Geoscience Reference
In-Depth Information
þ
2
Þ
2
Þ
¼
r
1
r
3
tan
ð
45
C cohesion
ð
ð
6
:
10
Þ
þ
2
Þ
2
þ
tan
ð
45
For the determination of the cohesive strength and the angle of internal friction a
series of experiments were done with different values of con
ning pressure (
˃
3
).
The Mohr Circle shows that as the con
ning pressure is increased, the stress as well
as the stress difference must be increased to produce rapture. A line which is the
tangent of the
. The angle that this
line makes with the horizontal axis of the diagram is the angle of internal friction,
Mohr Circle
'
is called as the
Mohr Envelope
'
'
'
/
(Fig.
5.2
). Along any potential plane of rupture within a rock:
l
¼
s=
n
¼ tan
/
ð
6
:
11
Þ
where
µ
is the coef
cient of internal friction,
˄
=
shearing stress along plane,
n =
normal stress along the lane,
/
=
the angle of internal friction.
The
˄
is at a maximum when
ʱ
=45
°
; whereas n is at a minimum when
ʱ
= 0 and
ʱ
°
˄
at a maximum when
combine to
make the shear stress most effective. Actual shear fracture makes an angle of less
than 45
=90
. Shear fracture develops when n and
with the greatest principal stress axis (Billings
1987
).
The intercept on the vertical axis,
˄
o
, is the cohesive strength of the rock. The
curve for the Mohr envelope is:
°
s
¼
s
o
þ r
n
tan
/
ð
6
:
12
Þ
where, the angle that fractures should theoretically make with the greatest principal
axis is
a
¼
45
/=
2
ð
6
:
13
Þ
So, if the angle of internal friction is 30
°
, the fractures would make the angle of
30
with the greatest principal stress axis. On the other hand the shear fracture
should theoretically form at 30
°
(Billings
1987
).
The frictional angle of a particular soil depends on various factors (Cernnica
1995
) like:
°
State of compaction and void ratio increasing the density. The relation is not
necessarily the linear one.
Coarseness, the shape of the particle and the angularity of the particle of the soil:
Angular grains interlock more effectively than rounded ones, thereby creating a
larger friction angle.
Mineralogical content of the soil: Hard gravel particles result in higher friction
angles. Soft grains which may crush more easily,
thereby reducing the
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