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

Dry Sand Cutting.
2
v s i VD
F g h w
With :
sin( ) sin( ) cos( )
VD
sin( ) sin( )
(5-17)
h b /hi
cos( ) sin( )
cos
sin( ) 2 sin( ) 2sin( ) sin
nr
nr
60
Shear Angle β vs. Blade Angle α
55
φ=25°
50
Shear Angle β (Degrees)
45
40
35
30
25
20
15
φ=30°
φ=35°
φ=40°
φ=45°
10
5
φ=50°
© S.A.M.
0
15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90
Blade Angle α (Degrees)
Figure 5-10: The shear angle β as a function of the blade angle α for hb/hi=2.
Figure 5-10, Figure 5-11 and Figure 5-12 show the shear angle and the cutting force coefficients for the alternative
shape of the layer cut. The difference with the standard configuration is small. Other configurations may exist, but
no big differences are expected. The model for dry sand or gravel can also be used for saturated sand, if the cutting
process is completely drained and there are no pore vacuum pressures. This only occurs if the permeability is very
high, which could be the case in gravel. Of course the dry density of the sand or gravel has to be replaced by the
submerged density of the sand or gravel, which is usually close to unity.
The shapes of the curves between the standard configuration and the alternative configuration are very similar.
The shear angle first increases with an increasing blade angle up to a maximum after which the shear angle
decreases with a further increasing shear angle. The shear angle also decreases with an increasing angle of internal
friction. It should be noted here that the external friction angle is assumed to be 2/3 of the internal friction angle.
The cutting forces become very high at large blade angles (close to 90°). Nature will find an alternative cutting
mechanism in this case which has been identified as the wedge mechanism. At which blade angle the wedge
mechanism will start to occur depends on the internal and external friction angles, but up to a blade angle of 60°
the model as described here can be applied. See Chapter 11: A Wedge in Dry Sand Cutting. for detailed information
on the wedge mechanism.
5.5. The Influence of Inertial Forces.
In the previous chapter the shear angle and the cutting forces are given for the influence of the weight only. This
will be appropriate for very small cutting velocities, but the question is of course; what is a very low cutting speed.
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