Axial testing and numerical modeling of square ... - NRC Research Press

1142

Axial testing and numerical modeling of square shaft helical piles under compressive and tensile loading Ben Livneh and M. Hesham El Naggar

Abstract: Helical piles are increasingly used to support and rehabilitate structures subjected to both tensile and compressive axial loads. This paper presents a detailed investigation into the axial performance of helical piles. The study encompasses 19 full-scale load tests in different soils and numerical modeling using finite element analysis. The ultimate load criteria and load transfer mechanisms for helical piles were examined. In addition, the relationship between the installation effort (torque) and pile capacity was explored to determine its suitability for predicting pile capacity. The piles tested were made of three circular pitched bearing plates welded at a spacing of three helical diameters to a solid-square, slender steel shaft. It is proposed to determine the ultimate pile capacity as the load corresponding to pile head movement equal to 8% of the largest helix diameter plus the pile elastic deflection. A torque correlation factor, KT = 33 m–1 for compression and KT = 24 m–1 for uplift, was established to relate the ultimate pile capacity to the installation torque. It was found that load transfer to the soil is predominantly through a cylindrical shear failure surface that follows the tapered profile of the interhelices soils and the bearing capacity of the lead helix in the direction of loading. Key words: helical screw piles, load transfer mechanism, failure criterion, individual bearing, cylindrical shear, torque correlation. Re´sume´ : Des pieux he´licoı¨daux sont utilise´s de plus en plus pour soutenir et re´habiliter des structures soumises a` des chargements axiaux tant en traction qu’en compression. Cet article pre´sente une e´tude de´taille´e sur la performance axiale des pieux he´licoı¨daux. L’e´tude comprend 19 essais de chargement a` pleine e´chelle dans diffe´rents sols, et une mode´lisation nume´rique au moyen d’une analyse en e´le´ments finis. On a examine´ le crite`re de chargement ultime et les me´canismes de transfert de chargement des pieux he´licoı¨daux. De plus, la relation entre l’effort d’installation (torque) et la capacite´ du pieu a e´te´ explore´e pour de´terminer sa pertinence pour pre´dire la capacite´ du pieu. Les pieux teste´s e´taient constitue´s de trois plaques circulaires portantes en forme de vis soude´es a` un espace de trois diame`tres d’he´lice a` un essieu carre´-solide e´lance´ en acier. On propose de de´terminer la capacite´ ultime du pieu comme e´tant la charge correspondant au mouvement de la teˆte e´gal a` 8 % du diame`tre de l’he´lice le plus grand plus la de´flexion e´lastique du pieu. Un facteur de corre´lation du torque, KT = 33 m–1 pour la compression et KT = 24 m–1 pour l’arrachement a e´te´ e´tabli pour mettre en relation la capacite´ ultime du pieu avec le torque d’installation. On a trouve´ que le transfert de charge au sol se fait de fac¸on pre´dominante le long d’une surface de rupture en cisaillement cylindrique qui suit le profil conique des sols entre les he´lices; et la capacite´ portante de l’he´lice de teˆte dans la direction du chargement. Mots-cle´s : pieux en forme de vis he´licoı¨dale, me´canisme de transfert de charge, crite`re de rupture, portance individuelle, cisaillement cylindrique, corre´lation de torque. [Traduit par la Re´daction]

Introduction Helical piles (also referred to as anchors, anchor piles, or screw piles) have most commonly been used as ‘‘anchors’’, to resist tensile loads in supporting structures such as lighthouse beacons, buried pipelines, utility poles, guyed towers, and transmission towers. In recent decades, their applications in engineering projects have expanded to both support and rehabilitate structures under tensile, compressive, and Received 3 November 2007. Accepted 30 March 2008. Published on the NRC Research Press Web site at cgj.nrc.ca on 31 July 2008. B. Livneh and M.H. El Naggar.1 Geotechnical Research Centre, Faculty of Engineering, The University of Western Ontario, London, ON N6A 5B9, Canada. 1Corresponding

author (e-mail: [email protected]).

Can. Geotech. J. 45: 1142–1155 (2008)

lateral loading. Given their current increase in application, however, the amount of available research and design methodologies to date are relatively limited in comparison with other, more conventional piling solutions, and the majority of relevant research has been focused solely on the uplift condition. Therefore, given the lack of design procedures, the application of helical piles, particularly for the compression case, is considered in this investigation. The combination of variable shaft length and variable helix diameter has expanded the range of projects for which helical piles may be suitable. Their installation method allows them to reach a great depth with the addition of extension segments in the field, and thus increases their versatility. Helical piles are installed almost vibration-free, through the use of mechanical torque, which reduces damage to adjacent structures, and they can be constructed without excavating soil or pouring concrete. This allows for

doi:10.1139/T08-044

#

2008 NRC Canada

Livneh and El Naggar

cleaner and quicker installation and makes them both environmentally friendly and cost effective. Early approaches towards the evaluation of helical anchor capacity involved examining the behaviour of shallow single plate anchors. Utilizing either assumed or observed failure surfaces within the soil adjacent to the pile, several studies characterize the failure geometry for anchors. Majer (1955), Mors (1959), and Ireland (1963) proposed highly idealized conical (reaching the surface at an angle of 908 + , where  is internal friction angle of the soil) and cylindrical failure surfaces. More recently, theoretical studies on anchors conducted by Vesic (1971), Rowe and Davis (1982), and Saeedy (1987) included limit equilibrium and finite element analyses, which most notably focused on the behaviour of the soil immediately contiguous to the anchor and on whether its state of stress provided evidence of resistance to anchor loading. Laboratory investigations of anchor behaviour and failure geometry include half-scale and full-scale laboratory models by Balla (1961), Sutherland (1965), Downs and Chieurzzi (1966), Meyerhof and Adams (1968), Clemence and Veesaert (1977), Sutherland et al. (1982), Murray and Geddes (1987), Weizhi and Fragaszy (1988), Hoyt and Clemence (1989), Ghaly and Hanna (1991), Ghaly et al. (1991), and Narasimha Rao et al. (1993). The results included estimations of a failure surface reaching the ground surface at angles between /4 and /2 to the vertical. The behaviours of shallow and deep anchors were classified through either a failure surface extending to the ground surface (shallow anchor behaviour), or a localized shearing failure (deep anchor behaviour). Based on laboratory results, Balla (1961) established a breakout factor as a dimensionless quantity related to the peak pullout load (H/D: where ‘‘H’’ is the depth of embedment of the uppermost helix and ‘‘D’’ is the diameter of the largest helix), which can also be used to classify shallow and deep anchors. Narasimha Rao et al. (1989) conducted an experimental program with multihelix anchors showing that pile ultimate uplift capacity increases with (i) the number of helical plates; (ii) decreasing soil moisture content; and (iii) increasing soil consistency index. The development of a cylindrical failure surface below the top helix was shown for piles with small helical spacing (i.e., S/D £ 3, where S is the space between helical plates and D is the average helical diameter). In this regard, the results of Narasimha Rao and Prasad (1991) and Narasimha Rao et al. (1993) were consistent with the findings of Mitsch and Clemence (1985), who presented results of both laboratory and field investigations on triple helix anchors. Mitsch and Clemence (1985) provided a method for estimating the uplift capacity of shallow and deep piles, dependent on pile embedment, helical spacing, and soil conditions. Aside from the empirical estimation of helical pile capacity through a correlation to installation torque, there presently exists two general theories describing the failure mechanism of multihelix anchors, namely through cylindrical shearing, involving the development of a failure surface between the interhelical soil, and through individual bearing of each helical plate, where each helix behaves independently. The distinction between these methods has significant

1143

implications on pile ultimate capacity and is of particular interest for this investigation.

Experimental investigation The main objective of this research is to evaluate the axial performance of helical piles by means of a full-scale loading program and the development of a numerical model. The specific objectives of the full-scale load testing program were (i) to determine the load transfer mechanism for compressive and tensile loading in different ground conditions; (ii) to define appropriate ultimate load criteria for helical piles; (iii) to evaluate the compressive and tensile capacity of tested helical piles based on these criteria; and (iv) to explore the relationship between the installation effort (torque) and the capacity of the pile and determine whether this relationship can be used as a predictor for the pile capacity and (or) performance acceptance of the pile. The numerical model was used to further address some of the research objectives, namely, to determine the load transfer mechanism and to establish a theoretical model to evaluate the capacity of helical piles under different loading conditions.

Pile description The ‘‘SS175 Chance foundation system’’ used in this evaluation is manufactured by AB Chance Company (Centralia, Mo) and it consists of three helical bearing plates (diameters 300 mm, 250 mm, and 200 mm – decreasing with depth) welded to a central shaft (44.5 mm) and it is defined as a segmented deep foundation system. Extension segments (or sections) are attached to the lead section with bolted couplings during installation to allow the system to bear upon soil at a desired depth. The helical shape of the bearing plates allows for minimum soil disturbance during installation and because each helix is a single 75 mm pitch of a screw thread, the system can literally screw into the ground. The path of each consecutive helix follows the same path as the preceding one during installation in such a scenario. The lead section of the pile (Fig. 1) supports the loads applied to the system by transferring them to the soil. The spacing between the plates is approximately three times the diameter of the lower plate (i.e., S/D & 3, or 750 mm and 600 mm with increasing depth), and it provides improved pile capacity as this preferred spacing is prescribed as the interval between the two governing failure mechanisms, namely individual bearing and cylindrical shearing (Hubbell Power Systems Inc. 2003).

Site investigation, pile installation, and loading apparatus The load testing program was conducted at two locations on the Environmental site at The University of Western Ontario, London. Two boreholes were performed using a hollow stem auger mounted on a rig. The soil profiles are composed of layers of clayey and sandy silts overlying deep deposits of either stiff silty clay (site 1) or dense-fine sand (site 2). The ground water table elevation in the site varied between 5.2 and 6.5 m below the ground surface (based on these boreholes and other boreholes in the site area performed before and after this testing program). The standard #

2008 NRC Canada

1144

Can. Geotech. J. Vol. 45, 2008

Fig. 1. Schematic of a typical pile lead section. f, internal friction angle of the soil.

Table 3. Summary of geotechnical properties of soil from site 1 at 2.4 m.

Table 1. Borehole and SPT results from site 1. Layer Stiff brown sandy clayey silt Very stiff brown clayey silt (W.T. depth) Stiff grey clayey silt Very stiff grey sandy clayey silt Dense grey silt

Depth (m) 2.4 4.1 5.8 7.3 >7.3

N-value 19 25 11 17 30

Note: W.T., water table; N-value, SPT value (i.e., number of blows).

Table 2. Borehole and SPT results from site 2. Layer Stiff brown sandy clayey silt Very stiff grey clayey silt (W.T. depth) Very stiff grey clayey silt, embedded gravel Dense grey fine sand, trace of silt

Depth (m) 2.6 4.1 5.2

N-value 34 21 20

>5.2

32

Note: W.T., water table; N-value, SPT value (i.e., number of blows).

penetration test (SPT) was conducted at each site to a minimum depth of 8 m, using a safety hammer with a rope and cathead. Advancing a split spoon sampler, the SPT results are provided in Table 1 and Table 2. Three consolidated undrained triaxial tests were conducted on spilt spoon soil samples retrieved at a depth of 2.4 m at site 1, to evaluate the total and effective shear strength parameters (undrained shear strength, cu, cohesion, c’, and angle of internal friction, ’). The results of this test along with the combined results of sieve and hydrometer analysis from this location are provided in Table 3. Complete logs of pile installation included readings of torque, taken at depth intervals of 0.3 m (1 ft). The profiles of installation torque throughout the depth of installation are shown in Fig. 2. Based on an empirical correlation factor, KT, the installation torque readings were used to estimate pile capacity, such that Qt = KTT (where Qt is the predicted pile capacity and T is the installation torque of the pile). The estimated capacity was used to prescribe the load increments in the testing program. This correlation has long been used in the field, with the rationale that installation torque is a measure of the energy required to overcome the shear strength of the soil and is hence directly related to pile capacity. During installation of piles to be tested in compression,

Gravel content (%) Sand content (%) Silt-clay content (%) Specific gravity Moisture content (%) Liquid limit Plastic limit Plasticity index Undrained shear strength, Su = cu (kPa) Undrained elastic modulus, Eu (MPa) Effective strength, c’ (kPa) Internal friction angle, ’ (8) Drained elastic modulus, E’ (MPa)

1.40 62.80 35.8 (38% clay and 62% silt) 2.85 23.50 29 25 4 60 60 10 28 54

the annular cavity (~90 mm) created by the square pile-shaft and the broad cross-section of the forged socket of the coupler means was constantly filled with a cementitious-based grout. After curing, the grout effectively increased the buckling resistance of the slender shaft by mobilizing the surrounding soil resistance, as well as provided additional rigidity to the connections. Reaction piles were installed at a distance of 2.7 m from the testing piles at roughly the same depth as the testing pile to effectively anchor the testing frame. Figure 3a illustrates the general layout for the setup for compression load testing. The figure shows the reaction frame, which consists of four reaction piles (in tension), the load beam (steel 600  242 I-beam), and two spreader beams (two steel 300  88 I-beams). The pile head was fixed using a 150 mm diameter hollow PVC pipe that extended approximately 1.3 m below the ground, around which was secured a 1 m ‘‘T-pipe’’ that was grouted and served as the pile cap; a flat, leveled surface for the loading jack. The load was measured using a calibrated load cell between the hydraulic jack and the loading frame and also through the measurements recorded on the hydraulic pressure of the loading jack. The apparatus for tension load testing is shown in Fig. 3b. The load readings were taken in a similar manner to the compression testing. For all cases, the displacements were monitored using three dial-gauges configured on the pile cap. #

2008 NRC Canada

Livneh and El Naggar Fig. 2. (a) Installation torque versus depth for piles at site 1. (b) Installation torque versus depth for all piles at site 2. (c) Installation torque versus depth for piles adjacent to site 1.

1145

The axial pile load tests were conducted according to ASTM D1143–81 (ASTM 1994) and ASTM D3689–90 (ASTM 1995) in which loads were applied in increments of approximately 10% of the estimated pile capacity in 5 min time intervals. In some cases, loading increased beyond the estimated pile capacity until continuous jacking was required to maintain the load or continuous creeping settlement was observed (i.e., failure).

Load testing program In total, 19 test piles were installed in two separate sites in the field. Seven of the test piles at site 1 were installed such that the lead sections rested within the upper clayey silt layers (approximately 5 m depth), and seven piles were installed such that the lead sections rested within the lower dense silt layer (approximately 9 m depth). At site 2, one pile was founded in clayey silt and four piles were installed such that all lead sections lay in sandy soil at a maximum depth of 7.8 m. According to the definitions proposed by Ilamparuthi et al. (2002) and by Meyerhof and Adams (1968), all piles tested in this evaluation are classified as ‘‘deep piles’’ based on their embedment depths and would hence experience a localized failure surface that does not extend to the ground surface.

Load and deflection data The pile capacity was estimated knowing its installation torque using a nominal value of KT = 33 m–1 (10 ft–1) for compression piles and KT = 26 m–1 (8 ft–1) for tension piles, based on the results of previous investigations (e.g., Hoyt and Clemence 1989). The load was applied in a minimum of 10 increments. For each load increment, the readings from the three dial gauges were taken and averaged. The incremental readings from the load cell were plotted against the averaged dial gauge readings to yield a load– deflection curve for each pile tested. These curves provided a useful tool to establish the ultimate pile capacity. The ultimate failure load for a pile may be defined as the load when the pile plunges, or settlement increases rapidly under sustained load (Prakash and Sharma 1990). Plunging failure typically involves settlements that far exceed the acceptable range for design and may not always be attained during a load test. If plunging does not occur clearly, another definition of ultimate load is needed. The load–movement curves for piles generally include three different regions: an initial linear region with large slope (i.e., high stiffness); a strongly nonlinear region with pile movements disproportionately larger for each load increment; and finally, a nearly linear region with small slope (i.e., low stiffness). The onset of failure in the load–movement curve is typically found within the nonlinear portion of the curve, between the initial linear–elastic portion and the final, nearlinear rapid failure section. It is within this region that the ultimate pile capacity is defined under most failure criteria. The special case of ‘‘plunging failure’’ describes a situation where the final, rapid-failure region of the load–movement curve is nearly horizontal (i.e., slope & 0). The ultimate load of the pile is taken to be the load that occurs at the onset of plunging for this special case. #

2008 NRC Canada

1146

Can. Geotech. J. Vol. 45, 2008

Fig. 3. (a) Depiction of load testing apparatus for compressive load application; beam positioning in relation to test pile and wood cribbing. (b) Depiction of load testing apparatus for tensile load application; beam positioning in relation to test pile and wood cribbing.

Failure criterion applied to load test results Based on the pile load–movement trends, it is noted that the behaviour was different for piles tested in tension and compression. The pile behaviour in the uplift case was initially very flexible, attributed to overcoming the slack of the loading apparatus (i.e., the reaction beam supported by wood cribbing, bearing on adjacent, relatively loose surficial soil). After undergoing large initial displacements of between 2 and 10 mm associated with the first load increment, these piles exhibited a curvilinear tendency until failure ensued, resulting in large displacements associated with each successive load increment in the nonlinear region. This trend was particularly pronounced for piles tested in clayey silt. Thus, it was necessary to exclude the initial ‘‘slack’’ displacement from the estimation of a failure criterion since this behaviour was the result of the testing apparatus and not the pile itself. For compressive loading, the initial linear–elastic region started from the beginning of the load test. Collectively, the near-linear failure region was achieved at a net displacement of greater than 8% of the largest helical diameter (i.e., 0.08D). Historically, estimates of pile capacity have been made considering various schemes related to pile geometry and the shape of the load–deflection curve, as depicted in Table 4. Most investigators consider some fraction of the characterstic pile dimension D (width for shallow foundations;

Table 4. Commonly used failure criteria for interpreting pile capacity (adapted from Zhang et al. 2005). Failure criterion AS-2159 (SAA 1995)

Davisson’s criterion (Davisson 1972) FDOT criterion (FDOT 1999) FHWA criterion (Reese and O’Neill 1988) ISSMFE criterion (ISSMFE 1985) and BS 8004 criterion (BSI 1986) Slope and tangent method (Butler and Hoy 1977)

Displacement at failure 50 mm at 1.5 times the design load and 30 mm at unloading 15 mm at serviceability load and 7 mm upon unloading PL D AE þ 120 þ 4 ðmmÞ PL AE

D þ 30 for piles with D > 0.61 m

5%D 10%D

Defined as the deflection at the intersection of tangents to the linear-elastic section and plunging failure section*

*Slope of plunging section to be equal to 1 in./40 kip (14.3 mm/100 kN).

diameter for piles), elastic displacement, or intersection of load–deflection tangents to define a failure criterion. Thus, given the unique geometry of helical piles, the failure criterion used to describe the amount of settlement experienced at the pile head at the ultimate pile load was related to the #

2008 NRC Canada

Livneh and El Naggar

largest  helical diameter, D, and elastic deflection of the pile PL AE , such that: ½1

S¼

PL þ 0:08D AE

1147 Fig. 4. (a) Tensile load–deflection curve for a pile tested in clayey silt. (b) Compressive load–deflection curve for a pile tested in dense silt. (c) Compressive load–deflection curve for a pile tested in sand.

where S is the settlement experienced at failure; P is the applied load at failure; L is the length of the pile; A is the cross-sectional area of the pile shaft; E is the Young’s modulus for the steel; and D is the diameter of the largest helix. Figure 4a shows the load–deflection curve and failure criterion for a pile tested in clayey silt in tension. The shape of this graph was characteristic of piles tested in tension and the failure criterion consistently fell within the nonlinear region for these curves. The load–deflection behaviour and failure criterion for a pile tested in dense silt in compression is presented in Fig. 4b. The plunging behaviour exhibited by this pile was exclusive to compression piles in dense silt. The typical load–deflection behaviour for nonplunging compression piles is observed in Fig. 4c. It is noted that the initial-linear region of load deflection curves for piles tested in clayey silt exhibited very steep slopes relative to other piles, while piles tested in sand showed a relatively steep, curvilinear tendency throughout the loading cycle. For all piles, the application of the proposed failure criterion led to the conclusion that piles installed in sand had the greatest ultimate capacity followed by dense silt and clayey silt. Additionally, compression piles carried greater loads than tension piles; and within the same soil layer, piles installed to a greater depth had higher ultimate capacities than shallower ones.

Installation torque – ultimate pile capacity relationship Various authors have confirmed a relationship between installation torque and ultimate pile capacity (Hoyt and Clemence 1989; Ghaly and Hanna 1991). Based on the load test results, Tables 5 and 6 summarize the load–torque correlation, KT, for compression and uplift, respectively. The bestfit line was translated to intercept the origin, while preserving the slope, yielding proposed values that are inherently conservative. The results from two load tests were not representative of the typical load–torque relationship: pile No. 3 due to the slight eccentricity caused by a misalignment of the loading system and pile No. 18 due to severe damage of its bottom helix caused by striking a cobble (which was visually confirmed upon retrieving the pile). Table 5 presents a ratio of installation torque to ultimate compressive capacity, KT, of between 35.3 m–1 (10.6 ft–1) and 62.1 m–1 (18.9 ft–1), excluding pile No. 3. The values of KT in dense and clayey silt range between 35.3 m–1 (10.6 ft–1) and 42.5 m–1 (13 ft–1), while in sand the value is greater than 60 m–1 (18.2 ft–1). The value of KT for tension piles varied between 21.3 m–1 (6.5 ft–1) and 36.3 m–1 (11.1 ft–1) as shown in Table 6. The upper range values correspond to piles tested in dense silt and sand and the lower range belongs to piles tested in clayey silt. The representative torque constants for piles tested in sand lies between 24.3 m–1 (7.4 ft–1) and 32.7 m–1 (10.0 ft–1). These values are in agreement with the findings reported in the literature. Figure 5 illustrates the relationship between ultimate com-

pressive capacity and the torque averaged over the final 1 m of installation. The curve confirms that the pile capacity is directly proportional to the installation torque and the slope of the curve represents the torque correlation constant, KT. Figure 6 shows the relationship between pile ultimate uplift capacity and the average installation torque over the final 1 m of installation. The curve shows a direct relationship #

2008 NRC Canada

1148

Can. Geotech. J. Vol. 45, 2008 Table 5. Pile capacity and torque constants for piles tested in compression. Pile No. 1 2 3 4 5 6 13 14

Site No. 1 1 1 1 1 1 2 2

Depth, D, of top helix (m) [ft] 7.6 [25] 7.6 [25] 7.6 [25] 3.4 [11] 3.0 [10] 3.0 [10] 5.8 [19] 6.1 [20]

Soil type Dense silt Dense silt Dense silt Clayey silt Clayey silt Clayey silt Sand Sand

Pile capacity (kN) [kip] 465 [104.6] 490 [110.2] 360 [80.9] 350 [78.7] 320 [72] 325 [73] 695 [156.2] 660 [148.4]

Average torque over last 1m (kNm) [lbft] 11.76 [8666] 11.54 [8500] 13.80 [10166] 9.95 [7333] 8.73 [6433] 8.60 [6333] 11.31 [8333] 10.63 [7833]

KT (m–1) [ft–1] 39.5 [12] 42.5 [13] 26.1 [8] 35.3 [10.6] 36.5 [11.1] 37.8 [11.5] 61.5 [18.7] 62.1 [18.9]

Note: Pile capacity observed at 8%D plus elastic displacement.

Table 6. Pile capacity and torque constants for piles tested in tension. Pile No. 7 8 9 16 20 10 17 18 15 12 19

Site No. 1 1 1 1a 2a 1 1b 1b 1a 2 2a

Depth, D, of top helix (m) [ft] 3.7 [12] 4.0 [13] 3.0 [10] 3.0 [10] 2.1 [7] 4.3 [14] 8.2 [27] 8.5 [28] 9.1 [30] 5.2 [17] 7.9 [26]

Soil type Clayey silt Clayey silt Clayey silt Clayey silt Clayey silt Clayey silt Dense silt Dense silt Dense Silt Sand Sand

Pile capacity (kN) [kip] 190 [42.8] 260 [58.3] 160 [36.0] 180 [40.5] 295 [66.2] 245 [55.0] 220 [49.5] 165 [37.0] 350 [78.7] 300 [67.4] 360 [80.9]

Average torque over last 1.5 m (kNm) [lbft] 8.91 [6570] 9.80 [7200] 6.55 [4800] 7.64 [5600] 10.10 [7400] 9.93 [7300] 7.07 [5200] 7.64 [5600] 9.63 [7100] 12.35 [9100] 10.99 [8100]

KT (m–1) [ft–1] 21.3 [6.5] 26.5 [8.1] 24.4 [7.5] 23.6 [7.3] 29.2 [9.0] 24.7 [7.6] 31.1 [9.5] 21.6 [6.6] 36.3 [11.1] 24.3 [7.4] 32.7 [10.0]

Note: Pile capacity observed at 8%D plus elastic displacement.

similar to that for compression piles. Plotted on the same scale, it yields however, a slightly smaller value of KT. For design purposes, the solid lines shown in Fig. 5 and Fig. 6 are proposed. Consistent with previous findings, installation torque averaged over the last 3 ft of installation was shown to be correlated with ultimate pile capacity. Beyond the inherent uncertainty of the condition of the soil beneath the lowest helix (compression case), this value provides a reasonable estimate of the strength of the soil surrounding the pile. Altogether, KT was found to be dependent on both soil strength (Fig. 2) as well as on loading direction. Values of KT tended to be higher (lower) in compression (tension) and varied directly with soil strength.

Further analysis Several of the piles tested in this investigation were instrumented with strain monitoring equipment. The results of the strain monitoring were limited to a great extent by the deleterious effects of pile installation. However, strain data obtained during load testing was used to verify load transfer in the development of a finite element model (FEM).

Finite element model development The main objective of modeling helical pile behaviour was to define the failure mechanism and load–transfer be-

haviour for each pile. Upon calibration–verification with the experimental data, the FEM provided insight into the effects of pile loading on the surrounding soil. Based on the findings of the model and full-scale load test results, a methodology for calculating pile capacity was developed. To account for the unique geometry of the problem a software program capable of realistically analyzing threedimensional soil–foundation interaction, namely the Plaxis 3D Foundation suite, was selected. To minimize boundary effects on pile responses, the lateral boundaries of the numerical model were placed at 4 m from the pile centre and the vertical (bottom) boundary was placed at 40 m below the ground surface. This allowed for a buffer of approximately 13 pile diameters (of largest helix) between the pile and any lateral boundary, and 30 m, or approximately 3 pile lengths in the vertical direction. The boundary conditions were as follows: (1) Vertical model boundaries with their normal in x-direction (i.e., parallel to the y–z plane) are fixed in the x-direction (ux = 0) and free in y- and z-directions. (2) Vertical model boundaries with their normal in z-direction (i.e., parallel to the x–y plane) are fixed in the z-direction (uz = 0) and free in x- and y-direction. (3) Vertical model boundaries with their normal neither in x- nor in z-direction (skewed boundary lines in a work plane) are fixed in the x- and z-directions (ux = uz = 0) and free in the y-direction. #

2008 NRC Canada

Livneh and El Naggar Fig. 5. Pile compressive capacity versus installation torque.

1149 Fig. 7. Distribution of wedge elements within the model and nodes and stress points in a typical 15-node wedge element. z, x, horizontal plane; h, vertical dimension.

Fig. 6. Pile uplift capacity versus installation torque.

grouted column associated with compression piles was ignored in the model, given the limited resistance provided, as well as its variable consistency in the field. The models were validated through a comparison with measured pile responses and strains along the pile during the load test.

Model input parameters

(4) The model bottom boundary is fixed in all directions (ux = uy = uz = 0). (5) The ‘‘ground surface’’ of the model is free in all directions. On average, each model consisted of approximately 10 000 elements (15-node wedge elements, with 6-noded boundary elements) with an average size of 0.528 m, as depicted in Fig. 7. The mesh was refined in the vicinity of the pile, that is, smaller dimension elements were generated, to improve the accuracy of the model. Interfaces are composed of 15-node interface elements of ‘‘virtual thickness’’ consisting of eight pairs of nodes, compatible with the 8-noded quadrilateral side of a soil element. Along degenerated soil elements, interface elements are composed of 6 node pairs, compatible with the triangular side of the degenerated soil element. Soil–pile interfaces are considered ‘‘smooth’’, in that minimal relative displacements at the interface are allowed. The numerical model was constructed to match the fullscale geometry of the pile in all regards excluding the helical shape of the bearing plates, which were modeled as circular discs rather than pitched plates. Additionally, the

The Mohr–Coulomb model was used to represent the soil behaviour, for which cohesion and friction angle values were obtained through limited triaxial test results and estimations based on SPT values. The soil parameters used in the model were ‘‘fine tuned’’ to enhance the match between the calculated and measured load–deflection values for each pile. The process of establishing the model’s soil parameters began by generating and loading a model for each pile at a given site. Considering initially both total and effective stress analyses, the high percentage of granular material (which exhibits relatively rapid drainage) and the relatively slow loading rate revealed that effective stress parameters were absolutely the most representative for the analyses at both sites. The load–deflection relationships resulting from the model simulations were plotted together with the load– deflection data obtained in the field for each pile. The model soil parameters were then adjusted slightly until there was sufficient agreement between load–deflection curves from the field and the model simulation results, for the majority of the piles on the same site. Figure 8 shows the load–deflection curves from the FEM and field load test for a pile tested in compression. Installed to a depth of approximately 4.5 m, this pile rested in two clayey silt layers. Because the measured and calculated load–deflection curves are in excellent agreement, as illustrated in Fig. 8, the soil properties used in this model are #

2008 NRC Canada

1150

considered to be representative of the soil properties of the two aforementioned soil layers for all other piles tested on site 1. This process was repeated in cases where piles were installed in different soil layers at the same site, until the entire soil stratigraphy was established and in good agreement for all piles. The input parameters used in the model are provided in Table 7 and Table 8. The high values of cohesion are indicative of overconsolidated soil.

Analysis of results The piles tested in the field were loaded beyond the onset of failure. In some cases, the failure detected in the FEM occurred at loads lower than those achieved in the field and as a result, the numerical analysis could not be performed past the onset of failure. This was primarily the result of the imposed failure condition, in effect, when the applied load had to be reduced in three successive calculation steps to reach equilibrium. Beyond this point, the ‘‘soil body’’ surrounding the pile collapsed due to the imbalance between incremental loads and soil shear strength; the result being large displacements for each successive, relatively small load increment. In light of this, the load–deflection curves generated by the FEM were loaded to a level that matched the field load–deflection curves at least to the onset of rapid failure in all cases.

Load transfer mechanism The interaction between the pile and surrounding soil was examined from the output of the numerical models, and the load transfer mechanism was established accordingly. Numerous analyses of the model output data were carried out to characterize pile behaviour. This included inspection of the state of stress within the soil in the vicinity of the pile during the load. It also included examination of the strain and displacement contours within the soil. Based on these analyses, a conservative estimate of the shape of the model failure surface was identified and an idealized failure mechanism was established. This was further used to define the load transfer mechanism of the pile and to develop a model to calculate the capacity of the helical piles.

Soil displacement Monitoring soil displacements is a widely used technique for estimating the failure surface of laboratory models. To employ this approach in the numerical study, the total soil displacements around the pile were noted at failure. The contours of soil displacement are provided in increments of 20% of total pile displacement in Figs. 9a and 9b for piles tested in compression and tension, respectively. These two piles were found to behave in a manner most characteristic of other piles under similar loading. The strain level beyond the final shown contours was negligible (3 < 1  10–4). Inspecting Fig. 9, the majority of the soil displacement occurs within a radial distance of 1.5 helical diameters (of largest helix) from the centre of the pile for both the tension and compression cases. Additionally, the displacement contours follow immediately outside the annulus region enclosing the tapered helical profile extending from the top large helix to the bottom small helix. For the compressive loading case (Fig. 9a), the radial ex-

Can. Geotech. J. Vol. 45, 2008

tent of displacement contours are greatest at the level of the top helix and are more pronounced for shallower piles. Above the top helix, the displacement follows a conical shape, reaching a maximum height of greater than one diameter of the uppermost helix. This region was shown to represent soil that is experiencing tensile stresses due to the downward movement of the pile. A deep region of displacement below the bottom helix was present for all compression piles extending to a depth of greater than two diameters of the lowest helix below the pile, which was likely due to bearing of the bottom helix on the soil below. The displacement contours for all compression piles suggest that the failure surface follows a tapered cylinder shape that roughly matches the interhelical profile. The load transfer mechanism for compressive loading may therefore simplify to a tapered pile-geometry extending between the top and bottom helices with the bottom helix essentially representing the ‘‘pile toe’’. The toe resistance in this case may contribute a significant portion of the pile capacity as the toe bears on minimally disturbed soil. For the case of uplift loading (Fig. 9b), all piles exhibit a large region of soil displacement that extends above the top helix to a height of greater than two diameters of the uppermost helix. This indicates significant bearing of the top helix on the above soil, as suggested in the literature. Similar to the compressive loading case, the greatest radial extent of the displacement contours was near the top helix. This region was somewhat dissimilar however, to the rupture surface proposed by Ilamparuthi et al. (2002), which projects outward from the top helix at an angle of 0.8. Based on the results of the present model, the breadth of the displacement region was slightly greater than the diameter of the top helix and tapered inward, rather than outward. However, it should be noted that the investigation of Ilamparuthi et al. (2002) was carried out on piles with lower embedment than the piles modeled here. Below the bottom helix, the displacement contours extended to a depth approximately equal to its diameter, enclosing a region of soil under tensile stresses. Therefore, the soil displacements for the uplift case suggest a tapered failure surface that follows the interhelical profile combined with substantial bearing of the top helix on the above soil.

State of stress The state of stress within the soil around the pile was noted at the failure load. The analysis of these stresses was helpful in characterizing the soil zone where the stresses in the soil approached the strength of the soil and failure was likely to occur. It is therefore most convenient to assess the state of stress in the soil in terms of the relative shear stress. The relative shear stress, trel, is defined as ½2

trel ¼

t tmax

where t* is the maximum value of shear stress (i.e., the radius of the Mohr stress circle). The parameter tmax is the maximum value of shear stress for the case where the Mohr’s circle expanded to touch the Coulomb failure envelope, keeping the intermediate principal stress constant. Thus a relative shear stress value of trel = 1 is indicative of soil failure. #

2008 NRC Canada

Livneh and El Naggar

1151

Fig. 8. Measured and computed load–deflection values for a compression pile in clayey silt.

Table 7. FEM soil properties at site 1. Layer Stiff brown sandy clayey silt Very stiff brown clayey silt (W.T. depth) Stiff grey clayey silt Very stiff grey sandy clayey silt Dense grey silt

Depth (m) 2.4 4.1 5.8 7.3 >7.3

g (kN/m3) 17.3 17.5 16.5 15 17

gsat (kN/m3) 17.3 18.5 18.5 18 19

c (kPa) 10 21 9 20 19

 (8) 28 27 23 30 34

E (kN/m2) 60 000 85 000 100 000 400 000 65 000

Note: W.T., water table; g, unit weight of the soil; gsat, saturated weight of the soil; c, cohesion of the soil; f, internal friction angle of the soil; E, Young’s modulus.

Table 8. FEM soil properties at site 2. Layer Stiff brown sandy clayey silt Very stiff grey clayey silt (W.T. depth) Dense grey fine sand, trace of silt

Depth (m) 2.6 5.2 >5.2

g (kN/m3) 18.5 17 18

gsat (kN/m3) 18.5 19 20

c (kPa) 22 23 6

 (8) 33 27 38

E (kN/m2) 40 000 300 000 100 000

Note: W.T., water table; g, unit weight of the soil; gsat, saturated weight of the soil; c, cohesion of the soil; f, internal friction angle of the soil; E, Young’s modulus.

Examining the relative shear stress of piles tested in compression reveals similarities to the soil displacement contours (Fig. 9a), however, the region of soil ‘‘approaching failure’’ tends to be much greater than that within a high concentration of soil displacement contours. Figure 10a shows a schematic of the full range of extent of the soil regions approaching shear failure (i.e., trel & 1) for all compression piles. Although the regions where the relative shear stress approaches soil strength overestimates the size of the failure region, they showed a consistent similarity to the shape of the soil displacement geometry and served to confirm the general geometry of the failure zone that was used to develop a design methodology. Similar to the compression case, Fig. 10b shows a schematic of the range of relative shear stress failure extents for

all tension piles. In a similar manner, these extents resembled and confirmed the displacement contour failure geometry, with only a slightly larger volume of soil considered to be approaching failure.

Design method for compressive loading applications Based on both measured and simulated behaviour of the helical piles considered in this investigation, a method for predicting the axial compressive capacity of the pile is presented.

Development of a failure surface The regions of highest density of displacement contours #

2008 NRC Canada

1152 Fig. 9. (a) Soil displacement contours for a compression pile as a percentage of total pile displacement at failure. (b) Soil displacement contours for a tension pile as a percentage of total pile displacement at failure.

Can. Geotech. J. Vol. 45, 2008

Calculation of pile capacity Under compression, it was shown that loads are transferred to the soil through two mechanisms: (i) shear resistance derived from a cylindrical failure surface along the interhelical soil profile, and (ii) bearing of the bottom helix on the soil below. A model is proposed for evaluating the contribution of each of these load transfer mechanisms to the pile capacity. El Naggar and Sakr (2000) developed a technique for predicting the axial compressive capacity of tapered piles installed in sand. In this model, a taper coefficient, Kt, was introduced to account for the taper effect on the skin friction, Qs, along the pile shaft, such that ½3

QsðtaperedÞ ¼

Zl

Kt Ks v0 tanðÞpdz

0

where Kt is the taper coefficient; Ks is the coefficient of lateral earth pressure; v0 is the effective overburden pressure; d is the pile–soil interface friction angle (in this case d = ; soil–soil interface); p is the pile perimeter; and l is the length of the pile shaft. The value of Kt is computed based on several factors, such as the ratio, Sr, of pile settlement to diameter (= Up/D), where pile settlement, Up, is evaluated using eq. [1], and Kt is given by (El Naggar and Sakr 2000) ½4

(i.e., greatest relative soil displacements) characterized the pile failure surface. Considering the smallest extents of the failure region to be representative ensures a consistent and conservative solution, which is vital for design and application. Therefore, the following observations established the geometry of the failure region for calculation of the compressive axial capacity of the system: (1) Between the lowermost two helices, the failure surface is observed to closely follow the profile of the helices and is considered as such for design. (2) At the level of the top helix, the failure surface is found to extend a minimum radial distance of 30% of its diameter away from the helix. This value is used in the calculations. (3) The extent of the failure surface above and below the top and bottom helices was found to be highly variable, and it is recommended that it be ignored for design purposes. Above the top helix, the soil was found to be in tension, which will not contribute significantly to pile capacity, while soil displacements below the bottom helix are attributed to the bearing resistance of this helix. (4) The theoretical toe bearing of the bottom helix is used in conjunction with the estimated shearing resistance between the helices to estimate pile capacity. These observations are summarized in Fig. 11. The taper angle, a, of the helices is approximately 2.128. The taper angle between the uppermost two helices is approximately 5.338 when considering the effect of the broad region of displaced soil contiguous to the top helix.

Kt ¼ A o þ

Bo Sr sv

where Ao and Bo depend on d, Ks, the elastic modulus of the soil, G, and the taper angle, a, given by ½5

Ao ¼

tanð þ ÞcotðÞ 1 þ 2tanðÞtanð þ Þ

Bo ¼

4GtanðÞtanð þ ÞcotðÞ ½1 þ 2tanðÞtanð þ ÞKs

In eq. [5], G is the shear modulus of the elastic soil; and z ¼ lnðr1 =rm Þ, in which rm is the average pile radius, and r1 is the radius at which the shear stress becomes negligible and is taken to be equal to 2.5/(1 – n), where n is Poisson’s ratio of the soil. The contribution of toe bearing from the bottom helix, Qp, was estimated using the approach outlined by Vesic (1963) for drilled shafts. The bearing capacity factors associated with drilled shafts were more representative of helical piles and the influence of their installation disturbance on surrounding soil. Therefore, the toe bearing capacity of the bottom helix was estimated by ½6

Qp ¼ Ap ðcNc þ q0 Nq Þ

Combining eqs. [3] and [6], and considering two tapered regions of cylindrical shearing resistance, the compressive capacity of the pile is estimated as ½7

Qu ¼ Qsð¼5:33 Þ þ Qsð¼2:12 Þ þ Qpðbottom helixÞ

The values of the pile capacity calculated using eq. [7] #

2008 NRC Canada

Livneh and El Naggar

1153

Fig. 10. (a) Schematic covering the minimum extents for soil surrounding compression piles that is approaching relative shear stress failure (i.e., trel = 1). (b) Schematic covering the minimum extents for soil surrounding tension piles that is approaching relative shear stress failure (i.e., trel = 1). D, diameter of the top helix; Qu, axial capacity of the pile.

Fig. 11. Schematic of pile failure components for compressive loading application. a, taper angle; D, diameter of the top helix; Qu, pile capacity (under compression); Qp, toe bearing capacity of the pile; Qs(tapered), skin friction capacity of the pile along the tapered failure surface.

are summarized in Table 9 and are compared with measured field values determined from the field load tests. The calculated capacities are found to be in good agreement with the measured values to within 12% in all cases. The results indicate that this method is suitable for design, as it consistently yields a conservative estimate of pile capacity. The

design capacity of the pile can be obtained from the ultimate capacity using an appropriate factor of safety.

Tension piles The mode of failure is slightly different in the uplift case as the effect of the tapered shaft does not improve pile capacity the way it does for the compression case (El Naggar and Wei 1999). Numerous existing techniques were examined to predict the tensile capacity of the helical piles tested; however, the method proposed by Mitsch and Clemence (1985) for deep piles was found to be the most consistent, to within approximately 20% of measured values for all piles (Table 10). This method predicts the uplift capacity of the pile by considering the algebraic sum of the bearing capacity of the uppermost helix and the frictional capacity developed at the interface of the interhelical soil using the average helical diameter. Pile spacing To ensure that the design capacity of each helical pile is fully mobilized, it is important to avoid interaction between adjacent piles through the soil. It was noted from the numerical models that the soil outside the final displacement contour (i.e., 20% of total pile displacement) experienced very low strain values; less than 3 = 1  10–4 and was less than 3 = 1  10–5 in many cases, that is, negligible for practical purposes. The maximum radial extent of the influence zone for a pile under compression was observed to reach a distance equal to two uppermost helical diameters (2D) from the centerline of the pile and two and a half uppermost helical diameters (2.5D) for piles under tensile loads. Therefore, for piles to mobilize their capacity fully and avoid interference between the influence zones of two adjacent piles, centre-to-centre spacing should be a minimum distance of #

2008 NRC Canada

1154

Can. Geotech. J. Vol. 45, 2008

Table 9. Comparison of measured and calculated bearing capacities of tested compression piles.

Compression piles Pile 1, dense silt Pile 2, dense silt Pile 4, clayey silt Pile 5, clayey silt Pile 6, clayey silt Pile 13, sand Pile 14, sand

Measured capacity, Qu (kN) 465 496 356 327 328 830 728

Calculated capacity, Qt (kN) 455 458 329 319 310 738 708

Capacity comparison Qt/Qu (%) 97.75 92.43 92.31 97.57 94.51 88.95 97.25

(2)

(3)

Table 10. Comparison of measured and calculated bearing capacities of tested tension piles.

Tension piles Pille 7, clayey silt Pile 8(7 ft.), clayey silt Pile 9, clayey silt Pille 10(7 ft.), clayey silt Pile 16, clayey silt Pile 20, clayey silt Pille 15, dense silt Pile 17, dense silt Pile 18*, dense silt Pille 12, sand Pile 19, sand

Measured capacity, Qu (kN) 226 285 181 305 250 356 381 256 178 378 406

Model capacity, Qt (kN) 175 260 170 285 235 226 350 232 160 322 356

Capacity comparison Qm/Qu (%) 77.43 91.23 93.92 93.44 94.00 63.48 91.86 90.63 89.89 85.19 87.68

(4)

(5)

*This performance is potentially misleading given the severe damage to its bottom helix.

4D for compression applications and 5D for tensile applications.

Model uncertainties The process of discretizing any continuous medium, such as soil in this case, with a finite number of elements, will contain some inherent approximations and inaccuracies. Additionally, the installation effects on the soil, which occurred in the field, cannot be accurately modeled by the software due to the absence of input data for the disturbed soil parameters. The accuracy of the analysis is also affected by ignoring the increase of stiffness with depth, thus failing to include both stress-dependency and stress-path dependency of stiffness or anisotropic stiffness. However, the stress state at failure is generally well described using the Mohr– Coulomb failure criterion with effective ’ and c’ parameters.

(6)

(7)

Conclusions A comprehensive investigation was conducted into the axial performance of square-shaft helical piles. The findings of the numerical model are in good agreement with the fullscale load test results, yielding the following noteworthy conclusions: (1) The load–deflection curves of the piles tested displayed typical trends, namely an initial linear segment, followed

by a highly nonlinear segment, and finally a near-linear, rapid-failure segment. This was particularly consistent and relevant for piles tested in compression, confirming the suitability of helical piles for axial compressive loading applications. A failure criterion was proposed to predict the ultimate load for the piles tested. For cases where plunging failure did not occur promptly, the ultimate load is defined as the load associated with deflection equal to 8% of the diameter of the largesthelix plus the elastic settlement PL of the pile AE þ 0:08D . The pile capacity was found to be proportional to the installation torque. Therefore, the empirical torque correlation coefficient Kt can be used to predict pile capacity. In compression the value of Kt ranged between 35 and 42 m–1 in dense and clayey silt, while in sand the value was greater than 60 m–1. In tension, the torque correlation coefficient was found to be 21.3 £ Kt £ 36.3 m–1, such that the upper range of values corresponded to piles tested in dense silt and sand and the lower range was for piles tested in clayey silt. Thus, the overall greater capacities of piles tested in compression translated into greater torque correlation factors The load transfer mechanism for all piles tested was found to be predominantly through a tapered cylindrical shear failure surface and bearing of the ‘‘lead helix’’ in the direction of loading. A method for estimating the axial compressive capacity of helical piles was developed as the sum of the end bearing and cylindrical shearing capacities of the pile. The resistance derived along the cylindrical shearing surface was subdivided into two regions, each with a different taper angel, a, and was computed based on the theory developed by El Naggar and Sakr (2000) for tapered piles. The first region has a taper angle of a = 5.338, extending from the top helix to the middle helix, with an upper diameter 30% greater than that of the top helix and a lower diameter equal to the diameter of the middle helix. The second region has a taper angle of a = 2.128 extending from the middle helix to the bottom helix with an upper and lower diameter equal to that of each respective helix. Finally, the end bearing of the bottom helix was computed using the bearing capacity factors presented by Vesic (1963) for drilled shafts. Estimates of pile capacity using this technique were shown to be conservative and accurate within 12% of measured values in all cases. The uplift capacity was developed in a slightly different manner and was most consistently computed by the method outlined by Mitsch and Clemence (1985). To avoid overlapping between the influence zones of adjacent helical piles, a minimum spacing of 4D and 5D was proposed for piles loaded in compression and tension, respectively.

Acknowledgements The donation of the helical piles by Hubbell Power Systems Inc. is greatly appreciated. The field installation of the helical piles by EBS Engineering and Construction is also greatly appreciated. #

2008 NRC Canada

Livneh and El Naggar

References ASTM. 1994. Standard test method for individual piles under static axial compressive load, D1143–81 (reapproved 1994). ASTM International, West Conshohocken, Pa. ASTM. 1995. Standard test method for individual piles under static axial tensile load, D3689–90 (reapproved 1995). ASTM International, West Conshohocken, Pa. Balla, A. 1961. The resistance to breaking-out of mushroom foundations for pylons. In Proceedings of the 5th International Conference of Soil Mechanics and Foundation Engineering, Paris, France, Vol. 1, pp. 569–576. BSI. 1986. British standard code of practice for foundations. BS 8004. British Standards Institution (BSI). London. Butler, H.D., and Hoy, H.E. 1977. The Texas quick-load method for foundation load testing – User’s manual. Rep. No. FHWAIP-77–8. Texas State Department of Highways and Public Transportation, Austin, Tex. Clemence, S.P.N., and Veesaert, C.J. 1977. Dynamic pullout resistance of anchors in sand. In Proceedings of the International Symposium On Soil-Structure Interaction, Roorkee, India. pp. 389–397. Davisson, M.T. 1972. High capacity piles. In Proceedings of Lecture Series of Innovations in Foundation Construction, ASCE, Illinois section, Chicago. pp. 81–112. Downs, D.I., and Chieurzzi, R. 1966. Transmission tower foundations. Journal of the Power Division, 92(P02): 91–114. El Naggar, M.H., and Sakr, M. 2000. Evaluation of axial performance of tapered piles from centrifuge tests. Canadian Geotechnical Journal, 37: 1295–1308. doi:10.1139/cgj-37-6-1295. El Naggar, M.H., and Wei, J.Q. 1999. Axial capacity of tapered piles established from model tests. Canadian Geotechnical Journal, 36: 1185–1194. doi:10.1139/cgj-36-6-1185. FDOT. 1999. Standard specifications for road and bridge construction. Florida Department of Transportation (FDOT). Tallahassee, Fla. Ghaly, A., and Hanna, A. 1991. Experimental and theoretical studies on installation torque of screw anchors. Canadian Geotechnical Journal, 28: 353–364. doi:10.1139/t91-046. Ghaly, A.M., Hanna, A.M., and Hanna, M.S. 1991. Uplift behavior of screw anchors in sand: I. Dry sand. Journal of Geotechnical Engineering, 117: 773–793. doi:10.1061/(ASCE)07339410(1991)117:5(773). Hoyt, R.M., and Clemence, S.P. 1989. Uplift capacity of helical anchors in soil. In Proceedings of the 12th International Conference on Soil Mechanics and Foundation Engineering (ISSMFE), Rio de Janeiro, Brazil. Vol. 2. pp. 1019–1022. Hubbell Power Systems Inc. 2003. Industry standards based on CHANCE multi-helix anchor specs. Bulletin 04–0301. Centralia, Mo. Ilamparuthi, K., Dickin, E.A., and Muthukrisnaiah, K. 2002. Experimental investigation of the uplift behaviour of circular plate anchors embedded in sand. Canadian Geotechnical Journal, 39(3): 648–664. doi:10.1139/t02-005. ISSMFE. 1985. Axial pile loading test – Part I: Static loading. Geotechnical Testing Journal, ASTM, 8(2): 79–80 Ireland, H.O. 1963. Discussion, uplift resistance of transmission tower footings. Journal of the Power Division, 89: 115–118.

1155 Majer, J. 1955. Zur berechnung von zugfundamenten. Osterreichische Bauzeitgschrift, 10: 85–90. [In German.] Meyerhof, G.G., and Adams, J.I. 1968. The ultimate uplift capacity of foundations. Canadian Geotechnical Journal, 5(4): 225–244. doi:10.1139/t68-024. Mitsch, M.P., and Clemence, S.P. 1985. The uplift capacity of helix anchors in sand. In Proceedings of the Uplift Behavior of Anchor Foundations in Soil, Detroit, Mich., 24 October 1985 Edited by S.P. Clemence. American Society of Civil Engineers. pp. 26–47. Mors, H. 1959. The behavior of mast foundations subjected to tensile forces. Bautechnik, 36: 367–378. Murray, E.J., and Geddes, J.D. 1987. Uplift of anchor plates in sand. Journal of Geotechnical Engineering, 113: 202–215. Narasimha Rao, S., and Prasad, Y.V.S.N. 1991. Estimation of uplift capacity of helical anchors in clays. Journal of Geotechnical Engineering, 199: 352–357. Narasimha Rao, S., Prasad, Y.V.S.N., Shetty, M.D., and Joshi, V.V. 1989. Uplift capacity of screw anchors. Geotechnical Engineering, 20: 139–159. Narasimha Rao, S., Prasad, Y.V.S.N., and Veeresh, C. 1993. Behaviour of embedded model screw anchors in soft clays. Ge´otechnique, 43: 605–614. Prakash, S., and Sharma, H.D. 1990. Pile foundations in engineering practice. John Wiley & Sons, New York. p. 824. Reese, L.C., and O’Neill, M.W. 1988. Drilled shafts: construction procedures and design methods, FHWA-HI-88–042. Federal Highway Administration, McLean, Va. Rowe, R.K., and Davis, E.H. 1982. The behaviour of anchor plates in sand. Ge´otechnique, 32: 25–41. SAA. 1995. Piling design and installation. Australian standard AS 2159. Standards Association of Australia (SAA), Homebush, NSW. Saeedy, H.S. 1987. Stability of circular vertical anchors. Canadian Geotechnical Journal, 24: 452–456. doi:10.1139/t87-056. Sutherland, H.B. 1965. Model studies for shaft raising through cohesionless soils. In Proceedings of the 6th International Conference on Soil Mechanics and Foundation Engineering, Montre´al, Que. Vol. 2, pp. 410–413. Sutherland, H.B., Finlay, T.W., and Fadl, M.O. 1982. Uplift capacity of embedded anchors in sand. In Proceedings of the 3rd International Conference on the Behavior of Offshore Structures, Massachusetts Institute of Technology, Cambridge, Mass. pp. 451–463. Vesic, A.S. 1963. Bearing capacity of deep foundations in sand. Highway Research Record, No. 39, Highway Research Board, National Academy of Science, Washington, D.C., pp. 112–153. Vesic, A.S. 1971. Breakout resistance of objects embedded in ocean bottom. Journal of the Soil Mechanics and Foundation Engineering Division, ASCE, 97: 1183–1205. Weizhi, S., and Fragaszy, R.J. 1988. Uplift testing of model anchors. Journal of Geotechnical Engineering, 114: 961–983. Zhang, L.M., Li, D.Q., and Wilson, H.T. 2005. Reliability of bored pile foundations considering bias in failure criteria. Canadian Geotechnical Journal, 42: 1086–1093. doi:10.1139/t05-044.

#

2008 NRC Canada