Geoscience Reference
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σ
'
=
σ
+
σ
'
cap
[6.15]
Therefore, Mohr-Coulomb's expression for a granular medium (
c
' = 0) becomes
=
σ
+
σ
tg
φ
=
σ
tg
φ
+
σ
tg
φ
[6.16]
cap
cap
= σ φ
is called “capillary cohesion”. It is dependent on
the degree of saturation and becomes zero when
The quantity
C
'
t g
cap
cap
S
= or
0
S
= .
1
For a material with a natural cohesion
na
C
(in the case of cementation), the total
cohesion, when the material is unsaturated, is (Figure 6.6)
C
=
C
+
C
tot
nat
cap
[6.17]
Recently, [SOU 06] generalized these calculations to the case of contact between
spheres of different diameters and with imperfect wetting (Figure 6.7). They
proposed the following analytical form to express the capillary force versus the
geometry of the pair of particles:
D
[6.18]
F
=
πγ
R R
+
exp
a
+
b
lg
1 2
R
2
where
R
and
R
are the particle radii and
D
is the interparticular distance.
−
0.53
1.1
V
[6.19]
a
=−
3
2
R
V
V
[6.20]
2
b
=−
0.148ln
−
0.96
θ
−
0.0082ln
+
0.48
3
3
R
R
2
2
V
[6.21]
c
=
0.0018ln
+
0.078
3
2
R
V
: volume of the liquid bridge
θ: contact angle
γ
lg
: water-air surface tension
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