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

6.13.6. Scale Effects.
The Delft Sand, Clay & Rock Cutting Model.
The soil mechanical research showed that the density of the sand increases slightly with the depth. Since both the
permeability and the volume strain, and less significant the other soil mechanical parameters, are influenced by
the density, it is important to know the size of this influence on the cutting forces (assuming that the twodimensional
cutting theory is a valid description of the process). If the two-dimensional cutting theory is a valid
description of the process, the dimensionless cutting forces will have to give the same results for similar geometric
ratios, independent of the dimensions and the layer-thickness, according to the equations for the non-cavitating
cutting process and the cavitating cutting process. The following blade configurations are used to research the
scaling influence:
1. A blade with a width of 150 mm wide and a height of 100 mm.
2. A blade with a width of 150 mm wide and a height of 150 mm.
3. A blade with a width of 150 mm wide and a height of 200 mm.
4. A blade with a width of 150 mm wide and a height of 300 mm.
The results of this research can be found in Table 6-4, where every value represents the average value of a number
of tests.
Table 6-4: Influence of the scale factor.
Configuration 1 2 3 4
hb/hi h = 0.10 0.15 0.20 0.30
30° 1 0.93 1.00 0.94 1.18
30° 2 1.23 1.00 1.06 1.13
30° 3 ---- 1.00 0.89 0.90
45° 1 0.95 1.00 1.13 ----
45° 2 0.89 1.00 1.05 1.30
45° 3 ---- 1.00 1.02 1.13
60° 1 0.91 1.00 ---- ----
60° 2 0.90 1.00 1.19 1.04
60° 3 1.02 1.00 1.13 1.21
The total cutting force ct with blade heights of 0.10 m (1), 0.15 m (2), 0.20 m (3) and 0.30 m (4) in proportion to
the cutting force at a blade height 0.15 m (2). The blade configurations are according chapter 6.13.4. Because the
influences of the gravity and inertia forces can disturb the character of the dimensionless forces compared to 0 to
0, the measured forces are first corrected for these influences. The forces in the table are in proportion to the forces
that occurred with blade configuration 2. The following conclusions can be drawn from the table:
1. There is a slight tendency to larger dimensionless forces with increasing dimensions of the blades and the
layer-thickness, which could be expected with the slightly increasing density.
2. For a blade angle of 30 and a blade-height / layer-thickness ratio of 2, large dimensionless forces are measured
for blade configuration 1. These are the tests with the thinnest layer-thickness of 25 mm. A probable cause
can be that the rounding of the blade tip in proportion with the layer-thickness is relatively large, leading to a
relatively large influence of this rounding on the cutting forces. This also explains the development of the
dimensionless forces at a blade angle of 30 and a blade-height / layer-thickness ratio of 3.
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