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

The Delft Sand, Clay & Rock Cutting Model.
a
h p h g z 10 hi
r= , r = or r ,
ch ch ch
b 1m i
w
1 1
i i i
p h
r = or r
2m b
2 2
ch i
w
g z 10 h
ch
i
b
(3-45)
Equation (3-46) can be derived for the occurrence of tensile failure under hyperbaric conditions. Under hyperbaric
conditions equation (3-46) will almost always be true, because of the terms with r1 and r2 which may become very
big (positive). So tensile failure will not be considered for hyperbaric conditions.
sin
sin
sin cos sin sin
r r2 r1 sin
sin
1
sin
c
cos
cos sin
sin
T
(3-46)
Analyzing equations (3-44) and (3-46) gives the following conclusions:
1. The first term of equations (3-44) and (3-46) is always positive.
2. If the sum of α+β+δ>π/2, in the second term of equation (3-44) and the fourth term of equation (3-46), these
terms are positive, which will be the case for normal cutting angles.
3. The second and third terms of equation (3-46) are always positive.
4. The last term in equations (3-44) and (3-46) is always negative.
5. Equation (3-44) may become negative and fulfill the condition for the Tear Type.
6. Equation (3-46) will never become negative under normal conditions, so under hyperbaric conditions the Tear
Type will never occur.
7. The Tear Type may occur with clay and rock under atmospheric conditions.
Figure 3-14: The forces on the layer cut.
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