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

Saturated Sand Cutting.
6.13.7. Comparison of Measurements versus Theory.
The results of the preceding three investigations are collected in Table 6-5, compared with the theory. Every value
is the average of a number of tests. In the table it can be found:
1. The dimensionless forces, the average from the several scales and blade widths.
2. As 1, but corrected for the gravity and inertia forces.
3. The theoretical dimensionless forces according to Appendix D to Appendix J.
Table 6-5: The total cutting force measured.
measured
calculated
not-corrected corrected theoretical
hb/hi c t t c t t c t t
30° 1 0.52 +13.3° 0.48 +17.1° 0.39 +28.3°
30° 2 0.56 +17.0° 0.53 +20.1° 0.43 +27.4°
30° 3 0.56 +24.8° 0.53 +28.2° 0.43 +27.3°
45° 1 0.71 + 4.9° 0.63 + 7.5° 0.49 +12.9°
45° 2 0.75 + 6.0° 0.66 + 8.0° 0.57 +10.7°
45° 3 0.76 + 5.1° 0.70 + 6.9° 0.61 + 9.9°
60° 1 1.06 + 1.2° 0.88 + 1.9° 0.69 - 0.7°
60° 2 1.00 - 2.4° 0.84 - 3.4° 0.83 - 3.2°
60° 3 0.99 - 3.4° 0.85 - 4.2° 0.91 - 4.6°
The total cutting force measured (not-corrected and corrected for the gravity and inertia forces) and the theoretical
total cutting forces (all dimensionless). The theoretical values for ct and t are based on an angle of internal friction
of 38, a soil/steel angle of friction of 30 and a weighted average permeability of approximately 0.000242 m/s
dependent on the weigh factor a 1. The total cutting force ct and the force direction t are determined according
chapter 6.12.4. The following conclusions can be drawn from this table:
1. The measured and corrected cutting forces are larger than the, according to the theory, calculated cutting
forces, at blade angles of 30 and 45. The differences become smaller with an increase in the blade angle and
when the blade-height / layer-thickness ratio increases.
2. For a blade angle of 60 the corrected measure forces agree well with the calculated forces.
3. The tendency towards larger forces with a larger blade-height / layer-thickness ratio (theory) is clearly present
with blade angles 30 and 45.
4. At a blade angle of 60 the forces seem to be less dependent of the blade-height / layer-thickness ratio.
5. The direction of the measured cutting forces agrees well with the theoretical determined direction. Only at the
blade angle of 30 the forces are slightly aimed more upward for the blade-height / layer-thickness ratios 1
and 2.
6. Neglecting the inertia forces, gravity, etc. introduces an error of at least 15% within the used velocity range.
This error occurs with the 60 blade, where the cutting velocity is the lowest of all cutting tests and is mainly
due to the gravity.
Considering that the sand, in the course of the execution of the tests, as a result of segregation, has obtained a
slightly coarser grain distribution and that the tests are performed with an increasing blade angle, can be concluded
that the test results show a good correlation with the theory. It has to be remarked, however, that the scale and side
effects can slightly disturb the good correlation between the theory and the measurements.
6.13.8. Location of the Resulting Cutting Force.
A quantity that is measured but has not been integrated in the theory is the location of the resulting cutting force.
This quantity can be of importance for the determination of the equilibrium of a drag head. The locations, of the
in this chapter performed tests, are listed in Table 6-6. Table 6-7 lists the dimensionless locations of the resulting
cutting force, in relation with the layer-thickness.
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