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Statistical evaluation of model factors in reliability calibration of high displacement helical piles under axial

loading

Journal: Canadian Geotechnical Journal

Manuscript ID cgj-2018-0754.R2

Manuscript Type: Article

Date Submitted by the Author: 03-Apr-2019

Complete List of Authors: Tang, Chong; National University of Singapore, Phoon, Kok-Kwang; National University of Singapore, Department of Civil & Environmental Engineering

Keyword: high displacement helical pile, model uncertainty, reliability-based design, load and resistance factor design, static load test

Is the invited manuscript for consideration in a Special

Issue? :Not applicable (regular submission)

https://mc06.manuscriptcentral.com/cgj-pubs

Canadian Geotechnical Journal

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1 Statistical evaluation of model factors in reliability calibration of high

2 displacement helical piles under axial loading

3 Chong Tang1 Kok-Kwang Phoon2

4 1Research fellow, Department of Civil and Environmental Engineering, National University of Singapore, Block

5 E1A, #07-03, 1Engineering Drive 2, Singapore 117576 (corresponding author), E-mail: [email protected]

6 2Professor, Department of Civil and Environmental Engineering, National University of Singapore, Block E1A,

7 #07-03, 1Engineering Drive 2, Singapore 117576, E-mail: [email protected]

8 Abstract: Industry survey suggests an increasing application of high displacement helical piles with greater

9 shaft and helix diameters to support various structures. In this paper, a database of 84 static load tests is

10 compiled and analyzed to evaluate the disturbance effect and characterize the model factors that can be used for

11 reliability-based limit state design. The measured capacity is defined as the load at a pile head settlement equal

12 to 5% of helix diameter. For similar helix configurations tested in the same site, the ratio of uplift to

13 compression capacity indicates a low degree of disturbance for very stiff clay (=0.8 – 1) and a medium degree of

14 disturbance for dense sand (=0.6 – 0.8). At the ultimate limit state, the model factor is defined as the ratio

15 between measured and calculated capacity, where three design guidelines are considered. A hyperbolic model

16 with two parameters is used to fit the load-displacement curves. At the serviceability limit state, the model factor

17 can be defined with the hyperbolic parameters. Based on the database, probabilistic distributions of the capacity

18 model factor and hyperbolic parameters are established. Finally, the capacity model statistics are applied to

19 calculate the resistance factor in the load and resistance factor design.

20 Keywords: high displacement helical pile, model uncertainty; reliability-based design, load and resistance factor

21 design, static load test

22

23 Introduction

24 A helical pile is prefabricated from a central steel shaft welded with steel plates that are moulded as a

25 helix with a carefully controlled pitch. It is installed by applying a torque and crowd (axial force) to

26 the pile head. The load is transferred from the central shaft to the surrounding soils through the

27 bearing helices, which is different from that for driven piles (Elsherbiny and El Naggar 2013;

28 Elkasabgy and El Naggar 2015). The industry survey of Clemence and Lutenegger (2015) showed a

29 dramatic growth in the use of helical piles over the past 25 years, due to the ease of installation and

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mailto:[email protected]

mailto:[email protected]

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30 low levels of noise and vibration. Moreover, helical piles allow immediate loading upon installation

31 and can be installed below the groundwater table without casing (Perko 2009). Yi and Lu (2015)

32 presented a detailed comparison of cost among three typical pile systems in Canada, such as helical

33 piles, driven piles, and cast-in-place piles. It is demonstrated that helical piles could save budget and

34 time in typical power substation project. Recently, it has been recognized that helical piles offer an

35 efficient solution for offshore foundations (Byrne and Houlsby 2015; Lutenegger 2017; Al-Baghdadi

36 2018; Spagnoli et al. 2019) and can be used for earthquake mitigation because of their slenderness,

37 higher damping ratios, ductility, and ability to resist uplift (Cerato et al. 2017; Sakr 2018; Elsawy et al.

38 2019).

39 Design of helical piles has gone through a remarkable evolution with the establishment of the

40 2007 Acceptance Criteria for Helical Foundations Systems and Devices (AC358). The latest edition is

41 AC358 Helical Pile Systems and Devices, which was approved in September 2017. Significant efforts

42 of several members of the Helical Piles and Tiebacks Committee (HPTC) led to the inclusion of

43 helical piles in the 2009 International Building Code (IBC) as a type of deep foundation (Clemence

44 and Lutenegger 2015). Also, helical piles have been written into Chapter 18 “Soils and Foundations”

45 of the 2014 New York City Building Code. Perlow (2011) stated that the volume of soil (Vs) displaced

46 by the central shaft will increase as the shaft diameter increases. Accordingly, helical piles are 𝑑

47 categorized into three groups by Perlow (2011): (1) low displacement (d≤89 mm, Vs≤0.025 m3/m), (2)

48 medium displacement (114 mm≤d≤178 mm, 0.025<Vs≤0.1 m3/m), and (3) high displacement (d≥219

49 mm, Vs>0.1 m3/m). In general, only high displacement helical piles with round shafts can provide

50 shaft resistance. Low displacement helical piles with square shafts will carve a diameter equal to or

51 larger than the hypotenuse of the shaft during installation and will not provide shaft resistance unless

52 post-grouted. The industry survey of Clemence and Lutenegger (2015) indicated an increasing use of

53 high displacement helical piles, owing to their advantages over driven piles. Nevertheless, the 2017

54 AC358 Acceptance Criteria has not been verified for the design of helical piles with shaft diameters

55 greater than 127 mm (i.e. medium to high displacement).

56 As similar to conventional driven piles, helical pile capacity can be calculated by indirect (or

57 theoretical), direct, or empirical methods (Tappenden 2007; Tappenden and Sego 2007). Indirect

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58 methods are based on the equations of bearing capacity and shaft resistance that are used to describe

59 the behaviour of piles in compression and buried anchors in uplift, where intermediate calculations of

60 soil parameters are required. Direct methods relate the unit end bearing and shaft resistance to the in

61 situ test results from cone penetration test (CPT) or standard penetration test (SPT). Empirical method

62 is associated with the correlation between the axial capacity and installation torque by a ratio Kt. The

63 accuracy in calculating the capacity was assessed by Hoyt and Clemence (1989), Tappenden (2007),

64 Tappenden and Sego (2007), Perko (2009), Cherry and Souissi (2010), Fateh et al. (2017), Tang and

65 Phoon (2018a). However, the study on high displacement helical piles is relatively limited. Tang et al.

66 (2018) collected 96 static load tests (where the installation torque is recorded) to examine the

67 applicability of the empirical torque-capacity correlation in the 2017 AC358 to high displacement

68 helical piles. Two cases should be cautiously considered, where the calculated capacity by the

69 empirical method significantly deviates from the measured value. The first refers to the soil around

70 the pile tip (not penetrated during installation but mobilized when the pile is under compression) that

71 is much stiffer than the soil penetrated by the pile (Elkasabgy and El Naggar 2015; Tang and Phoon

72 2018a). In this case, the compression resistance is not related to the final installation torque

73 (Elkasabgy and El Naggar 2015; Tang and Phoon 2018a). The second case is a helical pile installed at

74 a shallow depth, while the current Kt values were proposed for a deep failure mode under uplift (Tang

75 and Phoon 2018a). In practice, the empirical method is generally used as verification, because the

76 torque is only available after the installation. More studies are encouraged to calculate the axial

77 capacity of high displacement helical piles by indirect or direct methods.

78 Most engineers tend to use a factor of safety of 2 in design (Clemence and Lutenegger 2015).

79 This is the allowable stress design (ASD) method, as suggested in the Section 1810.3.3.1.9 “Helical

80 piles” in the 2018 International Building Code. The limitations of ASD were discussed by Kulhawy

81 and Phoon (2006, 2009) and Kulhawy (2010). Worldwide, geotechnical design codes are in the

82 transition from ASD to reliability-based design (RBD) (Fenton et al. 2016). The fourth edition of ISO

83 2394 (ISO 2015) contains a new informative Annex D, which clearly identifies the critical elements in

84 a geotechnical RBD procedure such as the characterization of geotechnical variability and model

85 uncertainty (Phoon et al. 2016). For low displacement helical piles, Tang and Phoon (2018a)

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86 characterized the model uncertainty and calibrated the resistance factor in the Load and Resistance

87 Factor Design (LRFD) that is the most popular simplified RBD format in North America. However,

88 the research for high displacement helical piles has not been carried out yet. This paper will also make

89 an effort to study this issue.

90 Therefore, the objectives of this article that is a companion paper to Tang and Phoon (2018a) for

91 low displacement helical piles are: (1) to develop a high quality database of high displacement helical

92 piles; (2) to define the measured capacity and calculate the capacity using the methods in the 4th

93 Canadian Foundation Engineering Manual (CFEM) (Canadian Geotechnical Society 2006), ISO

94 19901-4 (ISO 2016), and the guideline of the International Society for Helical Foundations (ISHF)

95 (Lutenegger 2015); (3) to quantify the deviation in capacity calculations by the ratio between the

96 measured and calculated capacity that is called a model factor; (4) to simulate the measured load-

97 displacement curves by a hyperbolic model with two parameters; (5) to establish the probabilistic

98 distributions of the capacity model factor and hyperbolic parameters; and (6) to calibrate the

99 resistance factor in LRFD with the derived capacity model statistics.

100 Failure mechanisms for axially loaded helical piles

101 The existence of bearing helices complicates the behaviour of helical piles, compared with

102 conventional driven piles. To calculate the axial capacity of helical piles, there are two aspects that

103 should be considered, including (1) shallow or deep failure under uplift and (2) interaction effect

104 within bearing helices.

105 Shallow or deep failure under uplift

106 For helical piles under uplift, there are two distinct mechanisms to describe the behaviour of the

107 uppermost helix that are shallow and deep failure. When a helical pile is installed at a shallow depth,

108 the bearing failure zone above the uppermost helix will extend to the ground surface, as evidenced by

109 the surface heave (Narasimha Rao et al. 1993). For deep helical piles, the bearing failure zone will be

110 confined within the soil medium (Merifield 2011; Wang et al. 2013; Tang et al. 2014). The

111 demarcation between shallow and deep failure is usually expressed as the critical embedment ratio

112 (Hu/D)crit, where Hu is the embedment depth of the uppermost helix and D is the helix diameter.

113 Meyerhof and Adams (1968) suggested (Hu/D)crit=3-9 for cohesionless soils with friction angle ϕ=25°-

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114 45°. Similar values were obtained by Ilamparuthi et al. (2002), where (Hu/D)crit=4.8 for loose sand, 5.9

115 for medium-dense sand, and 6.8 for dense sand. For a shallow anchor, a gently curved rupture surface

116 is emerged from the top edge of the anchor to the sand surface at 0.5ϕ to the vertical. For a deep

117 anchor, a balloon-shaped rupture surface above the anchor that is emerged at 0.8ϕ to the vertical is

118 observed. Centrifuge model tests of Hao et al. (2018) indicated (Hu/D)crit=9 for dense sand. Laboratory

119 small-scale model tests of Narasimha Rao et al. (1993) suggested (Hu/D)crit=4 for cohesive soils.

120 Numerical analyses of Merifield (2011) and Tang et al. (2014) indicated (Hu/D)crit=7. In helical pile

121 industry, it is frequently required that helical piles should be installed at a minimum depth of 5D

122 (Blessen et al. 2017; Hubbell, Inc. 2014).

123 Interaction effect within bearing helices

124 Critical spacing ratio

125 Because of the possible interaction effect within the bearing helices, significant studies have been

126 conducted to investigate the actual failure mechanism of helical piles (Narasimha Rao et al. 1989,

127 1991, and 1993; Zhang 1999; Lutenegger 2009; Elsherbiny and El Naggar 2013; Wang et al. 2013;

128 Elkasabgy and El Naggar 2015). In general, there are two primary models to describe the soil

129 behaviour within the bearing helices. The first model is the individual plate bearing in Fig. 1a and the

130 second model is the cylindrical shear failure in Fig. 1b. Note that Fig. 1 is illustrated for axial

131 compression. Two models are demarcated by the spacing ratio S/D, where S is the spacing between

132 adjacent helices.

133 On the basis of experimental (laboratory or in situ) or numerical studies, different (S/D)crit values

134 were suggested in the literature (Lanyi 2017). A summary of (S/D)crit is given in Table 1. For helical

135 piles under uplift, (S/D)crit=1-2 that was obtained from laboratory model tests in very soft to medium

136 stiff clay (Narasimha Rao et al. 1989, 1991, 1993; Narasimha Rao and Prasad 1993). Finite element

137 analyses of Merifield (2011) showed (S/D)crit=1.6. For uplift load tests on multi-helix piles with S/D≤3

138 in clay, Lutenegger (2009) opined that there is no distinct transition between two failure mechanisms.

139 Elsherbiny and El Naggar (2013) performed finite element analyses to show that (1) the individual

140 plate bearing is dominated regardless of S/D at a small load level; (2) a soil cylinder could develop as

141 the applied load increases; and (3) for a smaller S/D, there is more interaction between helices and the

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142 cylindrical shear failure may dominate the pile behaviour at a large load level. For helical piles under

143 uplift in kaolin clay, centrifuge model tests and large deformation finite element analyses in Wang et

144 al. (2013) implied that (1) the cylindrical shear failure is predominant when S/D≤3.2 (almost

145 independent of the soil strength and helix diameter) and (2) the individual plate bearing occurs as

146 S/D≥5. It should be pointed out that the helix diameter of 2.4 m in Wang et al. (2013) is much greater

147 than that is used in practice. Zhang (1999) carried out a set of field load tests and observed that (1) in

148 cohesive soils, the cylindrical shear failure is representative for helical piles with S/D<3 regardless of

149 loading type (i.e. uplift or compression) and (2) in cohesionless soils, the cylindrical shear failure is

150 more appropriate for helical piles with S/D≤2 under compression and for helical piles with S/D<3

151 under uplift. Field load tests on double-helix piles in layered strata of stiff clay and silty sand

152 demonstrated the individual plate bearing for S/D=1.5, which could be caused by the high degree of

153 installation disturbance and soil within the inter-helix region (Elkasabgy and El Naggar 2015). By

154 comparing the measured load-displacement curves for single- and double-helix piles with S/D=3 in

155 dense to very dense oil sand, Sakr (2009) implied that the individual plate bearing model is more

156 suitable.

157 Table 1 suggests (S/D)crit mainly ranges between 1.5 and 3. It seems to be difficult to provide a

158 unique (S/D)crit covering all possible design scenarios. This is because (S/D)crit could be dependent on

159 pile geometry, site stratigraphy, soil stiffness, installation disturbance, load type and the magnitude of

160 applied load (Elsherbiny and El Naggar 2013; Elkasabgy and El Naggar 2015). To simplify the

161 problem, CFEM-2006 and several helical pile design manuals (Blessen et al. 2017; Hubbell, Inc. 2014)

162 recommend that the individual plate bearing model is applicable for S/D≥3. Clemence and Lutenegger

163 (2015) showed that the individual plate bearing method is more widely used in design, because helical

164 piles are generally made with S/D=3. In the current work, the individual plate bearing method is used

165 for S/D≥3 and the cylindrical shear failure method is used for S/D<3.

166 Individual plate bearing

167 The individual plate bearing method assumes that the bearing failure occurs below (for compression)

168 or above (for uplift) each helix. The axial capacity (R) of a high displacement helical pile is calculated

169 as the summation of (1) the total helix capacity (Rt, which is the sum of the capacity from each helix

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170 Rh) and (2) the frictional resistance (Rf) mobilized by the shaft between the ground surface and the

171 uppermost helix (Adams and Klym 1972; Hoyt and Clemence 1989; Canadian Geotechnical Society

172 2006; Perko 2009; Elsherbiny and El Naggar 2013; Elkasabgy and El Naggar 2015):

173 (1)𝑅 = 𝑅t + 𝑅f = ∑𝑅h + 𝑅f = ∑𝐴h ∙ 𝑞t + ∑𝜋 ∙ 𝑑 ∙ ∆𝐿f ∙ 𝑓s

174 where Ah is the effective helix area (i.e. total helix area minus shaft area), qt is the unit end bearing

175 capacity provided by each helix, d is the shaft diameter, fs is the unit shaft friction, and ΔLf is the pile

176 segment length. The effective shaft length Heff, which is defined as the embedment depth of the

177 uppermost helix minus the diameter (Elsherbiny and El Naggar 2013; Elkasabgy and El Naggar 2015),

178 is usually used to calculate the shaft friction.

179 Cylindrical shear failure

180 In the cylindrical shear failure model, the axial capacity (R) of a high displacement helical pile is

181 computed as the sum of (1) the bearing capacity of the leading helix (Rh), (2) the shear capacity

182 developed along the soil cylinder circumscribed by the uppermost and lowermost helix (Rc), and (3)

183 the shaft friction (Rf) (Mitsch and Clemence 1985; Mooney et al. 1985; Perko 2009; Elsherbiny and El

184 Naggar 2013; Elkasabgy and El Naggar 2015):

185 (2)𝑅 = 𝑅h + 𝑅f + 𝑅c = 𝐴h ∙ 𝑞t + ∑𝜋 ∙ 𝑑 ∙ ∆𝐿f ∙ 𝑓s + ∑𝜋 ∙ 𝐷 ∙ ∆𝐿c ∙ 𝑓c

186 where ΔLc is the length of the soil cylinder, and fc is the unit shear capacity of the soil cylinder.

187 The central shaft could be a solid square bar (closed-end) mainly for small displacement helical

188 piles or a hollow pipe (open-end) for medium to high displacement helical piles. In axial compression,

189 the tip resistance of helical piles with closed-end can be estimated by the methods for conventional

190 displacement piles (Hannigan et al. 2016). For helical piles with open-end, the capacity from the pile

191 tip should be included within Eq. (1) and Eq. (2), because the soil will be pushed into the shaft during

192 installation. This phenomenon is soil plug, which has been extensively investigated for driven piles

193 with open-end (Randolph et al. 1992; Nicola and Randolph 1997; Kikuchi 2008; Seo and Kim 2018).

194 The effect of soil plug has been incorporated into four advanced CPT-based methods in Annex A of

195 ISO 19901-4:2016 for driven piles in sand. The study on the soil plug during helical pile installation is

196 absent that could be assumed as the case of driven piles with open-end. In this context, the tip

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197 resistance of high-displacement helical piles that should be important can be calculated using

198 available methods in the literature to estimate the tip resistance of driven piles with open-end (Sakr

199 2009, 2011a, 2012; Fateh et al. 2017).

200 Semi-empirical design methods

201 The design equations for the unit end bearing capacity of each helix (qt), unit shaft friction (fs), and

202 unit shear resistance along the soil cylinder surface (fc) are given in this section, with the

203 recommendations in three design guidelines such as CFEM-2006, ISHF-2015 and ISO 19901-4:2016.

204 Helix capacity

205 The unit end bearing capacity from each helix is commonly calculated by the Terzaghi’s bearing

206 capacity equation, which is given by:

207 (3)𝑞t = 𝑠uh ∙ 𝑁c

208 for cohesive soils and

209 (4)𝑞t = 𝜎′vh ∙ 𝑁q

210 for cohesionless soils, where suh is the operational undrained shear strength at the helix depth, Nc is the

211 undrained bearing capacity factor, σvh′ is the effective vertical stress at the helix depth, and Nq is the

212 drained bearing capacity factor.

213 The undrained bearing capacity factor Nc is commonly assumed to be 9. Bagheri and El Naggar

214 (2015) discussed that this value is suitable for helical piles under compression as the bearing capacity

215 is only controlled by the undrained cohesion. For helical piles under uplift, Nc would be greater than 9

216 (Martin and Randolph 2001; Merifield 2011; Bagheri and El Naggar 2015), because the effects of soil

217 weight and undrained cohesion are superimposed. With a database of helical piles in cohesive soils,

218 Young (2012) correlated the uplift Nc factor to the ratio H/D, where H is the embedment depth. The

219 limiting Nc value of 11.2 indicates the transition from the shallow to deep failure of the uppermost

220 helix (Merifield 2011; Tang et al. 2014).

221 Mitsch and Clemence (1985) presented the design chart of Nq for helical piles under uplift. Pérez

222 et al. (2018) demonstrated that using the Nq values of Mitsch and Clemence (1985) significantly

223 overestimates the uplift capacity. This is because these Nq factors were mainly calibrated against 1g

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224 small-scale model tests on plate anchors (g is the gravity acceleration), where the soil weight and

225 installation effect of helical piles on Nq are not considered (Pérez et al. 2018). Based on the centrifuge

226 model tests and numerical simulations, Pérez et al. (2018) developed a new analytical model for uplift

227 capacity of low displacement helical piles. It assumes a vertical plane of failure and the mobilized

228 friction angle on the plane of failure is the constant-volume value to consider the installation

229 disturbance.

230 Shaft friction

231 The unit shaft friction fs is frequently computed with the alpha method in Eq. (5) for cohesive soils

232 and the beta method in Eq. (6) for cohesionless soils:

233 (5)𝑓s = 𝛼 ∙ 𝑠us

234 (6)𝑓s = 𝐾s ∙ tan𝛿 ∙ 𝜎′v0 = 𝛽 ∙ 𝜎′v0

235 where α is the adhesion factor, sus is the operational undrained shear strength along the pile shaft, Ks is

236 the coefficient of lateral earth pressure which is assumed to be 2(1-sinϕ) in CFEM-2006, δ is the

237 friction angle along the shaft-soil interface, σv0′ is the effective vertical stress averaged along the shaft,

238 and β is an empirical coefficient relating fs to σv0′.

239 For similar helical piles tested in the same site, Sakr (2011a, 2012) observed that the initial parts

240 of the uplift and compression load-displacement curves are almost identical in which the shaft friction

241 is developed. It is reasonable to conclude that the shaft friction under compression or uplift loading

242 can be calculated by Eq. (5) or Eq. (6).

243 Shear resistance of soil cylinder

244 The unit shear capacity along the surface of soil cylinder is calculated in the way similar to that used

245 for the unit shaft friction, which is given below:

246 (7)𝑓c = 𝑠uc

247 for cohesive soils and

248 (8)𝑓c = 𝐾s ∙ tan𝜙s ∙ 𝜎′vc

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249 for cohesionless soils, where suc is the operational undrained shear strength over the soil cylinder

250 surface, ϕs is the mobilized friction angle along the soil cylinder surface, and σvc′ is the effective

251 vertical stress averaged over the soil cylinder surface.

252 Three design guidelines such as CFEM-2006, ISHF-2015, and ISO-19901-4:2016 are considered

253 in this study. The bearing capacity factors Nc and Nq and empirical shaft resistance coefficients α and

254 β are given in Table 2.

255 Consideration of soil disturbance and helix efficiency

256 It has been recognized that installation could significantly disturb the soil structure, change the soil

257 properties, and affect the helical pile capacity (Bagheri and El Naggar 2013, 2015; Lutenegger et al.

258 2014; Lutenegger and Tsuha 2015; Pérez et al. 2018; Tsuha et al. 2016; Weech and Howie 2001). For

259 uplift loading, the undrained shear strength should be reduced to consider the soil disturbance.

260 Lutenegger (2015) suggested a simple way with the soil sensitivity (St): (1) no reduction for St=1, (2)

261 15% reduction for St=2-4, (3) 25% reduction for St=5-10, and (4) 50% reduction for St>10. For

262 compression loading, the design guideline ISHF-2015 (Lutenegger 2015) suggested that the intact

263 undrained shear strength (sui) below the lowermost helix may be used, but a reduction should be made

264 for the undrained shear strength between the other helices. The following equation suggested by

265 Skempton (1950) can be used (Lutenegger 2015; Bagheri and El Naggar 2015):

266 (9)𝑠u = 𝑠ui ―0.5(𝑠ui ― 𝑠ur)

267 where sur is the remolded undrained shear strength that can be estimated with the soil sensitivity.

268 Another simple approach to consider the disturbance effect is using the disturbance factor (DF) that is

269 defined as the ratio of uplift to compression capacity (Perko 2009; Lutenegger and Tsuha 2015). In

270 Perko (2009), DF=0.87, where load tests for all piles (low to high displacement) and soils (fine- to

271 coarse-grain) were grouped together.

272 Furthermore, the design guideline ISHF-2015 stated that the bearing helices in cohesionless soils

273 do not contribute the same capacity and the efficiency of successive helices is diminished compared

274 with the leading helix. For double- and triple-helix piles, centrifuge model tests of Tsuha et al. (2012)

275 showed that the contributions of the second and third helix to the total uplift capacity of helical piles

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276 decreased with the increase of relative density and helix diameter. To calculate the helix capacity,

277 ISHF-2015 suggests (1) no reduction for the leading helix, (2) 20% reduction for the second helix,

278 and (3) 40% reduction for the third helix.

279 High displacement helical pile database

280 Collection of data

281 For the purpose of this work, 92 static load tests on high displacement helical piles under axial

282 loading are compiled from the literature (Tappenden 2007; Sakr 2008, 2009, 2011a, 2011b, 2012,

283 2013; Sakr et al. 2009; Elsherbiny and El Naggar 2013; Pardoski 2014; Elkasabgy and El Naggar

284 2015; Harnish and El Naggar 2017). These load tests are summarized below:

285 1. Tappenden (2007): 14 compression and 9 uplift load tests in 6 locations in Alberta and 1

286 location in British Columbia. CPT was carried out for soil investigation. Plunging failure was

287 observed in some load tests.

288 2. Sakr (2008): 2 compression and 2 uplift load tests in soft to firm clay or stiff high plastic clay

289 with silt located in northern Manitoba, Canada. The intact and remolded undrained shear

290 strength parameters sui and sur were measured by consolidated-isotropically undrained, triaxial

291 compression tests, where sui=30 kPa and sur=18 kPa for soft to firm clay and sui=60 kPa and

292 sur=30 kPa for stiff clay. Plunging failure was observed in load tests on helical piles C1, C2

293 and T2. For helical pile T1, the test was terminated at a displacement of 9 mm.

294 3. Sakr (2009): 4 compression and 5 uplift load tests in very dense oil sand located in north of

295 Fort McMurray, Alberta, Canada. The SPT blow count ranges from 26 to over 100. The wet

296 and dry unit weights are 21.6 and 18.1 kN/m3. The peak and residual friction angles are 50°

297 and 38° measured by triaxial compression tests on high quality and undisturbed samples.

298 Load tests in phase 1 for helical piles C1, C2, T1 and T2 were terminated at an axial load of

299 800 kN at a small displacement. Helical pile C3 tested in phase 2 showed plunging failure at a

300 displacement of about 50 mm.

301 4. Sakr et al. (2009): 1 compression and 1 uplift load tests in very dense sandy gravel soil

302 located in Anchorage, Alaska, USA. The SPT blow count varies from 40 to 110.

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303 5. Sakr (2011a): 4 uplift and 7 compression load tests in 4 different locations in northern Alberta,

304 Canada. The predominant geomaterial is dense to very dense sand. Either SPT or CPT was

305 performed for soil investigation. Among these load tests, pile ST32 reached plunging failure

306 at a displacement of 90 mm.

307 6. Sakr (2011b): 2 uplift load tests in loose to compact sand in Brookhaven, Upton, New York.

308 The SPT blow count varies between 9 and 24. Plunging failure was observed in load tests on

309 both piles T2 and T3.

310 7. Sakr (2012): 6 compression and 4 uplift load tests in 3 different locations in northern Alberta,

311 Canada. The soil is mainly cohesive such as glacial and clay shale. Geotechnical investigation

312 was performed by SPT or CPT. Plunging failure was observed in load tests on helical piles

313 ST62 and ST72.

314 8. Elsherbiny and El Naggar (2013): 4 compression tests in site A and site B. SPT was employed

315 for geotechnical investigation. Site A in northern Alberta, Canada, is cohesionless with SPT

316 blow count ranges between 10 and 24. Site B in northern Ontario, Canada, is cohesive with

317 SPT blow count ranges between 3 and 12.

318 9. Sakr (2013): 2 compression field load tests in cohesive soils in Ponoka, Alberta, Canada. Site

319 investigation was performed by CPT. The load-displacement behaviour of helical pile S4

320 indicated plunging failure.

321 10. Pardoski (2014): 3 compression field load tests in a site near Saskatoon, Saskatchewan,

322 Canada. The soil stratigraphy is a glacio-lacustrine deposit of silty clay, which is categorized

323 into a stiff clay. Based on the CPT results, the intact and remolded undrained shear strength

324 parameters are around 70 kPa and 35 kPa.

325 11. Elkasabgy and El Naggar (2015): 6 compression tests in Ponoka, Alberta, Canada. The

326 geomaterial is mainly composed of Pleistocene Stagnation Moraine glacial till. Laboratory,

327 SPT and CPT results were employed to evaluate the soil properties. Pile LS12 reached

328 plunging failure.

329 12. Butt et al. (2017): 3 compression and 3 uplift load tests on high displacement helical piles to

330 replace high voltage transmission line tower structures near Newark, New Jersey. Three site

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331 locations were considered. The soil stratigraphy is primarily consisted of normally

332 consolidated glacial lake clays and silts. SPT, CPT and laboratory tests were performed to

333 determine the intact and remolded undrained shear strength parameters. Plunging failure or

334 peak load can be clearly observed in all tests.

335 13. Harnish and El Naggar (2017): 6 compression and 4 uplift load tests in the yard of Helical

336 Pier Systems Inc. pile manufacturing facility in Lamont near Edmonton, Alberta, Canada. The

337 soil is mainly composed of glacial till. The intact and remolded shear strength profiles were

338 determined from CPT results, which increase with depth (sur=70-307 kPa and sui=74-600 kPa).

339 Plunging failure was identified in most load tests.

340 Full details on the collected load tests can be found in the references cited. All static load tests

341 were performed in North America (82 in Canada and 10 in the United States). The distribution and

342 range of the collected load tests are given in Table 3, where d=168-508 mm, D=356-1016 mm,

343 H/D=4.1-24, and S/D=1.5-4.5. The undrained shear strength su=24-300 kPa indicates soft to very hard

344 clay, while the friction angle ϕ=30-45° covers loose to very dense sand. The data are grouped into 34

345 uplift and 58 compression tests; 59 tests in cohesive soils and 33 tests in cohesionless soils; and 31

346 tests on single-helix piles and 61 tests on multi-helix piles.

347 Estimation of soil parameters

348 The calculation of helical pile capacity requires the soil parameters (i.e. soil weight, undrained shear

349 strength, and friction angle) that are directly obtained from laboratory tests or indirectly derived from

350 SPT or CPT results. The details can be found in Section 5.3 on “Evaluating soil properties for design”

351 in the Chance – Technical Design Manual (Hubbell, Inc. 2014).

352 Interpretation of load test results

353 All the load-displacement curves are illustrated in Fig. 2. Plunging failure is observed in some load

354 tests. It is reasonable to take the load where plunging failure occurs as the measured capacity. For the

355 other load tests, plunging failure is not easily identifiable, where a definition is commonly adopted to

356 interpret the measured capacity. For low displacement helical piles, the AC358 acceptance criterion

357 defines the measured capacity as the load when the net (total minus elastic) displacement is equal to

358 10% of helix diameter D. For high displacement helical piles, where the maximal helix diameter is

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359 1016 mm in the database, the 10% criterion corresponds to a large displacement. Sakr (2009) pointed

360 out that the 10% criterion is more suitable for low displacement helical piles, where helix capacity is

361 dominant. In helical pile industry, the method of O’Neill and Reese (1999) is commonly used, where

362 the measured capacity is interpreted as the load producing a pile head settlement equal to 5% of the

363 helix diameter D (Sakr 2009, 2011a, 2012, 2013; Pardoski 2014; Elkasabgy and El Naggar 2015;

364 Harnish and El Naggar 2017). When load tests are terminated at a displacement smaller than 5%D,

365 extrapolation is not recommended for model calibration (Lesny 2017), because (1) extrapolation could

366 considerably over-predict the pile capacity (Paikowsky and Tolosko 1999; Hasan et al. 2018) and (2)

367 the guideline to extrapolate the load-displacement curve is not established at present (NeSmith and

368 Siegel 2009). In this regard, 84 field load tests are selected, which are summarized in Tables A1 and

369 A2 in Appendix A with helical pile geometries, predominant soil conditions and interpreted capacities.

370 The test ID is retained for the ease of reference.

371 Following the work of Lutenegger and Tsuha (2015), the difference between the compression

372 and uplift capacity for high displacement helical piles with similar configurations that were tested in

373 the same site is studied. The values of the disturbance factor (DF) are given in Table 4 that provide an

374 indicator of the degree of installation disturbance. Note that in the case of high displacement helical

375 piles, the contribution of the tip resistance to the compression capacity could be significant. It will

376 produce a smaller ratio of the uplift to compression capacity. Because of this point, the DF values in

377 Table 4 are calculated with subtracting the tip capacity. For very stiff clay, most DF values vary

378 between 0.8 and 1, indicating a low degree of installation disturbance. For dense sand, most DF

379 values vary between 0.6 and 0.8, suggesting a medium degree of installation disturbance. These

380 observations are consistent with those of Lutenegger and Tsuha (2015).

381 Model statistics and application in LRFD calibration

382 Capacity model factor

383 The calculated capacities are compared with the measured capacities in Fig. 3 for cohesive soils and

384 in Fig. 4 for cohesionless soils. A considerable deviation is observed. In accordance with the guideline

385 in Annex D of ISO 2394:2015, the deviation is quantified as

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386 𝑀 =𝑅um

𝑅uc (10)

387 where M is the capacity model factor, Rum is the measured capacity, and Ruc is the calculated capacity.

388 The model factor itself is not constant, but takes a range of values. The simplest method to

389 characterize a random variable is to calculate the mean and coefficient of variation (COV). A mean

390 and COV of M close to 1 and 0 would represent a near perfect calculation model that does not exist in

391 geotechnical engineering, regardless of the numerical sophistication.

392 The mean and COV values are summarized in Table 5. For each group of loading and soil types,

393 similar model statistics are obtained for three design methods. For helical piles under compression in

394 cohesive soils, M=0.47-1.81 with mean=1.14 and COV=0.28 for CFEM-2006, M=0.4-1.46 with

395 mean=0.9 and COV=0.26 for ISHF-2015, and M=0.47-1.5 with mean=1 and COV=0.25. The

396 uncertainty in capacity calculations is largely attributed to: (1) assumed individual plate bearing and

397 cylindrical shear failure models that are simplified and idealized representation of the actual soil

398 failure within the bearing helices; (2) transformation model errors in the correlations used to

399 determine the undrained shear strength and friction angle; (3) imperfect consideration of the effect of

400 installation disturbance on soil properties; (4) empiricisms in the bearing capacity factors Nc and Nq

401 and the shaft resistance coefficients α and β; and (5) measurement errors in the procedure of static

402 load tests and the bias in the interpretation of measured capacity. Lesny (2017) stated that the model

403 factor M in Eq. (10) is a lumped variable covering different sources of uncertainties. Moreover, a

404 range of variation in M for helical piles in cohesionless soils is higher than that for helical piles in

405 cohesive soils. This may be due to the uncertainty in estimating the friction angle ϕ. Diaz-Segura

406 (2013) evaluated 60 methods to calculate the bearing capacity factor Nγ for footings on sand. It was

407 observed that the uncertainty in the estimation of ϕ leads to a range of variation in Nγ is higher than

408 that obtained by the 60 methods.

409 Some model statistics in the literature are discussed for comparison purposes. Tappenden (2007)

410 evaluated the LCPC method (Bustamante and Gianeselli 1982), which relate the unit end bearing and

411 shaft friction to the cone resistance from a CPT profile by scaling coefficients. Accurate predictions

412 were obtained for helical piles in firm to stiff clays with =0.8-1.2. For hard and very dense glacial 𝑀

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413 till materials, the LCPC method significantly overpredict the capacity, where the ratio of the

414 calculated to the measured capacity is in a range of 2.25 to 4.75. This is because the scaling

415 coefficients within the LCPC method can only be applicable for clay, silt, or chalk (Tappenden 2007).

416 In addition, the LCPC method was mainly developed with compression tests which will overpredict

417 the uplift capacity. The results of Tappenden (2007) also implied that the LCPC method may not be

418 applicable for shallow helical piles under uplift. Perko (2009) proposed SPT-based methods with the

419 past experience that relate helix capacity to the SPT blow count by empirical constants. The mean and

420 COV values are 0.82-1.34 and 0.32-0.61. Note that load tests used to calibrate the empirical constants

421 were mainly associated with low displacement helical piles. Fateh et al. (2017) used 37 static load

422 tests to evaluate four CPT-based methods in the Annex A of ISO 19901-4:2016 that were developed

423 for conventional driven piles, where mean=0.93-1.19 and COV=0.39-0.68. According to the

424 classification scheme proposed by Phoon and Tang (2019), three methods for helical pile capacity are

425 moderate conservative (mean=1 – 1.5) and medium dispersion (COV=0.3 – 0.6).

426 Application for LRFD calibration

427 Probabilistic distribution of the model factor M has been increasingly applied to calibrate the

428 resistance factor in LRFD of bridge foundations (Paikowsky et al. 2004, 2010; AbdelSalam et al.

429 2012; Ng and Fazia 2012; Abu-Farsakh et al. 2009, 2013; Ng et al. 2014; Seo et al. 2015; Motamed et

430 al. 2016; Reddy and Stuedlein 2017a; Tang and Phoon 2018a-d; Tang et al. 2019). Currently, high

431 displacement helical piles have not been widely used in bridge projects. Because of the viable

432 advantages (e.g., speed of installation, cost effectiveness, and high resistance to compression and

433 uplift loads), high displacement helical piles would provide an innovative foundation design option

434 for short and medium span bridges that are frequently supported by group of driven steel piles (Sakr

435 2010). The resistance factor in LRFD of high displacement helical piles is calibrated in this section.

436 The basic design equation for LRFD is written as (AASHTO 2007):

437 (11)𝜓 ∙ 𝑅n ≥ ∑𝛾i ∙ 𝑄ni

438 where ψ is the resistance factor, Rn is the nominal capacity, Qni is the ith nominal load component, and

439 γi is the load factor applied to Qni.

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440 The aim of LRFD is to calculate the resistance factor ψ to ensure that Eq. (11) is satisfied for a

441 target reliability index βT in which the resistance statistics, load factors and statistics (bias and COV)

442 are required. For the AASHTO strength limit state I (i.e. combination of the dead load QDL and live

443 load QLL), the load factors (γDL=1.25 and γLL=1.75), bias factors (λDL=1.08 and λLL=1.15), and COVs

444 (COVDL=0.13 and COVLL=0.18) from AASHTO (2007) are adopted. The bias factors λDL and λLL are

445 lognormally distributed. The resistance statistics are calculated in terms of the capacity model factor

446 M. Because the number of load tests for each helix configuration (single- or multi-helix) in each soil

447 type (cohesive or cohesionless) under compression or uplift is relatively limited, all data are treated as

448 one group. Fig. 5 presents the probability distribution of the model factor M for three methods. It

449 shows that a lognormal distribution fits the M samples better than a normal distribution. Hence, the

450 capacity bias M is modeled by a lognormal variable.

451 For lognormal distribution of load and resistance statistics, the resistance factor ψ can be simply

452 computed with the first-order second-moment method (Paikowsky et al. 2004, 2010):

453 𝜓 =

𝜆R ∙ (𝛾DL ∙ 𝜅 + 𝛾LL) ∙ [(1 + COV2DL + COV2

LL)(1 + COV2

R) ](𝜆DL ∙ 𝜅 + 𝜆LL) ∙ exp{𝛽T ∙ ln[(1 + COV2

R) ∙ (1 + COV2DL + COV2

LL)]} (12)

454 where κ is the ratio of the dead load QDL to the live load QLL, λR and COVR are the mean and COV of

455 the capacity model factor M that are given in Table 6.

456 The resistance factor for the dead to live load ratio κ=QDL/QLL=1-10 when βT=2.33 or 3 is

457 presented in Fig. 6. It is observed that there is a slight reduction in the resistance factor ψ as the load

458 ratio increases. When κ>3, ψ almost becomes constant. For CFEM-2006, ψ=0.63 at κ=1 and ψ=0.57 𝜅

459 at κ=4 (10% reduction), where βT=2.33. The target reliability index βT has a more significant influence

460 on ψ. For CFEM-2006, ψ=0.57 at βT=2.33 and ψ=0.44 at βT=3 (23% reduction). Paikowsky et al.

461 (2004) discussed that the resistance factor ψ alone does not provide a measure to evaluate the

462 efficiency of the design methods that can be evaluated through the ratio ψ/μ of the resistance factor ψ

463 to the mean model factor μ. The values for the efficiency factor ψ/μ are also given in Table 6.

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464 It would be important to notice that Foye et al. (2009) presented another rational framework to

465 compute the resistance factor, where the uncertainties within the design equations are individually

466 evaluated. In this study, calibration against pile load test data cannot identify different sources of

467 uncertainties in the problem, which are considered by a single model factor.

468 Hyperbolic model factors

469 The original load-displacement curves in Fig. 2 vary in a surprisingly wide range. When the applied

470 load is divided by the measured capacity, the scatter of the normalized curves significantly decreases

471 as seen in Fig. 7. Similar results have been obtained for small displacement helical piles under uplift

472 (Lutenegger 2008; Stuedlein and Uzielli 2014; Mosquera et al. 2016; Tang and Phoon 2018a). The

473 normalized curves can be simply fitted by the following equation:

474𝑄

𝑅um=

𝑠𝑎 + 𝑏 ∙ 𝑠 (13)

475 where s is displacement, a and b represent the initial slope and asymptote of the normalized curves,

476 which are determined by the least-squares regression of the measured load-displacement curves.

477 For a specified working load, the model factor in Eq. (10) can also be applied to characterize the

478 uncertainty in predicting pile settlement (Zhang et al. 2008; Zhang and Chu 2009; Abchir et al. 2016).

479 The limitation is the settlement model factor has to be re-evaluated when a different working load is

480 prescribed (Phoon and Kulhawy 2008). Eq. (13) is an improvement of Eq. (10), because (a, b) allows

481 the entire load-displacement curve to be captured, rather than one fixed working load point on the

482 curve. The probability distributions of the hyperbolic parameters are illustrated in Fig. 8. According to

483 the physical meaning, the parameter b is usually bounded within 0 and 1, which is modelled by a beta

484 variable in Fig. 8a. The parameter a is modeled by a gamma variable in Fig. 8b. For clarity, the

485 equations of the probability density functions and distribution parameters for beta and gamma

486 variables are given in Appendix B. For b, the distribution parameters ξ=7.55 and η=1.93. From Eq.

487 (B3), mean=0.8 and COV=0.16. For a, the distribution parameters ξ=2.01 and η=3.31. With Eq. (B4),

488 mean=6.63 and COV=0.7.

489 The scatter plots of the hyperbolic model factors are presented in Fig. 9, which are negatively

490 correlated. The correlation within all hyperbolic parameters is described by the Kendall’s tau

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491 coefficient ρτ=-0.67 that is more robust than the Pearson correlation, because smaller statistical

492 uncertainty is involved (Ching et al. 2016). Bivariate copula analysis is utilized to model the joint

493 probability distribution of the correlated hyperbolic parameters, which is implemented by the

494 computer program MvCAT developed by Sadegh et al. (2017). Both local optimization and Markov

495 Chain Monte Carlo (MCMC) simulation within a Bayesian framework are employed to estimate the

496 copula parameter θ. Sadegh et al. (2017) stated that “MCMC within Bayesian analysis not only

497 provide a robust estimation of the global optima, but also approximate the posterior distribution of the

498 selected copulas, which can be used to construct a prediction uncertainty range for the copulas.” The

499 maximum likelihood (best) estimations of θ from location optimization (black asterisk) and MCMC

500 within Bayesian analysis (black cross) and the associated posterior distribution (grey bines) are given

501 in Fig. 10. For Clayton (Fig. 10b) and Gumbel (Fig. 10d) copula, the copula parameters are located on

502 the boundary. It indicates the optimization algorithm fails to obtain the best-fit θ values with the

503 selected copulas, which are not appropriate (Sadegh et al. 2017). For Gaussian (Fig. 10a), Frank (Fig.

504 10c) and Plackett (Fig. 10e) copula, the copula parameters from local optimization and MCMC within

505 Bayesian analysis are close. The lowest value of Bayesian Information Criterion (BIC) is obtained for

506 Gaussian copula as seen in Table 7, which is thus adopted to simulate the hyperbolic parameters. The

507 results are illustrated in Fig. 9, where black cross for simulated parameters and red circle for measured

508 values. The samples of (a, b) are then used to simulate the normalized load-displacement curves in

509 Fig. 7, where black line for simulated curves and red line for measured curves. It is demonstrated that

510 the scatter and shape of the measured load-displacement curves are reasonably captured with the

511 developed probabilistic model for (a, b). It can be further employed to perform reliability calibration

512 of high displacement helical piles at serviceability limit state as presented in Phoon and Kulhawy

513 (2008), Huffman and Stuedlein (2014), Stuedlein and Uzielli (2014), Reddy and Stuedlein (2017b),

514 and Tang and Phoon (2018c).

515 Summary and conclusions

516 This paper compiled 84 full-scale static load tests on high displacement helical piles. The measured

517 capacity was defined as the load at a pile head settlement equal to 5% of helix diameter. For high

518 displacement helical piles in very stiff clay, the disturbance factor (i.e. DF in Table 4) that is the ratio

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519 of uplift to compression capacity varies between 0.8 and 1, implying a low degree of installation

520 disturbance. For high displacement helical piles in dense sand, the disturbance factor ranging between

521 0.6 and 0.8 indicates a medium degree of installation disturbance.

522 With the collected load tests, the statistics of the model factor that is a ratio between measured

523 and calculated capacity are similar, where mean=1.21 and COV=0.34 for CFEM-2006; mean=1.13

524 and COV=0.42 for ISHF-2015; mean=1.1 and COV=0.35 for ISO 19901-4:2016. It might be

525 reasonable to conclude that three methods can be used to calculate the axial capacity of high

526 displacement helical piles. They can be classified as moderate conservative (mean=1 – 1.5) and

527 medium dispersion (COV=0.3 – 0.6). Based on the model statistics, the resistance factor in LRFD of

528 high displacement helical piles was computed by the first-order second-moment method. A hyperbolic

529 model with two parameters was used to fit the measured load-displacement curves. The hyperbolic

530 parameters and are gamma and beta variables. Using the copula analysis that considers the 𝑎 𝑏

531 correlation between and , the measured load-displacement curves can be simulated reasonably. 𝑎 𝑏

532 Finally, it should be noted that the number of load test data for high displacement helical piles in

533 cohesive (or cohesionless) soils under compression (or uplift) is relatively small. The model statistics

534 (mean, COV or correlation) for each group of loading and soil types will be refined as more data

535 become available.

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List of Figure Caption

Fig. 1. Semi-empirical design methods: (a) individual plate bearing and (b) cylindrical shear method

Fig. 2. Measured load-displacement curves

Fig. 3. Comparison of calculated and measured capacity for cohesive soils

Fig. 4. Comparison of calculated and measured capacity for cohesionless soils

Fig. 5. Probability distribution of the capacity model factor

Fig. 6. Variation of the resistance factor with the ratio of the dead to live load

Fig. 7. Measured and simulated normalized load-displacement curves

Fig. 8. Probability distributions of hyperbolic model factors

Fig. 9. Scatter plot of hyperbolic model factors

Fig. 10. Maximum likelihood estimation and posterior distribution of copula parameter θ

Page 32 of 51



Draft

Fig. 1. Semi-empirical design methods: (a) Individual plate bearing and (b) cylindrical shear method

Page 33 of 51



Draft

0 25 50 75 100 125s (mm)

0

1000

2000

3000

4000

Q (

kN)

0 25 50 75 100 125 150s (mm)

0

1000

2000

3000

4000

Q (

kN)

(a) Compression (b) Uplift

Fig. 2. Measured load-displacement curves

Page 34 of 51



Draft102 103

Rum

(kN)

102

103

Ruc

(kN

)

CFEM-2006ISHF-2015ISO 19901-4:2016Equality line

102 103

Rum

(kN)

102

103

Ruc

(kN

)


103

Rum

(kN)

103Ruc

(kN

)


102 103

Rum

(kN)

102

103

Ruc

(kN

)


Fig. 3. Comparison of calculated and measured capacity for cohesive soils

(a) Single-helix (compression) (b) Multi-helix (compression)

(c) Single-helix (uplift)

(d) Multi-helix (uplift)

Page 35 of 51



Draft103

Rum

(kN)

103

Ruc

(kN

)CFEM-2006ISHF-2015ISO 19901-4:2016Equality line

103

Rum

(kN)

103

Ruc

(kN

)


103

Rum

(kN)

103

Ruc

(kN

)


102 103

Rum

(kN)

102

103

Ruc

(kN

)CFEM-2006ISHF-2015ISO 19901-4:2016Equality line

Fig. 4. Comparison of calculated and measured capacity for cohesionless soils

(c) Single-helix (uplift) (d) Multi-helix (uplift)

(b) Multi-helix (compression)(a) Single-helix (compression)

Page 36 of 51



Draft0 1 2 3

M

0.00010.001

0.01

0.10.250.5

0.750.9

0.99

0.9990.9999

Prob

abili

ty

NormalObserved M valuesLognormal

0 1 2 3M

0.00010.001

0.01

0.10.250.5

0.750.9

0.99

0.9990.9999

Prob

abili

ty


0 1 2 3 0M

0.00010.001

0.01

0.10.250.5

0.750.9

0.99

0.9990.9999

Prob

abili

ty


(a) CFEM-2006 (b) ISHF-2015

(c) ISO 19901-4:2016

Fig. 5. Probability distribution of capacity model factor

Page 37 of 51



Draft1 2 3 4 5 6 7 8 9 10

=QDL

/QLL

0.3

0.4

0.5

0.6

0.7

0.8CFEM-2006 (

T=2.33)

ISHF-2015 (T=2.33)

ISO 19901-4:2016 (T=2.33)

CFEM-2006 (T=3)

ISHF-2015 (T=3)

ISO 19901-4:2016 (T=3)

Fig. 6. Variation of the resistance factor with the ratio of the dead tolive load

Page 38 of 51



Draft0 25 50 75 100 125

s (mm)

0

0.4

0.8

1.2

1.6

2

Q/R

um

Fig. 7. Measured and simulated normalized load-displacement curves

Page 39 of 51



Draft0.4 0.5 0.6 0.7 0.8 0.9 1

b

0.005 0.01

0.05 0.1

0.25

0.5

0.75

0.9 0.95

0.99 0.995

0.999 0.99950.9999

Prob

abili

ty

Observed b valuesBeta distribution B ( , )

0 5 10 15 20a

0.005 0.01

0.05 0.1

0.25

0.5

0.75

0.9 0.95

0.99 0.995

Prob

abili

ty

Observed a valuesGamma distribution ( , )

=2.01, =3.31=6.63, COV=0.7

=7.55, =1.93=0.8, COV=0.16

Fig. 8. Probability distributions of hyperbolic model factors

Page 40 of 51



Draft0.2 0.4 0.6 0.8 1

b

0

5

10

15

20

25

30

35

40

a

Simulated (b, a)

Observed (b, a)

N = 73 = -0.67

Fig. 9. Scatter plot of hyperbolic model factors

Page 41 of 51



Draft

(a) Gaussian

-0.85 -0.8Copula parameter

0

0.1

0.2

0.3

0.4

Den

sity

(b) Clayton

0 0.05 0.1Copula parameter

0

0.1

0.2

0.3

0.4

Den

sity

(c) Frank

-10 -9 -8Copula parameter

0

0.1

0.2

0.3

0.4

Den

sity

(d) Gumbel

1 1.05 1.1Copula parameter

0

0.1

0.2

0.3

0.4

Den

sity

(e) Plackett

0.03 0.04 0.05Copula parameter

0

0.1

0.2

0.3

0.4

Den

sity

Fig. 10. Maximum likelihood estimation and posterior distribution of copula parameter

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List of Tables

Table 1. Summary of (S/D)crit marking the transition from the cylindrical shear to individual plate bearing failure

References Soil type Loading type (S/D)crit Analysis methodCFEM-2006 All All 3 Empirical assumption

Narasimha Rao et al. (1989)

Very soft clay Uplift 1.5


Soft to mediumstiff clay

Uplift 1-1.5

Narasimha Rao andPrasad (1993)

Soft marine clay

Uplift 1.5


Soft marine clay

Uplift 1.5-2

Laboratory model test

Merifield (2011) Clay Uplift 1.6 Finite element simulationWang et al. (2013) Kaolin clay Uplift 5 Centrifuge test/finite

element simulationUplift 3Cohesive

Compression 3Uplift 3

Zhang (1999)

CohesionlessCompression 2

Field load test

Tappenden (2007) All All 3 Field load testTappenden et al. (2009) Stiff clay Uplift 1.5 Field load test

Elkasabgy andEl Naggar (2015)

Stiff clay Compression 1.5 Field load test

Uplift 3Sakr (2009) Dense to verydense oil sand Compression 3

Field load test

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Table 2. Available design guidelines for the capacity of driven piles without bearing helicesDesign equations

Method Soil type Unite end bearing (qt) Unit shaft friction (fs)Clay Nc=9, D<0.5 m

Nc=7, 0.5≤D≤1 mNc=6, D>1 m

α=0.21+0.26pa/sus≤1CFEM-2006

Sand Nq=30-80Nq=50-120Nq=100-120

β=0.3-0.8, loose sandβ=0.6-1, medium sandβ=0.8-1.2, dense sand

Clay Nc=9 α=0.5(sus/σv0')-0.5, sus/σv0'≤1α=0.5(sus/σv0')-0.25, sus/σv0'>1

ISO 19901-4:2016

Sand qt≤qt,lim Nq=20, qt,lim=5 MPaNq=40, qt,lim=10 MPaNq=50, qt,lim=12 MPa

fs≤fs,lim β=0.37, fs,lim=81 kPa, DR=35-65%β=0.46, fs,lim=96 kPa, DR=65-85%β=0.56, fs,lim=115 kPa, DR=85-100%

ISHF-2015 Clay Nc=9 α=1, sus<24 kPaα=0.5, sus>72 kPaLinear interpolation of 0.5 and 124≤sus≤72 kPa

Sand Nq=0.5(12·ϕ)(ϕ/54) —Note: Nc is the undrained bearing capacity factor; α is the dimensionless adhesion factor; pa is the atmospheric pressure=101 kPa; sus the operational undrained shear strength mobilized along the shaft; Nq is the drained bearing capacity factor; β is the empirical factor relating the unit shaft friction to the average effective vertical stress σv0'; qt,lim is the limiting value of the unit end bearing capacity; fs,lim is the limiting value of the unit shaft friction; DR is the relative density; and ϕ is the internal friction angle. The Nq values in the ISHF guideline (Lutenegger 2015) is adopted from the Meyerhof’s Nq value divided by 2 to account for soil disturbance, which are widely used in practical design such as the Chance – Technical Design Manual (Hubbell, Inc. 2014).

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Table 3. Distributions and ranges of the collected load tests on high displacement helical pilesUplift Compression

Helix configuration Parameters Cohesive Cohesionless Cohesive CohesionlessNo. of load tests 4 6 13 8Range of H (m) 4.9-6.9 2.1-5.7 4.6-9 3.1-9.5Range of H/D 5.1-14 4.2-11.6 4.3-17.8 4.7-12

Range of d (mm) 168-406 168-406 168-508 168-508Range of D (mm) 457-914 406-914 457-1016 406-1016Range of su (kPa) 145-300 – 88-305 –

Single-helix

Range of ϕ (°) – 30-45 – 30-45No. of load tests 14 10 28 9

Number of helices n 2-6 2-3 2-6 2-3Range of H (m) 3-27.5 2.3-9.7 3-27.5 5-10.5Range of H/D 5.4-24 4.2-12 5.4-24 4.1-12Range of S/D 1.5-3 1.5-3 1.5-4.5 1.5-3

Range of d (mm) 168-406 168-406 168-406 178-406Range of D (mm) 356-1016 304-813 356-1016 356-813Range of su (kPa) 24-224 – 12-244 –

Multi-helix

Range of ϕ (°) – 30-39 – 32-39

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Table 4. Summary of the values of disturbance factor (DF) for high displacement helical pilesPile geometries Measured capacity (kN)

References Soil description H (m) d (mm) n D (mm) S/D Uplift Compression DFSakr (2009) Dense to very dense oil sand 5.1 178 1 406 – T3 560 C3 875 0.64Sakr (2011a) Medium to very dense sand 5.7 406 1 914 – ST21 1497 ST20 2094 0.71

Sakr et al. (2009) Very dense sandy gravel soil 3.1 168 1 508 – T1 534 C1 700 0.76Tappenden (2007) Hard clay till 5.9 273 1 762 – T7 800 C11 1018 0.79

Sakr (2012) Very stiff to very hard clay till 5.6 406 1 914 – ST14 1680 ST13 2030 0.83Harnish and El Naggar (2017) Glacial till 6.86 219 1 610 – T8S 1020 C8S 981 1.04

5 219 3 356 1.5 T4 360 C4 342 1.053 219 3 356 1.5 T5 190 C5 368 0.52

Tappenden (2007) Loose to compact silty sand

5 219 2 356 3 T6 360 C6 316 1.14Sakr (2009) Dense to very dense oil sand 4.9 178 2 406 3 T4 630 C4 935 0.67Sakr (2011a) Very dense sand 5 406 2 813 2 ST32 1880 ST31 1952 0.96

3 219 3 356 1.5 T2 140 C2 135 1.04Stiff silty clay5 219 2 356 3 T3 210 C3 185 1.14

Tappenden (2007)

Hard clay till 6 273 2 762 3 T8 1325 C12 1298 1.025.7 324 2 762 3 ST5 1195 ST6 1745 0.6814.1 406 2 813 2 ST62 1420 ST61 1496 0.95

Sakr (2012) Very stiff to very hard clay till

18.5 406 2 813 2 ST72 2100 ST71 2313 0.9127.5 324 6 914 2 TP1-T 747 TP1-C 840 0.8918.3 324 4 1016 2 TP2-T 836 TP2-C 1275 0.66

Butt et al. (2017) Normally consolidated glacial clay

27.5 324 5 1016 2 TP3-T 672 TP3-C 783 0.866.86 168 2 457 3 T6D 982 C6D 1095 0.9Harnish and El Naggar (2017) Glacial till6.86 219 2 610 3 T8D 1380 C8D 1433 0.96

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Table 5. Summary of model statistics for different loading and soil types and helix configurationsModel factor (M)

Loading type Soil type No. of load tests Design methods Range Mean COVCFEM-2006 0.47 – 1.81 1.14 0.28ISHF-2015 0.4 – 1.46 0.9 0.26

Cohesive 34

ISO 19901-4:2016 0.47 – 1.5 1 0.25CFEM-2006 0.51 – 2.86 1.27 0.49ISHF-2015 0.61 – 3.16 1.47 0.46

Compression

Cohesionless 13

ISO 19901-4:2016 0.64 – 2.44 1.16 0.48CFEM-2006 0.69 – 1.94 1.18 0.29ISHF-2015 0.54 – 1.58 0.97 0.26

Cohesive 18

ISO 19901-4:2016 0.58 – 1.66 1.06 0.28CFEM-2006 0.8 – 2.14 1.37 0.33ISHF-2015 0.94 – 2.34 1.58 0.32

Uplift

Cohesionless 13

ISO 19901-4:2016 0.64 – 2.02 1.35 0.34

Table 6. Calibrated LRFD resistance factors and efficiency factors for βT=2.33 and 3, where κ=QDL/QLL=4

βT=2.33 βT=3No. of load tests Design methods Mean (μ) COV ψ ψ/μ ψ ψ/μ

CFEM-2006 1.21 0.34 0.57 0.47 0.44 0.36ISHF-2015 1.13 0.42 0.45 0.4 0.33 0.29

78

ISO 19901-4:2016 1.1 0.35 0.51 0.46 0.39 0.35

Table 7. Copula analysis results for hyperbolic parametersθ values

Copulas Local optimization MCMC with Bayesian BIC valuesGaussian -0.86 -0.83 -687Clayton 0 0 -331Frank -9.26 -8.1 -647

Gumbel 1 1 -331Plackett 0.04 0.04 -678

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Appendix A. Field load test database of high displacement helical pilesTable A1. Static load tests in cohesive soils

ReferencesPredominant soil

conditionsTestID

Testtype Pile tip

su(kPa)

H(m)

d(mm) n

D(mm) S/D

Rum(kN) b a

Glacial till C6S C Open-end 244 6.86 168 1 457 – 644 0.93 2.47Glacial till C8S C Open-end 244 6.86 219 1 610 – 1064 0.84 5.48

Harnish andEl Naggar (2017)

Glacial till C10S C Open-end 244 6.25 273 1 762 – 1445 0.81 8.14Glacial till SS11 C Open-end – 6 324 1 610 – 894 0.78 6Elkasabgy and

El Naggar (2015) Glacial till LS12 C Open-end – 9 324 1 610 – 1952 0.86 4.64Very stiff to very hard clay till ST7 C Open-end 225 5.7 324 1 762 – 1540 0.62 12.2Very stiff to very hard clay till ST13 C Open-end 225 5.8 406 1 914 – 2292 0.9 9.12

Sakr (2012)

Very stiff to very hard clay till ST15 C Open-end 225 5.4 508 1 1016 – 2400 0.72 11.3Sakr (2013) Silty clay over glacial till S4 C Open-end 305 9 324 1 762 – 1906 0.9 3.37

Stiff silty clay C7 C Open-end 200 4.6 178 1 457 – 212 0.99 1.44Stiff silty clay C8 C Open-end 200 4.6 219 1 457 – 268 0.98 0.97Hard clay till C11 C Open-end 145 5.9 273 1 762 – 1094 0.61 10.6

Tappenden (2007)

Firm to stiff clay till over clay shale C13 C Open-end 300 7.5 219 1 400 – 1075 0.85 3.65Elsherbiny and

El Naggar (2013)Fill to silt and sand over silty clay PB-2 C Open-end 11.5 10 178 3 610 3 143 0.93 2.69

Glacial till C6D C Open-end 244 6.86 168 2 457 3 1144 0.94 2.73Glacial till C8D C Open-end 244 6.86 219 2 610 3 1516 0.86 5.56

Harnish andEl Naggar (2017)

Glacial till C10D C Open-end 244 6.25 273 2 762 3 1822 0.73 6.64Stiff silty clay C1 C Open-end 75 5 219 3 356 1.5 180 0.96 0.7Stiff silty clay C2 C Open-end 75 3 219 3 356 1.5 160 0.95 1.26Stiff silty clay C3 C Open-end 75 5 219 2 356 3 210 0.96 0.76Stiff silty clay C9 C Open-end 200 5.5 178 2 483 3.1 372 0.94 1.8

Hard clay till over clay shale C10 C Open-end 135 9.3 244 2 483 3.2 1177 0.93 2.03Hard clay till C12 C Open-end 145 6 273 2 762 3 1375 0.68 10.6

Tappenden (2007)

Firm to stiff silty clay C14 C Open-end 75 10.4 324 2 914 1.8 634 0.72 8Glacial till SD11 C Open-end – 6 324 2 610 1.5 1478 0.79 6.18Glacial till SD21 C Open-end – 6 324 2 610 3 1259 0.64 9.1Glacial till SD31 C Open-end – 6 324 2 610 4.5 1116 0.79 6.19

Elkasabgy andEl Naggar (2015)

Glacial till LD12 C Open-end – 9 324 2 610 1.5 2477 0.79 7.26Sakr (2012) Very stiff to very hard clay till ST6 C Open-end 225 5.7 324 2 762 3 1912 0.72 11.9

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Table A1 (continued).

ReferencesPredominant soil

conditionsTestID

Testtype Pile tip

su(kPa)

H(m)

d(mm) n

D(mm) S/D

Rum(kN) b a

Stiff to very stiff glacial till ST61 C Open-end 83 14.1 406 2 813 2 1630 0.78 6.94Sakr (2012)Stiff to hard glacial till ST71 C Open-end 117.5 18.5 406 2 813 2 2450 0.72 10.7

Sakr (2013) Silty clay over glacial till S3 C Open-end 305 9 324 2 762 1.5 2400 0.75 8.22Stiff clay C1 C Open-end 45 7.5 324 3 813 2.63 677 0.87 6.84Sakr (2008)

Soft to firm clay C2 C Open-end 24 10.8 324 4 864 2.65 772 0.89 5.34Glacio-lacustrine silty clay TP1 C Open-end 52.5 13.7 324 6 610 3 1068 – –Glacio-lacustrine silty clay TP2 C Open-end 51 13.9 324 6 610 3 970 0.93 2.37

Pardoski (2014)

Glacio-lacustrine silty clay TP3 C Open-end 56.5 14.6 324 2 610 3 623 – –Normally consolidated glacial clay TP1-C C Open-end 24 27.5 324 6 914 2 858 – –Normally consolidated glacial clay TP2-C C Open-end 38 18.3 324 4 1016 2 1303 0.9 6.31

Butt et al. (2017)

Normally consolidated glacial clay TP3-C C Open-end 24 27.5 324 5 1016 2 801 – –Sakr (2012) Very stiff to very hard clay till ST14 U Open-end 225 5.6 406 1 914 – 1680 0.87 7.62

Tappenden (2007) Hard clay till T7 U Open-end 145 5.9 273 1 762 – 800 0.77 8.53Glacial till T6S U Open-end 244 6.86 168 1 457 – 870 0.87 2.8Harnish and

El Naggar (2017) Glacial till T8S U Open-end 244 6.86 219 1 610 – 1020 0.84 2.7Very stiff to very hard clay till ST5 U Open-end 225 5.9 324 2 762 3 1195 0.79 9.33

Stiff to very stiff glacial till ST62 U Open-end 83 14.3 406 2 813 2 1420 0.9 3.91Sakr (2012)

Stiff to hard glacial till ST72 U Open-end 117.5 18.5 406 2 813 2 2100 0.83 8.52Sakr (2008) Soft to firm clay T2 U Open-end 24 7.9 219 3 711 3 445 0.83 2.92

Stiff silty clay T1 U Open-end 75 5 219 3 356 1.5 210 – –Stiff silty clay T2 U Open-end 75 3 219 3 356 1.5 140 – –Stiff silty clay T3 U Open-end 75 5 219 2 356 3 210 – –

Tappenden (2007)

Hard clay till T8 U Open-end 145 6 273 2 762 3 1325 0.72 8.44Glacial till T6D U Open-end 244 6.86 168 2 457 3 982 0.92 2.22Harnish and

El Naggar (2017) Glacial till T8D U Open-end 244 6.86 219 2 610 3 1380 0.87 4.12Normally consolidated glacial clay TP1-T U Open-end 24 27.5 324 6 914 2 747 – –Normally consolidated glacial clay TP2-T U Open-end 38 18.3 324 4 1016 2 836 – –

Butt et al. (2017)

Normally consolidated glacial clay TP3-T U Open-end 24 27.5 324 5 1016 2 672 – –

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Table A2. Static load tests in cohesionless soils

References Predominant soil conditionsTestID

Testtype Pile tip

ϕ(°)

H(m)

d(mm) n

D(mm) S/D

Rum(kN) b a

Sakr (2009) Dense to very dense oil sand C3 C Open-end 38 5.3 178 1 406 – 940 0.68 5.57Sakr et al. (2009) Very dense sandy gravel C1 C Open-end 45 3.1 168 1 508 – 734 0.7 7.93

Medium to very dense sand ST2 C Open-end 35 9.5 324 1 762 – 1892 0.55 18Medium to very dense sand ST20 C Open-end 35 6.1 406 1 914 – 2533 0.77 12.8

Sakr (2011a)

Medium to very dense sand ST22 C Open-end 35 5.75 508 1 1016 – 2200 0.68 11.6Sakr (2009) Dense to very dense oil sand C4 C Open-end 38 5.3 178 2 406 3 1000 0.43 11.4

Medium to very dense sand ST1 C Open-end 35 9 324 2 762 3 2030 0.52 19.6Dense to very dense sand ST24 C Open-end 34 5.95 406 2 813 2 2920 0.76 8.31

Very dense sand ST31 C Open-end 36 5 406 2 813 2 2320 0.66 10.4

Sakr (2011a)

Dense sand over very stiff glacial till ST41 C Open-end 36 10.5 406 2 813 2 2511 0.72 11.3Loose to compact silty sand C4 C Open-end 32 5 219 3 356 1.5 470 0.88 2.3Loose to compact silty sand C5 C Open-end 39 3 219 3 356 1.5 420 0.7 5.12

Tappenden (2007)

Loose to compact silty sand C6 C Open-end 32 5 219 2 356 3 380 0.83 2.36Tappenden (2007) Very dense sand till T9 U Open-end 38 4.9 406 1 762 – 2025 0.59 16

Sakr (2011a) Medium to very dense sand ST21 U Open-end 35 5.7 406 1 914 – 1497 0.79 7.67Sakr (2009) Dense to very dense oil sand T3 U Open-end 38 5.1 178 1 406 – 560 0.84 3.06Sakr (2011b) Loose to compact sand T2 U Open-end 30 2.1 168 1 406 – 93 0.91 1.44

Sakr et al. (2009) Very dense sandy gravel T1 U Open-end 45 3.2 168 1 508 – 534 0.82 4.42Medium to very dense sand ST3 U Open-end 35 9.5 324 2 762 3 1993 0.41 23.3Dense to very dense sand ST25 U Open-end 34 9.71 406 2 813 2 2900 0.67 12.5

Sakr (2011a)

Very dense sand ST32 U Open-end 36 5 406 2 813 2 1880 0.81 5.81Dense to very dense oil sand T4 U Open-end 38 4.9 178 2 406 3 630 0.75 4.75Sakr (2009)Dense to very dense oil sand T5 U Open-end 38 5.2 178 2 406 3 820 – –

Sakr (2011b) Loose to compact sand T3 U Open-end 30 2.3 168 2 304 2 80 0.86 1.75Loose to compact silty sand T4 U Open-end 32 5 219 3 356 1.5 360 0.9 1.65Loose to compact silty sand T5 U Open-end 39 3 219 3 356 1.5 365 0.95 2.08

Tappenden (2007)

Loose to compact silty sand T6 U Open-end 32 5 219 2 356 3 360 0.76 2.46Note:

1. C and U in the column of Test type mean Compression and Uplift loading test.2. In tests C9 and C10 of Tappenden (2007), D is an average value for two helix diameters D1=508 mm and D2=457 mm.

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Appendix B. Probability density functions for beta and gamma variables

The probability density functions are given in Eq. (B1) for beta variable and Eq. (B2) for gamma

variable.

𝑓(𝑥,𝜉,𝜂) =1

𝐵(𝜉,𝜂) ∙ 𝑥𝜉 ― 1 ∙ (1 ― 𝑥)𝜂 ― 1 (B1)

𝑓(𝑥,𝜉,𝜂) =𝜂𝜉 ∙ 𝑥𝜉 ― 1 ∙ 𝑒 ―𝜂 ∙ 𝑥

𝛤(𝜉) (B2)

where B(ξ, η) is the beta function, ξ and η are shape parameters for beta distribution, Γ(ξ) is the

gamma function, ξ and η are shape and scale parameters for gamma distribution. The mean μ and

variance σ2 are given in Eq. (B3) for beta variable and Eq. (B4) for gamma variable.

𝜇 =𝜉

𝜉 + 𝜂, 𝜎2 =𝜉 ∙ 𝜂

(𝜉 + 𝜂)2 ∙ (𝜉 + 𝜂 + 1) (B3)

(B4)𝜇 = 𝜉 ∙ 𝜂, 𝜎2 = 𝜉 ∙ 𝜂2

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