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

The Delft Sand, Clay & Rock Cutting Model.
If the material is now subjected to an external shear stress, four cases can be distinguished with respect to the strain
rate.
Figure 7-9: The probability of net activation in case 1.
The energy level Ea +N/2S is smaller than the limiting energy level El (Figure 7-9). The strain
rate equation is now:
Case 1:
T E a N
2 X k exp sinh
h i R T
2 S R
T
(7-10)
E
with: i 1 exp R T
Except for the coefficient i, necessary to ensure that the total probability remains 1, equation (7-10)
is identical to equation (7-6).
The activation energy Ea is less than the limiting energy El, but the energy level E+N/2S is
greater than the limiting energy level El (Figure 7-10).
Case 2:
The strain rate equation is now:
Ea
N E
X k T exp
exp
i R T 2S R T
R
T
(7-11)
h
The activation energy Ea is greater than the limiting energy El, but the energy level Ea -N/2S is
less than the limiting energy level El (Figure 7-11). The strain rate equation is now:
Case 3:
Ea
N E
X k T exp
exp
i R T 2S R T
R
T
(7-12)
h
Equation (7-12) appears to be identical to equation (7-11), but the boundary conditions differ.
Case 4:
The activation energy Ea is greater than the limiting energy El and the energy level Ea -N/2S is
greater than the limiting energy level El (Figure 7-12). The strain rate will be equal to zero in this
case.
The cases 1 and 2 are similar to the case considered by Mitchell (1976) and still do not permit true cohesion and
adhesion. Case 4 considers particles at rest without changing position within the particle matrix. Case 3 considers
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