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

The Delft Sand, Clay & Rock Cutting Model.
At large blade angles nature will look for an alternative mechanism, the wedge mechanism, which is discussed in
later chapters.
5.4. An Alternative Shape of the Layer Cut.
The shape of the layer cut will most probably be different with dry sand cutting compared to saturated sand cutting
or clay and rock cutting. First of all with dry sand cutting the cutting forces are determined by the weight of the
layer cut while with the other types of soil the weight can be neglected. Secondly in dry sand there are no forces
to keep the layer cut together, so the sand will move down if possible and the maximum slopes will be under the
angle of natural repose φnr (usually about 30°). Figure 5-9 shows this alternative shape of the layer cut. The line
D-E-F is the top of the sand, where the two marked areas have the same cross section.
Figure 5-9: The alternative shape of the layer cut.
The gravitational force (weight dry) follows, based on Figure 5-9, from:
sin( )
G s g hi
w
sin( )
h cos
b hi cos( ) hi
sin( )
sin( ) 2 sin( ) 2sin( ) sin
nr
nr
(5-15)
Based on the weight only of the soil, the forces can now be expressed as:
2
h s i HD
F g h w
With :
sin( ) sin( ) sin( )
HD
sin( ) sin( )
(5-16)
h b /hi
cos( ) sin( )
cos
sin( ) 2 sin( ) 2sin( ) sin
nr
nr
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