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

Which Cutting Mechanism for Which Kind of Soil?
The forces K1 and K2 on the blade, chisel or pick point are now:
K
K
1
2
W2
sin( ) W1
sin( ) G sin( )
sin( )
Icos( ) Ccos( ) A cos( )
sin( )
W2
sin( ) W1
sin( ) G sin( )
sin( )
Icos( ) Ccos( )
Acos( )
sin( )
(4-13)
(4-14)
The normal forces N1 on the shear plane and N2 on the blade are:
N 1 K1
cos
and N 2 K2
cos
(4-15)
The horizontal and vertical forces on the blade, chisel or pick point are:
F h W2
sin( ) K2
sin( ) Acos(
)
(4-16)
F W cos( ) K cos( ) Asin(
)
(4-17)
v 2
2
The equilibrium of moments around the blade tip is:
N
W
R G R N
W
1 1 1 3 2 2 2
R
(4-18)
Analyzing these equations results in the following conclusions:
At normal cutting angles in dredging, the argument of the cosine in the cohesive term of K1 is greater than 90
degrees, resulting in a small positive term as a whole. Together with the adhesive term, this gives a positive
normal stress on the shear plane. The minimum normal stress however equals the normal stress on the shear
plane, minus the radius of the Mohr circle, which is the cohesion. The result may be a negative minimum
normal stress. If this negative minimum normal stress is smaller than the negative tensile strength, the Tear
Type will occur. This occurrence depends on the ratio between the adhesive force to the cohesive force. A
large ratio will suppress the Tear Type.
The adhesive force on the blade is proportional to the (mobilized) length of the blade, so the Curling Type
may occur. The cohesive force on the shear plane is proportional to the (mobilized) cohesion, so the Tear
Type may occur. The occurrence of the Curling Type or Tear Type depends on the ratio of the adhesive
force to the cohesive force. A large ratio results in the Curling Type, a small ratio in the Tear Type.
When the argument of the sine in the denominator gets close to 180 degrees, the forces become very large. If
the argument is greater than 180 degrees, the forces would become negative. Since both conditions will not
happen in nature, nature will find another cutting mechanism, the wedge mechanism. In clay this is not likely
to occur, since there are only two angles in the argument of the sine in the denominator. It would require very
large blade angles to occur.
4.4. Cutting Rock Atmospheric.
Rock is the collection of materials where the grains are bonded chemically from very stiff clay, sandstone to very
hard basalt. It is difficult to give one definition of rock or stone and also the composition of the material can differ
strongly. Still it is interesting to see if the model used for sand and clay, which is based on the Coulomb model,
can be used for rock as well. Typical parameters for rock are the compressive strength UCS and the tensile strength
BTS and specifically the ratio between those two, which is a measure for how fractured the rock is. Rock also has
shear strength and because it consists of bonded grains it will have an internal friction angle and an external friction
angle. It can be assumed that the permeability of the rock is very low, so initially the pore pressures do no play a
role under atmospheric conditions. Since the absolute hydrostatic pressure, which would result in a cavitation
under pressure of the same magnitude can be neglected with respect to the compressive strength of the rock; the
pore pressures are usually neglected. This results in a material where gravity, inertia, pore pressures and adhesion
can be neglected.
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