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

A Wedge in Saturated Sand Cutting.
The normal force on the shear plane A-B is now:
W2 sin( ) W1 sin( )
N1
cos( )
sin( )
(12-7)
The normal force on the pseudo blade A-C is now:
W2 sin( ) W1 sin( )
N2
cos( )
sin( )
(12-8)
Now the force equilibrium on the wedge has to be solved. This is done by first taking the horizontal and vertical
force equilibrium on the wedge A-C-D.
The horizontal equilibrium of forces:
F W sin K sin K sin
h 4 4 e 3
W sin K sin 0
2 2
(12-9)
The vertical equilibrium of forces:
F W cos K cos W K cos
v 4 4 e 3 3
W cos K cos 0
2 2
(12-10)
The grain force K3 on the bottom of the wedge is now:
K
3
sin
W2 sin e K2 sin e
W sin W sin
sin
3 e 4 e
e
e
(12-11)
The grain force K4 on the blade is now:
K
4
sin
W2 sin K2 sin
e
W3 sin W4 sin
sin
e
(12-12)
From equation (12-12) the forces on the pseudo blade can be derived. On the pseudo blade a force component in
the direction of cutting velocity Fh and a force perpendicular to this direction Fv can be distinguished.
Fh W4 sin K4sin
e
(12-13)
F W cos K cos
(12-14)
v 4 4 e
12.3. Pore Pressures.
If the cutting process is assumed to be stationary, the water flow through the pores of the sand can be described in
a blade motions related coordinate system. The determination of the water vacuum pressures in the sand around
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