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Determination of Bearing Capacity of Open-Ended Piles
in Sand
Kyuho Paik1 and Rodrigo Salgado, M.ASCE2
Abstract: The bearing capacity of open-ended piles is affected by the degree of soil plugging, which is quantified by the incremental
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
capacity. In order to investigate this effect, model pile load tests were conducted on instrumented open-ended piles using a calibration
chamber. The results of these tests show that the IFR increases with increasing relative density and increasing horizontal stress. It can also
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
resistances increase with decreasing IFR. Based on the results of the model pile tests, new empirical relations for plug load capacity,
annulus load capacity, and shaft load capacity of open-ended piles are proposed. The proposed relations are applied to a full-scale pile load
test performed by the authors. In this load test, the pile was fully instrumented, and the IFR was continuously measured during pile
driving. A comparison between predicted and measured load capacities shows that the recommended relations produce satisfactory
predictions.
DOI: 10.1061/~ASCE!1090-0241~2003!129:1~46!
CE Database keywords: Bearing capacity; Pile load tests; Sand.
Introduction
When an open-ended pile is driven into the ground, a soil plug
may develop within the pile during driving, which may prevent or
partially restrict additional soil from entering the pile. It is known
that the driving resistance and the bearing capacity of open-ended
piles are governed to a large extent by this plugging effect.
Many design criteria for open-ended piles, based on field tests,
chamber tests or analytical methods, have been suggested @e.g.,
Klos and Tejchman 1977; Nishida et al. 1985; American Petroleum
Institute ~API! 1991; Randolph et al. 1991; Jardine et al.
1998#. For example, in the case of API RP2A ~1991!, which is
generally used for offshore foundation design, the bearing capacity
of an open-ended pile can only be estimated for either the fully
coring mode or the fully plugged mode of penetration. In practice,
most open-ended piles are driven into sands in a partially plugged
mode. Stefanoff and Boshinov ~1977! suggested the use of onedimensional
plug analysis, in which the soil plug is treated as a
series of horizontal thin discs and the force equilibrium condition
is applied to each disc, to calculate plug capacity of an openended
pile.
There have been modifications of one-dimensional plug analysis
to improve predictive accuracy, such as the introduction of the
concept of the wedged soil plug ~Murff et al. 1990; O’Neill and
Raines 1991; Randolph et al. 1991!. Many test results show that
the soil plug can be divided into a wedged plug zone and an
unwedged plug zone. While the wedged plug zone transfers load
to the soil plug, the unwedged plug zone transfers no load but
provides a surcharge pressure on top of the wedged plug zone.
However, it is not easy to apply the one-dimensional analysis to
practical cases, because of the sensitivity of the method to the
lateral earth pressure coefficient, which is not easily estimated
~Brucy et al. 1991; Leong and Randolph 1991!. De Nicola and
Randolph ~1997! addressed this by proposing a profile of the
lateral earth pressure coefficient K along the soil plug length.
An alternative design method can be based on the incremental
filling ratio ~IFR!. The degree of soil plugging is adequately quantified
using the IFR ~Paikowsky et al. 1989; Paik and Lee 1993!
defined as
IFR5
DL
DD
3100~%! (1)
where DL5increment of soil plug length ~L! corresponding to a
small increment DD of pile penetration depth D ~see Fig. 1!. The
fully plugged and fully coring modes correspond to IFR50 and
100%, respectively. A value of IFR between 0 and 100% means
that the pile is partially plugged. A series of model pile tests,
using a calibration chamber, were conducted on model openended
piles instrumented with strain gauges in order to investigate
the effect of IFR on the two components of bearing capacity: base
load capacity and shaft load capacity. Based on the calibration
chamber test results, empirical relationships between the IFR and
the components of pile load capacity are proposed. In order to
verify the accuracy of predictions made using the two empirical
relationships, a full-scale static pile load test was conducted on a
fully instrumented open-ended pile driven into dense sand. The
predicted pile load capacities are compared with the capacities
measured in the pile load test.
1Associate Professor, Dept. of Civil Engineering, Kwandong Univ.,
Kangwon-do 215-800, South Korea ~corresponding author!. E-mail:
pkh@kwandong.ac.kr
2Associate Professor, School of Civil Engineering, Purdue Univ., West
Lafayette, IN 47907-1284. E-mail: rodrigo@ecn.purdue.edu
Note. Discussion open until June 1, 2003. Separate discussions must
be submitted for individual papers. To extend the closing date by one
month, a written request must be filed with the ASCE Managing Editor.
The manuscript for this paper was submitted for review and possible
publication on July 23, 2001; approved on May 23, 2002. This paper is
part of the Journal of Geotechnical and Geoenvironmental Engineering,
Vol. 129, No. 1, January 1, 2003. ©ASCE, ISSN 1090-0241/2003/1-
46–57/$18.00.
46 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003
Soil Sample Preparation
Soil Properties
Han river sand, a subangular quartz sand, with D1050.17mm and
D5050.34 mm, was used for all the calibration chamber model
pile tests. The test sand is classified as poorly graded ~SP! in the
Unified Soil Classification System, so the maximum dry density
of the sand is near the low end of the typical range for sands. The
maximum and minimum dry unit weights of the sand were 15.89
and 13.04 kN/m3, respectively.
A series of laboratory tests were conducted to characterize the
sand. The results from these tests are summarized in Table 1. The
internal friction angle of the sand and the interface friction angle
between the sand and steel were measured from direct shear tests
under normal stresses of 40–240 kPa. The peak friction angles of
the sand with relative densities of 23, 56, and 90% were 34.8,
38.2, and 43.4°, respectively, and the critical-state friction angle
was 33.7°. The peak interface friction angles between the pile and
the sand were 17.0, 17.5, and 18.4° for DR523, 56, and 90%,
respectively, and the critical-state interface friction angle was
16.7°. This angle is lower than commonly reported values because
the test pile was made of stainless steel pipe with a very
smooth surface.
Calibration Chamber and Sample Preparation
All model pile tests were conducted in soil samples prepared
within a calibration chamber with a diameter of 775 and a height
of 1250 mm. In order to simulate various field stress conditions,
two rubber membranes, which can be controlled independently,
were installed on the bottom and inside the lateral walls of the
calibration chamber. The consolidation pressure applied to the
two rubber membranes was maintained constant by a regulator
panel throughout each pile test.
The soil samples were prepared by the raining method with a
constant fall height. The falling soil particles passed through a
sand diffuser composed of No. 8 and No. 10 sieves in order to
control flow uniformity and fall velocity. The soil samples had
DR523, 56, and 90%. After sample preparation, the samples
were consolidated to the desired stress state during approximately
30 h by compressed air transferred to the rubber membranes.
Measurements made in calibration chambers are subject to
chamber size effects. Many researchers have attempted to estimate
the chamber size needed for boundary effects on pile bearing
capacity or cone resistance to become negligible. Parkin and
Lunne ~1982! suggested 50 times the cone diameter as the minimum
chamber diameter for chamber size effect on cone penetration
resistance to become acceptably small. Salgado et al. ~1998!,
based on cavity expansion analyses, found that 100 times the cone
diameter was the minimum chamber diameter to reduce chamber
size effects on cone resistance to negligible levels. Diameters of
the chamber and test pile used in this study are 775 and 42.7 mm,
respectively. The lateral and bottom boundaries are located at a
distance equal to 18.2 pile radii from the pile axis and 23.0 pile
radii below the maximum depth reached by the pile base, respectively.
Considering the results of the research on chamber size
effects mentioned above, the size of the chamber used in this
study is not sufficiently large for chamber size effects on pile
bearing capacity to be neglected. The flexible boundary causes
lower radial stresses than those that would exist in the field. Accordingly,
the chamber tests done as part of this study produce
lower pile load capacities than those that would be observed in
the field. A correction for chamber size effects is then necessary.
It is discussed in a later section.
Model Piles and Test Program
Model Pile
An open-ended pile is generally driven into sands in a partially
plugged mode, and its bearing capacity is composed of plug load
capacity, annulus load capacity, and shaft load capacity. In order
to separate pile load capacity into its components, an instrumented
double-walled pile was used in the testing. A schematic
diagram of the pile is shown in Fig. 2. The model pile was made
of two very smooth stainless steel pipes with different diameters.
It had an outside diameter of 42.7 mm, inside diameter of 36.5
mm, and length of 908 mm.
The wall thickness of the test piles used in this study is larger
than those of piles typically used in practice. Szechy ~1959!
showed that the degree of soil plugging and bearing capacity of
two piles with different wall thicknesses do not differ in a significant
way ~with bearing capacity increasing only slightly with increasing
wall thickness!; only driving resistance depends significantly
upon the wall thickness. So the load capacity of the test
piles reported in this paper are probably larger, but only slightly
so, than what would be observed in the field.
Eighteen strain gauges were attached to the outside surface of
the inner pipe at nine different levels in order to measure the base
load capacity ~summation of plug and annulus load capacities!
Fig. 1. Definition of incremental filling ratio and plug length ratio
Table 1. Soil Properties of Test Sand
Property Value
Coefficient of uniformity Cu 2.21
Coefficient of gradation Cc 1.23
Maximum void ratio emax 0.986
Minimum void ratio emin 0.629
Minimum dry density gd,min 13.04 kN/m3
Maximum dry density gd,max 15.89 kN/m3
Specific gravity Gs 2.64
Peak friction angle fpeak 34.8–43.4°
Critical-state friction angle fc 33.7°
Peak interface friction angle d 17.0–18.4°
Critical-state interface friction angle dc 16.7°
JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003 / 47
from the load transfer curve along the inner pipe. Two strain
gauges were also attached to the outside surface of the outer pipe
in order to measure shaft load capacity. A gap of 4 mm between
the outer pipe and the pile toe, which was sealed with silicone,
prevented the base load from being transferred to the outer pipe.
The outer pipe, therefore, experienced only the shaft load.
Many researchers have relied on linear extrapolation to separate
the base load capacity into plug and annulus capacities ~Paik
and Lee 1993; Choi and O’Neill 1997; Lehane and Gavin 2001!.
Linear extrapolation would apply strictly only if the inside unit
friction between the pile and soil plug were constant between the
second lowest strain gauge and the pile base, as shown in Fig. 3.
In reality, the inside unit friction between the soil plug and the test
pile increases dramatically near the pile base. Use of linear extrapolation,
therefore, leads to an overestimation of annular resistance.
This overestimation increases as the distance between the
lowest strain gauge and the pile base increases. In part to avoid
this uncertainty, in this paper we use the base load capacity to
analyze the test results instead of the plug and annulus load capacities
separately. The base load capacity of the test pile was
obtained from the upper strain gauges located on the inner pipe,
for which the measured vertical loads reached a limit value ~Fig.
3!.
Test Program
Seven model pile tests were performed in dry soil samples with
three different relative densities and five different stress states.
Each test is identified by a symbol with three letters ~H high, M
medium, L low!, signifying the levels of the relative density, vertical
and horizontal stresses of the sample, respectively. A summary
of all model pile tests is presented in Table 2. Five model
pile tests were conducted in dense samples with DR590% and
five different stress states. Two model pile tests were conducted in
loose and medium samples consolidated to a vertical stress of
98.1 kPa and horizontal stress of 39.2 kPa. The model piles were
driven by a 39.2 N hammer falling from a height of 500 mm.
During pile driving, the soil plug length and the pile penetration
depth were measured at about 40 mm intervals, corresponding to
94% of the pile diameter, in order to calculate the IFR. The
change in soil plug length during pile driving was measured using
a ruler introduced through an opening at the top plate of the pile
~see Fig. 2!. In order to measure the soil plug length, driving
operations were suspended for no more than a minute each time.
Static pile load tests were performed when the pile base was
located at depths of 250, 420, 590, and 760 mm. The pile load
tests were continued until the pile settlement reached about 19
mm ~44% of the pile diameter!, at which point all the test piles
had reached a plunging limit state ~Fig. 4!. The ultimate load of
each test pile is defined as the load at a settlement of 4.27 mm,
corresponding to 10% of the pile diameter. The total load applied
to the pile head was measured by a load cell, and settlement of the
pile head was measured by two dial gauges. Details of the model
pile, sample preparation, and test program have been described by
Paik and Lee ~1993!.
Model Pile Test Results
Pile Drivability
Fig. 5~a! shows pile penetration depth versus hammer blow count
for all the test piles. As shown in the figure, the hammer blow
count per unit length of penetration increases as pile penetration
depth increases, since the penetration resistances acting on the
base and shaft of the piles during driving generally increase with
Fig. 2. Schematic of model pile
Fig. 3. Determination of plug and annulus loads
Table 2. Summary of Model Pile Test Program
Test
indicator
Initial
relative
density
~%!
Initial
vertical
stress
~kPa!
Initial
horizontal
stress
~kPa!
Initial
earth
pressure
coefficient
HLL 90 39.2 39.2 1.0
HML 90 68.6 39.2 0.6
HHL 90 98.1 39.2 0.4
HHM 90 98.1 68.6 0.7
HHH 90 98.1 98.1 1.0
MHL 56 98.1 39.2 0.4
LHL 23 98.1 39.2 0.4
48 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003
penetration depth. The vertical stress applied to the soil sample
had little effect on the cumulative blow count. However, the blow
count necessary to drive the pile to a certain depth decreased
rapidly with decreasing horizontal stress. It is also seen in Fig.
5~a! that the blow count necessary for driving the pile to some
required depth increases with increasing relative density.
Soil Plugging
The degree of soil plugging in an open-ended pile affects pile
behavior significantly. The IFR is a good indicator of the degree
of soil plugging. During the model pile tests, the IFR was measured
at increments of 40 mm of penetration. The change of the
soil plug length with pile penetration depth is plotted in Fig. 5~b!.
It is seen in the figure that the soil plug length developed during
pile driving increases as the horizontal stress of the soil sample
increases for the same relative density, and as the relative density
increases for the same stress. It can also be seen that every test
pile, during static load testing, advances in fully plugged mode,
irrespective of the initial soil condition and the degree of soil
plugging during pile driving. The static load tests appear as short
vertical lines in Fig. 5~b!, meaning that penetration depth increases
while soil plug length remains unchanged.
Fig. 6 shows changes of IFR with soil state ~relative density,
vertical stress, and horizontal stress!. Fig. 6~a! shows IFR versus
DR for tests with sv 8 598.1 kPa and K050.4. Fig. 6~b! shows IFR
versus sv 8 for tests with DR590% and sh8539.2 kPa. Fig. 6~c!
shows IFR versus sh8 for DR590% and sv 8 598.1 kPa. It is observed
that the IFR increases markedly with increasing relative
density and with increasing horizontal stress. These changes in
IFR reflect the decreasing amount of compaction of the soil plug
during pile driving as the relative density and stress level in the
soil increase. However, the IFR is relatively insensitive to
changes in the vertical stress applied to the soil sample. This
means that the IFR of an open-ended pile would be higher for an
overconsolidated sand than for a normally consolidated sand at
the same DR and sv 8 .
Fig. 7 shows IFR versus plug length ratio ~PLR! for the chamber
test results and for the test results of Szechy ~1959!; Klos and
Tejchman ~1977!; Brucy et al. ~1991!; and Paik et al. ~2002!. The
PLR is defined as the ratio of soil plug length to pile penetration
as ~see Fig. 1!
PLR5
L
D
(2)
In Fig. 7~b!, the data from Paik et al. ~2002! were obtained from
a full-scale pile with diameter of 356 mm driven into submerged
dense sands. The remaining data were obtained from model pile
tests using piles with various diameters driven into dry sand ranging
from loose to medium dense ~the diameter of each test pile is
indicated in the figure!. Fig. 7~a! shows that IFR, measured at the
final penetration depth, increases linearly with increasing PLR.
Fig. 4. Load–settlement curves from model pile load tests
Fig. 5. Driving test results: ~a! hammer blow count, and ~b! soil plug
length
JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003 / 49
The relationship between PLR and IFR for the calibration chamber
tests can be expressed as follows:
IFR~%!5109•PLR222 (3)
This equation slightly underestimates the IFR for PLR values
greater than 0.8 and slightly overestimates it for PLR values
lower than 0.7, as shown in Fig. 7~b!. In general, it is known that
the IFR is a better indicator of the degree of soil plugging than the
PLR ~Paikowsky et al. 1989; Paik and Lee 1993!. In the field,
however, it is easier to measure the PLR than the IFR. Eq. ~3! can
be used to estimate the IFR from the PLR, when only the PLR is
measured in the field.
Base and Shaft Load Capacities
The ultimate unit base resistance qb,c measured in the calibration
chamber is plotted versus relative density ~for sv 8 598.1 kPa and
K050.4), versus vertical stress ~for DR590% and sh8
539.2 kPa) and versus horizontal stress ~for DR590% and
Fig. 6. Incremental filling ratio versus ~a! relative density for sv8
598.1 kPa and K050.4; ~b! vertical stress for DR590% and sh8
539.2 kPa; and ~c! horizontal stress for DR590% and sv8
598.1 kPa
Fig. 7. Plug length ratio versus incremental filling ratio ~a! for chamber
test results, and ~b! for other test results
50 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003
sv 8 598.1 kPa) in Fig. 8. It is apparent that the ultimate unit base
resistance increases significantly with increasing relative density
and increasing horizontal stress, but is relatively insensitive to
vertical stress. This is consistent with experimental results of
Baldi et al. ~1981!; Houlsby and Hitchman ~1988!; and Vipulanandan
et al. ~1989!, which showed that cone resistance was a
function of lateral effective stress.
Fig. 9 shows the ultimate unit base resistance, normalized with
respect to the horizontal stress, versus IFR for different relative
densities, and the ultimate unit base resistance versus IFR for
dense sand. It can be seen in Figs. 9~a and b! that the ultimate unit
base resistance of open-ended piles increases with decreasing IFR
and that the rate of change of ultimate unit base resistance with
IFR increases with DR . It is also seen that the ultimate unit base
resistance increases with relative density at constant IFR.
Fig. 10 shows the ultimate unit shaft resistance f so,c measured
in the calibration chamber versus relative density, vertical stress,
and horizontal stress. Similarly to what is observed for ultimate
unit base resistance, the ultimate unit shaft resistance of an open-
Fig. 8. Unit base resistance versus ~a! relative density for sv8
598.1 kPa and K050.4; ~b! vertical stress for DR590% and sh8
539.2 kPa; and ~c! horizontal stress for DR590% and sv8
598.1 kPa
Fig. 9. Normalized unit base resistance versus incremental filling
ratio ~a! for sv8598.1 kPa and K050.4, and ~b! for DR590%
JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003 / 51
ended pile increases with both relative density and horizontal
stress, but is insensitive to the vertical stress. It is clear from Fig.
10~c! that the ultimate unit shaft resistance is linearly related to
the horizontal stress. The ultimate base and shaft load capacities
of the test piles are listed in Table 3.
Correction of Chamber Test Results for Chamber
Size Effects
Adjustment of Pile Diameter
Pile load capacities measured in a calibration chamber are different
from those measured in the field due to chamber size effects.
In order to use the calibration chamber test results for computation
of pile load capacity in the field, corrections for chamber size
effects were performed for every chamber test. In the estimation
of chamber size effects, the ratio of the chamber to the equivalent
diameter of the model pile used in the tests is required. The
equivalent diameter of an open-ended pile is the diameter that a
pile with solid cross-section would have to have in order to displace
the same soil volume during installation as the open-ended
pile. The equivalent diameter of open-ended piles varies with the
degree of soil plugging, because the soil displacement around the
pile due to pile driving increases with decreasing IFR ~Randolph
et al. 1979!. For example, if a pile is driven in fully coring mode,
the equivalent pile diameter is calculated from an equivalent area
equal to the annular area. If a pile is fully plugged during driving,
the gross cross-sectional area of the pile should be used. For piles
driven in a partially plugged mode, the equivalent pile diameter
can be determined through interpolation with respect to the IFR.
This is summarized, mathematically, as follows:
If IFR>100%, dp5A~d0 2 2di
2! (4a)
If IFR50%, dp5d0 (4b)
If 0%<IFR<100%,
dp5d02@d02A~d0 2 2di
2!#• IFR~%!
100
(4c)
in which dp5equivalent pile diameter; d05outer pile diameter;
and di5inner pile diameter.
Considering the pile driving mechanism of an open-ended pile,
the base load capacity of the pile depends on the IFR measured at
the final penetration depth. The shaft load capacity should be
related to the average value of the IFR measured during driving,
which is equal to the PLR at the pile penetration depth. In this
study, therefore, the equivalent pile diameters for each test were
computed for the base and shaft load capacities using Eqs. ~4!.
The IFR and PLR at the pile penetration depth are used for correction
of the base and the shaft load capacity, respectively.
Field Pile Load Capacity
Salgado et al. ~1998! conducted a theoretical analysis of chamber
size effect for cone penetration resistance in sand and quantified
the size effect as a function of soil state (DR and sh8) and chamber
to pile diameter ratio. According to their results, which also apply
to displacement piles, the ratio qc,cc /qc,ff of chamber to field cone
resistances for normally consolidated sands with DR523, 56,
Fig. 10. Unit shaft resistance versus ~a! relative density for sv8
598.1 kPa and K050.4; ~b! vertical stress for DR590% and sh8
539.2 kPa; and ~c! horizontal stress for DR590% and sv8
598.1 kPa
52 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003
90%, and diameter ratio in the 10–45 range can be approximated
as
qc,cc
qc,ff
5F1.08310223SDc
dp D10.31G for DR523% (5a)
qc,cc
qc,ff
5F1.02310223SDc
dp D10.24G for DR556% (5b)
qc,cc
qc,ff
5F7.79310233SDc
dp D10.27G for DR590% (5c)
In these equations, qc,cc5cone resistance measured in a calibration
chamber; qc,ff5field cone resistance; and Dc /dp5ratio of
chamber to equivalent pile diameter. The chamber size effect factors
for the base and shaft load capacities estimated by Eq. ~5! are
listed in Table 3. The field pile load capacity can then be obtained
by dividing the chamber pile load capacity by the corresponding
size effect factors.
New Design Equations for Load Capacity of
Open-Ended Piles
Base Load Capacity
Fig. 11 shows the ultimate unit field base resistance qb, f , normalized
with respect to the horizontal effective stress sh8 at the pile
base, versus IFR for piles driven into sands with various relative
densities. The figure shows that the normalized unit field base
resistance increases linearly with decreasing IFR. The relationship
between qb, f /sh8 and IFR can be expressed as
qb, f
ash8
5326– 295• IFR~%!
100
(6)
with a coefficient of determination r250.82. In this equation, the
a values, a function of the relative density, were obtained from
the calibration chamber tests as equal to 1.0 for dense sands, 0.6
for medium sands, and 0.25 for loose sands. In the case of fully
plugged piles ~IFR50!, which behave as closed-ended piles, unit
field base resistance is expressed as qb, f5326sh85130sv 8 for normally
consolidated dense sands with K050.4. This is consistent
with the unit base resistance of a closed-ended pile in dense sand
proposed by the Canadian foundation engineering manual ~CGS
1992!. In order to predict base load capacity of open-ended piles
using Eq. ~6!, it is necessary to know either the IFR or the soil
plug length at the final penetration depth @from which the IFR can
be estimated through Eq. ~3!#. A technique for measuring IFR
during pile installation will be described in a later section. Note
that Eq. ~6! should be used only for piles driven into sands, not
for piles installed using vibratory hammers.
Table 3. Summary of Model Pile Test Results and Size Effect Factors
Test
indicator
Test
depth
~mm!
Soil plug
length
~mm!
IFR
~%! PLR
Base load
capacity
~kN!
Shaft load
capacity
~kN!
Size Effect Factor
Base
load
Shaft
load
HLL 256 250 78.4 0.98 2.60 0.63 0.50 0.54
420 366 71.4 0.87 2.91 0.90 0.49 0.51
592 478 67.0 0.81 3.59 1.57 0.48 0.50
760 571 54.4 0.75 3.91 2.13 0.46 0.49
HML 250 251 88.0 1.00 2.50 0.50 0.52 0.54
420 373 76.3 0.89 2.85 0.81 0.50 0.52
589 483 69.0 0.82 3.67 1.39 0.48 0.50
760 583 57.4 0.77 4.30 2.23 0.47 0.49
HHL 250 251 84.2 1.00 2.42 0.53 0.51 0.54
420 369 73.0 0.88 2.81 0.90 0.49 0.51
590 477 69.5 0.81 3.54 1.65 0.48 0.50
758 575 60.0 0.76 4.29 2.05 0.47 0.49
HHM 252 255 87.9 1.01 3.09 0.70 0.52 0.55
420 381 78.6 0.90 3.57 1.45 0.50 0.52
591 501 73.9 0.85 4.66 2.49 0.49 0.51
761 614 72.1 0.81 4.91 3.60 0.49 0.50
HHH 251 266 92.6 1.06 4.53 1.36 0.53 0.56
420 398 82.9 0.95 4.66 2.46 0.51 0.53
590 521 79.8 0.88 5.40 3.93 0.50 0.52
760 644 77.8 0.85 5.78 5.70 0.50 0.51
MHL 247 236 75.9 0.96 1.82 0.28 0.53 0.58
419 347 67.4 0.83 2.17 0.49 0.51 0.55
589 445 60.5 0.76 2.41 0.65 0.50 0.53
757 532 53.9 0.70 2.82 1.00 0.49 0.52
LHL 247 224 71.1 0.91 1.01 0.18 0.61 0.66
419 319 56.5 0.76 1.23 0.36 0.58 0.62
581 401 52.4 0.69 1.46 0.59 0.57 0.60
756 472 42.6 0.62 1.56 0.66 0.56 0.59
JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003 / 53
Shaft Load Capacity
The average ultimate field unit shaft resistance f so, f for the model
piles, normalized with respect to K0sv 8 tan dc , is plotted versus
PLR in Fig. 12 for various relative densities. It can be seen in the
figure that the normalized ultimate field unit shaft resistance increases
with decreasing PLR. The field unit shaft resistance of
piles driven into dense sand can be expressed as follows:
f so, f
~K0sv 8 tan dc!b
57.224.8•PLR (7)
in which f so, f5average ultimate unit shaft resistance in the field;
K05lateral earth pressure coefficient before pile driving;
sv 8 5average vertical effective stress over the whole penetration
depth; dc5critical-state interface friction angle between the pile
and the soil; and b5function of the relative density. The b values
were obtained from the calibration chamber tests as equal to 1.0
for dense sands, 0.4 for medium sands, and 0.22 for loose sands.
In the case of closed-ended piles in normally consolidated dense
sands with K050.4, the normalized unit shaft resistance equals
7.2. This equation may be interpreted as implying that the lateral
stress on the closed-ended pile driven in dense sands is 7.2 times
higher than that before pile driving. This is consistent with the
lateral earth pressure coefficient of K52 – 3, which the Canadian
Foundation Engineering Manual ~CGS 1992! suggested for steel
piles with d520° driven into a normally consolidated dense sand.
Application of New Empirical Relations
Field Pile Load Test
A full-scale, field pile load test was performed on an instrumented
open-ended pile at Lagrange County in northern Indiana. The soil
at the site is gravelly sand with maximum and minimum dry unit
weights of 18.64 and 15.61 kN/m3, respectively. A 2.0 m thick fill
layer was removed before pile driving. The groundwater table is
at a depth of 3 m below the soil surface. Standard penetration test
and cone penetration test results indicate that the first 3 m of the
gravelly sand deposit are in a loose state (DR'30%), but the rest
of the deposit is in a dense to very dense state (DR'80%), as
shown in Fig. 13. Note that the fill originally present at the site
was removed before the piles were installed and tested, and Fig.
13 accordingly does not include data for the fill. The resulting
overconsolidation ratio ~OCR! is also shown in Fig. 13 as a function
of depth.
The test pile was an instrumented double-walled open-ended
pile, constituted of two pipes with different diameters, as shown
in Fig. 14. The open-ended pile had an outside diameter of 356
mm and wall thickness of 32 mm. In order to measure the base
and shaft load capacities directly, 20 strain gauges were attached
to the outer surface of the inner pipe and 18 to the outer surface of
the outer pipe. The open-ended pile was driven to a depth of 7.04
m using a single acting diesel hammer with a ram weight of 18.2
kN and a maximum hammer stroke of 3.12 m. The soil plug
length during pile driving was measured continuously using two
different weights, which were connected to each other by a steel
wire ~Fig. 15!. The heavier weight rested on top of the soil plug,
and the lighter weight hanged outside the pile. A scale marked on
the outside of the pile allowed measurement of the plug length. At
the final penetration depth, the IFR for the pile was 77.5%, indicating
a partially plugged condition, and the PLR was 0.82.
The load applied to the pile during the static load test was
measured using a 2 MN load cell, and the settlement of the pile
head was measured with two dial gauges. The residual loads after
pile driving and the loads induced at the base and shaft of the test
pile during the load test were independently measured by rezeroing
the values of all strain gauges attached to the test pile both
before pile driving and at the start of the static load test. The load
was applied to the pile head in increments of 147 kN, which were
decreased to 49–98 kN as the pile approached the limit load. The
load after each increment was maintained until the pile settlement
stabilized at less than 0.5 mm/h. The settlements at the pile head
were measured at 5, 15, 35, 55, 75, 95, and 120 min for each load
step. When the settlement did not stabilize within 120 min, the
settlement was measured only after stabilization ensued. Likewise,
strain values for the strain gauges attached to the inner and
outer pipes were measured after the settlement of the pile head
stabilized.
Static Load Test Results
Fig. 16 shows the load–settlement curves for the base and shaft
load capacities of the full-scale open-ended pile. As shown in the
figure, the shaft load capacity reached its limit value before the
Fig. 11. Normalized field unit base resistance versus incremental
filling ratio
Fig. 12. Normalized field unit shaft resistance versus incremental
filling ratio
54 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003
final load step. The ultimate total and base load capacities were
also determined as the loads at a settlement of 35.6 mm, corresponding
to 10% of the pile diameter. The ultimate base and shaft
load capacities not accounting for residual loads were 715 and
310 kN, respectively. The ultimate base and shaft load capacities
accounting for residual loads were 886 and 139 kN, respectively.
In practice, it is difficult to account for residual loads. Residual
loads are induced in every driven pile, but their magnitude depends
on several factors. The use of the unit base and shaft resistance
values that have been corrected for residual loads for designing
a different pile installed in a different sand site would
require estimation of the residual loads for that pile. This is very
difficult to do in practice. Accordingly, we base our suggested
design values of shaft and base resistances on the values measured
without any correction for residual loads, as is customary.
Comparison of Computed and Measured Capacities
The bearing capacity of the test pile was predicted using the empirical
relationships suggested in this study. Since the soil deposit
was overconsolidated by removal of the fill layer, the lateral earth
pressure coefficient K0 was taken as ~Mayne and Kulhawy 1982!
K05~12sin f!OCRsin f (8)
Saturated unit weights of the sand are gsat520.1 kN/m3 for the
loose sand and 21.2 kN/m3 for the dense sand, respectively. The
Fig. 13. Cone penetration test and standard penetration test results and overconsolidation ratio profile at test site
Fig. 14. Schematic of full-scale test pile Fig. 15. Measurement of soil plug length during pile driving
JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / JANUARY 2003 / 55
mean particle size is 0.4 mm. The critical state friction angle for
the sand obtained from triaxial compression tests is fc533.3°;
the interface friction angle between the pile and sand is taken as
dc52fc/3522.2°, which is adequate for typical pipe piles. At
the depth of the pile base, OCR51.41, and K0 results equal to
0.55. Using Eq. ~6!, the ultimate base load capacity Qbase can be
obtained as
qb, f
ash8
5326– 295• IFR~%!
100 5326– 295• 77.5
100597.4
Qbase5qb, fAb597.4•ash 8 Sp•d0 2
4 D
597.4~1.0!~0.553101.2!~0.0995!5539.4 kN
The ultimate shaft load capacity can be computed using Eq. ~7!.
The b values used in the calculations are 0.3 for the first 3 m in
loose sand and 1.0 for depth greater than 3 m in dense sands. The
variation of K0 with OCR along the whole depth of the pile was
considered in the calculations, which are summarized next
f so, f
~K0sv 8 tan dc!b
57.224.8•PLR57.224.8~0.82!53.26
Qshaft5f so, f•Aso53.26K0sv 8 tan dcb~pd0D!
53.26S~biKoisv8iDi!pd0 tan dc
53.26~0.3363.411.03191.3!p~0.356!tan 22.2°
5312.9 kN
in which D5penetration depth of the pile. Thus, the ultimate total
load capacity can be calculated as
Qtotal5Qbase1Qshaft5539.41312.95852.3 kN
The base and shaft load capacities predicted using Eqs. ~6! and
~7! were 75.4 and 100.9% of the ultimate values measured in the
pile load test, respectively. The predicted Qtotal5852.3 kN is a
reasonably close, conservative estimate of the measured value, as
shown in Fig. 17.
Summary and Conclusions
The bearing capacity of open-ended piles is affected by the degree
of soil plugging, which can be quantified through the IFR. Most
design criteria for open-ended piles do not consider the variation
of pile load capacity with IFR, and a standard technique for measuring
IFR during pile installation has not yet been proposed. In
this study, model pile tests were conducted using a calibration
chamber to investigate the effect of IFR on the pile load capacity,
and new empirical relations between the two components of pile
load capacity ~base and shaft load capacities! and IFR were proposed
based on the results of model pile tests.
The results of model pile tests show that the IFR decreases
with decreasing relative density and horizontal stress, but is independent
of the vertical stress. It is also seen that the IFR increases
linearly with the PLR, which is defined as the ratio of the soil
plug length to pile penetration depth, and can be estimated from
the PLR. The unit base resistance shows a tendency to increase
with decreasing IFR, and it does so at a rate that increases with
relative density. The unit shaft resistance, normalized with respect
to horizontal stress, increases with decreasing IFR and with increasing
relative density.
A full-scale pile load test was also conducted on a fully instrumented
open-ended pile driven into gravelly sand. The IFR for
the pile was continuously measured during pile driving. In order
to check the accuracy of predictions made with the proposed
equations, the equations were applied to the pile load test. Based
on the comparisons with the pile load test results, the proposed
equations appear to produce satisfactory predictions.
Acknowledgments
The research presented in this paper was performed in a period of
1 year spent by the first writer as a postdoctoral fellow at Purdue
University. The first writer is grateful for support received from
the Korea Science and Engineering Foundation. The field pile
load test done as part of this research was supported by INDOT
and FHWA through the Joint Transportation Research Program.
The assistance of Dr. Junhwan Lee and Bumjoo Kim with some
aspects of this research is appreciated.
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