Determination of Bearing Capacity of Open-Ended Piles
wnHfjF in Sand
__`6 W1 Kyuho Paik1 and Rodrigo Salgado, M.ASCE2
pg{cZ1/ Abstract: The bearing capacity of open-ended piles is affected by the degree of soil plugging, which is quantified by the incremental
"0J;H#Y"# 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
zB'_YwW capacity. In order to investigate this effect, model pile load tests were conducted on instrumented open-ended piles using a calibration
|
&/_{T chamber. The results of these tests show that the IFR increases with increasing relative density and increasing horizontal stress. It can also
#hXxrN 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
RhkTN'vO resistances increase with decreasing IFR. Based on the results of the model pile tests, new empirical relations for plug load capacity,
4X5KrecNr annulus load capacity, and shaft load capacity of open-ended piles are proposed. The proposed relations are applied to a full-scale pile load
m[s$) -T test performed by the authors. In this load test, the pile was fully instrumented, and the IFR was continuously measured during pile
VUZeC,FfO driving. A comparison between predicted and measured load capacities shows that the recommended relations produce satisfactory
Hh*
KcIRX predictions.
L#\5)mO.v DOI: 10.1061/~ASCE!1090-0241~2003!129:1~46!
wxy@XN"/i+ CE Database keywords: Bearing capacity; Pile load tests; Sand.
P<=1OWC Introduction
/ACau<U]t When an open-ended pile is driven into the ground, a soil plug
,>Dpt< may develop within the pile during driving, which may prevent or
@Y!B~ partially restrict additional soil from entering the pile. It is known
mQ2=t% that the driving resistance and the bearing capacity of open-ended
12tk$FcY8* piles are governed to a large extent by this plugging effect.
3ej[ Many design criteria for open-ended piles, based on field tests,
K?>sP%m) chamber tests or analytical methods, have been suggested @e.g.,
#x \YA#~ Klos and Tejchman 1977; Nishida et al. 1985; American Petroleum
ZP
]Ok Institute ~API! 1991; Randolph et al. 1991; Jardine et al.
?Cv([ ^Y.u 1998#. For example, in the case of API RP2A ~1991!, which is
8L5O5F' generally used for offshore foundation design, the bearing capacity
F:8@ ]tA& of an open-ended pile can only be estimated for either the fully
~Gl5O`w( coring mode or the fully plugged mode of penetration. In practice,
#X2wy$GTG most open-ended piles are driven into sands in a partially plugged
nK#%Od{GF mode. Stefanoff and Boshinov ~1977! suggested the use of onedimensional
dnkHx plug analysis, in which the soil plug is treated as a
15d'/f series of horizontal thin discs and the force equilibrium condition
*0'< DnGW is applied to each disc, to calculate plug capacity of an openended
xXSfYW pile.
@TJ There have been modifications of one-dimensional plug analysis
w!-MMT4y to improve predictive accuracy, such as the introduction of the
ua,!kyS concept of the wedged soil plug ~Murff et al. 1990; O’Neill and
LuVL<W Raines 1991; Randolph et al. 1991!. Many test results show that
3gtKD9RL: the soil plug can be divided into a wedged plug zone and an
gZ8JfA_\R( unwedged plug zone. While the wedged plug zone transfers load
}:(;mW8
D to the soil plug, the unwedged plug zone transfers no load but
`cPZsL provides a surcharge pressure on top of the wedged plug zone.
Q=Liy@/+! However, it is not easy to apply the one-dimensional analysis to
{u4AOM=) practical cases, because of the sensitivity of the method to the
@U9`V&])F[ lateral earth pressure coefficient, which is not easily estimated
.@$A~/ YU ~Brucy et al. 1991; Leong and Randolph 1991!. De Nicola and
,P=.x% Randolph ~1997! addressed this by proposing a profile of the
OxUc,%e9P lateral earth pressure coefficient K along the soil plug length.
5F#FC89Kk An alternative design method can be based on the incremental
O^@F?CG :1 filling ratio ~IFR!. The degree of soil plugging is adequately quantified
]}n|5 using the IFR ~Paikowsky et al. 1989; Paik and Lee 1993!
t:b}Mo0 defined as
JF=T_SH^U IFR5
$i1:--~2\ DL
]GD&EQ DD
AuZISb%6 3100~%! (1)
fNBI!= where DL5increment of soil plug length ~L! corresponding to a
Q7\j:. small increment DD of pile penetration depth D ~see Fig. 1!. The
taMcm}*T1 fully plugged and fully coring modes correspond to IFR50 and
tJmy}.t1 100%, respectively. A value of IFR between 0 and 100% means
)TEod!] that the pile is partially plugged. A series of model pile tests,
4BeHj~~ using a calibration chamber, were conducted on model openended
15OzO.Ud piles instrumented with strain gauges in order to investigate
1 hD(l6tG@ the effect of IFR on the two components of bearing capacity: base
x=kJlGT load capacity and shaft load capacity. Based on the calibration
.9?GKD chamber test results, empirical relationships between the IFR and
q/ (h{cq the components of pile load capacity are proposed. In order to
204"\mv verify the accuracy of predictions made using the two empirical
E<7$!P=z` relationships, a full-scale static pile load test was conducted on a
Yv0y8Vz@ fully instrumented open-ended pile driven into dense sand. The
Z[>fFg~N4 predicted pile load capacities are compared with the capacities
ct<XKqbI measured in the pile load test.
Gte\=0Wr 1Associate Professor, Dept. of Civil Engineering, Kwandong Univ.,
oTrit_@3 Kangwon-do 215-800, South Korea ~corresponding author!. E-mail:
oDayfyy4y) pkh@kwandong.ac.kr (G(M"S SC 2Associate Professor, School of Civil Engineering, Purdue Univ., West
2/\I/QkTs Lafayette, IN 47907-1284. E-mail:
rodrigo@ecn.purdue.edu sE
^YOT< Note. Discussion open until June 1, 2003. Separate discussions must
W }v
,6Oe be submitted for individual papers. To extend the closing date by one
{rn^ month, a written request must be filed with the ASCE Managing Editor.
9$D}j" The manuscript for this paper was submitted for review and possible
y>7 r;e publication on July 23, 2001; approved on May 23, 2002. This paper is
F>GPi!O part of the Journal of Geotechnical and Geoenvironmental Engineering,
A[F_x*S Vol. 129, No. 1, January 1, 2003. ©ASCE, ISSN 1090-0241/2003/1-
pl$wy}W- 46–57/$18.00.
RxNLn/?d@ 46 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003
?FwHqyFVlQ Soil Sample Preparation
C|[x],JCS Soil Properties
ddd2w Han river sand, a subangular quartz sand, with D1050.17mm and
<$d2m6 J D5050.34 mm, was used for all the calibration chamber model
yXqC pile tests. The test sand is classified as poorly graded ~SP! in the
7|jy:F,w% Unified Soil Classification System, so the maximum dry density
oTx>oM, of the sand is near the low end of the typical range for sands. The
q=-h#IF^ maximum and minimum dry unit weights of the sand were 15.89
p<?lF and 13.04 kN/m3, respectively.
B I=57 A series of laboratory tests were conducted to characterize the
JSmg6l?[u sand. The results from these tests are summarized in Table 1. The
| g1Cs internal friction angle of the sand and the interface friction angle
l/"!}wF between the sand and steel were measured from direct shear tests
7U^{xDg.b under normal stresses of 40–240 kPa. The peak friction angles of
sB$" mJ the sand with relative densities of 23, 56, and 90% were 34.8,
Onou:kmf1 38.2, and 43.4°, respectively, and the critical-state friction angle
PZO.$'L|7 was 33.7°. The peak interface friction angles between the pile and
k'+y the sand were 17.0, 17.5, and 18.4° for DR523, 56, and 90%,
Zj_2B_|WN# respectively, and the critical-state interface friction angle was
gZBKe!@a| 16.7°. This angle is lower than commonly reported values because
-yb7s2o the test pile was made of stainless steel pipe with a very
TK%q}bK, smooth surface.
TjI&8#AWBA Calibration Chamber and Sample Preparation
b80&${v All model pile tests were conducted in soil samples prepared
yE(<F2 within a calibration chamber with a diameter of 775 and a height
lY2~{Y|4s of 1250 mm. In order to simulate various field stress conditions,
R%q:]. two rubber membranes, which can be controlled independently,
'Yh`B8 were installed on the bottom and inside the lateral walls of the
RLzqpE<rJ calibration chamber. The consolidation pressure applied to the
s^4wn:*$zd two rubber membranes was maintained constant by a regulator
f.bw A x panel throughout each pile test.
9U4[o<G]= The soil samples were prepared by the raining method with a
XBB>" constant fall height. The falling soil particles passed through a
uH,/S4?X sand diffuser composed of No. 8 and No. 10 sieves in order to
:$gs7<z{rm control flow uniformity and fall velocity. The soil samples had
7G*rxn"d DR523, 56, and 90%. After sample preparation, the samples
&9z`AY]> were consolidated to the desired stress state during approximately
xg 8R>j 30 h by compressed air transferred to the rubber membranes.
;PnN$g]Q Measurements made in calibration chambers are subject to
PgHmOs chamber size effects. Many researchers have attempted to estimate
7oc Ng the chamber size needed for boundary effects on pile bearing
%d40us8 E capacity or cone resistance to become negligible. Parkin and
%4t?X Lunne ~1982! suggested 50 times the cone diameter as the minimum
<:T/hm$ chamber diameter for chamber size effect on cone penetration
F! Cn'* resistance to become acceptably small. Salgado et al. ~1998!,
BE],PCpPr based on cavity expansion analyses, found that 100 times the cone
aQf2}kD diameter was the minimum chamber diameter to reduce chamber
e@S$[,8 size effects on cone resistance to negligible levels. Diameters of
:eT\XtxM~{ the chamber and test pile used in this study are 775 and 42.7 mm,
/q,=!&f2 respectively. The lateral and bottom boundaries are located at a
2(Yg',aMY- distance equal to 18.2 pile radii from the pile axis and 23.0 pile
B&<5VjZ\ radii below the maximum depth reached by the pile base, respectively.
N}<!k#d
E Considering the results of the research on chamber size
@F*z/E}e effects mentioned above, the size of the chamber used in this
2X*n93AQi study is not sufficiently large for chamber size effects on pile
cIC/3g}] bearing capacity to be neglected. The flexible boundary causes
q/Ji}NGm lower radial stresses than those that would exist in the field. Accordingly,
Om>?"=yD E the chamber tests done as part of this study produce
uFhPNR2l lower pile load capacities than those that would be observed in
L/,gD.h^ the field. A correction for chamber size effects is then necessary.
g1_z=(i`Z It is discussed in a later section.
,fN <I Model Piles and Test Program
9ZR"Lo>3e+ Model Pile
nh80"Ny5 An open-ended pile is generally driven into sands in a partially
"gzn%k[D9m plugged mode, and its bearing capacity is composed of plug load
.*xO/pn capacity, annulus load capacity, and shaft load capacity. In order
g_k95k3V' to separate pile load capacity into its components, an instrumented
mwN"Cu4t double-walled pile was used in the testing. A schematic
qJO6m-
diagram of the pile is shown in Fig. 2. The model pile was made
(l9jczi of two very smooth stainless steel pipes with different diameters.
6}0_o[23 It had an outside diameter of 42.7 mm, inside diameter of 36.5
mG@[~w+ mm, and length of 908 mm.
iTs"RW The wall thickness of the test piles used in this study is larger
w5rtYTI than those of piles typically used in practice. Szechy ~1959!
^,?>6O showed that the degree of soil plugging and bearing capacity of
vjh'<5w9Wi two piles with different wall thicknesses do not differ in a significant
&5sPw^{,H way ~with bearing capacity increasing only slightly with increasing
6W3."}; wall thickness!; only driving resistance depends significantly
f)gV2f0t upon the wall thickness. So the load capacity of the test
c* ~0R? piles reported in this paper are probably larger, but only slightly
$: 1/`m19 so, than what would be observed in the field.
o1b.a*SZ Eighteen strain gauges were attached to the outside surface of
%[ *+ the inner pipe at nine different levels in order to measure the base
Xc^(e?L4 load capacity ~summation of plug and annulus load capacities!
"*V'
Fig. 1. Definition of incremental filling ratio and plug length ratio
T+rym8.p Table 1. Soil Properties of Test Sand
KL9JA;" Property Value
p]?eIovi Coefficient of uniformity Cu 2.21
Zy{hYHQ Coefficient of gradation Cc 1.23
rg#/kd<?[V Maximum void ratio emax 0.986
yd'cLZd<} Minimum void ratio emin 0.629
H!,V7R Minimum dry density gd,min 13.04 kN/m3
-]Mk}
z$ Maximum dry density gd,max 15.89 kN/m3
&e#pL`N Specific gravity Gs 2.64
*UJB*r Peak friction angle fpeak 34.8–43.4°
z|Xt'?9&n Critical-state friction angle fc 33.7°
$P#+Y,r~\ Peak interface friction angle d 17.0–18.4°
3,{;wJ
Z Critical-state interface friction angle dc 16.7°
s?nj@:4 JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003 / 47
7lJ8<EP9
u from the load transfer curve along the inner pipe. Two strain
bNtOqhi gauges were also attached to the outside surface of the outer pipe
.L^;aL in order to measure shaft load capacity. A gap of 4 mm between
iEy2z+/"^ the outer pipe and the pile toe, which was sealed with silicone,
Wf%)::G*uR prevented the base load from being transferred to the outer pipe.
'd;aAG The outer pipe, therefore, experienced only the shaft load.
wN6sica| Many researchers have relied on linear extrapolation to separate
9ao?\]&t the base load capacity into plug and annulus capacities ~Paik
mz;ExV16 and Lee 1993; Choi and O’Neill 1997; Lehane and Gavin 2001!.
xlgT1b:6 Linear extrapolation would apply strictly only if the inside unit
*/TO$ ^s friction between the pile and soil plug were constant between the
F8{T/YhZ second lowest strain gauge and the pile base, as shown in Fig. 3.
P9Eh,j0_ In reality, the inside unit friction between the soil plug and the test
upJy,|5 pile increases dramatically near the pile base. Use of linear extrapolation,
m}: X\G(6Q therefore, leads to an overestimation of annular resistance.
`Pwf?_2n- This overestimation increases as the distance between the
3O2vY1Y2 lowest strain gauge and the pile base increases. In part to avoid
Et}%sdS this uncertainty, in this paper we use the base load capacity to
Y2N$&]O{ analyze the test results instead of the plug and annulus load capacities
,'l.u?SKyd separately. The base load capacity of the test pile was
Bxj4rC[ obtained from the upper strain gauges located on the inner pipe,
x}d5Y for which the measured vertical loads reached a limit value ~Fig.
YYkgm:[ 3!.
@cm[]]f'l Test Program
KpS=oFX{} Seven model pile tests were performed in dry soil samples with
irjHPuhcG three different relative densities and five different stress states.
Ls.g\Gl3 Each test is identified by a symbol with three letters ~H high, M
BP4vOZ0$ medium, L low!, signifying the levels of the relative density, vertical
C)9-{Yp and horizontal stresses of the sample, respectively. A summary
9+5F(pd( of all model pile tests is presented in Table 2. Five model
,p\*cHB9 pile tests were conducted in dense samples with DR590% and
tEibxE five different stress states. Two model pile tests were conducted in
@e7_&EGR? loose and medium samples consolidated to a vertical stress of
Z vyF"4QN 98.1 kPa and horizontal stress of 39.2 kPa. The model piles were
&;GoCU Le driven by a 39.2 N hammer falling from a height of 500 mm.
@OHNz!Lj:d During pile driving, the soil plug length and the pile penetration
q zo)\, depth were measured at about 40 mm intervals, corresponding to
(.{. " 94% of the pile diameter, in order to calculate the IFR. The
SxC(:k2b; change in soil plug length during pile driving was measured using
wc~ 9zh a ruler introduced through an opening at the top plate of the pile
fKua om9 ~see Fig. 2!. In order to measure the soil plug length, driving
<!|=_W6 operations were suspended for no more than a minute each time.
Tm~jYgJ Static pile load tests were performed when the pile base was
~IQjQz? located at depths of 250, 420, 590, and 760 mm. The pile load
e+@.n tests were continued until the pile settlement reached about 19
xu;^F mm ~44% of the pile diameter!, at which point all the test piles
$.B}zY{ had reached a plunging limit state ~Fig. 4!. The ultimate load of
*y>| each test pile is defined as the load at a settlement of 4.27 mm,
MUN:}S corresponding to 10% of the pile diameter. The total load applied
2fPMZ7Zd3 to the pile head was measured by a load cell, and settlement of the
d{C8}U pile head was measured by two dial gauges. Details of the model
)S_%Ip pile, sample preparation, and test program have been described by
"DJ%Yo Paik and Lee ~1993!.
o9v9
bL+X Model Pile Test Results
sn@)L ~$V Pile Drivability
H@k$sZ. Fig. 5~a! shows pile penetration depth versus hammer blow count
A+3=OBpkW0 for all the test piles. As shown in the figure, the hammer blow
6M8(KN^ count per unit length of penetration increases as pile penetration
+OUM 4y depth increases, since the penetration resistances acting on the
WxF@'kdn*, base and shaft of the piles during driving generally increase with
6AmFl< Fig. 2. Schematic of model pile
.:, 9Tf Fig. 3. Determination of plug and annulus loads
GuJIN"P] Table 2. Summary of Model Pile Test Program
Fd9Z7C Test
%E2C4UbY indicator
ra\|c>[% Initial
Ob-k`@_| relative
wtGb3D"am density
@{8805Dp ~%!
It^_?oiK Initial
}HZ'i;~r|9 vertical
aK9zw stress
zPb"6%1B ~kPa!
jTY{MY Jh Initial
QOF'SEq"k horizontal
jY\YSQ stress
#DHeEE ~kPa!
\G1(r=fU Initial
Al]z= earth
C6b(\#g( pressure
mHC36ba coefficient
mDU-;3OqF HLL 90 39.2 39.2 1.0
H0mDs7 HML 90 68.6 39.2 0.6
_]=, U.a=/ HHL 90 98.1 39.2 0.4
#.\X%! HHM 90 98.1 68.6 0.7
gH/k}M7tA# HHH 90 98.1 98.1 1.0
k+cHx799 MHL 56 98.1 39.2 0.4
z[_Gg8e LHL 23 98.1 39.2 0.4
{pB9T3ry] 48 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003
,1e@Y~eZ penetration depth. The vertical stress applied to the soil sample
CB?H`R pC. had little effect on the cumulative blow count. However, the blow
{eo?vA8SE count necessary to drive the pile to a certain depth decreased
q]t^6m&- rapidly with decreasing horizontal stress. It is also seen in Fig.
BH=CoD. 5~a! that the blow count necessary for driving the pile to some
<i1P ~ required depth increases with increasing relative density.
cV)~%e/ Soil Plugging
%AuS8'Uf The degree of soil plugging in an open-ended pile affects pile
rx;zd ? behavior significantly. The IFR is a good indicator of the degree
aw/5#(1R of soil plugging. During the model pile tests, the IFR was measured
h%@#jvh?4 at increments of 40 mm of penetration. The change of the
b~FmX soil plug length with pile penetration depth is plotted in Fig. 5~b!.
(*Y ENT} It is seen in the figure that the soil plug length developed during
bjq2XP?LL pile driving increases as the horizontal stress of the soil sample
(tP^F)}e5 increases for the same relative density, and as the relative density
uM~j increases for the same stress. It can also be seen that every test
uc;QSVWGy8 pile, during static load testing, advances in fully plugged mode,
^zaN?0%S33 irrespective of the initial soil condition and the degree of soil
`{I-E5x plugging during pile driving. The static load tests appear as short
_Msaub!N vertical lines in Fig. 5~b!, meaning that penetration depth increases
x;*KRO while soil plug length remains unchanged.
jDc5p3D&[] Fig. 6 shows changes of IFR with soil state ~relative density,
Ok~\ vertical stress, and horizontal stress!. Fig. 6~a! shows IFR versus
.{W)E DR for tests with sv 8 598.1 kPa and K050.4. Fig. 6~b! shows IFR
-vC?bumR% versus sv 8 for tests with DR590% and sh8539.2 kPa. Fig. 6~c!
3bPvL/\Lb shows IFR versus sh8 for DR590% and sv 8 598.1 kPa. It is observed
V|fs"HY that the IFR increases markedly with increasing relative
[VP~~*b density and with increasing horizontal stress. These changes in
c8jq.y v IFR reflect the decreasing amount of compaction of the soil plug
) 4'@=q during pile driving as the relative density and stress level in the
^UK6q2[ soil increase. However, the IFR is relatively insensitive to
pc%_:> changes in the vertical stress applied to the soil sample. This
4%k_c79> means that the IFR of an open-ended pile would be higher for an
"$BWP overconsolidated sand than for a normally consolidated sand at
+P <Lo I the same DR and sv 8 .
C,D~2G Fig. 7 shows IFR versus plug length ratio ~PLR! for the chamber
QRv2%^L test results and for the test results of Szechy ~1959!; Klos and
",T-'>h$2R Tejchman ~1977!; Brucy et al. ~1991!; and Paik et al. ~2002!. The
"L" 6jT PLR is defined as the ratio of soil plug length to pile penetration
;=6~,k) as ~see Fig. 1!
5<ycF_ PLR5
5q?ZuAAA L
oa|nQ`[ D
kSw.Q2ao (2)
?79ABm
a In Fig. 7~b!, the data from Paik et al. ~2002! were obtained from
YX_p3 a full-scale pile with diameter of 356 mm driven into submerged
6(}8[i: dense sands. The remaining data were obtained from model pile
mko<J0|4 tests using piles with various diameters driven into dry sand ranging
[?hc.COE from loose to medium dense ~the diameter of each test pile is
dLm~]V3 indicated in the figure!. Fig. 7~a! shows that IFR, measured at the
7>J8\= final penetration depth, increases linearly with increasing PLR.
!}^{W)h[ Fig. 4. Load–settlement curves from model pile load tests
y8un&LP Fig. 5. Driving test results: ~a! hammer blow count, and ~b! soil plug
pemb2HQ'4j length
@vaK-&|#$ JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003 / 49
70:a2m The relationship between PLR and IFR for the calibration chamber
d1#;>MiU tests can be expressed as follows:
}ya9 +?I IFR~%!5109PLR222 (3)
jxr~cp?4 This equation slightly underestimates the IFR for PLR values
8:,l+[\ greater than 0.8 and slightly overestimates it for PLR values
7PZ0 lower than 0.7, as shown in Fig. 7~b!. In general, it is known that
i1?H*:] the IFR is a better indicator of the degree of soil plugging than the
;p#)z/zZ PLR ~Paikowsky et al. 1989; Paik and Lee 1993!. In the field,
1G+42>?<1 however, it is easier to measure the PLR than the IFR. Eq. ~3! can
>_]j{}~\k be used to estimate the IFR from the PLR, when only the PLR is
b{t'Doe measured in the field.
R$=UJ}> Base and Shaft Load Capacities
]dc^@}1bN The ultimate unit base resistance qb,c measured in the calibration
^'~+ w3M@ chamber is plotted versus relative density ~for sv 8 598.1 kPa and
RUmJ=i'4/ K050.4), versus vertical stress ~for DR590% and sh8
v*1UNXU\ 539.2 kPa) and versus horizontal stress ~for DR590% and
K<KyX8$P0 Fig. 6. Incremental filling ratio versus ~a! relative density for sv8
Qj?FUxw 598.1 kPa and K050.4; ~b! vertical stress for DR590% and sh8
*S_eYKSl 539.2 kPa; and ~c! horizontal stress for DR590% and sv8
|?SK.1pW 598.1 kPa
mh!;W=|/" Fig. 7. Plug length ratio versus incremental filling ratio ~a! for chamber
&CFHH"OsT test results, and ~b! for other test results
T"XP`gk 50 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003
bH&Cbme90- sv 8 598.1 kPa) in Fig. 8. It is apparent that the ultimate unit base
Ex~[Hk4ow resistance increases significantly with increasing relative density
` IiAtS and increasing horizontal stress, but is relatively insensitive to
]C-hl}iq vertical stress. This is consistent with experimental results of
UfSWdR) Baldi et al. ~1981!; Houlsby and Hitchman ~1988!; and Vipulanandan
_pM&Ya et al. ~1989!, which showed that cone resistance was a
jAmAT/ 1 function of lateral effective stress.
!L+*.k: Fig. 9 shows the ultimate unit base resistance, normalized with
GmB7@-[QA% respect to the horizontal stress, versus IFR for different relative
6yKr5t H4 densities, and the ultimate unit base resistance versus IFR for
.
Yg)|/ dense sand. It can be seen in Figs. 9~a and b! that the ultimate unit
0 }k[s+^ base resistance of open-ended piles increases with decreasing IFR
n3-u.Fb and that the rate of change of ultimate unit base resistance with
T%Vii*?M IFR increases with DR . It is also seen that the ultimate unit base
;OQ{ resistance increases with relative density at constant IFR.
pm,&