Axial Capacity of Piles in Sand | Foundation Engineering - Civil Engineering (CE) PDF Download

 Page 1


 
 
 
 
 
 
 
 
 
AXIAL CAPACITY OF PIPE PILES IN SAND 
 
 
ABSTRACT 
 
Axial capacity of piles in sand depend on a variety of factors relating to soil 
properties, type of pile, the method of installation and the nature of loading.  This 
paper examines physical phenomena that occur during pile installation and 
influence pile capacity.  These physical phenomena include grain crushing, pile 
shaking, stress-redistribution and plugging.  To better understand the method of 
capacity prediction, each parameter and the associated uncertainty is revisited.  It is 
evident that these factors are inter-related and sometimes compensating.  Attention 
is drawn to the influence that pile installation procedures can have on pile capacities 
and the need for field experience with various pile installation procedures for 
designers is highlighted.  In summary, while the various available methods of pile 
capacity prediction are deceptively simple to use, the associated uncertainty of each 
method cannot be ignored.   
 
INTRODUCTION 
 
While in the past, large diameter steel pipe piles were used extensively for offshore 
oil platforms, more recently, with the ready availability of heavy hammers, their 
usage has gained popularity for the construction of new and the retrofit of existing 
bridges over relatively deep waters.  In the 1990’s, the American Petroleum 
Institute (API) singled out the prediction of axial capacity of piles in sand as the 
most uncertain aspect in the design of fixed steel pile jacket platforms.  The 
commonly used method for analyses of axial load capacity of pipe piles in sand 
(API, 1993) has undergone continual refinements in past decades, however, 
statistical studies of pile load test data have shown that the margin of error between 
the calculated and measured capacities is still significant, particularly for open-
ended pipe piles (Toolan et al., 1990).  The function of this paper is to re-examine 
the commonly used method of analysis of such piles and to enumerate deficiencies 
and limitations inherent to this method.  It includes a discussion of the soil 
parameters, their suitability in the analyses, and the effects of various phenomena 
occurring during pile driving on load capacity. 
 
 
 
Page 2


 
 
 
 
 
 
 
 
 
AXIAL CAPACITY OF PIPE PILES IN SAND 
 
 
ABSTRACT 
 
Axial capacity of piles in sand depend on a variety of factors relating to soil 
properties, type of pile, the method of installation and the nature of loading.  This 
paper examines physical phenomena that occur during pile installation and 
influence pile capacity.  These physical phenomena include grain crushing, pile 
shaking, stress-redistribution and plugging.  To better understand the method of 
capacity prediction, each parameter and the associated uncertainty is revisited.  It is 
evident that these factors are inter-related and sometimes compensating.  Attention 
is drawn to the influence that pile installation procedures can have on pile capacities 
and the need for field experience with various pile installation procedures for 
designers is highlighted.  In summary, while the various available methods of pile 
capacity prediction are deceptively simple to use, the associated uncertainty of each 
method cannot be ignored.   
 
INTRODUCTION 
 
While in the past, large diameter steel pipe piles were used extensively for offshore 
oil platforms, more recently, with the ready availability of heavy hammers, their 
usage has gained popularity for the construction of new and the retrofit of existing 
bridges over relatively deep waters.  In the 1990’s, the American Petroleum 
Institute (API) singled out the prediction of axial capacity of piles in sand as the 
most uncertain aspect in the design of fixed steel pile jacket platforms.  The 
commonly used method for analyses of axial load capacity of pipe piles in sand 
(API, 1993) has undergone continual refinements in past decades, however, 
statistical studies of pile load test data have shown that the margin of error between 
the calculated and measured capacities is still significant, particularly for open-
ended pipe piles (Toolan et al., 1990).  The function of this paper is to re-examine 
the commonly used method of analysis of such piles and to enumerate deficiencies 
and limitations inherent to this method.  It includes a discussion of the soil 
parameters, their suitability in the analyses, and the effects of various phenomena 
occurring during pile driving on load capacity. 
 
 
 
 
ANALYTICAL METHOD 
 
The ultimate axial capacity of a pile in compression is illustrated in Figure 1 and 
calculated using Equation (1): 
 
Q
uc
 = Q
s
 + Q
p
 – W
p
  (1) 
where, Q
uc
 is the ultimate axial capacity in compression; Q
s
 is the side shear 
capacity; Q
p
 is the end bearing capacity; and W
p
 is the weight of the pile.  Q
uc
 is 
positive in compression; Q
s
 and Q
p
 are positive upwards.  For calculating pile 
capacity in tension, Equation (2) is used: 
 
Q
ut
 = Q
s
 + W
p
 (2) 
where, Q
ut
 is positive in tension and Q
s
 is positive downwards.  The end bearing Q
p
 
is taken as zero in the case of tensile capacity.  The pile weight, W
p
 in both of the 
above equations, should be the net pile weight, i.e., the total weight of the pile 
minus the total weight of the displaced soil and water. 
 
The side-shear capacity Q
s
 is calculated by dividing the soil into layers with the 
load transfer in each layer being calculated separately.  The side shear is calculated 
using Equation (3): 
Q
s
 = S (f
si
.?A
i
) (3) 
where, f
si 
is the local side shear stress between the pile and the surrounding soil in 
layer “i”, and ?A
i 
is the area of the side of the pile in layer i.  The side area is equal 
to the circumference of the pile times the length of the pile in layer “i”.  The local 
side shear stress on the pile-soil interface f
si
, is given by Equation (4): 
 
f
si 
= K s´ tan (d) (4) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 1:  Axial Capacity Calculations 
 
where, K is the coefficient of lateral earth pressure (ratio of horizontal to vertical 
normal effective stress), s´ is the vertical effective overburden pressure at the 
f
si
= K s’tan d
q
p
 = s’N
q
 
Q
uc
Q = Qp + Qs - Wp 
Wp
Page 3


 
 
 
 
 
 
 
 
 
AXIAL CAPACITY OF PIPE PILES IN SAND 
 
 
ABSTRACT 
 
Axial capacity of piles in sand depend on a variety of factors relating to soil 
properties, type of pile, the method of installation and the nature of loading.  This 
paper examines physical phenomena that occur during pile installation and 
influence pile capacity.  These physical phenomena include grain crushing, pile 
shaking, stress-redistribution and plugging.  To better understand the method of 
capacity prediction, each parameter and the associated uncertainty is revisited.  It is 
evident that these factors are inter-related and sometimes compensating.  Attention 
is drawn to the influence that pile installation procedures can have on pile capacities 
and the need for field experience with various pile installation procedures for 
designers is highlighted.  In summary, while the various available methods of pile 
capacity prediction are deceptively simple to use, the associated uncertainty of each 
method cannot be ignored.   
 
INTRODUCTION 
 
While in the past, large diameter steel pipe piles were used extensively for offshore 
oil platforms, more recently, with the ready availability of heavy hammers, their 
usage has gained popularity for the construction of new and the retrofit of existing 
bridges over relatively deep waters.  In the 1990’s, the American Petroleum 
Institute (API) singled out the prediction of axial capacity of piles in sand as the 
most uncertain aspect in the design of fixed steel pile jacket platforms.  The 
commonly used method for analyses of axial load capacity of pipe piles in sand 
(API, 1993) has undergone continual refinements in past decades, however, 
statistical studies of pile load test data have shown that the margin of error between 
the calculated and measured capacities is still significant, particularly for open-
ended pipe piles (Toolan et al., 1990).  The function of this paper is to re-examine 
the commonly used method of analysis of such piles and to enumerate deficiencies 
and limitations inherent to this method.  It includes a discussion of the soil 
parameters, their suitability in the analyses, and the effects of various phenomena 
occurring during pile driving on load capacity. 
 
 
 
 
ANALYTICAL METHOD 
 
The ultimate axial capacity of a pile in compression is illustrated in Figure 1 and 
calculated using Equation (1): 
 
Q
uc
 = Q
s
 + Q
p
 – W
p
  (1) 
where, Q
uc
 is the ultimate axial capacity in compression; Q
s
 is the side shear 
capacity; Q
p
 is the end bearing capacity; and W
p
 is the weight of the pile.  Q
uc
 is 
positive in compression; Q
s
 and Q
p
 are positive upwards.  For calculating pile 
capacity in tension, Equation (2) is used: 
 
Q
ut
 = Q
s
 + W
p
 (2) 
where, Q
ut
 is positive in tension and Q
s
 is positive downwards.  The end bearing Q
p
 
is taken as zero in the case of tensile capacity.  The pile weight, W
p
 in both of the 
above equations, should be the net pile weight, i.e., the total weight of the pile 
minus the total weight of the displaced soil and water. 
 
The side-shear capacity Q
s
 is calculated by dividing the soil into layers with the 
load transfer in each layer being calculated separately.  The side shear is calculated 
using Equation (3): 
Q
s
 = S (f
si
.?A
i
) (3) 
where, f
si 
is the local side shear stress between the pile and the surrounding soil in 
layer “i”, and ?A
i 
is the area of the side of the pile in layer i.  The side area is equal 
to the circumference of the pile times the length of the pile in layer “i”.  The local 
side shear stress on the pile-soil interface f
si
, is given by Equation (4): 
 
f
si 
= K s´ tan (d) (4) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 1:  Axial Capacity Calculations 
 
where, K is the coefficient of lateral earth pressure (ratio of horizontal to vertical 
normal effective stress), s´ is the vertical effective overburden pressure at the 
f
si
= K s’tan d
q
p
 = s’N
q
 
Q
uc
Q = Qp + Qs - Wp 
Wp
 
middle of each layer, and d, is the angle of friction between the surrounding soil and 
the pile wall.  API recommends a value of K of 1.0 for full-displacement piles and 
0.8 for non-displacement piles, for both tension and compression loads.  In addition, 
API recommends a limiting maximum value of unit friction, denoted as f
lim
. 
 
The capacity of the tip in end bearing is calculated from the bearing capacity 
equation: 
 
Q
p
 = q
p
 A
p
 (5) 
where, A
p
 is the cross-sectional area of the pile tip, and q
p
 is defined as the unit net 
end bearing pressure between the pile tip and the soil.  The value of q
p
 is limited to 
q
lim
.  In turn, 
q
p
 = s´N (6) 
where, N
q
 is a bearing capacity factor and s´ is the free-field effective overburden 
pressure at the elevation of the tip.  For API-RP 2A, the values of the various 
parameters (N
q
, d, f
lim
, q
lim
) are correlated with the soil type and relative density and 
are presented in Table 1.  The tip capacity for plugged open-ended pipe piles is 
equal to that of a closed-ended pile of an equal diameter.  In the case where the pile 
is driven unplugged, the tip capacity is simply taken as the capacity in end bearing 
of the annular rim of the open-ended pile.  However, the total capacity is increased 
by the lesser of the total internal shaft friction and the end bearing of the plug.  The 
values of angle of friction and lateral earth pressure coefficient used to calculate the 
internal side-shear capacity are assumed to be the same as those used for external 
side-shear capacity. 
 
Table 1:  Proposed Values for estimation of Axial Capacity of Steel Pipe Piles 
in Sands (API-1993) 
 
 
Density Soil Type 
d   
(deg) 
Limiting Skin 
Friction f
lim
 
(ksf) 
Bearing 
Capacity 
Factor, N
q
 
Limiting End 
Bearing Stress 
q
lim
 (ksf) 
Very loose Sand 15 1.0 8 40 
Loose Sand/Silt  47.9 kPa  1916 kPa 
Medium Silt     
Loose Sand 20 1.4 12 60 
Medium Sand/Silt  67.0 kPa  2873 kPa 
Dense Silt     
Medium Sand 25 1.7 20 100 
Dense Sand/Silt  81.4 kPa  4788 kPa 
Dense Sand 30 2.0 40 200 
Very Dense Sand/Silt  95.8 kPa  9576 kPa 
Dense Gravel 35 2.4 50 250 
Very Dense Sand  114.9 kPa  11970 kPa 
Page 4


 
 
 
 
 
 
 
 
 
AXIAL CAPACITY OF PIPE PILES IN SAND 
 
 
ABSTRACT 
 
Axial capacity of piles in sand depend on a variety of factors relating to soil 
properties, type of pile, the method of installation and the nature of loading.  This 
paper examines physical phenomena that occur during pile installation and 
influence pile capacity.  These physical phenomena include grain crushing, pile 
shaking, stress-redistribution and plugging.  To better understand the method of 
capacity prediction, each parameter and the associated uncertainty is revisited.  It is 
evident that these factors are inter-related and sometimes compensating.  Attention 
is drawn to the influence that pile installation procedures can have on pile capacities 
and the need for field experience with various pile installation procedures for 
designers is highlighted.  In summary, while the various available methods of pile 
capacity prediction are deceptively simple to use, the associated uncertainty of each 
method cannot be ignored.   
 
INTRODUCTION 
 
While in the past, large diameter steel pipe piles were used extensively for offshore 
oil platforms, more recently, with the ready availability of heavy hammers, their 
usage has gained popularity for the construction of new and the retrofit of existing 
bridges over relatively deep waters.  In the 1990’s, the American Petroleum 
Institute (API) singled out the prediction of axial capacity of piles in sand as the 
most uncertain aspect in the design of fixed steel pile jacket platforms.  The 
commonly used method for analyses of axial load capacity of pipe piles in sand 
(API, 1993) has undergone continual refinements in past decades, however, 
statistical studies of pile load test data have shown that the margin of error between 
the calculated and measured capacities is still significant, particularly for open-
ended pipe piles (Toolan et al., 1990).  The function of this paper is to re-examine 
the commonly used method of analysis of such piles and to enumerate deficiencies 
and limitations inherent to this method.  It includes a discussion of the soil 
parameters, their suitability in the analyses, and the effects of various phenomena 
occurring during pile driving on load capacity. 
 
 
 
 
ANALYTICAL METHOD 
 
The ultimate axial capacity of a pile in compression is illustrated in Figure 1 and 
calculated using Equation (1): 
 
Q
uc
 = Q
s
 + Q
p
 – W
p
  (1) 
where, Q
uc
 is the ultimate axial capacity in compression; Q
s
 is the side shear 
capacity; Q
p
 is the end bearing capacity; and W
p
 is the weight of the pile.  Q
uc
 is 
positive in compression; Q
s
 and Q
p
 are positive upwards.  For calculating pile 
capacity in tension, Equation (2) is used: 
 
Q
ut
 = Q
s
 + W
p
 (2) 
where, Q
ut
 is positive in tension and Q
s
 is positive downwards.  The end bearing Q
p
 
is taken as zero in the case of tensile capacity.  The pile weight, W
p
 in both of the 
above equations, should be the net pile weight, i.e., the total weight of the pile 
minus the total weight of the displaced soil and water. 
 
The side-shear capacity Q
s
 is calculated by dividing the soil into layers with the 
load transfer in each layer being calculated separately.  The side shear is calculated 
using Equation (3): 
Q
s
 = S (f
si
.?A
i
) (3) 
where, f
si 
is the local side shear stress between the pile and the surrounding soil in 
layer “i”, and ?A
i 
is the area of the side of the pile in layer i.  The side area is equal 
to the circumference of the pile times the length of the pile in layer “i”.  The local 
side shear stress on the pile-soil interface f
si
, is given by Equation (4): 
 
f
si 
= K s´ tan (d) (4) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 1:  Axial Capacity Calculations 
 
where, K is the coefficient of lateral earth pressure (ratio of horizontal to vertical 
normal effective stress), s´ is the vertical effective overburden pressure at the 
f
si
= K s’tan d
q
p
 = s’N
q
 
Q
uc
Q = Qp + Qs - Wp 
Wp
 
middle of each layer, and d, is the angle of friction between the surrounding soil and 
the pile wall.  API recommends a value of K of 1.0 for full-displacement piles and 
0.8 for non-displacement piles, for both tension and compression loads.  In addition, 
API recommends a limiting maximum value of unit friction, denoted as f
lim
. 
 
The capacity of the tip in end bearing is calculated from the bearing capacity 
equation: 
 
Q
p
 = q
p
 A
p
 (5) 
where, A
p
 is the cross-sectional area of the pile tip, and q
p
 is defined as the unit net 
end bearing pressure between the pile tip and the soil.  The value of q
p
 is limited to 
q
lim
.  In turn, 
q
p
 = s´N (6) 
where, N
q
 is a bearing capacity factor and s´ is the free-field effective overburden 
pressure at the elevation of the tip.  For API-RP 2A, the values of the various 
parameters (N
q
, d, f
lim
, q
lim
) are correlated with the soil type and relative density and 
are presented in Table 1.  The tip capacity for plugged open-ended pipe piles is 
equal to that of a closed-ended pile of an equal diameter.  In the case where the pile 
is driven unplugged, the tip capacity is simply taken as the capacity in end bearing 
of the annular rim of the open-ended pile.  However, the total capacity is increased 
by the lesser of the total internal shaft friction and the end bearing of the plug.  The 
values of angle of friction and lateral earth pressure coefficient used to calculate the 
internal side-shear capacity are assumed to be the same as those used for external 
side-shear capacity. 
 
Table 1:  Proposed Values for estimation of Axial Capacity of Steel Pipe Piles 
in Sands (API-1993) 
 
 
Density Soil Type 
d   
(deg) 
Limiting Skin 
Friction f
lim
 
(ksf) 
Bearing 
Capacity 
Factor, N
q
 
Limiting End 
Bearing Stress 
q
lim
 (ksf) 
Very loose Sand 15 1.0 8 40 
Loose Sand/Silt  47.9 kPa  1916 kPa 
Medium Silt     
Loose Sand 20 1.4 12 60 
Medium Sand/Silt  67.0 kPa  2873 kPa 
Dense Silt     
Medium Sand 25 1.7 20 100 
Dense Sand/Silt  81.4 kPa  4788 kPa 
Dense Sand 30 2.0 40 200 
Very Dense Sand/Silt  95.8 kPa  9576 kPa 
Dense Gravel 35 2.4 50 250 
Very Dense Sand  114.9 kPa  11970 kPa 
 
FIELD PERFORMANCE 
 
Several researchers (Olson and Dennis, 1982, Briaud and Tucker, 1988, and Kraft, 
1991) have compiled data from pile load tests from all over the world.  Iskander 
(1995) has shown that on a plot of measured versus computed capacities, there is 
large scatter, with the computed capacity varying from as low as 13% to as high as 
357% of the measured capacity.  Clearly, the method is unsafe in some cases and 
uneconomical in others.  The consensus of experts is that the method is overly 
conservative by 20%-40% (Lacasse, 1990).  Iskander (1995), Lings (1985) and 
Toolan et al. (1990) have also shown that the method may underestimate the 
capacities of shorter piles while significantly overestimating the capacities of longer 
piles.  Others (Pelletier et al., 1993) have argued that the apparent length effects are 
due to differing installation methods and removal of soil plugs.  Data from various 
available case histories (Kraft, 1990) is presented in Figure 2.  It can be seen that 
based on the 46 load tests, the ratio of the  measured to the calculated capacities 
follows roughly a skewed normal distribution.  Probability plot using a lognormal 
(base 10) distribution for these same data presented in Figure 2b shows a better fit. 
 
 
 
 
Figure 2a:  Comparison of Measured Capacity (Qm) and Predicted Capacity 
(Qc) in Compression.  (b): Lognormal Probability Plot for Qm/Qc 
 
SOIL PARAMETERS 
 
Angle of Friction:  During pile driving, the high stresses that develop near the soil-
pile interface crush the sand grains.  The nature and extent of crushing is unknown.  
Inspection of steel piles pulled out of the ground has shown that sand grains 
sometimes get embedded in the steel surface of the pile (Vesic, 1967a).  Crushing 
of the soil particles, along with soil displacement and densification invariably lead 
to different stress-strain behavior.  It is therefore concluded that the angle of friction 
d differs from the one obtained from soil investigations and laboratory tests.  
Meanwhile, the stresses inside the soil plug and the load transfer between the inner 
pile wall and the soil plug are also not known.  The phenomenon of arching and 
locking-up of stress is known to occur in the soil core (Randolph et al., 1990).  
4.1 3.7 3.3 2.9 2.5 2.1 1.7 1.3 0.9 0.5
20
10
0
Qmeasured /Qcalculated
Frequency
110
 1
 5
10
20
30
40
50
60
70
80
90
95
99
Qm/Qc
Percent
AD* 0.649
Goodness of Fit
Lognormal base 10 Probability Plot for Qm/Qc
ML Estimates - 95% CI
Location
Scale
0.0723460
0.174114
ML Estimates
Page 5


 
 
 
 
 
 
 
 
 
AXIAL CAPACITY OF PIPE PILES IN SAND 
 
 
ABSTRACT 
 
Axial capacity of piles in sand depend on a variety of factors relating to soil 
properties, type of pile, the method of installation and the nature of loading.  This 
paper examines physical phenomena that occur during pile installation and 
influence pile capacity.  These physical phenomena include grain crushing, pile 
shaking, stress-redistribution and plugging.  To better understand the method of 
capacity prediction, each parameter and the associated uncertainty is revisited.  It is 
evident that these factors are inter-related and sometimes compensating.  Attention 
is drawn to the influence that pile installation procedures can have on pile capacities 
and the need for field experience with various pile installation procedures for 
designers is highlighted.  In summary, while the various available methods of pile 
capacity prediction are deceptively simple to use, the associated uncertainty of each 
method cannot be ignored.   
 
INTRODUCTION 
 
While in the past, large diameter steel pipe piles were used extensively for offshore 
oil platforms, more recently, with the ready availability of heavy hammers, their 
usage has gained popularity for the construction of new and the retrofit of existing 
bridges over relatively deep waters.  In the 1990’s, the American Petroleum 
Institute (API) singled out the prediction of axial capacity of piles in sand as the 
most uncertain aspect in the design of fixed steel pile jacket platforms.  The 
commonly used method for analyses of axial load capacity of pipe piles in sand 
(API, 1993) has undergone continual refinements in past decades, however, 
statistical studies of pile load test data have shown that the margin of error between 
the calculated and measured capacities is still significant, particularly for open-
ended pipe piles (Toolan et al., 1990).  The function of this paper is to re-examine 
the commonly used method of analysis of such piles and to enumerate deficiencies 
and limitations inherent to this method.  It includes a discussion of the soil 
parameters, their suitability in the analyses, and the effects of various phenomena 
occurring during pile driving on load capacity. 
 
 
 
 
ANALYTICAL METHOD 
 
The ultimate axial capacity of a pile in compression is illustrated in Figure 1 and 
calculated using Equation (1): 
 
Q
uc
 = Q
s
 + Q
p
 – W
p
  (1) 
where, Q
uc
 is the ultimate axial capacity in compression; Q
s
 is the side shear 
capacity; Q
p
 is the end bearing capacity; and W
p
 is the weight of the pile.  Q
uc
 is 
positive in compression; Q
s
 and Q
p
 are positive upwards.  For calculating pile 
capacity in tension, Equation (2) is used: 
 
Q
ut
 = Q
s
 + W
p
 (2) 
where, Q
ut
 is positive in tension and Q
s
 is positive downwards.  The end bearing Q
p
 
is taken as zero in the case of tensile capacity.  The pile weight, W
p
 in both of the 
above equations, should be the net pile weight, i.e., the total weight of the pile 
minus the total weight of the displaced soil and water. 
 
The side-shear capacity Q
s
 is calculated by dividing the soil into layers with the 
load transfer in each layer being calculated separately.  The side shear is calculated 
using Equation (3): 
Q
s
 = S (f
si
.?A
i
) (3) 
where, f
si 
is the local side shear stress between the pile and the surrounding soil in 
layer “i”, and ?A
i 
is the area of the side of the pile in layer i.  The side area is equal 
to the circumference of the pile times the length of the pile in layer “i”.  The local 
side shear stress on the pile-soil interface f
si
, is given by Equation (4): 
 
f
si 
= K s´ tan (d) (4) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 1:  Axial Capacity Calculations 
 
where, K is the coefficient of lateral earth pressure (ratio of horizontal to vertical 
normal effective stress), s´ is the vertical effective overburden pressure at the 
f
si
= K s’tan d
q
p
 = s’N
q
 
Q
uc
Q = Qp + Qs - Wp 
Wp
 
middle of each layer, and d, is the angle of friction between the surrounding soil and 
the pile wall.  API recommends a value of K of 1.0 for full-displacement piles and 
0.8 for non-displacement piles, for both tension and compression loads.  In addition, 
API recommends a limiting maximum value of unit friction, denoted as f
lim
. 
 
The capacity of the tip in end bearing is calculated from the bearing capacity 
equation: 
 
Q
p
 = q
p
 A
p
 (5) 
where, A
p
 is the cross-sectional area of the pile tip, and q
p
 is defined as the unit net 
end bearing pressure between the pile tip and the soil.  The value of q
p
 is limited to 
q
lim
.  In turn, 
q
p
 = s´N (6) 
where, N
q
 is a bearing capacity factor and s´ is the free-field effective overburden 
pressure at the elevation of the tip.  For API-RP 2A, the values of the various 
parameters (N
q
, d, f
lim
, q
lim
) are correlated with the soil type and relative density and 
are presented in Table 1.  The tip capacity for plugged open-ended pipe piles is 
equal to that of a closed-ended pile of an equal diameter.  In the case where the pile 
is driven unplugged, the tip capacity is simply taken as the capacity in end bearing 
of the annular rim of the open-ended pile.  However, the total capacity is increased 
by the lesser of the total internal shaft friction and the end bearing of the plug.  The 
values of angle of friction and lateral earth pressure coefficient used to calculate the 
internal side-shear capacity are assumed to be the same as those used for external 
side-shear capacity. 
 
Table 1:  Proposed Values for estimation of Axial Capacity of Steel Pipe Piles 
in Sands (API-1993) 
 
 
Density Soil Type 
d   
(deg) 
Limiting Skin 
Friction f
lim
 
(ksf) 
Bearing 
Capacity 
Factor, N
q
 
Limiting End 
Bearing Stress 
q
lim
 (ksf) 
Very loose Sand 15 1.0 8 40 
Loose Sand/Silt  47.9 kPa  1916 kPa 
Medium Silt     
Loose Sand 20 1.4 12 60 
Medium Sand/Silt  67.0 kPa  2873 kPa 
Dense Silt     
Medium Sand 25 1.7 20 100 
Dense Sand/Silt  81.4 kPa  4788 kPa 
Dense Sand 30 2.0 40 200 
Very Dense Sand/Silt  95.8 kPa  9576 kPa 
Dense Gravel 35 2.4 50 250 
Very Dense Sand  114.9 kPa  11970 kPa 
 
FIELD PERFORMANCE 
 
Several researchers (Olson and Dennis, 1982, Briaud and Tucker, 1988, and Kraft, 
1991) have compiled data from pile load tests from all over the world.  Iskander 
(1995) has shown that on a plot of measured versus computed capacities, there is 
large scatter, with the computed capacity varying from as low as 13% to as high as 
357% of the measured capacity.  Clearly, the method is unsafe in some cases and 
uneconomical in others.  The consensus of experts is that the method is overly 
conservative by 20%-40% (Lacasse, 1990).  Iskander (1995), Lings (1985) and 
Toolan et al. (1990) have also shown that the method may underestimate the 
capacities of shorter piles while significantly overestimating the capacities of longer 
piles.  Others (Pelletier et al., 1993) have argued that the apparent length effects are 
due to differing installation methods and removal of soil plugs.  Data from various 
available case histories (Kraft, 1990) is presented in Figure 2.  It can be seen that 
based on the 46 load tests, the ratio of the  measured to the calculated capacities 
follows roughly a skewed normal distribution.  Probability plot using a lognormal 
(base 10) distribution for these same data presented in Figure 2b shows a better fit. 
 
 
 
 
Figure 2a:  Comparison of Measured Capacity (Qm) and Predicted Capacity 
(Qc) in Compression.  (b): Lognormal Probability Plot for Qm/Qc 
 
SOIL PARAMETERS 
 
Angle of Friction:  During pile driving, the high stresses that develop near the soil-
pile interface crush the sand grains.  The nature and extent of crushing is unknown.  
Inspection of steel piles pulled out of the ground has shown that sand grains 
sometimes get embedded in the steel surface of the pile (Vesic, 1967a).  Crushing 
of the soil particles, along with soil displacement and densification invariably lead 
to different stress-strain behavior.  It is therefore concluded that the angle of friction 
d differs from the one obtained from soil investigations and laboratory tests.  
Meanwhile, the stresses inside the soil plug and the load transfer between the inner 
pile wall and the soil plug are also not known.  The phenomenon of arching and 
locking-up of stress is known to occur in the soil core (Randolph et al., 1990).  
4.1 3.7 3.3 2.9 2.5 2.1 1.7 1.3 0.9 0.5
20
10
0
Qmeasured /Qcalculated
Frequency
110
 1
 5
10
20
30
40
50
60
70
80
90
95
99
Qm/Qc
Percent
AD* 0.649
Goodness of Fit
Lognormal base 10 Probability Plot for Qm/Qc
ML Estimates - 95% CI
Location
Scale
0.0723460
0.174114
ML Estimates
 
From tests on sand plugs in the laboratory (Kishida et al., 1977), it is evident that 
the angle of friction between the inner soil and the pile is different from the one on 
the outer side. 
 
Vertical Effective Stress:  The vertical effective overburden pressure is not the 
same as the free-field vertical effective stress because the initial state of stress in the 
field is altered, first by pile driving and then by load transfer at the pile-soil 
interface.  Analyses in which the soil is treated as an elastic homogeneous medium 
show the introduction of a vertical effective stress field in the surrounding soil due 
to load-transfer from the pile (Randolph, 1985).  Development of residual stresses 
in the soil due to pile driving has been discussed at length by Fellenius et al. (1995).  
In summary, the use of free-field stresses in the analysis does not model actual 
conditions. 
 
Bearing Capacity Factor:  The theoretical value of the bearing capacity factor N
q
 
depends on the angle of internal friction, f, and the assumption of the failure pattern 
of the slip surface.  The lack of knowledge of the actual failure surface makes the 
use of theoretical bearing capacity factors seem dubious.  Meyerhof (1976) has 
shown by analysis of load test data that the semi-empirical bearing capacity factor 
N
q
 works well for piles no longer than 15 to 20 pile diameters.   
 
 
Figure 3:  Bearing Capacity Factors Proposed by Various Researchers  
(Vesic, 1967). 
 
There is a wide range of theoretical values of bearing capacity factors suggested by 
various authors (Figure 3).  The values of N
q
 suggested by Berezantsev et al. (1961) 
are used in the API RP-2A.  Even if the failure surface chosen by Berezantsev is 
assumed to be correct, the lack of knowledge of the actual stresses at the failure 
surface and the stress-dependency of the angle of internal friction, f, make it 
difficult to choose the actual value of N
q
. 
 
Soil Compressibility:  The sand immediately below the pile tip compresses to 
mobilize the tip resistance.  The downward displacement causes the sand adjacent