The Behaviour of Batter Piles under Uplift Loads

Abstract

In this paper, experimental work was carried out in the laboratories of the University of Baghdad on single
batter piles. These piles are constructed in sand and subjected to uplift loads of different inclinations. It was found that the uplift capacity of vertical and batter piles under inclined pulls increased with increasing the inclination of pull with the vertical and with a maximum at horizontal pull. It was also found that the vertical pile has ultimate uplift load greater than batter piles, but at the same time, a negative batter pile has greater ultimate uplift load than positive batter pile f or all load inclinations.

Full text

International Conference on Geotechnical Engineering October 3-6, 2004, Sharjah – UAE
105
The Behaviour of Batter Piles under Uplift Loads
Yousif. J. al – Shakarchi Mohammed Yousif Fattah
myf_1968@yahoo.com
Ihsan K. Kashat
Civil Engineering Department,
College of Eng., University of
Baghdad, Baghdad, Iraq.
Lecturer, Building and
Construction Department,
University of Technology,
Baghdad, Iraq.
Civil Engineering Department,
College of Eng., University of
Baghdad, Baghdad, Iraq.
ABSTRACT: In this paper, experimental work was carried out in the laboratories of the University of Baghdad on single
batter piles. These piles are constructed in sand and subjected to uplift loads of different inclinations. It was found that
the uplift capacity of vertical and batter piles under inclined pulls increased with increasing the inclination of pull with
the vertical and with a maximum at horizontal pull. It was also found that the vertical pile has ultimate uplift load greater
than batter piles, but at the same time, a negative batter pile has greater ultimate uplift load than positive batter pile for all
load inclinations.
KEY WORDS: Batter pile, uplift load, sand, experimental work.
INTRODUCTION
Batter piles are used to support structures subjected to
large lateral loads, or if the upper foundation stratum will
not adequately resist lateral movement of vertical piles.
Piles may be battered in opposite directions or used in
combination with vertical piles. The axial load on a batter
pile should not exceed the allowable design load for a
vertical pile. It is very difficult to drive piles with a batter
greater than 1 horizontal to 2 vertical. The driving
efficiency of the hammer is decreased as the batter
increases, (EM 1110-2-2906, 1991).
In sands, the use of the same procedures employed in
compression loading is recommended for uplift, with the
exception that the ultimate load should be reduced to 70
percent of the maximum compression value, (Mosher and
Dawkins, 2000).
PILES UNDER UPLIFT LOADS
Meyerhof and Ranjan (1972) made uplift tests on vertical
and batter piles with different embedded lengths. The
results indicated that as the inclination of pull increases,
the uplift failure load increases with maximum at (α = 90
o
)
for both vertical and batter piles.
Meyerhof (1973) carried out tests on inclined piles axially
loaded. The results showed that for the same depth of
embedment and soil conditions and a given inclination of
pull, the uplift capacity of axially loaded inclined piles
exceeds the uplift capacity of axially loaded vertical ones.
Moreover, while the uplift capacity of such axially loaded
inclined piles generally increases as the inclination
increases, the corresponding uplift capacity of vertical
piles decreases as the inclination of the pull from the
vertical increases.
Testing Apparatus:
The testing apparatus consist of (see Plate 1):
1. The Loading Unit:
The loading unit consists of two main frames, each
main frame consists of two parts. The first main frame
carries the raining system and the horizontal part of
the second main frame. It consists of a horizontal
movable upper part connected rigidly to the fixed
vertical steel columns by means of bolts and nuts
which are connected rigidly to the ground by means of
roll bolts (as shown in Plate 2).
The second main frame consists mainly of steel angles
welded with thick plates and hollowed in
predetermined points to carry the screw jack (in case
of compression) or to carry the pulleys (in case of
uplift).
This frame also consists of a portable horizontal part
connected rigidly with the fixed vertical part and with
the portable upper part of the first main frame by
means of bolts and nuts.
2. The single pile Model:
The model piles used are made of steel. The pile used
consists of two parts. The first main part is the 30 cm
embedded part which is made rough by sandpaper
glued on its surface. The second main part is the upper
portable part screwed in the first main part and
hollowed at a distance 3 cm above the sand surface
for load application.
3. The sand box:
A wooden container with inner dimensions of (80 cm
x 80 cm x 80 cm) was used to keep the sand layers.
The inner faces of the wooden box were covered with
two sheets of polythene with a thin film of grease oil
between them to reduce the friction generated
between the sand and the inner faces of the box. Steel
plates were fixed at the sides of the sand box to fix the
clamps and the steel angle which carry the dial
gauges.

International Conference on Geotechnical Engineering October 3-6, 2004, Sharjah – UAE
106
4. The density control system:
It consists of a steel frame with a pulley fixed at its
top with a cable of (3 mm) diameter passes through
the pulley carrying small container. It feeds a single
hose with a screen of (3.2 mm) openings used to break
the falling sand during raining in order to have the
same intensity and to distribute the sand particles
uniformly. The sand flow was controlled by a valve at
the exit of the container. The cable was pulled by the
revolving of a fixed pulley to assure a constant height
for the sand raining.
5. The measuring system:
A - Displacement measurement:
Two (0.002 mm per division) sensitive dial gauges
placed on a wooden cap were used to measure the
vertical and horizontal displacements. These gauges
were fixed rigidly at the same level of load application
using steel angle, small clamps and steel shafts.
B – Load measurement:
The loading frame was equipped with pulleys in
predetermined points in the second main frame for
adjusting the required inclination of pull. The load
was applied through a steel wire (2 mm diameter for
single pile test) with one end connected to an eye-
hook on the pile top through a swivel arrangement and
the other end to a hanger.
The wire was passed over the fixed pulleys, which
was freely moved by a ball bearing fixed on its
centers. The load was applied by adding dead weights
on the hanger at the end of the wire. Also the angle of
loading was from vertical (α = 0
o
) to horizontal (α =
90
o
) in increments of (15
o
), (Kashat, 1990).
Sand Properties
The grain size distribution curve for the sand used is
shown in Figure 1. The specific gravity is equal to
(2.65). The dry density was kept approximately
constant using the raining technique at 19.12 kN/m
3
.
Using the triaxial compression test, the angle of
internal friction of the sand was found to be (38
o
) for
single uplift tests.
Testing Program
The testing program was planned to consist of the
following tests:
1. Seven uplift tests were conducted on vertical
piles with depth of embedment (L = 30 cm),
eccentricity (e = 6 cm), diameter (b = 1.5 cm).
The load inclination was varied from vertical (α
= 0
o
) to horizontal (α = 90
o
) in increments of
(15
o
) as shown in Figure 2-a.
2. Fourteen uplift tests were conducted on positive
batter piles with length of embedment (L = 30
cm), eccentricity (e = 6 cm) and diameter (b = 1.5
cm). The load inclination was varied from
vertical (α = 0
o
) to horizontal (α = 90
o
) in
increments of (15
o
) and batter angle β of (30
o
) as
shown in Figure 2-b.
Plate 1. Testing apparatus.

International Conference on Geotechnical Engineering October 3-6, 2004, Sharjah – UAE
107
Plate 2. The loading unit.
1&2- first main frame 3&4- second main frame.
1- horizontal portable upper part. 2- fixed vertical column.
3- portable horizontal part. 4- fixed vertical part.
3. Fourteen uplift tests were conducted on negative
batter piles with length of embedment (L = 30
cm), eccentricity (e = 3 cm) and diameter (b = 1.5
cm). The load inclination was varied from
vertical (α = 0
o
) to horizontal (α = 90
o
) in
increments of (15
o
) and batter angle β of (-30
o
) as
shown in Figure 2-c.
The Failure Surface
The following results were obtained from the photographs
taken to study the layout of the failure surface for single
vertical and batter piles subjected to inclined uplift loads.
Plate 3 presents the observed failure surface for single
vertical pile under uplift load with depth of embedment of
(L = 30 cm) and under a load inclination α equlas to (30
o
)
with the vertical and (e/L = 0.3).
During the stages of loading, the sand around the pile
moves downward with a rate at the same side of loading
higher than the rate of the opposite side. No movements of
sand were observed under the pile base. The stressed zone
around the pile had a diameter nearly equals to (3 – 4) the
pile diameter.
DEFINITIONS
The Ultimate Inclined Uplift Load, Puαα:
It is the pullout force of the pile.
Normalized Load (Puαα / Puo):
It is the ratio of the ultimate inclined uplift load to the
ultimate vertical uplift load.
Ultimate Uplift Load Determination:
There is rear information in the literature about the way for
determining the ultimate inclined uplift load on piles. In
this work, it is assumed that the pullout force is the
ultimate uplift load for the following reasons:
1. Piles under small inclinations of loads were governed
by the vertical displacement in which only a few
points with a little magnitude could be recorded.
When the inclined uplift load was increased, the
upward displacement of the pile top increases
continuously without any increase of pull at a rate far
out of proportion to the rate of increase of pull till the
pile is pulled out so that no failure point could be
recorded. The same thing happened at higher
inclination of load so that only short load-
displacement curves with a few points could be
recorded.
2. Using pull-out force as ultimate uplift load coincides
nearly with other investigators.
Figures 3 to 5 show the load-displacement curves
for vertical and batter piles of (± 30
o
).

International Conference on Geotechnical Engineering October 3-6, 2004, Sharjah – UAE
108
Fig. 1. Grain size distribution for the tested sand.
0.0010.0100.1001.00010.000
Grain Diameter (mm)
0
10
20
30
40
50
60
70
80
90
100
% Passing by Weight
Gravel
Sand
Coarse to Medium
Fine
Fines
Silt Clay
U. S. Standard Sieve Sizes
Cu = D60/D10
= (0.63 / 0.23) = 2.74 < 6
(Uniform Sand)
Pu
α
α
L
e
b
e/L = 0.2
e = 6 cm
L = 30 cm
b = 1.5 cm
α =
γ =
(0, 15, 30, 45, 60, 75, 90)
degrees
19.12 kN/m
3
φ = 38
o
(a) - Single vertical pile under uplift load.
Pu
α
α
L
e
b
e/L = 0.2
e = 6 cm
L = 30 cm
b = 1.5 cm
α =
γ =
(0, 15, 30, 45, 60, 75, 90)
degrees
19.12 kN/m
3
φ = 38
o
(b) - Positive batter pile under uplift load.
β
β =
+ 30
o

International Conference on Geotechnical Engineering October 3-6, 2004, Sharjah – UAE
109
Fig. 2. Single pile program of testing under uplift load.
Fig. 2 . (Continued)
Plate 3. Observed shape of failure surface for single vertical pile under
uplift load (α = 30
o
).
Effect of load inclination angle, αα:
Figure 6 presents that as the inclination of pull with
vertical α increases, the ultimate uplift load increases with
a maximum at α equals to (90
o
). It is shown that the
vertical pile has greater ultimate uplift load for all load
inclinations than negative and positive batter piles except
when α was greater than (75
o
) with the vertical, thereafter
the negative batter pile has greater ultimate uplift load than
others. At the same time, a negative batter pile has greater
ultimate uplift load than a positive batter pile for all load
inclinations. These results are similar to those obtained by
Meyerhof and Ranjan (1972).
Figure 7 shows clearly that the ratios of the ultimate
horizontal uplift load to the ultimate vertical uplift load
(Pu
90
/Pu
o
) are 265 %, 224 % and 195 % for negative,
vertical and positive batter piles, respectively.
COMPARISON OF EXPERIMENTAL RESULTS
WITH THEORETICAL ONES
Meyerhof and Ranjan Procedure
According to Meyerhof and Ranjan (1972), the uplift
failure load varies roughly in the form of an ellipse from
vertical to horizontal. The general equation can be written
in the form:
1sin
P
P
cos
P
P
2
un
u
2
uo
u
=α+α
αα
(1)
where:
P
uα
= Inclined uplift load at angle of pull, α,
P
uo
= Vertical uplift load, and
P
un
= Horizontal load.
Pu
α
α
L
e
b
e/L = 0.2
e = 6 cm
L = 30 cm
b = 1.5 cm
α =
γ =
(0, 15, 30, 45, 60, 75, 90)
degrees
19.12 kN/m
3
φ = 38
o
(c) - Negative batter pile under uplift load.
β
β =
- 30
o

International Conference on Geotechnical Engineering October 3-6, 2004, Sharjah – UAE
110
The vertical uplift load can be determined by the equation (Meyerhof and Ranjan, 1972):
Fig. 3. Displacement vs. uplift load for vertical pile with various load
inclinations (L/b = 20).
Fig. 4. Displacement vs. uplift load for negative batter pile with different load
inclinations (L/b = 20), β = - 30
o
.
0 2 4 6 8 10 12
Displacement (mm)
0
4
8
12
16
20
24
28
32
Uplift Load, Pu (kg)
= 0 (Vertical Disp.)
= 30 (Horizontal Disp.)
= 60 (Horizontal Disp.)
= 90 (Horizontal Disp.)
α
α
α
α
α
o
o
o
o
e/L = 0.2
0 2 4 6 8 10 12
Displacement (mm)
0
4
8
12
16
20
24
28
32
36
Uplift Load, Pu (kg)
= 0 (Vertical Disp.)
= 30 (Horizontal Disp.)
= 60 (Horizontal Disp.)
= 90 (Horizontal Disp.)
α
α
α
α
α
o
o
o
o
e/L = 0.2
0 2 4 6 8 10 12
Displacement (mm)
0
4
8
12
16
20
24
Uplift Load, Pu (kg)
= 0 (Vertical Disp.)
= 30 (Horizontal Disp.)
= 60 (Horizontal Disp.)
= 90 (Horizontal Disp.)
α
α
α
α
α
o
o
o
o
e/L = 0.2

International Conference on Geotechnical Engineering October 3-6, 2004, Sharjah – UAE
111
Fig. 5. Displacement vs. uplift load for positive batter pile with different load
inclinations (L/b = 20), β = + 30
o
.
δπγ+=
tan.b.K..D.
2
1
WP
s
2
puo
(2)
where: W
p
= weight of the pile,
D = depth of embedment of the pole,
b = diameter of pile
Ks = average coefficient of earth
pressure on the shaft, and
δ = soil-pile friction angle.
Using Equation (1), the results in Table 1 are obtained.
Meyerhof (1973) Procedure
The ultimate uplift load of vertical pile
can be written in
the form:
α+
γ
=
α
cosWb.K.D.
2
P
'
b
2
u
(3)
The vertical uplift coefficients K
b
′
is 8 while the horizontal
uplift coefficient is 12. The uplift coefficient for other load
inclinations can be found by interpolation. The theoretical
and experimental results are shown in Table 2.
The results obtained using Eq.1 are plotted against
experimental results are shown in Figure 8. It is clear to
say that:
1. The results obtained by Meyerhof’s equation (1973)
gives good agreement with the present experimental
results.
2. The differences between theoretical to experimental
results increase with increasing the load inclination as
shown in Figure 9.
3. No eccentricity factor can be conducted due to the
limited data available in the literature.
Axially Loaded Piles
According to Meyerhof (1973), the ultimate uplift load for
axially loaded pile can be expressed in terms of uplift skin
friction using Eq.4:
As.tan.Ku.PPu
'
o
δ= (4)
where:
As = the embedded pile surface area.
The uplift coefficient K
u
is a function of the angle of
internal friction and the load inclination angle, α. The
results are shown in Table 3.
The experimental and theoretical results are plotted in
Figure 10. It is shown that increasing the batter pile angle,
the difference between experimental and theoretical load
increases with increasing the batter angle.
Table 1. Theoretical and experimental results of piles under uplift load using Meyerhof and Ranjan
(1972) equation.
α
o
e/L
Theoretical Puα
(kg)
Experimenal Puα
(kg)
0
30
60
0.2
0.2
0.2
4.88
5.65
8.28
13.0
15.4
19.8
)4(A.tan.K.PP
su
'
ou
δ=
0 15 30 45 60 75 90
Inclination of Load, (degree)
8
12
16
20
24
28
32
Uplift Load, Pu (kg)
α
α
= + 30
= 0
= - 30
β
β
β
o
o
o
e/L = 0.2
0 15 30 45 60 75 90
Inclination of Load, (degree)
0
40
80
120
160
200
240
280
(Pu /Puo) x 100
α
α
= + 30
= 0
= - 30
β
β
β
o
o
o
e/L = 0.2
Fig. 6. Inclination of load vs. uplift load for
vertical batter pile, (L/b = 20).
Fig. 7. Inclination of load vs. ratio of inclined
uplift load to vertical uplift load for
vertical batter pile, (L/b = 20).

International Conference on Geotechnical Engineering October 3-6, 2004, Sharjah – UAE
112
90 0.2 10.79 29.0
Table 2. Theoretical and experimental results for single vertical pile under uplift load using Meyerhof
(1973) equation.
α
o
e/L
Theoretical P
uα
(kg)
Experimenal P
uα
(kg)
0
30
60
90
0.2
0.2
0.2
0.2
12.40
13.56
14.67
15.48
13.0
15.4
19.8
29.0
Table 3. Theoretical and experimental results for axially loaded piles using Meyerhof (1973)
equation.
α = β
o
K
u
Theoretical P
uβ
(kg)
Experimental P
uβ
(kg)
0
30
0.2
0.2
9.24
7.28
13.0
12.5
Fig. 8. Ultimate uplift load from test vs. ultimate uplift load from the theory
of Meyerhof and Ranjan (1972) and Meyerhof (1973).
0 4 8 12 16 20 24 28 32
Ultimate Uplift Load from Test (kg)
0
4
8
12
16
20
24
28
32
Ultimate Uplift Load from tTheory (kg)
Meyerhof and Ranjan (1972)
Meyerhof (1973)
Das (1999)
1
1
2
2
3
3
4
4
1 = 0
2 = 30
3 = 60
4 = 90
α
α
α
α
o
o
o
o
0 30 60 90
Inclination of Load, (Deg.)
80
120
160
200
240
280
Pu, exp. / Pu, theor.) x 100
Meyerhof (1973)
Meyerhof and Ranjan (1972)
0 10 20 3
0
Batter Pile Angle, (Deg.)
120
130
140
150
160
170
180
190
200
Pu ,exp. / Pu ,theor.) x 100
α
α
e/L = 0.2
β
Fig. 9. Inclination of load vs. uplift load for
vertical and batter piles, (L/b = 20),
β = ± 30
o
.
Fig. 10. Inclination of load vs. ratio of
inclined uplift load to vertical
uplift load for vertical and

International Conference on Geotechnical Engineering October 3-6, 2004, Sharjah – UAE
113
Das (1999) Procedure
When piles are embedded in granular soils (cohesion, c =
0), the net ultimate uplift capacity (T
un
) is (Das and Seely,
1975):
∫
=
L
o
uun
dz)pf(T (5)
where: f
u
= unit skin friction during uplift.
P = perimeter of pile cross section.
The unit skin friction during uplift, f
u
, usually varies as
shown in Figure 11a. It increases linearly to depth of z =
L
cr
, beyond that it remains constant. For z ≤ L
cr
:
δσ= tanKf
'
vuu
(6)
where: K
u
= uplift coefficient,
σ
v
′
= effective vertical stress at a depth z, and
δ = soil-pile friction angle.
The variation of the uplift coefficient with soil friction
angle φ is given in Figure 11b. Based on experience, Das
(1999) suggested that the values of L
cr
and δ appear to
depend on the relative density of soil. Figure 11c shows
the approximate nature of these variations with the relative
density of soil. For calculating the net ultimate uplift
capacity of piles, the following procedure was suggested,
(Das, 1999):
1. Depending on the relative density of the soil, and
using Figure 11c, the value of L
cr
is obtained.
2. If the length of the pile, L, is less than or equal to L
cr
:
∫ ∫
δσ==
L
o
L
0
u
'
vuun
dz)tanK(pdz)pf(T (7)
In dry soils, σ
v
′
= γ.z (where γ = unit weight of soil), so:
∫
δσ=
L
o
u
'
vun
dz)tanK(pT
∫
δγ=δγ=
L
0
u
2
u
tanKL.p
2
1
dz.tanzK.p (8)
The values of K
u
and δ are obtained from Figures 11b
and c.
3. For L > L
cr
:
[ ]



∫
+δσ=
∫






∫ ∫
+==
Lcr
0
u
'
v
L
0
L
0
L
Lcr
uuuun
dztanKp
dzfdzfpdzfpT
[
]
∫
δσ
=
L
Lcr
u
)Lcrzat(
'
v
dztanK (9)
For dry soils, Eq. 9 simplifies to:
)LL(tanKL.ptanKL.p
2
1
T
crucrucrun
−δγ+δγ=
(10)
For the piles used in this work, the embeddment was in
sand with (φ = 38
o
and Dr = 75 %, γ
dry
= 19.12 kN/m
3
), L
= 30 cm and b = 1.5 cm.
Using Figure 11:
cr
b
L






= 14.5, L
cr
= 14.5 x 1.5 = 21.75 cm.
φ
δ
= 1.0 , δ = 1.0 x 38 = 38
o
Ku = 2.3
From Eq. 8:
T
un
= ½(1.5x4x10
-2
)(19.12)(0.2175)
2
(2.3) tan(38
o
) +
(1.5x4x10
-2
)(19.12)(0.2175)
x(2.3)(0.3-0.2175) tan(38
o
)
T
un
= 0.1087 kN = 10.87 kg
This value is shown in Figure 8.
CONCLUSIONS:
Based on the objective results obtained throughout this
work, the following conclusions can be made:
1. The uplift capacity of vertical and batter piles under
inclined pulls increased with increasing the inclination
of pull with the vertical and with a maximum at
horizontal pull.
2. A vertical pile has ultimate uplift load greater than
batter piles, but at the same time, a negative batter pile
has greater ultimate uplift load than positive batter
pile for all load inclinations.
3. During the stages of loading, the sand around the pile
moves downward with a rate at the same side of
loading higher than the rate of the opposite side. No
movements of sand were observed under the pile base.
The stressed zone around the pile had a diameter
nearly equals to (3 – 4) the pile diameter.
REFERENCES:
Das, B. M., (1999). (Principles of Foundation
Engineering), 4
th
Edition, PWS Publishing.
EM 1110-2-2906, (1991). (Design of Pile Foundations),
Engineer Manual, U.S. Army corps of Engineers,
Washington.
Das, B. M. and Seely, G. R., (1975). (Uplift Capacity of
Buried Model Piles in Snad), Journal of the Geotechnical
Engineering Division, ASCE, Vol. 101, No. GT10, p.p.
1091-1094.
Kashat, I. K., (1990). (Effect of Load Inclination on the
Behaviour of Pile), M.Sc. thesis, University of Baghdad.

International Conference on Geotechnical Engineering October 3-6, 2004, Sharjah – UAE
114
Meyerhof, G. G., (1973). (Uplift Resistance of Inclined
Anchors and Piles), Proceedings of the 8
th
International
Conference on Soil Mechanics and Foundation
Engineering, Moscow, Vol. 2, p.p. 167-172.
Meyerhof, G. G. and Ranjan, G., (1972). (The Bearing
Capacity of Rigid Piles Under Inclined Loads in Sand -I-
Vertical Piles), Canadian Geotechnical Journal, Vol. 9,
p.p. 430-446.
Mosher, L. and Dawkins, W. P., (2000), (Theoretical
Manual for Pile Foundations), U.S. Army Corps of
Engineers, Engineer Research and Development Center.
Lcr
z
fu
L
20 30 40 50
Skin Friction Angle, (deg)
0
1
2
3
4
Ku
φ
(a)
(b)
Fig. 11 Procedure of determination of uplift capacity of piles in sand (after Das,
1999), a) Nature of variation of f
u
b) uplift coefficient Ku
c) Variation of δ/φ and (L/D) with relative density of soil.
0 20 40 60 80 100
Relative Density of Soil (%)
0.0
0.4
0.8
1.2
1.6
(L/D)cr
0
(δ/φ)
4
8
12
16
δ/φ
(L/D)cr
( c )