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

The Delft Sand, Clay & Rock Cutting Model.
The length of the blade D-C is:
hb
D C L4
sin
(12-34)
The distance between the blade edge and the wedge side A-C (perpendicular) is:
(12-35)
L L sin
5 3
The distance from point A and the line L5 is:
(12-36)
L L cos
6 3
The arm of the acting point of N2 and W2 is now:
L7 L6 R2
(12-37)
The equilibrium of moments can be determined using all those distances:
M N 4 W 4 R 4 N 3 W 3 R 3 N 2 W 2 L 7 S 2 L 5 0
(12-38)
Equation (12-38) still contains the unknown arms R2, R3 and R4. Based on the FEM calculations for the pore
pressures, values of 0.35·L2, 0.55·L3 and 0.32·L4 are found, Ma (2001). Figure 12-19 shows the moments on the
wedge with respect to the cutting edge as a function of the wedge angle θ for different values of the shear angle β
and a blade angle α of 90º. The moment is zero for a wedge angle θ between 50º and 55º.
2.0
Moment versus Wedge Angle
1.6
1.2
0.8
Moment
0.4
0.0
-0.4
-0.8
-1.2
-1.6
-2.0
45 47 49 51 53 55 57 59 61 63 65
Wedge Angle (deg.)
Beta=15 deg. Beta=20 deg. Beta=25 deg. Beta=30 deg.
Figure 12-19: Moment versus wedge angle θ by using polynomial regression for:
α=90 0 ; β=15 0 ,20 0 ,25 0 ,30 0 ; δ=28 0 ; φ=42 0 ; hi=1; hb=3; ki/kmax=0.25
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