3440
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
where
q
uv
(
e,
α=0)
= average ultimate vertical load per unit area of
the foundation with load eccentricity
e
and load inclination α =
0,
q
uv
(
e=
0
,
α=0)
= average ultimate bearing capacity with centric
vertical load,
R
= reduction factor,
b
and
c
= functions of
D
f
/
B
only and independent of soil friction angle
. The variation of
b
and
c
with
D
f
/
B
[Eq. (7)] is given in Table 1.
Table 1. Variation of
b
and
c
with
D
f
/
B
—
Analysis of Purkayastha and Char (1977)
D
f
/
B
b
c
0
0.25
0.5
1.0
1.862
1.811
1.754
1.820
0.73
0.785
0.80
0.888
For
D
f
/
B
between zero and 1, the average values of
b
and
c
are
about 1.81 and 0.8 respectively. So Eq. (7) can be approximated
as,
8.0
)0 ,0 (
)0 ,(
8.11
B
e
R
q
q
euv
euv
(8)
Saran and Agarwal (1991) performed a limit equilibrium
analysis to evaluate the ultimate bearing capacity of strip
foundation subjected to eccentrically inclined load. According
to this analysis, for a foundation on granular soil,
) , / (
) , / (
) , / (
2
1
Be
Beq
Beu
NB
Nq
q
(9)
where
q
u
(
e
/
B
,α)
= average inclined load per unit area with load
eccentricity ratio
e
/
B
and load inclination α,
N
q
(
e
/
B
,α)
and
N
γ(
e
/
B
,α)
= bearing capacity factors expressed in terms of load
eccentricity
e
and inclined at an angle α to the vertical. They are
available in tabular and graphical form in the original paper of
Saran and Agarwal (1991).
The purpose of the present study is to present several
laboratory model test results for the average ultimate inclined
load per unit area of a strip foundation,
q
u
(
e
,α)
, supported by
dense sand [i.e.
q
uv
(
e,
α)
/cosα]. A reduction factor has been
proposed to estimate
q
u
(
e
,α)
at a given
D
f
/
B
from the ultimate
bearing capacity with centric vertical loading
q
uv
(
e=
0
,
α=0)
at
similar
D
f
/
B
.
2 LABORATORY MODEL TESTS
Laboratory model tests were conducted using a poorly graded
sand with effective size
D
10
= 0.325 mm, uniformity coefficient
C
u
= 1.45 and coefficient of gradation
C
c
= 1.15. The model
tests were conducted in a tank measuring 1.0 m (length)
0.504
m (width)
0.655 m (height). The two length sides of the tank
were made of 12mm thick high strength fiberglass. All four
sides of the tank were braced to avoid bulging during testing.
The model foundation measured 100 mm (width
B
)
500 mm
(length
L
)
30mm (thickness
t
) and was made from a mild steel
plate. The bottom of the footing was made rough by applying
glue and then rolling the steel plate over sand. Since the width
of the test tank and the length of the model foundation were
approximately the same, a plane strain condition roughly
existed during the tests.
Sand was poured into the test tank in layers of 25 mm from a
fixed height by raining technique to achieve the desired average
unit weight of compaction. The height of fall was fixed by
making several trials in the test tank prior to the model test to
achieve the desired unit weight of sand. The model foundation
was placed at a desired
D
f
/
B
ratio at the middle of the box.
Load to the model foundation was applied by a loading
assembly which was capable of applying eccentrically inclined
load. It consisted of three units: (a) the electrical control panel,
(b) hydraulic power pack and (c) loading device. The loading
device was a combination of a beam, four cylinders, four
supporting columns and a base. The hydraulic cylinder was the
device that converted fluid power into linear mechanical force
and motion. It converted fluid energy to an output force in a
linear direction for executing different jobs. The capacity of the
hydraulic cylinder in universal static loading setup was 100 kN.
The load could be applied to the model foundation in the range
of 0 to 100 kN with an accuracy of 1 N. The inclination of the
load could be changed by forward and backward movement of
the cylinder. The inclination of the load remained intact
throughout the testing period by the provision of the check
valve. Settlement of the model foundation was measured by dial
gauges placed on two edges along the width side of the model
foundation.
The average values of the various parameters during the
model tests are given in Table 2.
Table 2. Model Test Parameters
Parameters
Values
Unit weight of compaction of sand
Relative density of compaction
Soil friction angle
D
f
/
B
e
/
B
Load inclination α
14.36 kN/m
3
69%
40.8
0, 0.5, 1
0, 0.05, 0.1, 0.15
0, 5
, 10
, 15
, 20
3 MODEL TEST RESULTS
Based on the load-settlement curves, the average ultimate
inclined loads per unit area of the foundation
q
u
(
e
,α)
(=
Q
u
/
B
; see
Fig. 1) obtained from the present tests are given in Table 3.
4 ANALYSIS OF MODEL TEST RESULTS
Based on Eqs. (5), 6) and (7), it was assumed that, for a given
D
f
/
B
,
n
m
eBDu
eBDu
B
e a
q
q
RF
f
f
1
1
factor
reduction
)0 ,0 , /
(
) , , /
(
(10)
In order to determine the values of
a
,
m
and
n
, the following
procedure was used:
Step 1
: For vertical loading conditions (i.e.
=0), Eq. (10)
takes the form
m
B
e a
RF
1
(11)
With
= 0 and, for a given
D
f
/
B
, regression analyses were
performed to obtain the magnitudes of
a
and
m
.
Step 2
: Using the values of
a
and
m
obtained in Step 1 and
Eq. (10), for a given
D
f
/
B
, a regression analysis was performed
to obtain the value of
n
for
> 0°.
The values of
a
,
m
and
n
obtained from analyses described
above are given below,
D
f
/
B
= 0
―
a
= 2.23,
m
= 0.81,
n
= 1.98
D
f
/
B
= 0.5
―
a
= 2.0,
m
= 0.88,
n
= 1.23
D
f
/
B
= 1.0
―
a
= 1.76,
m
= 0.92,
n
= 0.97
From the values of
a
,
m
and
n
, It can be seen that the variations
of
a
and
m
with
D
f
/
B
are very minimal; however, the value of
n
decreases with the increase in embedment ratio. The average
values of
a
and
m
are 1.97 and 0.87 respectively.
