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

7.8.2. Wismer & Luth (1972B).
The Delft Sand, Clay & Rock Cutting Model.
Wismer & Luth (1972B) investigated rate effects in soil cutting in dry sand, clay and loam. For clay and loam they
distinguished two rate effects, the inertial forces and the strengthening effect. For cutting velocities as known in
dredging (up to 5-6 m/sec), the inertial forces can be neglected compared to the static cutting forces (low cutting
velocities) and compared to the strengthening effect. Wismer & Luth (1972B) carried out experiments with blade
angles of 30°, 60° and 90°, blades of 0.19·0.29 m, 0.127·0.193 m and 0.0762·0.117 m (7.5·11.45 inch, 5.0·7.6
inch and 3.0·4.59 inch) and layer thicknesses from 0.0225-0.0762 m (0.9-3.0 inch). They did the experiments in
two types of clay. Unfortunately they did not mention the cohesion and adhesion, but the mentioned a cone
resistance. However, based on their graphs the cohesion could be deducted. The cone index 27 clay should have
had a cohesion of about 22.5 kPa and an adhesion of 11.25 kPa, the cone index 42 clay a cohesion of 34 kPa and
an adhesion of 17 kPa. The strengthening factor of Wismer & Luth (1972B) can be rewritten in SI Units, using the
reference strain rate of 0.03/sec, giving the following equation for the strengthening factor.
vc
h
0.03
i
y s with: s
0.1
(7-106)
Figure 7-49 shows the theoretical strengthening factors based on the average of equations (7-34) and (7-35) and
for the above equation for the minimum and maximum layer thickness, giving a range for the strengthening factor
and comparing the Miedema (1992) equation with the Wismer & Luth (1972B) equation. The figure also shows
the results of 5 series of tests as carried out by Wismer & Luth (1972B) with a 30° blade. The two equations match
well up to cutting velocities of 1.5 m/sec, but this may differ for other configurations. At high cutting velocities
the Wismer & Luth (1972B) equation gives larger strengthening factors. Both equations give a good correlation
with the experiments, but of course the number of experiments is limited. A realistic strengthening factor for
practical cutting velocities in dredging is a factor 2. In other words, a factor of about 2 should be used to multiply
the static measured cohesion, adhesion and tensile strength.
It should be mentioned that the above equation is modified compared with the original Wismer & Luth (1972B)
equation. They used the ratio cutting velocity to blade width to get the correct dimension for strain rate, here the
ratio cutting velocity to layer thickness is used, which seems to be more appropriate. The constant of 0.03 is the
constant found from the experiments of Hatamura & Chijiiwa (1977B).
3.0
Strengthening Factor λ vs. Cutting Velocity v c
Labda Miedema 1
2.8
Strengthening Factor λ (-)
2.6
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
Labda Miedema 2
Labda Wismer &
Luth 1
Labda Wismer &
Luth 2
W&L Series 1
W&L Series 2
W&L Series 3
W&L Series 4
W&L Series 5
0.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Cutting Velocity v c (m/sec)
© S.A.M.
Figure 7-49: The strengthening factor.
Page 238 of 454 TOC Copyright © Dr.ir. S.A. Miedema