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

The Delft Sand, Clay & Rock Cutting Model.
Figure 6-54: An example of pore pressure measurements versus the theory. ......................................................183
Figure 6-55: An example of the forces measured versus the theory. ...................................................................184
Figure 6-56: An example of the measured signals (forces and pore pressures). ..................................................185
Figure 6-57: F h, F v, F d and E sp as a function of the cutting velocity and the layer thickness, without deviation.186
Figure 6-58: F h, F v, F d and E sp as a function of the cutting velocity and the layer thickness, with deviation. .....187
Figure 7-1: The cutting process, definitions. ........................................................................................................191
Figure 7-2: The Curling Type in clay. ..................................................................................................................192
Figure 7-3: The Flow Type in clay.......................................................................................................................192
Figure 7-4: The Tear Type in clay. ......................................................................................................................192
Figure 7-5: The Boltzman probability distribution. .............................................................................................193
Figure 7-6: The probability of exceeding an energy level Ea. .............................................................................193
Figure 7-7: The probability of net activation in direction of force. ......................................................................194
Figure 7-8: The adapted Boltzman probability distribution. ................................................................................195
Figure 7-9: The probability of net activation in case 1. .......................................................................................196
Figure 7-10: The probability of net activation in case 2. .....................................................................................197
Figure 7-11: The probability of net activation in case 3. .....................................................................................197
Figure 7-12: The probability of net activation in case 4. .....................................................................................197
Figure 7-13: Shear stress as a function of strain rate with the horizontal axis logarithmic. .................................201
Figure 7-14: Shear stress as a function of strain rate with logarithmic axis. ........................................................201
Figure 7-15: Comparison of 3 rheological models. ..............................................................................................202
Figure 7-16: Abelev & Valent (2010) data. .........................................................................................................203
Figure 7-17: Comparison of the model developed with the v/d Schrieck (1996) model. .....................................205
Figure 7-18: The Flow Type cutting mechanism when cutting clay. ...................................................................207
Figure 7-19: The forces on the layer cut in clay. ..................................................................................................207
Figure 7-20: The forces on the blade in clay. .......................................................................................................207
Figure 7-21: The shear angle as a function of the blade angle and the ac ratio r. ................................................212
Figure 7-22: The blade angle α + the shear angle β. ............................................................................................212
Figure 7-23: The horizontal cutting force coefficient λ HF as a function of the blade angle and the ac ratio r. ....213
Figure 7-24: The vertical cutting force coefficient λ VF as a function of the blade angle and the ac ratio r. .........213
Figure 7-25: Specific energy and production in clay for a 60 degree blade. ........................................................214
Figure 7-26: The Tear Type cutting mechanism in clay. .....................................................................................215
Figure 7-27: The transition Flow Type vs. Tear Type. ........................................................................................218
Figure 7-28: The Mohr circles when cutting clay. ...............................................................................................218
Figure 7-29: The shear angle β vs. the blade angle α for the Tear Type. .............................................................220
Figure 7-30: The horizontal cutting force coefficient λ HT/r T. ...............................................................................220
Figure 7-31: The vertical cutting force coefficient λ VT/r T. ...................................................................................221
Figure 7-32: The vertical cutting force coefficient λ VT/r T zoomed. ......................................................................221
Figure 7-33: The Curling Type cutting mechanism when cutting clay. ...............................................................222
Figure 7-34: The equilibrium of moments on the layer cut in clay. .....................................................................227
Figure 7-35: The shear angle β for the Curling Type. ..........................................................................................228
Figure 7-36: The horizontal cutting force coefficient λ HC. ...................................................................................228
Figure 7-37: The vertical cutting force coefficient λ VC. .......................................................................................229
Figure 7-38: The ratio h b/h i at the transition Flow Type/Curling Type. ...............................................................229
Figure 7-39: Horizontal force; cohesion c=1 kPa, adhesion a=1 kPa, tensile strength σ T=-0.3 kPa, blade height
h b=0.1 m, blade angle α=55° .........................................................................................................230
Figure 7-40: Vertical force; Cohesion c=1 kPa, adhesion a=1 kPa, tensile strength σ T=-0.3 kPa, blade height h b=0.1
m, blade angle α=55°.....................................................................................................................231
Figure 7-41: The Mohr circles for h i=0.1 m, two possibilities. ............................................................................231
Figure 7-42: The Mohr circles for h i=0.5 m, only tensile failure possible. ..........................................................232
Figure 7-43: The specific energy E sp in clay as a function of the compressive strength (UCS). ..........................233
Figure 7-44: The shear angles measured and calculated. .....................................................................................235
Figure 7-45: The total cutting force measured and calculated. ............................................................................235
Figure 7-46: The direction of the total cutting force measured and calculated. ...................................................236
Figure 7-47: The 60 degree experiments. .............................................................................................................236
Figure 7-48: The 30 degree experiment. ..............................................................................................................237
Figure 7-49: The strengthening factor. .................................................................................................................238
Figure 8-1: Ductile and brittle cutting Verhoef (1997). .......................................................................................241
Figure 8-2: The stress-strain curves for ductile and brittle failure. ......................................................................242
Figure 8-3: The Chip Type. ..................................................................................................................................243
Figure 8-4: Failure envelopre according to Verhoef (1997) (Figure 9.4) of intact rock. .....................................243
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