The Delft Sand, Clay & Rock Cutting Model, 2019a

The Delft Sand, Clay & Rock Cutting Model.
Figure 2-58 gives a summary of the Mohr circles for Active and Passive failure for a soil with cohesion.
Figure 2-58: The Mohr circles for active and passive failure for a soil
with cohesion.
Some equations for a soil with cohesion in the active state:
Failure will occur if:
1
v
h
sin
2
1
ccot v
2
h
(2-118)
This can also be written as:
v h v h
sin c cos
0
2 2
(2-119)
Using this equation the value of σh can be expressed into σv:
1 sin cos
2c K 2c K
1 sin 1 sin
h v a v a
(2-120)
On the other hand, the value of σv can also be expressed into σh:
1 sin cos
2c K 2c K
1 sin 1 sin
v h p h p
(2-121)
For the passive state the stresses σv and σh should be reversed.
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