896
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
conducting 80 CK
o
D tests. It is important to emphasize that p
′
i
and
I
D
are the in-situ (before shearing) mean effective stress and relative
density values. The sand used in these tests is local sand called
Silivri Sand. In order to have the same grain size distribution in all
tests, this sand was sieved and prepared with the standard grain size
distribution of Ottawa sand (
Table 1
).
Table 1. Properties of the test sand.
Sand
G
s
C
u
C
c
e
max
e
min
Silivri sand with Ottawa
distribution (SP)
2.67
2.16
1.45
0.96
0.56
Samples were prepared by dry pluviation. Several tests were
conducted at different OCRs (1,2,4,8) to consider the influence
of unloading on dilation. Overconsolidated samples were
unloaded under K
o
conditions.
3 TEST RESULTS
3.1 Dilatancy as a function of p
′
i
and I
D
Dilatancy angle is calculated from the test results using the
relationship proposed by Schanz and Vermeer (1996).
=
⁄ 2 −
⁄
⁄
(3)
The relationship given in Eq. 3 is preferred since it is
specifically developed for triaxial testing conditions. As the
goal is to investigate the uncoupled effects p
′
i
and I
D
on
ψ
, test
results are divided into several I
D
ranges. In other words, p
i
′
-
ψ
relationships are defined separately for each 0.05 increment in
I
D
(i.e. a single p
i
′
-
ψ
relationship is defined for the tests with
0.65
≤
I
D
<0.70, and this p
i
′
-
ψ
relationship is considered to be
applicable for I
D
=0.675). The reason for choosing the I
D
increment to be 0.05 is because this much variation in I
D
is
within the measurement margin of error. So for each I
D
range,
the tangents of calculated
ψ
values (tan
ψ
) are plotted against the
corresponding end of consolidation (in-situ) mean effective
stresses that are normalized with the atmospheric pressure
(p
i
′
/p
a
). The tan
ψ
-(p
′
i
/p
a
) relationships obtained for three
different I
D
ranges are shown in Figure 1 as examples. For all
tan
ψ
-(p
i
′
/p
a
), the relationships that yield the greatest coefficient
of determination (R
2
) are used.
As it can be observed in Figure 1, tan
ψ
-(p
i
′
/p
a
) can be
considered to be approximately a linear relationship. Therefore,
it is defined using line equation as follows:
=
′
⁄ +
(4)
Here in Eq. 4,
α
ψ
and
β
ψ
are unitless fitting parameters. The
variations of
α
ψ
and
β
ψ
with I
D
are plotted in Figure 2. It can be
seen that the value of
α
ψ
is approximately constant and
β
ψ
varies linearly with I
D
. However, in order to propose functions
that would be applicable to all soils,
α
ψ
and
β
ψ
are defined as
linear functions:
=
+
(5)
=
+
(6)
Constants a
ψ
, b
ψ
, m
ψ
, and n
ψ
are fitting parameters. As a
result, a general equation can be written with the form given
below.
=
+
′
⁄ +
+
(7)
Figure 1. Tan
ψ
-(p
′
i
/p
a
) relationships for two different I
D
ranges for
Silivri sand.
However, for the soil tested, their values are given in Figure
2. According to Figure 2, a
ψ
=0, b
ψ
=-0.06, m
ψ
=0.353, and n
ψ
=0.
Hence, the dilatancy equation for Silivri Sand with Ottawa
distribution can be written as
=
′
⁄ +
= −0.06
⁄ + 0.353
(8)
Figure 2.
α
ψ
-I
D
and
β
ψ
-I
D
relationships for Silivri sand.
When the test results are analyzed considering the influence
of OCR, it is noticed that unloading has no effect on the dilatant
behavior. Thus, OCR does not affect the proposed equations.
3.2 Influence of dilatancy on peak friction angle
Peak friction angle (
φ′
) is a function of critical state friction
angle (
φ′
crit
) and dilatancy which can be defined as in Eq. 9.
= ′
+
(9)
Here, the parameter r defines the proportion of dilatancy
contribution to the frictional strength of the material. Up until
now, researchers defined parameter r as a soil dependent
constant. However, in this study the influences of I
D
and p
′
on
parameter r are also investigated. The same method of
uncoupling the influences of I
D
and p
′
is also used here.
Accordingly, for each 0.05 increment of I
D
, corresponding r-p
′
relationships are obtained. The results for 0.70
≤
I
D
<0.75 and
0.90
≤
I
D
<0.95 ranges are given in Figure 3 as examples.
