Geoscience Reference
In-Depth Information
2.3.4 Friction Angle (
φ
) and Cohesion (c)
The shear strength of the soil is described as the function of normal stress on the
slip surface, cohesion, and angle of internal friction. The angle of internal friction
(
φ
) and cohesion are the two important physical properties of the soil which
determines angle of rupture, shearing strength, safety factor as well as stability
condition of the slope materials. A Mohr Stress Circle was developed to obtain
angle of internal friction and angle of rupture through confining pressure (
˃
3
) and
compressive stress (
˃
1
) with the centre on the horizontal axis; the centre of the
circle was obviously (
˃
1
+
˃
3
)/2 and the radius was (
˃
1
-
˃
3
)/2. The values of
con
ning pressure,
˃
3
, and compressive stress,
˃
1
were plotted on horizontal axis
where stress difference is
˃
1
−
˃
3
. On a plane parallel to the greatest principal stress
axis (2
ʱ
= 0) the normal stress across the plane was
˃
3
and the shearing stress was
0. If the plane makes an angle of 45
°
with the greatest principal stress axis
(2
ʱ
= 90), the shearing stress is at a maximum and the normal stress is (
˃
1
+
˃
3
)/2. If
the plane makes an angle of 90
°
with the greatest principal stress axis (2
˃
= 180
°
),
the shearing stress is 0 and the normal stress is
˃
1
.
Cohesion (C) is the attraction of particles to each other which is not directly
governed by a friction law but does provide a measure of strength of a material.
Thus sands do not exhibit cohesion, while soil which contains clay show cohesion.
It can be measured, as in soil mechanics, by the Mohr-Coulomb Equation.
2
þ
2
Þ ¼
r
1
r
3
tan
45
C cohesion
ð
ð
2
:
7
Þ
þ
2
2
þ
tan
45
The cohesion of the soil varies from place to place due to variation in the
presence of cementing materials which helps to combine soil particles tightly. This
is the bonding of the particles with each other. The natural bonding of the soil
particles are influenced and loosened by the presence of lubricating agent (water
and ice particles) and ensure the materials to collapse. The friction angle of sand-
stone under dry condition varies from 26
°
to 35
°
and under wet condition 25
°
-
34
°
.
Fine-grained granite provides the friction angle of 31
°
-
35
°
and 29
°
-
31
°
for dry and
wet condition respectively. In case of gneiss, friction angle is 26
°
-
29
°
for dry and
23
for wet condition (Barton and Choubey
1977
). The above mentioned
lithological compositions are available in the Shivkhola Watershed and laboratory
test of 50 soil samples shows that the friction angle ranges between 18
°
-
26
°
°
and 32
°
(Appendix C).
At Lower Paglajhora and 14 Miles Bustee, the geo-technical properties of soil
are very much conducive to soil slip (Table
2.13
). In the present study the friction
angle for the concerned material varies from 18
(Fig.
2.14
). Around
Tindharia and Lower Paglajhora friction angle ranges between 18
°
and 22
°
. A steep
slope will decline by slope failure to an angle of repose slope to attain short term
stability. This concept leads to the concept of limiting or Threshold slope angle. It is
clearly observed from the
°
to 32
°
figure that middle section, extreme lower most part,
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