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UNIFIED DESIGN OF PILED FOUNDATIONS WITH EMPHASIS ON SETTLEMENT ANALYSIS
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ABSTRACT
Design of a piled foundation rarely includes a settlement analysis and
is usually limited to determining that the factor of safety on pile capacity is equal to
an at least value. This approach is uneconomical and, sometimes, unsafe. Every
design of a piled foundation should establish the resistance distribution along the pile,
determine the location of the force equilibrium (the neutral plane), estimate the
magnitude of dragload from accumulated negative skin friction at the neutral plane,
evaluate the length of the zone where the shear forces change from negative to
positive direction, establish the load-movement relation for the pile toe and the load
distribution in the pile at the time that settlement becomes an issue for the design,
and, finally, perform a settlement analysis. The settlement analysis of a piled
foundation must distinguish between settlement due to movements caused by external
load on the piles and settlement due to causes other than the load on the piles. A
fundamental realization of the design approach is that pile toe capacity is a
misconception. Each of the mentioned points is addressed in the paper, and a design
approach for the design of piled foundations and piled rafts is presented. Examples
and case histories are included showing the distribution of measured and calculated
resistance distribution along the piles and settlement of soil and piles.
INTRODUCTION
The most common reason for placing foundations on piles as opposed to on
spread footings, rafts, or other types, is to minimize foundation settlement. Yet, the
design of a piled foundation rarely includes a settlement analysis. Of old, the
common notion is that, if capacity is safe, nature takes care of the rest. This “designby-
faith” approach is frequently uneconomical and wasteful — neither is it always
safe. In addition to determining capacity, settlement analysis must be a part of every
design of a piled foundation. For a group of piles bearing in rock or glacial till, this
1 Bengt H. Fellenius, Dr. Tech., P.Eng. 1905 Alexander Street SE, Calgary, Alberta, T2G 4J3
Tel.: (403) 920-0752; e-address: <Bengt[at]Fellenius.net>
Bengt H. Fellenius — Unified Design of Piled Foundations with Emphasis on Settlement Analysis
Page 2
may merely be an assessment of the fact that no adverse settlement will occur. For
other conditions, settlement assessment requires detailed analysis. Similar to the
design of any type of foundation, a proper settlement analysis necessitates that soil
profile and pore water regime are well established and that influence of fills, loads
from other foundations, excavations, and changes in groundwater table are included
in the calculations. For piled foundations, however, it is necessary to take into
account additional factors, such as the distribution of pile shaft and toe resistances at
long-term equilibrium between loads at the pile head, drag load at the location of the
neutral plane due to accumulated negative skin friction, the length of the zone above
and below the neutral plane within which the shear forces along the pile shaft change
from negative direction to positive direction, the load-movement relation for the pile
toe, and the load distribution in the pile. Moreover, a settlement analysis must
distinguish between settlement due to movements caused by external loads from the
supported structure and settlement due to causes other than the external load.
PILE CAPACITY AND RESIDUAL LOAD
Pile capacity is a basic aspect of the pile design and analysis. Capacity is the
ultimate resistance of the pile, the load beyond which movement becomes excessive
or progressive for little increase of load, as observed, for example, in a static loading
test. The capacity is easy to determine in the case of a pile having no toe resistance
and a shaft resistance with elastic-plastic response to loading, such as the typical pile
load-movement curve presented in Fig. 1A. The curve is determined in a simulation
of a static loading test on a 300 mm diameter, 15 m long closed-toe steel pipe pile in
uniform soil. The capacity value is obvious from the plunging behavior of the shaftbearing
pile, i.e., the continuous movement for no load increase. As indicated in
Fig. 1B, however, once toe resistance comes into play, the load-movement curve no
longer demonstrates a plunging behavior.
Fig. 1A Load-movement for a 100 % Fig. 1B Load-movement for a pile with
shaft-bearing pile equal shaft and toe resistances
0
200
400
600
800
1,000
0 5 10 15 20 25 30
MOVEMENT (mm)
LOAD (KN)
ONLY SHAFT
RESISTANCE
OFFSET
LIMIT LOAD
LINE PARALLEL THE
ELASTIC LINE, EA/L
0
200
400
600
800
1,000
0 5 10 15 20 25 30
MOVEMENT (mm)
LOAD (KN)
50 % SHAFT RESISTANCE
50 % TOE RESISTANCE
Offset
Limit
10% of Pile
Diameter
Bengt H. Fellenius — Unified Design of Piled Foundations with Emphasis on Settlement Analysis
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The load-movement curve shown in Fig. 1B is representative of the same pile
when the resistance is assumed to be 50 % from shaft resistance and 50 % from toe
resistance. The soil parameters for the calculations behind Fig. 1B are chosen so as to
have the Offset Limit equal to the capacity of the shaft-bearing pile (Fig. 1A). The
load-movement curve in Fig. 1B does not show any tendency toward “plunging” or
any obvious load value that could be considered to be the capacity of the pile. For
such cases, the practice is either to simply consider the capacity to be the load that
generated a movement equal to 10 % of the pile diameter (30 mm in this case), or to
select a value of pile capacity by a definition applied to the curvature of the loadmovement.
Several such definitions are in use, the most common in North America is
the Davisson Offset Limit Load, which is the load at the intersection with the loadmovement
curve and a line parallel with the elastic line of the pile rising from the
movement axis at a value equal to 4 mm plus the pile diameter divided by 120. The
multitude of failure definitions is a consequence of the futility of forcing an ultimate
resistance theory onto a situation where it does not apply. Obviously, there is more to
determining pile capacity than selecting an arbitrarily defined point on a curve.
The load-movement response of a pile is the combination of the results of three
developments. First, the shaft resistance, which in most cases does develop an
ultimate resistance and a failure mode. Second, the shortening of the pile, which is a
more or less linear response to the applied load. Third, the toe response, which does
not display an ultimate resistance. The latter statement can be understood on
realizing that a pile toe is but a footing supporting a long column, and the loadmovement
behavior of a pile toe is similar to that of footings, as discussed next.
The concept of ultimate resistance was developed many years ago from
observations of large scale footings in clay and model footings in sand. Loading tests
on small-scale or large-scale footings on clay were performed at rates of loading such
that pore pressures developed increasingly as the test progressed, causing the
effective strength to reduce to the point that a failure resulted. This does not happen
when the loading rate is so slow that excess pore pressures dissipate as fast as they
develop. Moreover, with regard to the small-scale tests in sand, it was not realized at
the time that the soil response of tests on small footings placed on the surface of a
sand is always in a dilative mode: the sand expands, loses density, and loses strength
as the test progresses (Altaee and Fellenius 1994). In contrast, no failure has been
observed for buried footings, small or large.
For example, Ismael (1985) performed footing tests in fine compact sand on
square footings with sides of 0.25 m, 0.50 m, 0.75 m, and 1.00 m at a depth of 1.0 m,
2.8 m above the groundwater table. The results in terms of measured stress versus
movement as a percentage of the footing widths are shown in Fig. 2A. Notice that the
curves are gently curving with no break or other indication of failure despite the
movements being as large as 10 % to 15 % of the footing side. Similar results were
presented by Briaud and Gibbens (1994) for footings placed well above the
groundwater table in a slightly preconsolidated, silty fine sand. The natural void ratio
of the sand was 0.8. The footing sides were 1.0 m, 1.5 m, 2.0 m, and 3.0 m. Two of
the footings were 3.0 m wide. The results of the test are presented in Fig. 2B. It is
noteworthy that no indication of failure is indicated despite the large movements.
Bengt H. Fellenius — Unified Design of Piled Foundations with Emphasis on Settlement Analysis
Page 4
Fig. 2A Stress vs. movement for four footings Fig. 2B Stress vs. movement for five footings
(data from Ismael 1985) (data from Briaud and Gibbens 1994)
The recently developed O-cell test (Osterberg 1998) has enabled direct
observations of the response of a pile toe to increasing load and shown that the virgin
load-movement response of the pile toe is in the shape of a gentle curve gradually
bending over and displaying no kinks or sudden changes of slope; very much similar
to that of a footing. Plainly, bearing capacity as a concept does not apply to the
response of a pile toe to load.
That the concept of pile bearing capacity is specious does not mean that the
application of the concept of a bearing capacity of a pile would be wrong. The
approach is well-established in engineering practice. However, the practice would do
well to recognize the fallacies involved as demonstrated in the following.
Figure 3 presents two load-movement curves produced by simulation of a static
loading test using identical pile and soil input. The only difference between the
calculation of the two curves is that no residual load was assumed present in the pile
represented by the lower curve, whereas for the upper curve a residual load
amounting to one-third of the “ultimate” toe resistance was assumed. (The term
“residual load” refers to the load present in a pile immediately before the start of a
static loading test). The Offset Limit line (“Davisson line”) has been added to show
more clearly how much difference — in this case 20% — the presence of residual
load can have on the interpretation of the results of a test.
To calculate the load-movement curves, the shaft and toe resistance responses
were input expressed in “t-z” and “q z” curves as indicated in Fig. 4. The q-z curve
(used for the Fig. 1B simulation) is in the shape of a gentle curve gradually bending
over without reaching a peak—typical for a pile toe response. Both of the two t-z
curves have a distinct peak, however. The “no-strain-softening” t-z curve used for
the simulations in Figs. 1A and 1B shows a shear resistance having a slight trend to
0
400
800
1,200
1,600
2,000
0 5 10 15 20
MOVEMENT/WITDH ( % )
S T R E S S ( KPa )
0.25 m width
0.50 m width
0.75 m width
1.00 m width
0
400
800
1,200
1,600
2,000
0 5 10 15 20
MOVEMENT/WIDTH (%)
S T R E S S ( KPa )
1.0 m w idth
1.5 m w idth
2.5 m w idth
3.0 m w idth
3.0 m w idth
Bengt H. Fellenius — Unified Design of Piled Foundations with Emphasis on Settlement Analysis
Page 5
strain hardening beyond the peak. The second t-z curve shows a strain-softening
response beyond the peak, which load-movement behavior is typical for pile shaft
resistance in most soils. The results of a simulation employing this t-z curve are
presented in Fig. 5. As in Fig. 3, the upper load-movement curve in Fig. 5 includes
the effect of residual load and the difference between the two curves is similar to
those of Figs. 1 and 3 (to facilitate the comparison, the curves shown in Fig. 3 are
indicated also in Fig. 5). The curves show that the gradual increase of toe resistance
is compensated by the simultaneous gradual decrease of shaft resistance. Notice, an
eye-balling of the curves would now suggest that the Offset Limit would be a
reasonable “failure load” to interpret from test results.
Fig. 3 Load-movement curves for pile unaffected Fig. 4 Shaft and toe response t-z
and affected by residual load and q-z curves (normalized load)
Fig. 5 Load-movement curves for using the strain-softening
t-z curve, unaffected and affected by residual load
Despite the fact that the existence of residual load has been observed and
reported several times (e.g., Hunter and Davisson 1969; Gregersen et al. 1973;
0
200
400
600
800
1,000
0 5 10 15 20 25 30
MOVEMENT (mm)
LOAD (KN)
No Residual
Load
Residual Load
present
OFFSET
LIMIT LOAD
No Strain Softening
0
100
0 10 20 30 40 50
MOVEMENT (mm)
NORMALIZED LOAD
Maximum head
movement in test t-z
no strain softening
t-z
with strain
q-z softening
Pile toe
response
%
0
200
400
600
800
1,000
0 5 10 15 20 25 30
MOVEMENT (mm)
LOAD (KN)
With Strain Softening
Residual
Load present
No Residual
Load
OFFSET
LIMIT LOAD
Bengt H. Fellenius — Unified Design of Piled Foundations with Emphasis on Settlement Analysis
Page 6
Fellenius and Samson 1976; Holloway et al. 1978), many are under the fallacious
impression that its effect is marginal and, anyway, limited to piles in clay. Thus, they
are led to think that residual load can be neglected in the analysis of the results from
loading tests on instrumented piles. The effect is far from marginal, however, nor is it
limited to piles in clay. Figs. 6 and 7 show results of a static loading test on an
instrumented 280 mm diameter precast concrete pile driven 16 m into sand
(Gregersen et al. 1973).
Fig. 6 Load-movements for head, toe, and shaft Fig. 7 Measured distributions of
of an instrumented pile in sand (data from residual load and true load
Gregersen et al. 1973) (data from Gregersen et al. 1973)
Note the gradual, almost linear increase of the toe load and the reduction in shaft
resistance for pile head movements beyond 40 mm shown in Fig. 6. The initial stiffer
shape of the curve is an effect of the driving having densified the sand immediately
below the pile toe. The increase of toe resistance beyond the 10 mm pile head
movement is about equal to the simultaneous decrease of shaft resistance and results
in the appearance of plunging failure for the load-movement curve of the pile head at
a 500 KN maximum load. Note also that each time the pile head was unloaded, the
load remaining increased, showing that the preceding load cycle had added to the
residual load in the pile.
The pile was instrumented at several levels and Gregersen et al., (1973) measured
the load distribution in the pile immediately before and during the static loading test.
Fig. 7 presents the distribution measured immediately before, the “residual load”, and
the load distribution at the 500 KN maximum load, the “true load”. The difference
between the two curves, (the curve marked “True minus Residual”) is the measured
imposed increase of load in the pile at the maximum test load. This is what would
have been mistakenly considered the “true” load distribution had they not looked for
the residual load but assigned all gage readings at the start of the test to be “zero
readings”, that is, the readings for zero load in the pile.
0
100
200
300
400
500
600
0 10 20 30 40 50 60 70
MOVEMENT OF PILE HEAD (mm)
LOAD (KN)
HEAD
SHAFT
TOE
0
2
4
6
8
10
12
14
16
18
0 100 200 300 400 500 600
LOAD (KN)
DEPTH (m)
True
Residual
True minus
Residual
Bengt H. Fellenius — Unified Design of Piled Foundations with Emphasis on Settlement Analysis
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The residual load in the pile can be explained as partially introduced by the
driving of the pile and partially be due to recovery (re-consolidation) of the soil from
the disturbance caused by the pile driving. However, residual load for piles in sand is
not restricted to driven piles, which is illustrated in Fig. 8, presenting the load
distribution in a 0.9 m diameter, instrumented bored pile in sand.
Fig. 8 Measured load increase from the start of a static loading test in
sand with evaluated distributions of residual load and true load.
(data from Baker et al. 1993, analyzed by Fellenius, 2001)
Measurements of residual load is mostly obtained from observation of load
distribution for piles in clay with the objective of studying the development of drag
load. Usually no static loading test is performed. However, the term “drag load” is
just the term for “residual load” when no static loading test is performed. The
mechanics are identical.
For example, Fellenius and Broms (1969) and Fellenius (1972) measured the
load distribution in two 300 mm diameter, 53 m long, instrumented piles driven
through about 40 m of clay and into sand. The area was virgin, untouched by
construction since it rose from the sea after the end of the Ice Age. The load
distribution was measured immediately and during a long time following the driving.
The measured distributions are presented in Fig. 9, showing that immediately after
driving the loads were about equal to the own weight of the piles themselves. The
dissipation of the pore pressures induced in the driving over the next 154 days
resulted in the build-up of load in the pile. Somewhat surprisingly, the build-up of
load continued also after the induced pore pressures had dissipated, and Fig. 9
includes also the distribution measured at 496 days after the end-of-driving, 342 days
later. The continued load increase is considered due to a small regional settlement of
about a millimetre per year coinciding with the isostatic land heave of about the same
magnitude. Had a static loading test been performed at any one of these times after
driving, the measured drag loads would have been the residual load in the piles.
0.0
2.0
4.0
6.0
8.0
10.0
12.0
0 1,000 2,000 3,000 4,000 5,000
LOAD (KN)
DEPTH (m)
PILE 4
True
Distribution
Residual
Load
Measured
Distribution
Bengt H. Fellenius — Unified Design of Piled Foundations with Emphasis on Settlement Analysis
Page 8
Fig. 9 Load distributions measured in two piles immediately,
154 days, and 496 days after the end of driving. (Data
from Fellenius and Broms 1972; Fellenius 1972)
An additional example is presented in Fig. 10, which shows results of a static
loading test on a driven, 45 m long, 406 mm diameter, instrumented steel pipe pile in
soft clay (Fellenius et al. 2004). The test was performed 46 days after the pile was
installed when the induced pore pressures had dissipated. Note that if the residual
load had not been considered in the evaluation of the test data, that is, if the gages had
been “zeroed” at the start of the test, the loads measured during the tests would have
been thought to be representative for the true load distribution. Then, the evaluation
would have mistakenly concluded that there was no shaft resistance along the
lower 12 m length of the pile.
Already a small movement will be sufficient to develop shear forces along a pile.
Such movement is the result of a large number of influences associated with the
driving of piles, drilling and grouting of bored piles, curing of the concrete grout,
reconsolidation of the soil around the pile, etc., as well as effect of environmental
events at the site, such as ongoing settlement. It is not the purpose of this paper to
dwell on what causes the development of residual load, only to indicate that if
residual load is disregarded in the analysis of the results of a static loading test, the
results of the analysis will be in error.
Residual load is built up by accumulation of negative direction shear forces along
the upper part of the pile that is in equilibrium with accumulation of positive direction
shear forces along the lower part. The length along the pile (the shear transition zone)
where the shear direction changes from negative to positive direction can be short or
long.
0
10
20
30
40
50
60
0 200 400 600 800
FORCE AT GAGE (KN)
DEPTH (m)
PILE OWN WEIGHT
0 Days
154 Days
496 Days
CLAY
SAND
Bengt H. Fellenius — Unified Design of Piled Foundations with Emphasis on Settlement Analysis
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Fig. 10 Load distributions measured in a static loading test
on a 45 m long pile in clay. (Fellenius et al. 2004)
Shear resistance along a pile is governed by effective stress and is approximately
proportional to the overburden effective stress. Therefore, the ultimate shaft
resistance distribution in a homogenous, uniform soil will be in the shape of a curve
similar to the ultimate resistance curve shown in Fig. 11A, which shape can be
determined in a test performed on an instrumented pile.
The toe resistance portion of the ultimate resistance, shown level with the pile toe
in Fig. 11A, is the resistance mobilized in the static loading test, typically at a toe
movement of about 10 mm. As made clear in the foregoing, before the start of the
test, the pile will have become subjected to a residual load — sometimes a significant
amount, sometimes negligible. To illustrate the statement, the figure indicates two
distributions of residual load. The first curve represents the case of small relative soil
movements, where full residual shaft shear is only mobilized near the ground surface
(negative direction) and near the pile toe (positive direction). The shear forces are not
fully mobilized along the middle portion of the pile, the zone of shear direction
change— the “transfer zone”. The second curve is typical of where larger relative
soil movement have caused the shear forces to become fully mobilized over a longer
length of the pile, leaving a shorter transfer zone.
If the gages in the pile had been “zeroed” immediately before the start of the
static loading test, and only the test-applied loads considered in the final reporting of
the distribution, the so-determined distribution may be grossly in error. Fig. 11B
shows the “true distribution” curve, which combines the residual load and test applied
loads, and the “false distribution”, which appears when the residual load is neglected.
Published case histories on results of loading tests on instrumented piles have
0
5
10
15
20
25
30
35
40
45
50
0 500 1000 1500 2000 2500
LOAD (KN)
DEPTH (m)
Added during test
Residual
True Load
Clay
Sa
nd
Bengt H. Fellenius — Unified Design of Piled Foundations with Emphasis on Settlement Analysis
Page 10
frequently neglected to include residual load, which has given rise to fallacies such as
the “critical depth” (Fellenius and Altaee 1995).
Fig. 11A Distributions of ultimate resistance Fig. 11B True and false ultimate
and residual load resistance distributions
NEGATIVE SKIN FRICTION, DRAG LOAD, AND DOWNDRAG
Several important papers have published presenting measurements of load
distribution in instrumented piles with emphasis on drag load, e.g., Bjerrum et al 1965
and 1969; Darvall et al. 1969; Endo et al. 1969; Fellenius and Broms 1969; Fellenius
1972; Clemente 1979 and 1981; Bozozuk 1981, Leung et al. 1991).
The case history paper by Endo et al. (1969) is a comprehensive field study of
drag load and downdrag on piles and demonstrates the interaction between the forces
in the pile, the settlement, and the pile toe penetration. The paper presents the results
of measurements on instrumented, 610 mm diameter, 43 m long, single, driven steel
piles, as well as settlements of the piles and surrounding soil during a period of
almost two years (672 days). The soil profile at the site consisted of thick alluvium
over a buried aquifer: a 9 m thick layer of silty sand followed by silt to a depth of
about 25 m underlain by alternating layers of silt and sandy silt to a depth of 41 m
followed by sand. Two piles were driven closed-toe and one was driven open-toe.
The end-of-driving penetration resistance was light, about 20 mm for the last blow.
The groundwater table was located about 1 m below the ground surface. The
pore water pressure at the site was affected by pumping in the lower silt layer to
obtain water for an industrial plant, which created a downward gradient at the site.
The difference in terms of head of water between the groundwater table and the sand
0
5
10
15
20
25
0 500 1000 1500 2000
LOAD
DEPTH
Qult/ Rult
Residual
Toe Load
True Ultimate
Resistance
Transfer
Zones
0
5
10
15
20
25
0 500 1000 1500 2000
LOAD
DEPTH
True
Ultimate
Resistance
False
Ultimate
Resistance
Mobilized Toe
Resistance
Qult/ Rult
Bengt H. Fellenius — Unified Design of Piled Foundations with Emphasis on Settlement Analysis
Page 11
layer at the depth of 40 m was about 30 m. The ensuing consolidation of the soils
caused the soil to settle and hang on the piles, creating drag load and downdrag.
Fig. 12A presents a compilation of the load distributions measured in three piles
672 days after the driving, denoted Piles oE43, cE43, and cB43. All three piles
developed a neutral plane shortly below 30 m depth. The load distributions in the two
closed-toe piles are very similar. For these two, the drag load is about 3,000 KN, in
equilibrium with the sum of positive shaft resistance of about 1,500 KN and toe
resistance of about 1,500 KN. Had a static loading test been included in the study,
the shaft resistance of the full length of the piles would have been about 4,500 KN.
The load distributions are particularly interesting when related to the settlement
distributions measured both in the soil and for the piles. Fig. 12B presents settlement
measurements taken 124 days, 490 days, and 672 days from one pile, Pile cE43, after
the end of driving. Note that the point where the relative movement between the pile
and the soil is zero (i.e., where the soil and the pile settlement curves intersect) is
approximately level with the depth of the force equilibrium — the neutral plane.
Fig. 12B shows that the settlement of the ground surface 672 days after the end of
driving was 120 mm. At this time, the settlement (of soil and pile) at the neutral
plane was about 30 mm, and the settlement of the pile head was 53 mm, consisting of
the settlement at the neutral plane plus about 13 mm of pile shortening between the
pile head and the neutral plane due to the drag load.
Fig. 12 Load distributions in three pipe piles 672 days and settlement distributions at
124 days, 490 days, and 672 days after driving (data from Endo et al. 1969).
During the 672 days of measurements, the relative difference between the
settlement of the soil at the pile toe and the pile toe increased slightly, that is, the net
pile toe penetration into the sand increased. The records also show that the pile toe
0
5
10
15
20
25
30
35
40
45
50
0 500 1,000 1,500 2,000 2,500 3,000 3,500
LOAD (KN)
DEOTH (m)
oE43
cE43
cB43
0
5
10
15
20
25
30
35
40
45
50
0 50 100 150
SETTLEMENT (mm)
Soil 124 Days
Soil 490 Days
Soil 672 Days
Pile 124 Days
Pile 490 Days
Pile 672 Days
NEUTRAL PLANE
Closed-toe
Piles
Open-toe
Pile
S
a
n
d
S
i
l
t
a
n
d
C
l
a
y
S
a
n
d
Soil
Pile
Pile cE43
A B
Bengt H. Fellenius — Unified Design of Piled Foundations with Emphasis on Settlement Analysis
Page 12
load increased. In Fig. 13, the measured pile toe loads have been plotted versus net
pile toe penetration, as measured on the 124 day, 490 day and 672 day after the
driving of the piles. The first measurements taken at the end-of-driving, indicate that
the pile toe was subjected to an initial residual toe load corresponding to an initial toe
movement of approximately 8 mm.
Fig. 13 Pile toe load-movement — the q-z function. (data from Endo et al. 1969)
The load-movement curve indicates a practically linear relationship between the
load and the penetration. Obviously, had the settlement been larger, the pile net
penetration would have been larger, too, which would have mobilized a larger pile toe
resistance, which, in turn, would have lowered the location of the force equilibrium.
Collectively, the case records established that
1. Shaft shear (negative skin friction as well as shaft resistance) is governed
by effective stresses and requires very small soil movement relative the
pile surface to become mobilized. Indeed, Bjerrum et al. (1969) reported
that about the same magnitude drag load was measured for a few
millimetre of settlement at the ground surface as for 2 m of settlement.
2. For high capacity toe-bearing piles, large drag loads were measured and,
for these piles, the observed pile settlement consisted mainly of pile
shortening for the loads.
3. A pile subjected to drag load has a load distribution consisting of negative
skin friction accumulating in the upper portion of the pile in equilibrium
with positive shaft resistance along the lower portion of the pile plus toe
resistance. The zone where the shear forces transfer from negative to
positive direction can be short or long depending on the magnitude of the
soil movements and the relative stiffness of the pile and the soil. The
picture is the same as that for the distribution of residual load shown in
Fig. 11A. Indeed, had Endo et al. (1969) polished off their superb study
with a static loading test, the drag load would have become the residual
load for the test.
0
400
800
1,200
1,600
0 5 10 15 20 25 30
TOE MOVEMENT — Measured increase of penetration into the soil (mm)
TOE LOAD (KN)
Pile cE43
q - z
function
124 Days
490 Days 672 Days
?
Bengt H. Fellenius — Unified Design of Piled Foundations with Emphasis on Settlement Analysis
Page 13
4. The location where the downward acting forces are equal to the upward
acting forces is where there is no movement between the pile and the soil.
The location is called “plane of force equilibrium” or “neutral plane”. At
this location, the pile and the soil settle equally, which is a very important
insight for pile group design.
5. If appreciable soil settlement occurs at the neutral plane, the pile(s) will
be subjected to downdrag, an undesirable condition for most piled
foundations.
6. The location of the neutral plane is entirely a function of the conditions
for the force equilibrium and is not a function of the magnitude of
settlement in any other regard than the force equilibrium is a function of
the pile toe penetration into the soils at the pile toe, which in turn is
governed by the magnitude of settlement at the neutral plane.
7. Where soil settlements are small, the transition zone is long and where the
soil settlements are large, the transition zone is short. All other things
equal, the drag load is larger in the second case.
8. Live loads (transient loads) will reduce or eliminate the drag load.
9. Negative skin friction will develop whether or not an external load is
applied to the pile head. The external dead load and the drag load will
combine and the maximum load in the pile will occur at the neutral plane.
10. The larger the pile toe resistance, the lower neutral plane.
11. A thin coat of bitumen will drastically reduce the shear force between the
pile surface and the soil and reduce the negative skin friction (and reduce
the positive shaft resistance and pile bearing capacity).
Because of the word “load” in “drag load”, some are led to believe the drag load
to be just another load similar to the loads applied from the structure supported on the
piles. However, the drag load is only of concern for the structural strength of a pile.
In contrast to the external loads (the loads from the supported structure), the drag load
is of no consequence for the bearing capacity or settlement of the pile or pile group.
Simply, the drag load is no more a negative aspect for a pile than the prestress is for a
prestressed concrete pile. Indeed, a pile subjected to considerable drag load is stiffer
than a pile that is not subjected to much drag load and will display smaller
deformation for variations of the load applied to the pile head. Downdrag, on the
other hand, is an important settlement problem that has to be carefully addressed in a
design. The author has termed the design approach “The unified design of piled
foundations for capacity, settlement, dragload, and downdrag” (Fellenius 1984 1989).