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

Basic Soil Mechanics.
2.11. Summary.
Figure 2-57 gives a summary of the Mohr circles for Active and Passive failure of a cohesion less soil.
Figure 2-57: The Mohr circles for active and passive failure for a
cohesion less soil.
Some equations for a cohesion less soil in the active state:
Failure will occur if:
1
v
h
sin
2
1
v
h
2
(2-114)
This can also be written as:
v h v h
sin
0
2 2
(2-115)
Using this equation the value of σh can be expressed into σv:
1
sin
K
1
sin
h v a v
(2-116)
On the other hand, the value of σv can also be expressed into σh:
1
sin
K
1
sin
v h p h
(2-117)
For the passive state the stresses σv and σh should be reversed.
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