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

A Wedge in Clay Cutting.
on the equilibrium of forces and the equilibrium of moments. So for now the mobilized adhesive force Am is used
in the equations.
The horizontal equilibrium of forces on the wedge:
F h N 4 sin A m cos C 2 cos N 2 sin
C 3 0
(13-7)
The vertical equilibrium of forces on the wedge:
F v N 4 cos A m sin C 2 sin N 2 cos
N 3 0
(13-8)
To derive N4:
Multiply the horizontal equilibrium equation with sin(α).
N sin sin A cos sin C cos sin
4 m 2
N sin sin C sin 0
2 3
(13-9)
Multiply the vertical equilibrium equation with cos(α).
N cos cos A sin cos C sin cos
4 m 2
N cos cos N cos 0
2 3
(13-10)
Now add up the two resulting equations in order to get an expression for N4.
N C sin N cos C sin N cos
(13-11)
4 2 2 3 3
The mobilized adhesive force Am can be derived according to:
First multiply the horizontal equilibrium equation with cos(α).
N sin cos A cos cos C cos cos
4 m 2
N sin cos C cos 0
2 3
(13-12)
Now multiply the vertical equilibrium equation with sin(α):
N cos sin A sin sin C sin sin
4 m 2
N cos sin N sin 0
2 3
(13-13)
Subtracting the two resulting equations gives the equation for the mobilized adhesive force.
A C cos N sin C cos N sin
(13-14)
m 2 2 3 3
This can also be rewritten as an equation for the normal force N3 on the bottom of the wedge.
N N cos A sin C sin N cos
(13-15)
3 4 m 2 2
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