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

Rock Cutting: Atmospheric Conditions.
8.9. Resulting Forces & Mohr Circles.
1.60
Horizontal Cutting Force F h vs. Tensile Strength BTS-UTS
1.40
Fh Flow, Shear or
Crushed Type
Horizontal Cutting Force F h (MN)
1.20
1.00
0.80
0.60
0.40
Fh Tear Type -
Beta Flow Type
Fh Tear Type -
Beta Tear Type
Lower Limit BTS-
UTS Chip Type
Upper Limit BTS-
UTS Chip Type
0.20
Fh Chip Type
0.00
0 5 10 15 20 25
-Tensile Strength BTS-UTS (MPa)
© S.A.M.
Figure 8-49: Horizontal cutting force: α=60 º, UCS=100 MPa, φ=20º, hi=0.1 m & w=0.1 m.
Vertical Cutting Force F v vs. Tensile Strength BTS-UTS
0.40
0.35
Fv Flow, Shear or
Crushed Type
Vertical Cutting Force F v (MN)
0.30
0.25
0.20
0.15
0.10
Fv Tear Type -
Beta Flow Type
Fv Tear Type -
Beta Tear Type
Lower Limit BTS-
UTS Chip Type
Upper Limit BTS-
UTS Chip Type
0.05
Fv Chip Type
0.00
0 5 10 15 20 25
-Tensile Strength BTS-UTS (MPa)
© S.A.M.
Figure 8-50: Vertical cutting force: α=60 º, UCS=100 MPa, φ=20º, hi=0.1 m & w=0.1 m.
Figure 8-49 and Figure 8-50 show the horizontal and vertical cutting forces. The transition tensile failure/shear
failure occurs at a tensile strength of about -8.5 MPa, so 8.5% of the UCS value. From a tensile strength of -8.5
MPa (8.5% UCS) to -20 MPa (20% UCS), both tensile failure and shear failure are possible. Below a tensile
strength of -20 MPa (20% UCS) only shear failure is possible. Figure 8-51 and Figure 8-52 show the Mohr circles
for tensile strengths of -8.5 MPa (8.5% UCS) and -20 MPa (20% UCS). One can see that with a tensile strength of
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