898
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
Figure 6.
α
ψ
-I
D
and
β
ψ
-I
D
relationships for Erksak sand.
Evidently, when the parameters of Erksak sand (a
ψ
=0, b
ψ
=-
0.012, m
ψ
=0.687, n
ψ
=0) are inserted into Eq. 7, the following
function is obtained.
= −0.012
⁄ + 0.687
(14)
When Equations 8 and 14 are compared, it can be seen that
for both soils the same form of tan
ψ
-(p
′
i
/p
a
) relationship is
obtained.
The influence of dilatancy on the frictional behavior is also
investigated. For the r parameter, the obtained
α
r
-I
D
and
β
r
-I
D
relationships are given in Figure 7.
Figure 7.
α
r
-I
D
and
β
r
-I
D
relationships for Erksak sand.
As it can be observed from Figure 7, the same form of the
r=
g
(p
′
i
,I
D
) function shown in Eq. 13 can also be defined for
Erksak sand. Of course, the line-fitting parameters are clearly
different but this can be attributed to the differences in the grain
shape, size and distribution between the two sands. Erksak sand
is obviously more uniform compared to Silivri sand with
Ottawa grading. The difference between e
max
and e
min
is greater
for Silivri sand than it is for Erksak sand. It might be proposed
that the uniformities of sands control the influence of dilatant
behavior on strength, but this proposition requires further
testing on different sands with varying uniformities.
5 CONCLUSIONS
In this paper, dilatancy angle and its influence on friction angle
are quantified for cohesionless soils. This is achieved by
analyzing the results of an extensive triaxial testing program on
K
o
-consolidated cohesionless soils. The results are arranged in a
way that allows the observation of the uncoupled effects of the
influential parameters; I
D
and p
′
i
. Moreover, it has been shown
that OCR does not affect dilatant behavior. Even though the
general form of the
ψ
=
f
(p
′
i
,I
D
) function is given in Eq. 7, the
present data suggests a simpler version as shown in Eq. 8:
=
′
⁄ +
(r.8)
The data from Silivri sand with Ottawa grading and Erksak
sand, both support the Eq. 8 form of
ψ
=
f
(p
′
i
,I
D
) function. Here,
b
ψ
and m
ψ
are soil dependent unitless constants. For now, there
is not sufficient data to correlate the values of b
ψ
and m
ψ
to
grain shape, grain size distribution, and mineralogy. However, it
is believed that, as the corresponding constants for different
soils are obtained, it would be possible to link b
ψ
and m
ψ
to
mineralogy, grain shape, and grain size distribution
characteristics. Similarly, the influence of dilatancy angle on the
peak friction angle of the soil is defined. This influence is again
a function of p
′
i
and I
D
. As a result, peak friction angle can be
calculated by using Eq. 9 and Eq. 13.
In order to obtain the constants for Eq. 8 and Eq. 13, it is
sufficient to conduct 12 triaxial tests on clean cohesionless
sands. The most important advantage of the proposed equations
is that the dilatancy and peak friction angles are calculated using
directly measurable and/or calculable soil parameters. This
attribute significantly increases the practicality of the dilatancy
and peak friction angle calculations. Once the required
parameters are defined for a specific soil, it will be possible to
calculate the variations in dilatancy and friction angle just by
tracking the changes in stress state and volumetric state.
6 ACKNOWLEDGEMENTS
Authors would like to acknowledge the Scientific and
Technological Research Council of Turkey (TUBITAK) for
providing financial support to this project under TUBITAK
Project 110M595.
7 REFERENCES
Abadkon A. 2012.
Strength and Dilatancy of Anisotropic Cohesionless
Soils
. Ph.D. Thesis. Bogazici University, Istanbul, Turkey.
Bolton M. D. 1986. Strength and dilatancy of sands.
Géotechnique
36
(1), 65-78.
Chakraborty T. and Salgado R. 2010. Dilatancy and Shear Strength of
Sand at Low Confining Pressures.
ASCE Journal of Geotechnical
and Geoenvironmental Engineering
136 (3), 527-532.
Cinicioglu O. and Abadkon A. 2012. Anizotropik Kohezyonsuz
Zeminlerin Mukavemet ve Genle
ş
im Özellikleri. 14th National
Congress on Soil Mech & Foundation Eng, October 4-5, Isparta,
Turkey (in Turkish).
De Josselin de Jong G. 1976. Rowe’s stress-dilatancy relation based on
friction.
Géotechnique
26 (3), 527-534.
Rowe P. W. 1962. The stress-dilatancy relation for static equilibrium of
an assembly of particles in contact.
Proc. R. Soc. A,
269 (1339),
500-527.
Vaid Y. P. and Sasitharan S. 1992. The Strength and Dilatancy of Sand.
Canadian Geotechnical Journal
29 (3), 522-526.
Schanz T. and Vermeer P. A. 1996. Angle of friction and dilatancy of
sand.
Géotechnique
46 (1), 145-151.
Taylor D. W. 1948.
Fundamentals of Soil Mechanics
. John Wiley and
Sons, New York.