Determination of Bearing Capacity of Open-Ended Piles
`[&%fTW+ in Sand
yBCLS550 Kyuho Paik1 and Rodrigo Salgado, M.ASCE2
JkEITuTth Abstract: The bearing capacity of open-ended piles is affected by the degree of soil plugging, which is quantified by the incremental
DFbhy filling ratio ~IFR!. There is not at present a design criterion for open-ended piles that explicitly considers the effect of IFR on pile load
l15Z8hYhj capacity. In order to investigate this effect, model pile load tests were conducted on instrumented open-ended piles using a calibration
,va2:V
chamber. The results of these tests show that the IFR increases with increasing relative density and increasing horizontal stress. It can also
yJ>Bc be seen that the IFR increases linearly with the plug length ratio ~PLR! and can be estimated from the PLR. The unit base and shaft
wn.UjxX. resistances increase with decreasing IFR. Based on the results of the model pile tests, new empirical relations for plug load capacity,
`NQ;|! annulus load capacity, and shaft load capacity of open-ended piles are proposed. The proposed relations are applied to a full-scale pile load
QJ%N80 test performed by the authors. In this load test, the pile was fully instrumented, and the IFR was continuously measured during pile
w}YcAnuB{% driving. A comparison between predicted and measured load capacities shows that the recommended relations produce satisfactory
im9Pj b% predictions.
;3iWV"&_A DOI: 10.1061/~ASCE!1090-0241~2003!129:1~46!
`[h&Q0Du6 CE Database keywords: Bearing capacity; Pile load tests; Sand.
R*H-QH/H1 Introduction
]l"9B'XR When an open-ended pile is driven into the ground, a soil plug
L lD=c may develop within the pile during driving, which may prevent or
K."W/A! partially restrict additional soil from entering the pile. It is known
S
rhBU6K that the driving resistance and the bearing capacity of open-ended
{5 3#Xd piles are governed to a large extent by this plugging effect.
EgRuB@lw76 Many design criteria for open-ended piles, based on field tests,
hP_{$c{4:g chamber tests or analytical methods, have been suggested @e.g.,
#@F Klos and Tejchman 1977; Nishida et al. 1985; American Petroleum
9fYof Institute ~API! 1991; Randolph et al. 1991; Jardine et al.
TpYdIt9#> 1998#. For example, in the case of API RP2A ~1991!, which is
F5H]$AjW generally used for offshore foundation design, the bearing capacity
HP=5a. of an open-ended pile can only be estimated for either the fully
M
9 N'Hk= coring mode or the fully plugged mode of penetration. In practice,
Xif>ZL?aXb most open-ended piles are driven into sands in a partially plugged
(S_1C, mode. Stefanoff and Boshinov ~1977! suggested the use of onedimensional
IH"_6s#$& plug analysis, in which the soil plug is treated as a
`ghNS series of horizontal thin discs and the force equilibrium condition
xs?]DJj is applied to each disc, to calculate plug capacity of an openended
@>F`;'_*z pile.
O`_]n There have been modifications of one-dimensional plug analysis
U%K gLg# to improve predictive accuracy, such as the introduction of the
aN';_tGvK concept of the wedged soil plug ~Murff et al. 1990; O’Neill and
N.vkM`Z Raines 1991; Randolph et al. 1991!. Many test results show that
R8|FqBs
the soil plug can be divided into a wedged plug zone and an
+D?Re%HI unwedged plug zone. While the wedged plug zone transfers load
KcM+8W\
to the soil plug, the unwedged plug zone transfers no load but
XUK%O8N#9 provides a surcharge pressure on top of the wedged plug zone.
-3SRGr However, it is not easy to apply the one-dimensional analysis to
i x_a practical cases, because of the sensitivity of the method to the
p+;x&h)[l lateral earth pressure coefficient, which is not easily estimated
+WvW#wpH ~Brucy et al. 1991; Leong and Randolph 1991!. De Nicola and
} 7i}dyQv} Randolph ~1997! addressed this by proposing a profile of the
^AT#A<{1( lateral earth pressure coefficient K along the soil plug length.
@9g!5dcT An alternative design method can be based on the incremental
lgC^32y filling ratio ~IFR!. The degree of soil plugging is adequately quantified
DCgiTT\ using the IFR ~Paikowsky et al. 1989; Paik and Lee 1993!
):V)Hrq?x defined as
787}s`,} IFR5
Oe0dC9H DL
_<jccQ DD
XRn+6fn| 3100~%! (1)
6M bMAh5> where DL5increment of soil plug length ~L! corresponding to a
8u Z4[ small increment DD of pile penetration depth D ~see Fig. 1!. The
V6b) fully plugged and fully coring modes correspond to IFR50 and
_2eL3xXha. 100%, respectively. A value of IFR between 0 and 100% means
)J&!>GP that the pile is partially plugged. A series of model pile tests,
c#pVN](? using a calibration chamber, were conducted on model openended
30h1)nQ$h} piles instrumented with strain gauges in order to investigate
;{rl
Y> the effect of IFR on the two components of bearing capacity: base
pXe]hnY load capacity and shaft load capacity. Based on the calibration
NTSKmCvQG chamber test results, empirical relationships between the IFR and
Rp.FG the components of pile load capacity are proposed. In order to
e(k$k>? verify the accuracy of predictions made using the two empirical
7P DD relationships, a full-scale static pile load test was conducted on a
DO?
bJ01 fully instrumented open-ended pile driven into dense sand. The
u_S>`I predicted pile load capacities are compared with the capacities
NAfu$7 measured in the pile load test.
q?oJ=]m" 1Associate Professor, Dept. of Civil Engineering, Kwandong Univ.,
nHB`<B Kangwon-do 215-800, South Korea ~corresponding author!. E-mail:
4\Cb4jq%/ pkh@kwandong.ac.kr G/8G`teAZ 2Associate Professor, School of Civil Engineering, Purdue Univ., West
:w4I+*] Lafayette, IN 47907-1284. E-mail:
rodrigo@ecn.purdue.edu JmVha!<qk Note. Discussion open until June 1, 2003. Separate discussions must
|Vc:o_n7 be submitted for individual papers. To extend the closing date by one
>V3pYRA month, a written request must be filed with the ASCE Managing Editor.
I[ I]C9D The manuscript for this paper was submitted for review and possible
kN$L8U8f publication on July 23, 2001; approved on May 23, 2002. This paper is
LWP&Si*j part of the Journal of Geotechnical and Geoenvironmental Engineering,
DYCXzFAa Vol. 129, No. 1, January 1, 2003. ©ASCE, ISSN 1090-0241/2003/1-
2@f E! 46–57/$18.00.
*!+?%e{;b 46 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003
_xXDvBU Soil Sample Preparation
a<{+
JU5 Soil Properties
J""N:X!1 Han river sand, a subangular quartz sand, with D1050.17mm and
_:9-x;0H2 D5050.34 mm, was used for all the calibration chamber model
;?:X_C pile tests. The test sand is classified as poorly graded ~SP! in the
wB W]w Unified Soil Classification System, so the maximum dry density
V~qlg1h of the sand is near the low end of the typical range for sands. The
s)|l-I maximum and minimum dry unit weights of the sand were 15.89
#FV `*G
and 13.04 kN/m3, respectively.
tL@m5M%:N2 A series of laboratory tests were conducted to characterize the
;hp?wb sand. The results from these tests are summarized in Table 1. The
>a1ovKF internal friction angle of the sand and the interface friction angle
?HaUT(\j between the sand and steel were measured from direct shear tests
`'<&<P under normal stresses of 40–240 kPa. The peak friction angles of
'D;'Pr] the sand with relative densities of 23, 56, and 90% were 34.8,
@g'SH:} 38.2, and 43.4°, respectively, and the critical-state friction angle
Nh|QYxOP was 33.7°. The peak interface friction angles between the pile and
<ba+7CK]w the sand were 17.0, 17.5, and 18.4° for DR523, 56, and 90%,
RJZ4fl respectively, and the critical-state interface friction angle was
Fh$Xcz~i 16.7°. This angle is lower than commonly reported values because
cX/["AM the test pile was made of stainless steel pipe with a very
^aO\WKkA smooth surface.
ni x1_Wo; Calibration Chamber and Sample Preparation
\muC_9ke All model pile tests were conducted in soil samples prepared
K.jm>]'z4; within a calibration chamber with a diameter of 775 and a height
kzLtI w&. of 1250 mm. In order to simulate various field stress conditions,
lGP'OY"Q two rubber membranes, which can be controlled independently,
&za~=+ were installed on the bottom and inside the lateral walls of the
ZX!u\O|w calibration chamber. The consolidation pressure applied to the
hgi9%>oUB two rubber membranes was maintained constant by a regulator
K%"cVqb2V panel throughout each pile test.
sGD b< The soil samples were prepared by the raining method with a
*QpKeI constant fall height. The falling soil particles passed through a
+EBoFeeIG sand diffuser composed of No. 8 and No. 10 sieves in order to
f<0nj? control flow uniformity and fall velocity. The soil samples had
ROHr%'owgL DR523, 56, and 90%. After sample preparation, the samples
?#917M were consolidated to the desired stress state during approximately
%L$P']%t@ 30 h by compressed air transferred to the rubber membranes.
vMOit,{ Measurements made in calibration chambers are subject to
3#Hx^H chamber size effects. Many researchers have attempted to estimate
<C_FI` wk the chamber size needed for boundary effects on pile bearing
Zj8aD-1]U^ capacity or cone resistance to become negligible. Parkin and
! G+/8Q^ Lunne ~1982! suggested 50 times the cone diameter as the minimum
U ]6Hml;l chamber diameter for chamber size effect on cone penetration
UN}jpu<h resistance to become acceptably small. Salgado et al. ~1998!,
T9+ ?A
l based on cavity expansion analyses, found that 100 times the cone
~IKPi==@, diameter was the minimum chamber diameter to reduce chamber
hOSkxdi*^ size effects on cone resistance to negligible levels. Diameters of
RT)*H>| the chamber and test pile used in this study are 775 and 42.7 mm,
=N zA2td respectively. The lateral and bottom boundaries are located at a
h4^
a#%$ distance equal to 18.2 pile radii from the pile axis and 23.0 pile
-3<5,Q{G+ radii below the maximum depth reached by the pile base, respectively.
vWwnC)5 Considering the results of the research on chamber size
\ oIVE+L/P effects mentioned above, the size of the chamber used in this
X|7Y|0o study is not sufficiently large for chamber size effects on pile
\}e1\MiZ bearing capacity to be neglected. The flexible boundary causes
Oj*3'?<7= lower radial stresses than those that would exist in the field. Accordingly,
bG0t7~!{E the chamber tests done as part of this study produce
_KkLH\1g$ lower pile load capacities than those that would be observed in
A8R}W= the field. A correction for chamber size effects is then necessary.
O9k9hRE]z It is discussed in a later section.
98os4}r Model Piles and Test Program
r^k:$wJbRK Model Pile
1v4( An open-ended pile is generally driven into sands in a partially
cFoDR plugged mode, and its bearing capacity is composed of plug load
B{SzC=4f} capacity, annulus load capacity, and shaft load capacity. In order
TK;*:K8oe to separate pile load capacity into its components, an instrumented
8uX1('+T* double-walled pile was used in the testing. A schematic
p_jDnb# diagram of the pile is shown in Fig. 2. The model pile was made
g(Jzu' of two very smooth stainless steel pipes with different diameters.
E
VBB:*q6 It had an outside diameter of 42.7 mm, inside diameter of 36.5
wNW9xmS mm, and length of 908 mm.
i(JBBE" The wall thickness of the test piles used in this study is larger
Y$ ;C@I than those of piles typically used in practice. Szechy ~1959!
vb}; _/#? showed that the degree of soil plugging and bearing capacity of
2hRaYX,g two piles with different wall thicknesses do not differ in a significant
|.Bb Pfe8f way ~with bearing capacity increasing only slightly with increasing
}06
wall thickness!; only driving resistance depends significantly
M ,8r{[2 upon the wall thickness. So the load capacity of the test
RvYH(!pQ piles reported in this paper are probably larger, but only slightly
_{o=I?+] so, than what would be observed in the field.
31y=Ar"" Eighteen strain gauges were attached to the outside surface of
*Ri?mEv
hF the inner pipe at nine different levels in order to measure the base
/}Y>_87 load capacity ~summation of plug and annulus load capacities!
W$0<a@ Fig. 1. Definition of incremental filling ratio and plug length ratio
!c\d(u Table 1. Soil Properties of Test Sand
0!rU,74I= Property Value
2@o_7w98 Coefficient of uniformity Cu 2.21
s!09Pxc Coefficient of gradation Cc 1.23
PY.c$)az> Maximum void ratio emax 0.986
7{:| ) Minimum void ratio emin 0.629
]S[zD|U% Minimum dry density gd,min 13.04 kN/m3
0}c*u) , Maximum dry density gd,max 15.89 kN/m3
n< [np;\ Specific gravity Gs 2.64
,ORZtj Peak friction angle fpeak 34.8–43.4°
f8)D| Critical-state friction angle fc 33.7°
0yXUVKq3 Peak interface friction angle d 17.0–18.4°
-@G|i$! Critical-state interface friction angle dc 16.7°
_n2PoE:5@P JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003 / 47
= Ow}MX from the load transfer curve along the inner pipe. Two strain
[zK|OMxoV gauges were also attached to the outside surface of the outer pipe
V#|#%
8 in order to measure shaft load capacity. A gap of 4 mm between
/g712\?M4 the outer pipe and the pile toe, which was sealed with silicone,
LGPy>,! prevented the base load from being transferred to the outer pipe.
m~#S76!w The outer pipe, therefore, experienced only the shaft load.
'Ol}nmJ'n Many researchers have relied on linear extrapolation to separate
l2=.;7IV the base load capacity into plug and annulus capacities ~Paik
X",fp and Lee 1993; Choi and O’Neill 1997; Lehane and Gavin 2001!.
nbw&+dcJ8 Linear extrapolation would apply strictly only if the inside unit
y yrCO"eh friction between the pile and soil plug were constant between the
t/_w} second lowest strain gauge and the pile base, as shown in Fig. 3.
/H@k;o In reality, the inside unit friction between the soil plug and the test
tsU.c"^n pile increases dramatically near the pile base. Use of linear extrapolation,
s'ntf therefore, leads to an overestimation of annular resistance.
SZ~Ti|^ This overestimation increases as the distance between the
@h([c lowest strain gauge and the pile base increases. In part to avoid
{Zjnf6d] this uncertainty, in this paper we use the base load capacity to
=lS~2C analyze the test results instead of the plug and annulus load capacities
rOB-2@- separately. The base load capacity of the test pile was
8^$}!9B~JZ obtained from the upper strain gauges located on the inner pipe,
Us M|OH5k for which the measured vertical loads reached a limit value ~Fig.
?y'KX]/ 3!.
ss% ahs Test Program
7<AHQ<#@ Seven model pile tests were performed in dry soil samples with
J+[&:]=P three different relative densities and five different stress states.
vd SV6p.d Each test is identified by a symbol with three letters ~H high, M
9]VUQl9gh medium, L low!, signifying the levels of the relative density, vertical
sZPPS&KoP3 and horizontal stresses of the sample, respectively. A summary
A"\kdxC of all model pile tests is presented in Table 2. Five model
85m[^WGyh pile tests were conducted in dense samples with DR590% and
Q4TI '/ five different stress states. Two model pile tests were conducted in
B=7bQli} loose and medium samples consolidated to a vertical stress of
$91c9z;f^ 98.1 kPa and horizontal stress of 39.2 kPa. The model piles were
,JN2q]QPP driven by a 39.2 N hammer falling from a height of 500 mm.
AR]y p{NS During pile driving, the soil plug length and the pile penetration
RhnSQe depth were measured at about 40 mm intervals, corresponding to
{IYfq)c 94% of the pile diameter, in order to calculate the IFR. The
d[w 'j/{ change in soil plug length during pile driving was measured using
S$+vRX7 a ruler introduced through an opening at the top plate of the pile
3)zanoYHi ~see Fig. 2!. In order to measure the soil plug length, driving
.Frc:Y{ operations were suspended for no more than a minute each time.
Va\dMv-b Static pile load tests were performed when the pile base was
?zQ\u{]= located at depths of 250, 420, 590, and 760 mm. The pile load
:f ybH)* tests were continued until the pile settlement reached about 19
0V"r$7(} mm ~44% of the pile diameter!, at which point all the test piles
9loWh5_1Z had reached a plunging limit state ~Fig. 4!. The ultimate load of
d47b&.v8e each test pile is defined as the load at a settlement of 4.27 mm,
A$WE:<^ corresponding to 10% of the pile diameter. The total load applied
m7zen530 to the pile head was measured by a load cell, and settlement of the
VThcG(
NF pile head was measured by two dial gauges. Details of the model
^L+*}4Dr pile, sample preparation, and test program have been described by
wRgmw
4 Paik and Lee ~1993!.
(8qMF{ Model Pile Test Results
KIC5U50J Pile Drivability
m(s(2wq"f Fig. 5~a! shows pile penetration depth versus hammer blow count
(\, <RC\ for all the test piles. As shown in the figure, the hammer blow
7$<.I#x count per unit length of penetration increases as pile penetration
Ig}G"GR depth increases, since the penetration resistances acting on the
|t+M/C0y/ base and shaft of the piles during driving generally increase with
_BO:~x Fig. 2. Schematic of model pile
) DXN|<A Fig. 3. Determination of plug and annulus loads
Z"#eN(v.N Table 2. Summary of Model Pile Test Program
R*a5bKr Test
0B fqEAl indicator
{*,~,iq Initial
6zh<PETa03 relative
G6(kwv4 density
W2/FGJD ~%!
gNF8&T Initial
^`~M f vertical
RO[Ko-m|/N stress
hTcy;zLLS ~kPa!
A<P3X/i Initial
%|E'cdvkX horizontal
OzY55 stress
!+T\}1f7d ~kPa!
#[0:5$-[ Initial
Ck;O59A"&- earth
gw~%jD-2 pressure
Xou1X$$z coefficient
&7z79#1NS HLL 90 39.2 39.2 1.0
IN=pki|. HML 90 68.6 39.2 0.6
pm$2*!1F( HHL 90 98.1 39.2 0.4
n@n608 HHM 90 98.1 68.6 0.7
W%LTcm HHH 90 98.1 98.1 1.0
2{;&c MHL 56 98.1 39.2 0.4
?#;
oqH< LHL 23 98.1 39.2 0.4
jJFWPD]u 48 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003
0q'd }D W penetration depth. The vertical stress applied to the soil sample
>dKK [E/[d had little effect on the cumulative blow count. However, the blow
j1_ E^ count necessary to drive the pile to a certain depth decreased
7pMl:\ rapidly with decreasing horizontal stress. It is also seen in Fig.
r@N 0%JZZ 5~a! that the blow count necessary for driving the pile to some
!wiW#PR required depth increases with increasing relative density.
(t&]u7Atr Soil Plugging
Y.`
{]rC The degree of soil plugging in an open-ended pile affects pile
2VmQ%y6e" behavior significantly. The IFR is a good indicator of the degree
5\93-e of soil plugging. During the model pile tests, the IFR was measured
mr:;Wwd at increments of 40 mm of penetration. The change of the
}$M 2XF soil plug length with pile penetration depth is plotted in Fig. 5~b!.
UjibQl3:m It is seen in the figure that the soil plug length developed during
&:}e`u@5| pile driving increases as the horizontal stress of the soil sample
Y g>W.wA increases for the same relative density, and as the relative density
nk.Y#+1) increases for the same stress. It can also be seen that every test
z ogtIn) pile, during static load testing, advances in fully plugged mode,
@X`~r8& irrespective of the initial soil condition and the degree of soil
AA][}lU:5 plugging during pile driving. The static load tests appear as short
[MSLVTR vertical lines in Fig. 5~b!, meaning that penetration depth increases
k.bzh. while soil plug length remains unchanged.
w-2&6o<n- Fig. 6 shows changes of IFR with soil state ~relative density,
pR_cI]{=SA vertical stress, and horizontal stress!. Fig. 6~a! shows IFR versus
)|;*[S4 DR for tests with sv 8 598.1 kPa and K050.4. Fig. 6~b! shows IFR
OLXkiesK{ versus sv 8 for tests with DR590% and sh8539.2 kPa. Fig. 6~c!
+pYrA qmO- shows IFR versus sh8 for DR590% and sv 8 598.1 kPa. It is observed
vZV+24YWb that the IFR increases markedly with increasing relative
WrK!]17or density and with increasing horizontal stress. These changes in
*r!f! eA: IFR reflect the decreasing amount of compaction of the soil plug
iO=xx|d during pile driving as the relative density and stress level in the
]D^ dQ%{ soil increase. However, the IFR is relatively insensitive to
2}j2Bhc changes in the vertical stress applied to the soil sample. This
F\1nc"K/( means that the IFR of an open-ended pile would be higher for an
zx^]3} overconsolidated sand than for a normally consolidated sand at
kTQ:k
}%B the same DR and sv 8 .
j`^':! Fig. 7 shows IFR versus plug length ratio ~PLR! for the chamber
:PtpIVAosg test results and for the test results of Szechy ~1959!; Klos and
MhC74G Tejchman ~1977!; Brucy et al. ~1991!; and Paik et al. ~2002!. The
Lm+!/e PLR is defined as the ratio of soil plug length to pile penetration
'G6TSl as ~see Fig. 1!
70_T;K6 PLR5
Rf@D]+v L
8D]:>[|E D
?7-#iC` (2)
~45u
a In Fig. 7~b!, the data from Paik et al. ~2002! were obtained from
$;un$ko6% a full-scale pile with diameter of 356 mm driven into submerged
j&E4|g ( dense sands. The remaining data were obtained from model pile
Q0~5h?V' tests using piles with various diameters driven into dry sand ranging
.lu:S;JSnS from loose to medium dense ~the diameter of each test pile is
\3K 6NA!L indicated in the figure!. Fig. 7~a! shows that IFR, measured at the
a?' 3 final penetration depth, increases linearly with increasing PLR.
|Y3!Lix Fig. 4. Load–settlement curves from model pile load tests
iHjo3_g)n Fig. 5. Driving test results: ~a! hammer blow count, and ~b! soil plug
#oMbE<//" length
O{8"f\* JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003 / 49
}yqRz6=YB The relationship between PLR and IFR for the calibration chamber
20m6-rkI<} tests can be expressed as follows:
6h>8^l IFR~%!5109PLR222 (3)
THHrGvb This equation slightly underestimates the IFR for PLR values
>7!aZO greater than 0.8 and slightly overestimates it for PLR values
UwtOlV:G{ lower than 0.7, as shown in Fig. 7~b!. In general, it is known that
@_YEK3l]l the IFR is a better indicator of the degree of soil plugging than the
#1Mk9sxo PLR ~Paikowsky et al. 1989; Paik and Lee 1993!. In the field,
OXDlwbwL however, it is easier to measure the PLR than the IFR. Eq. ~3! can
Gb61X6 be used to estimate the IFR from the PLR, when only the PLR is
jIE>t5 fy measured in the field.
BEvSX|M>x Base and Shaft Load Capacities
A{h
hnrr8 The ultimate unit base resistance qb,c measured in the calibration
(Br$(XJoK} chamber is plotted versus relative density ~for sv 8 598.1 kPa and
Orh5d7+S K050.4), versus vertical stress ~for DR590% and sh8
$}oQ=+c5 539.2 kPa) and versus horizontal stress ~for DR590% and
%9M; MK Fig. 6. Incremental filling ratio versus ~a! relative density for sv8
el!Bi>b9c! 598.1 kPa and K050.4; ~b! vertical stress for DR590% and sh8
M)Rp+uQ 539.2 kPa; and ~c! horizontal stress for DR590% and sv8
y:4Sw#M%( 598.1 kPa
+ WPi} Fig. 7. Plug length ratio versus incremental filling ratio ~a! for chamber
q`1t*<sk test results, and ~b! for other test results
q^sMJ 50 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003
x+B~ t4A sv 8 598.1 kPa) in Fig. 8. It is apparent that the ultimate unit base
7~\Dzcfk"P resistance increases significantly with increasing relative density
Tp`)cdcC[ and increasing horizontal stress, but is relatively insensitive to
37p0*%a": vertical stress. This is consistent with experimental results of
qIjC-#a=m Baldi et al. ~1981!; Houlsby and Hitchman ~1988!; and Vipulanandan
+^YV>; et al. ~1989!, which showed that cone resistance was a
UQ|0Aqwq function of lateral effective stress.
-Kg@Sj/U}R Fig. 9 shows the ultimate unit base resistance, normalized with
yD1*^~ loJ respect to the horizontal stress, versus IFR for different relative
R,Zuy(g densities, and the ultimate unit base resistance versus IFR for
(m;P,* dense sand. It can be seen in Figs. 9~a and b! that the ultimate unit
H[@}ri< base resistance of open-ended piles increases with decreasing IFR
gbpm:: and that the rate of change of ultimate unit base resistance with
n!Y.?mU6 IFR increases with DR . It is also seen that the ultimate unit base
HKOJkbVZ2^ resistance increases with relative density at constant IFR.
BT>*xZLpS Fig. 10 shows the ultimate unit shaft resistance f so,c measured
vzi=[A in the calibration chamber versus relative density, vertical stress,
qjR;c&
q R and horizontal stress. Similarly to what is observed for ultimate
EfDo%H^!j unit base resistance, the ultimate unit shaft resistance of an open-
5[l3]HOO Fig. 8. Unit base resistance versus ~a! relative density for sv8
/<:9NP'^ 598.1 kPa and K050.4; ~b! vertical stress for DR590% and sh8
(i *1M 539.2 kPa; and ~c! horizontal stress for DR590% and sv8
Byldt 598.1 kPa
2IjqTL Fig. 9. Normalized unit base resistance versus incremental filling
mf}?z21vD ratio ~a! for sv8598.1 kPa and K050.4, and ~b! for DR590%
83R"!w18 JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003 / 51
ls*^3^O ended pile increases with both relative density and horizontal
,6t0w|@-k stress, but is insensitive to the vertical stress. It is clear from Fig.
WDzov9ot 10~c! that the ultimate unit shaft resistance is linearly related to
I">z#@CT the horizontal stress. The ultimate base and shaft load capacities
Ch;EnN< of the test piles are listed in Table 3.
k9^P#l@p Correction of Chamber Test Results for Chamber
vpXS!o>/Sn Size Effects
1M3U)U Adjustment of Pile Diameter
fd+kr# Pile load capacities measured in a calibration chamber are different
_|A)ueY from those measured in the field due to chamber size effects.
Q;5\( 0w5 In order to use the calibration chamber test results for computation
1GEE ^Eu of pile load capacity in the field, corrections for chamber size
(^Nf;E effects were performed for every chamber test. In the estimation
#v&&GuF of chamber size effects, the ratio of the chamber to the equivalent
/o|@]SAe. diameter of the model pile used in the tests is required. The
7FMHz.ZRE equivalent diameter of an open-ended pile is the diameter that a
9MHb<~F pile with solid cross-section would have to have in order to displace
PFPfLxna the same soil volume during installation as the open-ended
H[>_LYZ8 pile. The equivalent diameter of open-ended piles varies with the
x[(2}Qd degree of soil plugging, because the soil displacement around the
.mok.f<G_m pile due to pile driving increases with decreasing IFR ~Randolph
MH !CzV& et al. 1979!. For example, if a pile is driven in fully coring mode,
5lU`o the equivalent pile diameter is calculated from an equivalent area
@F,HyCSN equal to the annular area. If a pile is fully plugged during driving,
^1Yx'ua' the gross cross-sectional area of the pile should be used. For piles
<M$hj6.tn driven in a partially plugged mode, the equivalent pile diameter
(j-(fS can be determined through interpolation with respect to the IFR.
KO5Q;H This is summarized, mathematically, as follows:
DJ<c If IFR>100%, dp5A~d0 2 2di
'm2,7] 2! (4a)
cA/2,i If IFR50%, dp5d0 (4b)
&rNXn?>b If 0%<IFR<100%,
U3za}3 dp5d02@d02A~d0 2 2di
^
1J;SO| 2!# IFR~%!
W
B!$qie\ 100
.qVdo+M%F (4c)
1%-?e``. in which dp5equivalent pile diameter; d05outer pile diameter;
BR0bf5T/ and di5inner pile diameter.
_O rE{ Considering the pile driving mechanism of an open-ended pile,
(+^1'?C8 the base load capacity of the pile depends on the IFR measured at
IsRsjhg8x the final penetration depth. The shaft load capacity should be
KX9ZwsC0 related to the average value of the IFR measured during driving,
X`aED\#\h which is equal to the PLR at the pile penetration depth. In this
w1KQ9H* study, therefore, the equivalent pile diameters for each test were
R/b=!< computed for the base and shaft load capacities using Eqs. ~4!.
-_314j=`/ The IFR and PLR at the pile penetration depth are used for correction
3[e@mcO of the base and the shaft load capacity, respectively.
R 7{r Y Field Pile Load Capacity
KK] >0QAY Salgado et al. ~1998! conducted a theoretical analysis of chamber
ntF(K/~Y size effect for cone penetration resistance in sand and quantified
9Q.j
< the size effect as a function of soil state (DR and sh8) and chamber
z?gJHN< to pile diameter ratio. According to their results, which also apply
&c\8`# 6 to displacement piles, the ratio qc,cc /qc,ff of chamber to field cone
L9kSeBt resistances for normally consolidated sands with DR523, 56,
xv%}xeEV Fig. 10. Unit shaft resistance versus ~a! relative density for sv8
';lO[B 598.1 kPa and K050.4; ~b! vertical stress for DR590% and sh8
5o72X k 539.2 kPa; and ~c! horizontal stress for DR590% and sv8
[]Fy[G.)H 598.1 kPa
8WyG49eic 52 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003
XG[%oL 90%, and diameter ratio in the 10–45 range can be approximated
3(}?f as
nut7b qc,cc
e1IuobT qc,ff
<y'ttxeS 5F1.08310223SDc
!PQRlgcG dp D10.31G for DR523% (5a)
$"UAJ - qc,cc
;{ezK8FJ}@ qc,ff
6@$[x* V 5F1.02310223SDc
zeua`jQ dp D10.24G for DR556% (5b)
m0#hG
x qc,cc
|/(5GX,X qc,ff
wXZ-%,R-D 5F7.79310233SDc
Th8Q~*v dp D10.27G for DR590% (5c)
rcbixOT In these equations, qc,cc5cone resistance measured in a calibration
1";~"p2( chamber; qc,ff5field cone resistance; and Dc /dp5ratio of
$_ NaxV chamber to equivalent pile diameter. The chamber size effect factors
+amvQ];?Q8 for the base and shaft load capacities estimated by Eq. ~5! are
zH_q6@4 listed in Table 3. The field pile load capacity can then be obtained
Qz<-xe`o8] by dividing the chamber pile load capacity by the corresponding
H}@|ucM"\ size effect factors.
f^]AyU;F: New Design Equations for Load Capacity of
@<2pYIi8 Open-Ended Piles
%MIu;u FR Base Load Capacity
9@j~1G%^ Fig. 11 shows the ultimate unit field base resistance qb, f , normalized
m<yA]
';s with respect to the horizontal effective stress sh8 at the pile
!Q#b4 f base, versus IFR for piles driven into sands with various relative
xvkof
'Q) densities. The figure shows that the normalized unit field base
EW!$D resistance increases linearly with decreasing IFR. The relationship
~U1iB between qb, f /sh8 and IFR can be expressed as
?1{`~)" qb, f
y>OZ<!` ash8
d!d
3r W;A 5326– 295 IFR~%!
pta%%8": 100
Cam}:'a/` (6)
Y}Dp{ with a coefficient of determination r250.82. In this equation, the
NqWHR~& a values, a function of the relative density, were obtained from
70NHU;&N the calibration chamber tests as equal to 1.0 for dense sands, 0.6
GBQb({ for medium sands, and 0.25 for loose sands. In the case of fully
-3V~YhG plugged piles ~IFR50!, which behave as closed-ended piles, unit
.
9
NS field base resistance is expressed as qb, f5326sh85130sv 8 for normally
Y1~SGg7(@ consolidated dense sands with K050.4. This is consistent
G"[pr%? with the unit base resistance of a closed-ended pile in dense sand
StL[\9~: proposed by the Canadian foundation engineering manual ~CGS
) T1oDk 1992!. In order to predict base load capacity of open-ended piles
J){\h-4 using Eq. ~6!, it is necessary to know either the IFR or the soil
Zz-;jkX) plug length at the final penetration depth @from which the IFR can
c #!6 be estimated through Eq. ~3!#. A technique for measuring IFR
xdM#>z`; during pile installation will be described in a later section. Note
nnNg^<[k3 that Eq. ~6! should be used only for piles driven into sands, not
-X[[
OR9+ for piles installed using vibratory hammers.
Ltw7b Table 3. Summary of Model Pile Test Results and Size Effect Factors
E,fp=. Test
C6M/$_l&a indicator
[J`G`s! Test
E?mp6R]}% depth
5Nb_K`Vp* ~mm!
aTm.10{^ Soil plug
%`1vIr(7 length
0_
\ g ~mm!
c.Y8CD.tqL IFR
mv.I.EL ~%! PLR
1^#Q/J, Base load
C<t>m_t9 capacity
wKlCx ~kN!
KL mB Shaft load
mv?H]i`N capacity
1$VI\} ~kN!
:"^<
aLj Size Effect Factor
(VAL.v* Base
PJ@ ,01 load
GKhwn&qCKb Shaft
1!wEXH( load
{l&2Kd* HLL 256 250 78.4 0.98 2.60 0.63 0.50 0.54
?1:/
6 420 366 71.4 0.87 2.91 0.90 0.49 0.51
TY\"@(Q|G 592 478 67.0 0.81 3.59 1.57 0.48 0.50
eKz~viM' 760 571 54.4 0.75 3.91 2.13 0.46 0.49
KdJx#Lc HML 250 251 88.0 1.00 2.50 0.50 0.52 0.54
>Ro n+
oe 420 373 76.3 0.89 2.85 0.81 0.50 0.52
(I
ds<n" 589 483 69.0 0.82 3.67 1.39 0.48 0.50
&]F|U3 760 583 57.4 0.77 4.30 2.23 0.47 0.49
TDE1z>h+" HHL 250 251 84.2 1.00 2.42 0.53 0.51 0.54
7B\(r~f`t 420 369 73.0 0.88 2.81 0.90 0.49 0.51
w00\1'-Kz 590 477 69.5 0.81 3.54 1.65 0.48 0.50
%OW9cqL>l 758 575 60.0 0.76 4.29 2.05 0.47 0.49
fsc~$^.~\ HHM 252 255 87.9 1.01 3.09 0.70 0.52 0.55
.0E4c8R\X 420 381 78.6 0.90 3.57 1.45 0.50 0.52
/_OZ1jX 591 501 73.9 0.85 4.66 2.49 0.49 0.51
rY?F6'} 761 614 72.1 0.81 4.91 3.60 0.49 0.50
F]A~~P HHH 251 266 92.6 1.06 4.53 1.36 0.53 0.56
{dx /p-Tv 420 398 82.9 0.95 4.66 2.46 0.51 0.53
~!-8l&C 590 521 79.8 0.88 5.40 3.93 0.50 0.52
^s~n[ 760 644 77.8 0.85 5.78 5.70 0.50 0.51
&9_\E{o%] MHL 247 236 75.9 0.96 1.82 0.28 0.53 0.58
;3}EBcw) 419 347 67.4 0.83 2.17 0.49 0.51 0.55
Y0yO`W4 589 445 60.5 0.76 2.41 0.65 0.50 0.53
>^f)|0dn)E 757 532 53.9 0.70 2.82 1.00 0.49 0.52
?U/Wio$@ LHL 247 224 71.1 0.91 1.01 0.18 0.61 0.66
'#i]SU&* 419 319 56.5 0.76 1.23 0.36 0.58 0.62
1R%`i'$/ 581 401 52.4 0.69 1.46 0.59 0.57 0.60
$:E}Nj]{& 756 472 42.6 0.62 1.56 0.66 0.56 0.59
fk7Cf"[w JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003 / 53
ho]!G498 Shaft Load Capacity
EY&C[= The average ultimate field unit shaft resistance f so, f for the model
Qy^z *s piles, normalized with respect to K0sv 8 tan dc , is plotted versus
o+_/)c PLR in Fig. 12 for various relative densities. It can be seen in the
Wj j2J8B figure that the normalized ultimate field unit shaft resistance increases
hRa(<Z K with decreasing PLR. The field unit shaft resistance of
#O9*$eMw piles driven into dense sand can be expressed as follows:
?)[zLnxc& f so, f
T
E&Q6 ~K0sv 8 tan dc!b
(d'j'U:C 57.224.8PLR (7)
NC.P2^% in which f so, f5average ultimate unit shaft resistance in the field;
NVc!g K05lateral earth pressure coefficient before pile driving;
"-QRkif sv 8 5average vertical effective stress over the whole penetration
k g,ys4 depth; dc5critical-state interface friction angle between the pile
q= yZx) and the soil; and b5function of the relative density. The b values
&:;;u\ were obtained from the calibration chamber tests as equal to 1.0
{pe7]P? for dense sands, 0.4 for medium sands, and 0.22 for loose sands.
n;kciTD%wK In the case of closed-ended piles in normally consolidated dense
.5!sOOs$P sands with K050.4, the normalized unit shaft resistance equals
rbK#a)7 7.2. This equation may be interpreted as implying that the lateral
nK h%E-c stress on the closed-ended pile driven in dense sands is 7.2 times
'y6!%k* higher than that before pile driving. This is consistent with the
v*H &