the Soil Mechanics and Foundations Division, ASCE, 89(SM3): 1–34. O’Neill, M.W., and Raines, R.D. 1991. Load transfer for pipe piles in highly pressured dense sand. Journal of Geotechnical Engineering, ASCE, 117(8): 1208–1226. Randolph, M.F., Dolwin, J., and Beck, R.1994. Design of driven piles in sand. Géotechnique, 44(3): 427–448. Sakr, M., and El Naggar, M.H. 2003. Centrifuge modeling of tapered piles in sand. Geotechnical Testing Journal, 26(1): 22–35. Sakr, M., El Naggar, M.H., and Nehdi, M. 2004. Novel toe driving for pipe pile installation and performance of FRP pile segments. Canadian Geotechnical Journal. Accepted for publication. Terzaghi, K. 1942. Discussion of the progress report of the committee on the bearing value of pile foundations. Proceedings of the American Society of Civil Engineers, 68: 311–323. Vesic, A.S. 1970. Tests on instrumented piles, Ogeechee River site. Journal of the Soil Mechanics and Foundations Division, ASCE, 96(SM2): 561–584. Vipulanandan, C., Wong, D., Ochoa, M., and O’Neill, M.W. 1989. Modeling of displacement piles in sand using a pressure chamber. In Foundation engineering: current principles and practice. Vol. 1. Edited by F.H. Kulhawy. American Society of Civil Engineers, New York. pp. 526–541. Wei, J., and El Naggar, M.H. 1998. Experimental study of axial behaviour of tapered piles. Canadian Geotechnical Journal, 35: 641–654. Yu, H.S., and Houlsby, G. 1991. Finite cavity expansion in dilatant soils: Part 1. Loading analysis. Géotechnique, 41(2): 173–183. Zil’berberg, S.D., and Sherstnev, A.D. 1990. Construction of compaction tapered pile foundation (from the experience of the Vladspetsstroi trust). Soil Mechanics and Foundation Engineering, 27(3): 96–101.

© 2004 NRC Canada
