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

The Delft Sand, Clay & Rock Cutting Model.
7.3.7. Resulting Equations for the Cutting Process.
The strain rate is the rate of change of the strain with respect to time and can be defined as a velocity divided by a
characteristic length. For the cutting process it is important to relate the strain rate to the cutting (deformation)
velocity vc and the layer thickness hi. Since the deformation velocity is different for the cohesion in the shear plane
and the adhesion on the blade, two different equations are found for the strain rate as a function of the cutting
velocity.
v
c
sin
1.4 h
i sin
c
(7-32)
a
v
c
sin
1.4 h i sin
(7-33)
This results in the following two equations for the multiplication factor for cohesion (internal shear strength) and
adhesion (external shear strength). With τy the cohesion at zero strain rate.
c
v
sin
c
1.4
0
h i sin
y 0
1 ln 1
a
v
sin
c
1.4
0
h i sin
y 0
1 ln 1
(7-34)
(7-35)
With:
0 / y 0.1428, 0 0.03
(7-36)
Van der Schrieck (1996) published a graph showing the effect of the deformation rate on the specific energy when
cutting clay. Although the shape of the curves found are a bit different from the shape of the curves found with
equations (7-34) and (7-35), the multiplication factor for, in dredging common deformation rates, is about 2. This
factor matches the factor found with the above equations.
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