Determination of Bearing Capacity of Open-Ended Piles
a&wl- in Sand
~qco -b Kyuho Paik1 and Rodrigo Salgado, M.ASCE2
R279=sO,J Abstract: The bearing capacity of open-ended piles is affected by the degree of soil plugging, which is quantified by the incremental
o;_v' 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
^5j9WV capacity. In order to investigate this effect, model pile load tests were conducted on instrumented open-ended piles using a calibration
A$[@AY$MI chamber. The results of these tests show that the IFR increases with increasing relative density and increasing horizontal stress. It can also
k +&LOb7 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
iS=}| 8" resistances increase with decreasing IFR. Based on the results of the model pile tests, new empirical relations for plug load capacity,
WPpl9)Qc annulus load capacity, and shaft load capacity of open-ended piles are proposed. The proposed relations are applied to a full-scale pile load
^'6!)y# test performed by the authors. In this load test, the pile was fully instrumented, and the IFR was continuously measured during pile
(A/V(.! driving. A comparison between predicted and measured load capacities shows that the recommended relations produce satisfactory
^hRos predictions.
MU%C_d%. DOI: 10.1061/~ASCE!1090-0241~2003!129:1~46!
X0Xs"--} CE Database keywords: Bearing capacity; Pile load tests; Sand.
C!%BW%"R Introduction
g' H!%< When an open-ended pile is driven into the ground, a soil plug
0bS\VUB( may develop within the pile during driving, which may prevent or
W32bBzhL partially restrict additional soil from entering the pile. It is known
.K XpB7: that the driving resistance and the bearing capacity of open-ended
f9X*bEl9;` piles are governed to a large extent by this plugging effect.
`=vL?w^QS Many design criteria for open-ended piles, based on field tests,
pRc@0^G chamber tests or analytical methods, have been suggested @e.g.,
YRAWylm Klos and Tejchman 1977; Nishida et al. 1985; American Petroleum
aQ46euth Institute ~API! 1991; Randolph et al. 1991; Jardine et al.
AEe*A+ 1998#. For example, in the case of API RP2A ~1991!, which is
Mw*R~OX generally used for offshore foundation design, the bearing capacity
x.xfMM2n of an open-ended pile can only be estimated for either the fully
&v'e;W coring mode or the fully plugged mode of penetration. In practice,
ja#E}`wC4 most open-ended piles are driven into sands in a partially plugged
=Y?M#3P.I mode. Stefanoff and Boshinov ~1977! suggested the use of onedimensional
^ejU=0+cN plug analysis, in which the soil plug is treated as a
ZGH2 series of horizontal thin discs and the force equilibrium condition
_U|s!60' is applied to each disc, to calculate plug capacity of an openended
?8)_, pile.
}{ J<Wzw There have been modifications of one-dimensional plug analysis
CES^
c-. k to improve predictive accuracy, such as the introduction of the
+F]X concept of the wedged soil plug ~Murff et al. 1990; O’Neill and
q 6%jCt2' Raines 1991; Randolph et al. 1991!. Many test results show that
^8ZVB.Fv the soil plug can be divided into a wedged plug zone and an
zdlysr# unwedged plug zone. While the wedged plug zone transfers load
&C`t(e to the soil plug, the unwedged plug zone transfers no load but
B|/=E470G provides a surcharge pressure on top of the wedged plug zone.
=3_I;Lw However, it is not easy to apply the one-dimensional analysis to
&CV%+ practical cases, because of the sensitivity of the method to the
>Ke4lO" lateral earth pressure coefficient, which is not easily estimated
>RG
}u ~Brucy et al. 1991; Leong and Randolph 1991!. De Nicola and
V{HP8f91 Randolph ~1997! addressed this by proposing a profile of the
;*{y!pgb lateral earth pressure coefficient K along the soil plug length.
Ugp[Ugr An alternative design method can be based on the incremental
w[S2
]< filling ratio ~IFR!. The degree of soil plugging is adequately quantified
Q"h/o"-h using the IFR ~Paikowsky et al. 1989; Paik and Lee 1993!
"W?<BpV~@! defined as
1(CpTaa IFR5
jSsbLa@ DL
BA4qQCS;5 DD
K.Nun)< 3100~%! (1)
sk5h_[tK where DL5increment of soil plug length ~L! corresponding to a
.J6Oiv.E small increment DD of pile penetration depth D ~see Fig. 1!. The
%AwR 4"M fully plugged and fully coring modes correspond to IFR50 and
a^hDxeG 100%, respectively. A value of IFR between 0 and 100% means
)$p<BL U that the pile is partially plugged. A series of model pile tests,
s5_[[:c=^ using a calibration chamber, were conducted on model openended
<7NY.zvwk] piles instrumented with strain gauges in order to investigate
u0(H! the effect of IFR on the two components of bearing capacity: base
t:B~P,r load capacity and shaft load capacity. Based on the calibration
a/A$
MXZ_ chamber test results, empirical relationships between the IFR and
'H+H4( the components of pile load capacity are proposed. In order to
b_ +dNoB verify the accuracy of predictions made using the two empirical
;7Cb!v1 relationships, a full-scale static pile load test was conducted on a
4E/Q+^? fully instrumented open-ended pile driven into dense sand. The
!ba /]A/ predicted pile load capacities are compared with the capacities
|75>8; measured in the pile load test.
e <2?O 1Associate Professor, Dept. of Civil Engineering, Kwandong Univ.,
FR"yGx#$ Kangwon-do 215-800, South Korea ~corresponding author!. E-mail:
D/[(}o( pkh@kwandong.ac.kr owM3Gz%?UA 2Associate Professor, School of Civil Engineering, Purdue Univ., West
:y^0]In Lafayette, IN 47907-1284. E-mail:
rodrigo@ecn.purdue.edu scZdDbL6+ Note. Discussion open until June 1, 2003. Separate discussions must
iOXxxP%# be submitted for individual papers. To extend the closing date by one
1AiqB Rs month, a written request must be filed with the ASCE Managing Editor.
29p`G1n The manuscript for this paper was submitted for review and possible
=|_:H$94 publication on July 23, 2001; approved on May 23, 2002. This paper is
{>$i)B part of the Journal of Geotechnical and Geoenvironmental Engineering,
BV_rk^}Ur Vol. 129, No. 1, January 1, 2003. ©ASCE, ISSN 1090-0241/2003/1-
1W*%}!&Gm 46–57/$18.00.
" |ZC2Zu< 46 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003
fn(<
<FA) Soil Sample Preparation
/D2
cY> Soil Properties
AWsy9 Han river sand, a subangular quartz sand, with D1050.17mm and
,kS3Ioj D5050.34 mm, was used for all the calibration chamber model
Qa-]IKOs pile tests. The test sand is classified as poorly graded ~SP! in the
{6d)|';% Unified Soil Classification System, so the maximum dry density
Jm0o[4 of the sand is near the low end of the typical range for sands. The
l-4+{6lz maximum and minimum dry unit weights of the sand were 15.89
n3Uw6gLD and 13.04 kN/m3, respectively.
i8 t% v A series of laboratory tests were conducted to characterize the
2IDN?Mw sand. The results from these tests are summarized in Table 1. The
Vm\ly;v'R internal friction angle of the sand and the interface friction angle
[HNWM/ff7+ between the sand and steel were measured from direct shear tests
r: Ij\YQ under normal stresses of 40–240 kPa. The peak friction angles of
t6m&+N the sand with relative densities of 23, 56, and 90% were 34.8,
?5@!r>i=< 38.2, and 43.4°, respectively, and the critical-state friction angle
A9qbE was 33.7°. The peak interface friction angles between the pile and
=LLix .
> the sand were 17.0, 17.5, and 18.4° for DR523, 56, and 90%,
3,;;C( respectively, and the critical-state interface friction angle was
$hv o^$ 16.7°. This angle is lower than commonly reported values because
b7;`A~{9v the test pile was made of stainless steel pipe with a very
KA^r,Iw smooth surface.
?VUW.- Calibration Chamber and Sample Preparation
E&js`24 & All model pile tests were conducted in soil samples prepared
W%$sA}O within a calibration chamber with a diameter of 775 and a height
l@:|OGD;8 of 1250 mm. In order to simulate various field stress conditions,
J4Yu|E<& two rubber membranes, which can be controlled independently,
NHI(}Ea|] were installed on the bottom and inside the lateral walls of the
%2)B.qTp& calibration chamber. The consolidation pressure applied to the
r5#8Vzr two rubber membranes was maintained constant by a regulator
P[Q3z$I} panel throughout each pile test.
NW$_w The soil samples were prepared by the raining method with a
z''ITX)oG constant fall height. The falling soil particles passed through a
rt +a/:4+ sand diffuser composed of No. 8 and No. 10 sieves in order to
~%.<rc0 control flow uniformity and fall velocity. The soil samples had
*SP@`)\D DR523, 56, and 90%. After sample preparation, the samples
.r=F'i}-j* were consolidated to the desired stress state during approximately
_c:}i\8R 30 h by compressed air transferred to the rubber membranes.
OH+kN/Fd Measurements made in calibration chambers are subject to
A!xx#+M chamber size effects. Many researchers have attempted to estimate
Wycood* the chamber size needed for boundary effects on pile bearing
=H8
LBM capacity or cone resistance to become negligible. Parkin and
J%9)&aW Lunne ~1982! suggested 50 times the cone diameter as the minimum
I;u1mywd chamber diameter for chamber size effect on cone penetration
Xu[(hT6 resistance to become acceptably small. Salgado et al. ~1998!,
VDnN2)Km* based on cavity expansion analyses, found that 100 times the cone
Qg^Ga0Lf6 diameter was the minimum chamber diameter to reduce chamber
eW"L") size effects on cone resistance to negligible levels. Diameters of
yAyq-G"sO the chamber and test pile used in this study are 775 and 42.7 mm,
?^f=7e8] respectively. The lateral and bottom boundaries are located at a
^*-6PV#Z distance equal to 18.2 pile radii from the pile axis and 23.0 pile
e"I+5r", radii below the maximum depth reached by the pile base, respectively.
6 +2M$3_U Considering the results of the research on chamber size
u[Ij4h. effects mentioned above, the size of the chamber used in this
>5%;NI5
G study is not sufficiently large for chamber size effects on pile
0UbY0sYo bearing capacity to be neglected. The flexible boundary causes
~d.Z.AD lower radial stresses than those that would exist in the field. Accordingly,
C*C;n4 AT the chamber tests done as part of this study produce
q
eW{Cl~ lower pile load capacities than those that would be observed in
3 *g>kRMJ the field. A correction for chamber size effects is then necessary.
j
o +- It is discussed in a later section.
7k<6oM1 Model Piles and Test Program
r9\7I7z Model Pile
+xL*`fn An open-ended pile is generally driven into sands in a partially
v-utDQT3 plugged mode, and its bearing capacity is composed of plug load
V]{^}AKc capacity, annulus load capacity, and shaft load capacity. In order
PKxI09B to separate pile load capacity into its components, an instrumented
jeu|9{iTVu double-walled pile was used in the testing. A schematic
a7~%( L@r diagram of the pile is shown in Fig. 2. The model pile was made
B)v|A of two very smooth stainless steel pipes with different diameters.
AJJa<c+j It had an outside diameter of 42.7 mm, inside diameter of 36.5
Ow3t2G mm, and length of 908 mm.
G*y!
Q The wall thickness of the test piles used in this study is larger
1x'H# than those of piles typically used in practice. Szechy ~1959!
+m>)q4e showed that the degree of soil plugging and bearing capacity of
Yvn*evO4 two piles with different wall thicknesses do not differ in a significant
4S7#B way ~with bearing capacity increasing only slightly with increasing
zKllwIfi wall thickness!; only driving resistance depends significantly
m|by^40A( upon the wall thickness. So the load capacity of the test
.{8?eze[m piles reported in this paper are probably larger, but only slightly
C"
2K U* so, than what would be observed in the field.
s`$YY_ Eighteen strain gauges were attached to the outside surface of
0e,U&B<W the inner pipe at nine different levels in order to measure the base
b;2[E/JKB load capacity ~summation of plug and annulus load capacities!
x o{y9VS Fig. 1. Definition of incremental filling ratio and plug length ratio
RF|r@/S Table 1. Soil Properties of Test Sand
Hgk@I; Property Value
;i>(r;ZM Coefficient of uniformity Cu 2.21
&e%eIz Coefficient of gradation Cc 1.23
]fdxpqz Maximum void ratio emax 0.986
=3H*% Minimum void ratio emin 0.629
86f8b{_e" Minimum dry density gd,min 13.04 kN/m3
hf1h*x^J Maximum dry density gd,max 15.89 kN/m3
2E$K='H:, Specific gravity Gs 2.64
_7bQR7s Peak friction angle fpeak 34.8–43.4°
C9VtRq Critical-state friction angle fc 33.7°
jiGXFM2 Peak interface friction angle d 17.0–18.4°
XlaGR2-% Critical-state interface friction angle dc 16.7°
=c34MY(#X JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003 / 47
IA3m.Vxj ^ from the load transfer curve along the inner pipe. Two strain
jFH wu* gauges were also attached to the outside surface of the outer pipe
@p2XaqZ in order to measure shaft load capacity. A gap of 4 mm between
!;U;5 e=0 the outer pipe and the pile toe, which was sealed with silicone,
OBEHUJ5 prevented the base load from being transferred to the outer pipe.
B'QcD The outer pipe, therefore, experienced only the shaft load.
\<kQ::o1y Many researchers have relied on linear extrapolation to separate
'S'Z-7h>0 the base load capacity into plug and annulus capacities ~Paik
hx$bY and Lee 1993; Choi and O’Neill 1997; Lehane and Gavin 2001!.
9lR- Linear extrapolation would apply strictly only if the inside unit
jG^f_w friction between the pile and soil plug were constant between the
Q*W$!ZUT second lowest strain gauge and the pile base, as shown in Fig. 3.
ZQI;b0C In reality, the inside unit friction between the soil plug and the test
r-'CB pile increases dramatically near the pile base. Use of linear extrapolation,
Lz:Q6 therefore, leads to an overestimation of annular resistance.
r=cm(AHF This overestimation increases as the distance between the
557%^)v lowest strain gauge and the pile base increases. In part to avoid
z>A;|iL this uncertainty, in this paper we use the base load capacity to
,b,t^xX>) analyze the test results instead of the plug and annulus load capacities
pdq5EUdS separately. The base load capacity of the test pile was
/`+ubFXc obtained from the upper strain gauges located on the inner pipe,
fI"OzIJV for which the measured vertical loads reached a limit value ~Fig.
xO
6$:o- 3!.
rGgP9
( Test Program
YGsg0I't Seven model pile tests were performed in dry soil samples with
eEZZ0NNe; three different relative densities and five different stress states.
_`d=0l*8 Each test is identified by a symbol with three letters ~H high, M
%j.
*YvveW medium, L low!, signifying the levels of the relative density, vertical
_BPp=(| and horizontal stresses of the sample, respectively. A summary
rL23^}+^` of all model pile tests is presented in Table 2. Five model
3hPp1wZd pile tests were conducted in dense samples with DR590% and
eQ80Kf~ five different stress states. Two model pile tests were conducted in
/?B%,$~ loose and medium samples consolidated to a vertical stress of
.gs:.X)TG9 98.1 kPa and horizontal stress of 39.2 kPa. The model piles were
=
6.i.(L_S driven by a 39.2 N hammer falling from a height of 500 mm.
!D~\uW1b During pile driving, the soil plug length and the pile penetration
>7(7 depth were measured at about 40 mm intervals, corresponding to
' )~G2Ys 94% of the pile diameter, in order to calculate the IFR. The
N/8_0]Gf change in soil plug length during pile driving was measured using
aBT8mK -. a ruler introduced through an opening at the top plate of the pile
Zd~Q@+sH ~see Fig. 2!. In order to measure the soil plug length, driving
|TRl>1rv operations were suspended for no more than a minute each time.
wak`Jte=}m Static pile load tests were performed when the pile base was
Sp./*h\} located at depths of 250, 420, 590, and 760 mm. The pile load
KF}_|~~T tests were continued until the pile settlement reached about 19
aSH =|Jnc mm ~44% of the pile diameter!, at which point all the test piles
evro]&N{ had reached a plunging limit state ~Fig. 4!. The ultimate load of
h{.x:pPXy each test pile is defined as the load at a settlement of 4.27 mm,
@q <d^]po corresponding to 10% of the pile diameter. The total load applied
~4=XYYcka to the pile head was measured by a load cell, and settlement of the
5O]eD84B pile head was measured by two dial gauges. Details of the model
XEb+Z7L 1 pile, sample preparation, and test program have been described by
i/aj;t Paik and Lee ~1993!.
%R@&8 Model Pile Test Results
4mwLlYZ Pile Drivability
6'\VPjt Fig. 5~a! shows pile penetration depth versus hammer blow count
r`A|2(h5B for all the test piles. As shown in the figure, the hammer blow
2^ kK2D$o count per unit length of penetration increases as pile penetration
O_^
uLp depth increases, since the penetration resistances acting on the
Dfw%Bu base and shaft of the piles during driving generally increase with
uE^5o\To Fig. 2. Schematic of model pile
o0#zk Fig. 3. Determination of plug and annulus loads
vg-'MG Table 2. Summary of Model Pile Test Program
2O
"
~k Test
9ve)+Lk indicator
=fcRH:B: Initial
bw*D!mm, relative
Bt(U,nFB density
R7ExMJw ~%!
yPT\9"/ Initial
Mk|*=#e; vertical
Mq4>Mu stress
](SqLTB+? ~kPa!
&n9srs Initial
4]m?8j)
6b horizontal
VCc57Bo stress
g7O,
< ~kPa!
d;E
(^l Initial
F?hGt]o earth
Dt
Ry%fA_ pressure
'OvyQ/T
coefficient
#r;uM+ HLL 90 39.2 39.2 1.0
T74."Lo# HML 90 68.6 39.2 0.6
*vP:+] HHL 90 98.1 39.2 0.4
mmBZ}V+&= HHM 90 98.1 68.6 0.7
%lqrq<Xn HHH 90 98.1 98.1 1.0
7^n{BsN MHL 56 98.1 39.2 0.4
"Tc[1{eI LHL 23 98.1 39.2 0.4
"<1-9CMl 48 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003
MVZ9x% penetration depth. The vertical stress applied to the soil sample
28=L9q
had little effect on the cumulative blow count. However, the blow
c*Q6k<SKR count necessary to drive the pile to a certain depth decreased
Fu"@)xw/-q rapidly with decreasing horizontal stress. It is also seen in Fig.
_{48s8V 5~a! that the blow count necessary for driving the pile to some
D}L4uz? required depth increases with increasing relative density.
f<l.%B Soil Plugging
pb}4{]sI The degree of soil plugging in an open-ended pile affects pile
cDqj&:$e behavior significantly. The IFR is a good indicator of the degree
q-4#)EnW of soil plugging. During the model pile tests, the IFR was measured
y>|AX/n at increments of 40 mm of penetration. The change of the
)ioIn`g^- soil plug length with pile penetration depth is plotted in Fig. 5~b!.
~PiCA It is seen in the figure that the soil plug length developed during
8I%N^G pile driving increases as the horizontal stress of the soil sample
"MU)8$d increases for the same relative density, and as the relative density
g%2twq_ increases for the same stress. It can also be seen that every test
Zm#qW2a]P pile, during static load testing, advances in fully plugged mode,
*&vi3#ur irrespective of the initial soil condition and the degree of soil
{6brVN.V plugging during pile driving. The static load tests appear as short
q($fl7}Y vertical lines in Fig. 5~b!, meaning that penetration depth increases
r:9H>4m while soil plug length remains unchanged.
Uiu9o]n Fig. 6 shows changes of IFR with soil state ~relative density,
hSfLNvK
vertical stress, and horizontal stress!. Fig. 6~a! shows IFR versus
R4Si{J*O DR for tests with sv 8 598.1 kPa and K050.4. Fig. 6~b! shows IFR
4Vrx9 sA1 versus sv 8 for tests with DR590% and sh8539.2 kPa. Fig. 6~c!
]WZi + shows IFR versus sh8 for DR590% and sv 8 598.1 kPa. It is observed
H\ONv=}7I that the IFR increases markedly with increasing relative
uc-Go
6W density and with increasing horizontal stress. These changes in
$,#,yl ol IFR reflect the decreasing amount of compaction of the soil plug
?*A"#0 during pile driving as the relative density and stress level in the
"RM vWuNt soil increase. However, the IFR is relatively insensitive to
kU$M 8J. changes in the vertical stress applied to the soil sample. This
70{fl
4J5 means that the IFR of an open-ended pile would be higher for an
qr[+^*Ha overconsolidated sand than for a normally consolidated sand at
6v9A7g;4. the same DR and sv 8 .
U&<w{cuA Fig. 7 shows IFR versus plug length ratio ~PLR! for the chamber
@iD5X.c test results and for the test results of Szechy ~1959!; Klos and
XqK\'8]\Mw Tejchman ~1977!; Brucy et al. ~1991!; and Paik et al. ~2002!. The
N~@VZbS(6 PLR is defined as the ratio of soil plug length to pile penetration
P
g1EE"N@ as ~see Fig. 1!
ZeYkZzN PLR5
\J?5Kl[*c L
5N4[hQrVJ D
5,1q% (2)
x8wal[6 In Fig. 7~b!, the data from Paik et al. ~2002! were obtained from
RXU#.=xvy a full-scale pile with diameter of 356 mm driven into submerged
8/* 6&#- dense sands. The remaining data were obtained from model pile
PM!7ci tests using piles with various diameters driven into dry sand ranging
/"%QIy'{ from loose to medium dense ~the diameter of each test pile is
w=S7zzL) indicated in the figure!. Fig. 7~a! shows that IFR, measured at the
C/je5 final penetration depth, increases linearly with increasing PLR.
Z,bv D'u Fig. 4. Load–settlement curves from model pile load tests
1WMwTBHy+ Fig. 5. Driving test results: ~a! hammer blow count, and ~b! soil plug
FI|@=l;_ length
Q8r 7 JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003 / 49
a,U@ !}K The relationship between PLR and IFR for the calibration chamber
sCF7K=a tests can be expressed as follows:
U<lCK!85[ IFR~%!5109PLR222 (3)
Cq, hzi- This equation slightly underestimates the IFR for PLR values
]kd )j greater than 0.8 and slightly overestimates it for PLR values
%aeQL;# V lower than 0.7, as shown in Fig. 7~b!. In general, it is known that
hf1f the IFR is a better indicator of the degree of soil plugging than the
4? a!6 PLR ~Paikowsky et al. 1989; Paik and Lee 1993!. In the field,
$@blP<I however, it is easier to measure the PLR than the IFR. Eq. ~3! can
M1f^Lx be used to estimate the IFR from the PLR, when only the PLR is
#Ua+P(1q measured in the field.
044*@a5f Base and Shaft Load Capacities
#815h,nP+ The ultimate unit base resistance qb,c measured in the calibration
`+(|$?C u chamber is plotted versus relative density ~for sv 8 598.1 kPa and
*R6n+d K050.4), versus vertical stress ~for DR590% and sh8
uoe5@j2 539.2 kPa) and versus horizontal stress ~for DR590% and
,~_)Cf#CB Fig. 6. Incremental filling ratio versus ~a! relative density for sv8
}Rc8\, 598.1 kPa and K050.4; ~b! vertical stress for DR590% and sh8
$*{$90Q 539.2 kPa; and ~c! horizontal stress for DR590% and sv8
uUczD 8y 598.1 kPa
o(/(`/ Fig. 7. Plug length ratio versus incremental filling ratio ~a! for chamber
zaVDe9B,7 test results, and ~b! for other test results
3T3p[q4 50 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003
J0U9zI4 sv 8 598.1 kPa) in Fig. 8. It is apparent that the ultimate unit base
5M{DJ/q resistance increases significantly with increasing relative density
_r}oYs%1 and increasing horizontal stress, but is relatively insensitive to
.bYDj&]P{ vertical stress. This is consistent with experimental results of
fFfH9 cl! Baldi et al. ~1981!; Houlsby and Hitchman ~1988!; and Vipulanandan
.FnO et al. ~1989!, which showed that cone resistance was a
dsP1Zq function of lateral effective stress.
2b]'KiX Fig. 9 shows the ultimate unit base resistance, normalized with
,Jf)A/_ respect to the horizontal stress, versus IFR for different relative
_F *("
o densities, and the ultimate unit base resistance versus IFR for
"b!QE2bRO dense sand. It can be seen in Figs. 9~a and b! that the ultimate unit
O\T base resistance of open-ended piles increases with decreasing IFR
cf|<~7 and that the rate of change of ultimate unit base resistance with
jG0{>P#+ IFR increases with DR . It is also seen that the ultimate unit base
K'%,dn resistance increases with relative density at constant IFR.
N2VF_[l Fig. 10 shows the ultimate unit shaft resistance f so,c measured
j:0VtJo~ in the calibration chamber versus relative density, vertical stress,
7"r7F#D=G and horizontal stress. Similarly to what is observed for ultimate
?'K}bmdt}. unit base resistance, the ultimate unit shaft resistance of an open-
2oAPJUPOJ Fig. 8. Unit base resistance versus ~a! relative density for sv8
9BGPq) # 598.1 kPa and K050.4; ~b! vertical stress for DR590% and sh8
>qjr7 vx 539.2 kPa; and ~c! horizontal stress for DR590% and sv8
?rQMOJR 598.1 kPa
TD-d5P^Kek Fig. 9. Normalized unit base resistance versus incremental filling
*0y+=,"QU ratio ~a! for sv8598.1 kPa and K050.4, and ~b! for DR590%
!UD62yw~ JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003 / 51
qoMYiF}/e ended pile increases with both relative density and horizontal
"RH2% stress, but is insensitive to the vertical stress. It is clear from Fig.
B:tST( 10~c! that the ultimate unit shaft resistance is linearly related to
n]x4twZ the horizontal stress. The ultimate base and shaft load capacities
2C %{A of the test piles are listed in Table 3.
9o P8| <+ Correction of Chamber Test Results for Chamber
`"M=Z Vk Size Effects
}Xs=x6Mj Adjustment of Pile Diameter
~\K+)(\SNp Pile load capacities measured in a calibration chamber are different
$.(>Sj1 from those measured in the field due to chamber size effects.
d'Z|+lq: In order to use the calibration chamber test results for computation
'=x of pile load capacity in the field, corrections for chamber size
/MSz{ %v effects were performed for every chamber test. In the estimation
#
3uXgZi of chamber size effects, the ratio of the chamber to the equivalent
@4h .? diameter of the model pile used in the tests is required. The
W
k'()N equivalent diameter of an open-ended pile is the diameter that a
'oHtg
@ pile with solid cross-section would have to have in order to displace
r,i^-jv; the same soil volume during installation as the open-ended
c\.4I4uy pile. The equivalent diameter of open-ended piles varies with the
[Y*p
I&f degree of soil plugging, because the soil displacement around the
El0|.dW pile due to pile driving increases with decreasing IFR ~Randolph
IQdiVj et al. 1979!. For example, if a pile is driven in fully coring mode,
&oYX093di the equivalent pile diameter is calculated from an equivalent area
m$A|Sx&sG$ equal to the annular area. If a pile is fully plugged during driving,
^MUtmzh the gross cross-sectional area of the pile should be used. For piles
hkv&Od, driven in a partially plugged mode, the equivalent pile diameter
suaTXKjyk+ can be determined through interpolation with respect to the IFR.
G F,/<R # This is summarized, mathematically, as follows:
kwK<?\D If IFR>100%, dp5A~d0 2 2di
(ui"vLk8PP 2! (4a)
bWwc2##7jo If IFR50%, dp5d0 (4b)
s9qr;}U.` If 0%<IFR<100%,
d/- f] dp5d02@d02A~d0 2 2di
|>GtClL 2!# IFR~%!
+WK!}xZR 100
>! wX%QHH (4c)
Gs.id^Sf in which dp5equivalent pile diameter; d05outer pile diameter;
<"AP&J'H and di5inner pile diameter.
^{-J Y Considering the pile driving mechanism of an open-ended pile,
e0+N1kY the base load capacity of the pile depends on the IFR measured at
\8=>l?P the final penetration depth. The shaft load capacity should be
+Ld4e] related to the average value of the IFR measured during driving,
+l2{EiQw which is equal to the PLR at the pile penetration depth. In this
hPx=3L$ study, therefore, the equivalent pile diameters for each test were
Wze\z
computed for the base and shaft load capacities using Eqs. ~4!.
:^1 Xfc" The IFR and PLR at the pile penetration depth are used for correction
{G/4#r
2> of the base and the shaft load capacity, respectively.
6N :fq Field Pile Load Capacity
%-i2MK'A Salgado et al. ~1998! conducted a theoretical analysis of chamber
lycY1 lK size effect for cone penetration resistance in sand and quantified
$=TFTSO the size effect as a function of soil state (DR and sh8) and chamber
:u` to pile diameter ratio. According to their results, which also apply
9EK5#_L[= to displacement piles, the ratio qc,cc /qc,ff of chamber to field cone
-j`tBv) resistances for normally consolidated sands with DR523, 56,
Qy*`s Fig. 10. Unit shaft resistance versus ~a! relative density for sv8
65\'(99yU 598.1 kPa and K050.4; ~b! vertical stress for DR590% and sh8
<E|i3\[p 539.2 kPa; and ~c! horizontal stress for DR590% and sv8
w=s:eM@ 598.1 kPa
|t6 :4'] 52 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003
Gt$PBlq0 90%, and diameter ratio in the 10–45 range can be approximated
VXO.S)v2J as
b *Ca*! qc,cc
y_M,p?]^, qc,ff
m](q,65 2 5F1.08310223SDc
tHmV4 H$ dp D10.31G for DR523% (5a)
dO!B=/ qc,cc
cD'|zH] qc,ff
LMaY}m> 5F1.02310223SDc
H`OJN. dp D10.24G for DR556% (5b)
AP9>_0= qc,cc
`Y,<[ Lnr qc,ff
om{aws; 5F7.79310233SDc
xM_+vN*( dp D10.27G for DR590% (5c)
!'(QF9%Q In these equations, qc,cc5cone resistance measured in a calibration
-r%k)4_ chamber; qc,ff5field cone resistance; and Dc /dp5ratio of
s:*" b' chamber to equivalent pile diameter. The chamber size effect factors
Su]p6B for the base and shaft load capacities estimated by Eq. ~5! are
QFU1l"(qGk listed in Table 3. The field pile load capacity can then be obtained
S?u@3PyJm by dividing the chamber pile load capacity by the corresponding
~IQw?a.E size effect factors.
ok/{ w New Design Equations for Load Capacity of
f5,!,]XO Open-Ended Piles
[Mp8" Base Load Capacity
/EV _Y|(- Fig. 11 shows the ultimate unit field base resistance qb, f , normalized
frUO+ with respect to the horizontal effective stress sh8 at the pile
F~x>\?iN base, versus IFR for piles driven into sands with various relative
W5R / densities. The figure shows that the normalized unit field base
>_SqM! ^v resistance increases linearly with decreasing IFR. The relationship
V2IurDE between qb, f /sh8 and IFR can be expressed as
YxWA]
yL qb, f
;0-Y), ash8
*#7]PA Qw 5326– 295 IFR~%!
hYSf;cG}A 100
>M^4p (6)
1hW"#>f7 with a coefficient of determination r250.82. In this equation, the
X%
X
&< a values, a function of the relative density, were obtained from
l G $s( the calibration chamber tests as equal to 1.0 for dense sands, 0.6
N_R(i3c6U! for medium sands, and 0.25 for loose sands. In the case of fully
PEPf=sm plugged piles ~IFR50!, which behave as closed-ended piles, unit
FwqaWEk field base resistance is expressed as qb, f5326sh85130sv 8 for normally
!b8.XGo consolidated dense sands with K050.4. This is consistent
mcq.*at with the unit base resistance of a closed-ended pile in dense sand
^(~%'f proposed by the Canadian foundation engineering manual ~CGS
agj_l}=gO 1992!. In order to predict base load capacity of open-ended piles
pvY BhTz0 using Eq. ~6!, it is necessary to know either the IFR or the soil
"RLv{D<)J, plug length at the final penetration depth @from which the IFR can
}$Z0v` be estimated through Eq. ~3!#. A technique for measuring IFR
)=%TIkeF during pile installation will be described in a later section. Note
`!@d$*:' that Eq. ~6! should be used only for piles driven into sands, not
Q<T+t0G\O- for piles installed using vibratory hammers.
UQ}#=[)2e Table 3. Summary of Model Pile Test Results and Size Effect Factors
H,0Io Test
l9#@4Os indicator
XxLauJP
K Test
E@_]L<Z depth
kn&>4/') ~mm!
aM|;3j1p Soil plug
VRD:PVz length
mY&(&'2T" ~mm!
fzjAP7 y IFR
B3'-: ~%! PLR
%JPBD]&M Base load
Ft 6{g
JBG capacity
!pxOhO.V ~kN!
GL'l "L Shaft load
!z2 KQ
4C capacity
~TYpq;rq ~kN!
_m*FHi Size Effect Factor
,racmxnv Base
S,vh load
P@FE3g Shaft
5F$~ZDu load
pB'{_{8aA HLL 256 250 78.4 0.98 2.60 0.63 0.50 0.54
/q5!p0fH* 420 366 71.4 0.87 2.91 0.90 0.49 0.51
nR8r$2B+t 592 478 67.0 0.81 3.59 1.57 0.48 0.50
\k.W
F|~ 760 571 54.4 0.75 3.91 2.13 0.46 0.49
CkR
95* HML 250 251 88.0 1.00 2.50 0.50 0.52 0.54
Y(B3M=j 420 373 76.3 0.89 2.85 0.81 0.50 0.52
v@QfxV2 589 483 69.0 0.82 3.67 1.39 0.48 0.50
{'z( 760 583 57.4 0.77 4.30 2.23 0.47 0.49
Dbw{E:pq HHL 250 251 84.2 1.00 2.42 0.53 0.51 0.54
Cq[<CPAS 420 369 73.0 0.88 2.81 0.90 0.49 0.51
T!Nv 590 477 69.5 0.81 3.54 1.65 0.48 0.50
f"R'Q|7D 758 575 60.0 0.76 4.29 2.05 0.47 0.49
v,d'SR. HHM 252 255 87.9 1.01 3.09 0.70 0.52 0.55
4WP@ F0@n3 420 381 78.6 0.90 3.57 1.45 0.50 0.52
<lTLz$QE
591 501 73.9 0.85 4.66 2.49 0.49 0.51
"=,IbC 761 614 72.1 0.81 4.91 3.60 0.49 0.50
>hO9b;F} HHH 251 266 92.6 1.06 4.53 1.36 0.53 0.56
p(.z#o# 420 398 82.9 0.95 4.66 2.46 0.51 0.53
97vQM 590 521 79.8 0.88 5.40 3.93 0.50 0.52
Ru@ { b` 760 644 77.8 0.85 5.78 5.70 0.50 0.51
"Z)zKg MHL 247 236 75.9 0.96 1.82 0.28 0.53 0.58
>E9 k5 419 347 67.4 0.83 2.17 0.49 0.51 0.55
R\-]t{t` 589 445 60.5 0.76 2.41 0.65 0.50 0.53
L~E|c/ 757 532 53.9 0.70 2.82 1.00 0.49 0.52
rIeOli:< LHL 247 224 71.1 0.91 1.01 0.18 0.61 0.66
[oOV@GE 419 319 56.5 0.76 1.23 0.36 0.58 0.62
nQ#NW8*Fs 581 401 52.4 0.69 1.46 0.59 0.57 0.60
5#~E[dr 756 472 42.6 0.62 1.56 0.66 0.56 0.59
eI1C0Uz1
JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003 / 53
=@!s[ Shaft Load Capacity
5xhYOwQBo The average ultimate field unit shaft resistance f so, f for the model
;s?,QvE{r# piles, normalized with respect to K0sv 8 tan dc , is plotted versus
PO*0jO;% PLR in Fig. 12 for various relative densities. It can be seen in the
,c|Ai(U figure that the normalized ultimate field unit shaft resistance increases
I ;F\'P)e with decreasing PLR. The field unit shaft resistance of
)yUSuK(Vu piles driven into dense sand can be expressed as follows:
v)JS4KS f so, f
xM?tdQ~VHY ~K0sv 8 tan dc!b
SW7AG;c= 57.224.8PLR (7)
AI]lG]q8 in which f so, f5average ultimate unit shaft resistance in the field;
$l_\9J913 K05lateral earth pressure coefficient before pile driving;
RG:_:%@%} sv 8 5average vertical effective stress over the whole penetration
~p
x2kHZ depth; dc5critical-state interface friction angle between the pile
]/7#[ and the soil; and b5function of the relative density. The b values
APyH.] mQ were obtained from the calibration chamber tests as equal to 1.0
;N!opg))d< for dense sands, 0.4 for medium sands, and 0.22 for loose sands.
{?Cm In the case of closed-ended piles in normally consolidated dense
()Qq7/ sands with K050.4, the normalized unit shaft resistance equals
(W#^-*$R 7.2. This equation may be interpreted as implying that the lateral
()<?^lr33 stress on the closed-ended pile driven in dense sands is 7.2 times
\
*A!@T higher than that before pile driving. This is consistent with the
+kq+x6& lateral earth pressure coefficient of K52 – 3, which the Canadian
[}5mi?v Foundation Engineering Manual ~CGS 1992! suggested for steel
J2k4k piles with d520° driven into a normally consolidated dense sand.
Q1(4l?X@ Application of New Empirical Relations
=+H,} Field Pile Load Test
xF*i+'2 A full-scale, field pile load test was performed on an instrumented
f,Am;:\ | open-ended pile at Lagrange County in northern Indiana. The soil
xdMY2u at the site is gravelly sand with maximum and minimum dry unit
p9&gKIO_m weights of 18.64 and 15.61 kN/m3, respectively. A 2.0 m thick fill
uW4.Q_O!H layer was removed before pile driving. The groundwater table is
Us_1 #$p, at a depth of 3 m below the soil surface. Standard penetration test
UDPn4q and cone penetration test results indicate that the first 3 m of the
9{Igw"9ck gravelly sand deposit are in a loose state (DR'30%), but the rest
"YVr/u of the deposit is in a dense to very dense state (DR'80%), as
)!FheoR shown in Fig. 13. Note that the fill originally present at the site
f[?JLp
was removed before the piles were installed and tested, and Fig.
SQ<{X/5 13 accordingly does not include data for the fill. The resulting
ep{/m-h(!_ overconsolidation ratio ~OCR! is also shown in Fig. 13 as a function
Hxn#vAc of depth.
3@* ~>H The test pile was an instrumented double-walled open-ended
w9Nk8OsL pile, constituted of two pipes with different diameters, as shown
/K;A bE in Fig. 14. The open-ended pile had an outside diameter of 356
X?] Mzcu mm and wall thickness of 32 mm. In order to measure the base
i%MR<M and shaft load capacities directly, 20 strain gauges were attached
|w -s{L3@+ to the outer surface of the inner pipe and 18 to the outer surface of
9l,8:%X_ the outer pipe. The open-ended pile was driven to a depth of 7.04
2#8PM-3" m using a single acting diesel hammer with a ram weight of 18.2
YVk
+zt~S kN and a maximum hammer stroke of 3.12 m. The soil plug
n.,ZgLx[" length during pile driving was measured continuously using two
)iZhE"?z different weights, which were connected to each other by a steel
F5{GMn;j wire ~Fig. 15!. The heavier weight rested on top of the soil plug,
y,c\'}*H and the lighter weight hanged outside the pile. A scale marked on
ssmJ?sl the outside of the pile allowed measurement of the plug length. At
]SN5&S the final penetration depth, the IFR for the pile was 77.5%, indicating
}IQ! [T5 a partially plugged condition, and the PLR was 0.82.
(~(FQ:L%U The load applied to the pile during the static load test was
1uzK(j8w measured using a 2 MN load cell, and the settlement of the pile
^}kYJvqA head was measured with two dial gauges. The residual loads after
QRF:6bAxsL pile driving and the loads induced at the base and shaft of the test
G#='*vOtO pile during the load test were independently measured by rezeroing
yK mHTjX= the values of all strain gauges attached to the test pile both
,S?:lQuK5 before pile driving and at the start of the static load test. The load
knWI7 was applied to the pile head in increments of 147 kN, which were
[TT:^F(Y decreased to 49–98 kN as the pile approached the limit load. The
RG/P] load after each increment was maintained until the pile settlement
Ey_mK\' stabilized at less than 0.5 mm/h. The settlements at the pile head
$$R-> were measured at 5, 15, 35, 55, 75, 95, and 120 min for each load
!H @nAz step. When the settlement did not stabilize within 120 min, the
syb$% settlement was measured only after stabilization ensued. Likewise,
MN>U jFA strain values for the strain gauges attached to the inner and
luz,z(
v outer pipes were measured after the settlement of the pile head
z] |Y stabilized.
vmW`}FKW Static Load Test Results
T n,Ifo3 Fig. 16 shows the load–settlement curves for the base and shaft
`2'*E\ load capacities of the full-scale open-ended pile. As shown in the
MF$NcU figure, the shaft load capacity reached its limit value before the
eqpnh^0}d Fig. 11. Normalized field unit base resistance versus incremental
r?`7i' filling ratio
-Q1~lN m: Fig. 12. Normalized field unit shaft resistance versus incremental
x/ P\qI filling ratio
w8>h6x" 54 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003
71\53Qr#U final load step. The ultimate total and base load capacities were
ghWWJx9 also determined as the loads at a settlement of 35.6 mm, corresponding
&:g:7l]g to 10% of the pile diameter. The ultimate base and shaft
3PGAUQR#"q load capacities not accounting for residual loads were 715 and
@U18Dj[ 310 kN, respectively. The ultimate base and shaft load capacities
7M~sol[* accounting for residual loads were 886 and 139 kN, respectively.
fCx( In practice, it is difficult to account for residual loads. Residual
'{UKO7 loads are induced in every driven pile, but their magnitude depends
nV7Vc; on several factors. The use of the unit base and shaft resistance
_0v+'&bz values that have been corrected for residual loads for designing
O`c50yY a different pile installed in a different sand site would
oD V6[e require estimation of the residual loads for that pile. This is very
o(oOB difficult to do in practice. Accordingly, we base our suggested
-1,0hmn=+ design values of shaft and base resistances on the values measured
nq]6S$3
6 without any correction for residual loads, as is customary.
[p9v#\G; [ Comparison of Computed and Measured Capacities
8rH6L:]S The bearing capacity of the test pile was predicted using the empirical
WN+i 3hC relationships suggested in this study. Since the soil deposit
GeTk/tU was overconsolidated by removal of the fill layer, the lateral earth
o]4\Geg$ pressure coefficient K0 was taken as ~Mayne and Kulhawy 1982!
ve
ysW(z K05~12sin f!OCRsin f (8)
\~ChbPnc Saturated unit weights of the sand are gsat520.1 kN/m3 for the
|MFAP!rycS loose sand and 21.2 kN/m3 for the dense sand, respectively. The
2Qp}f^ Fig. 13. Cone penetration test and standard penetration test results and overconsolidation ratio profile at test site
? +L, Fig. 14. Schematic of full-scale test pile Fig. 15. Measurement of soil plug length during pile driving
m+hI3@j JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003 / 55
)pH+ibR mean particle size is 0.4 mm. The critical state friction angle for
b&+zAt. the sand obtained from triaxial compression tests is fc533.3°;
gHLI>ew*QR the interface friction angle between the pile and sand is taken as
aX^T[ dc52fc/3522.2°, which is adequate for typical pipe piles. At
hc3hU the depth of the pile base, OCR51.41, and K0 results equal to
5,1<A@H 0.55. Using Eq. ~6!, the ultimate base load capacity Qbase can be
::oFL#+ obtained as
t1adS:)s qb, f
e~SK*vR%] ash8
n" Ie> 5326– 295 IFR~%!
'\I(n|\ 100 5326– 295 77.5
TC?B_;a 100597.4
TwPQ8}pj? Qbase5qb, fAb597.4ash 8 Spd0 2
I_ mus<sE 4 D
x,,y}_YX 597.4~1.0!~0.553101.2!~0.0995!5539.4 kN
/h0bBP The ultimate shaft load capacity can be computed using Eq. ~7!.
Dcvul4Q The b values used in the calculations are 0.3 for the first 3 m in
\b"rf697, loose sand and 1.0 for depth greater than 3 m in dense sands. The
"l56?@- x variation of K0 with OCR along the whole depth of the pile was
v_!6S|
considered in the calculations, which are summarized next
eBrNhE-[G] f so, f
JpC'(N ~K0sv 8 tan dc!b
OOqT 0wN 57.224.8PLR57.224.8~0.82!53.26
32[}@f2q Qshaft5f so, fAso53.26K0sv 8 tan dcb~pd0D!
<:v+<)K 53.26S~biKoisv8iDi!pd0 tan dc
mVZh_R=a 53.26~0.3363.411.03191.3!p~0.356!tan 22.2°
" CT}34l 5312.9 kN
Y<xqws in which D5penetration depth of the pile. Thus, the ultimate total
$N=&D_Q load capacity can be calculated as
Jj-\Eb? Qtotal5Qbase1Qshaft5539.41312.95852.3 kN
2tq2 The base and shaft load capacities predicted using Eqs. ~6! and
+
Q-b} ~7! were 75.4 and 100.9% of the ultimate values measured in the
:<qe2Z5k pile load test, respectively. The predicted Qtotal5852.3 kN is a
IL].!9 reasonably close, conservative estimate of the measured value, as
UCLM*`M shown in Fig. 17.
q-JTGCFl Summary and Conclusions
VsQ|t/|# The bearing capacity of open-ended piles is affected by the degree
M~taZt4 of soil plugging, which can be quantified through the IFR. Most
?F"o+]i+^ design criteria for open-ended piles do not consider the variation
iS$[dC ?N of pile load capacity with IFR, and a standard technique for measuring
SyvoN,;Q IFR during pile installation has not yet been proposed. In
+/ukS6>gr this study, model pile tests were conducted using a calibration
,X?/FAcb chamber to investigate the effect of IFR on the pile load capacity,
(C!p2f and new empirical relations between the two components of pile
=}`d load capacity ~base and shaft load capacities! and IFR were proposed
UBaXS_c\ based on the results of model pile tests.
3oCI1>k The results of model pile tests show that the IFR decreases
Pd91<L with decreasing relative density and horizontal stress, but is independent
!mNst$-H4 of the vertical stress. It is also seen that the IFR increases
{"ST
hTZ linearly with the PLR, which is defined as the ratio of the soil
tIuM9D{P plug length to pile penetration depth, and can be estimated from
9M96$i`P the PLR. The unit base resistance shows a tendency to increase
s6 yvq#: with decreasing IFR, and it does so at a rate that increases with
<0CjEsAB] relative density. The unit shaft resistance, normalized with respect
pR
S! to horizontal stress, increases with decreasing IFR and with increasing
s@\3|e5g relative density.
h*S"]ye5 A full-scale pile load test was also conducted on a fully instrumented
C >*z^6Gz open-ended pile driven into gravelly sand. The IFR for
@Q74 the pile was continuously measured during pile driving. In order
]Ur/DRNS to check the accuracy of predictions made with the proposed
gu
k,GF9p] equations, the equations were applied to the pile load test. Based
7Nq<
o5 on the comparisons with the pile load test results, the proposed
C]L)nCOBX equations appear to produce satisfactory predictions.
hi8q?4jE Acknowledgments
*qpu!z2m|| The research presented in this paper was performed in a period of
b'z
$S+ 1 year spent by the first writer as a postdoctoral fellow at Purdue
,->ihxf University. The first writer is grateful for support received from
(p{X.X+ the Korea Science and Engineering Foundation. The field pile
fbq$:Q44 load test done as part of this research was supported by INDOT
q[$>\Nfg>B and FHWA through the Joint Transportation Research Program.
dSGdK
$ XA The assistance of Dr. Junhwan Lee and Bumjoo Kim with some
k1B
](@xt aspects of this research is appreciated.
iXWHI3
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Fig. 16. Load settlement curves from field pile load test
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