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

The Delft Sand, Clay & Rock Cutting Model.
Figure 2-51: Active soil failure. .............................................................................................................................61
Figure 2-52: The Mohr circle for active soil failure. ..............................................................................................64
Figure 2-53: An example of active soil failure, Utah copper mine landslide (photoblog.nbcnews.com). .............64
Figure 2-54: Passive soil failure. ............................................................................................................................65
Figure 2-55: The Mohr circle for passive soil failure. ............................................................................................68
Figure 2-56: An example of passive soil failure, the Komatsu D65PX-15 (www.youtube.com). .........................68
Figure 2-57: The Mohr circles for active and passive failure for a cohesion less soil. .........................................69
Figure 2-58: The Mohr circles for active and passive failure for a soil with cohesion. ........................................70
Figure 2-59: The coefficients of active and passive soil failure K a & K p. ..............................................................71
Figure 2-60: The coefficient of active soil failure K a. ............................................................................................72
Figure 2-61: The coefficient of passive soil failure K p. .........................................................................................72
Figure 3-1: The Curling Type, the Flow Type, the Tear Type, the Shear Type, the Crushed Type and the Chip
Type. ...............................................................................................................................................75
Figure 3-2: The cutting process, definitions. ..........................................................................................................76
Figure 3-3: The Flow Type ....................................................................................................................................77
Figure 3-4: The Shear Type ...................................................................................................................................77
Figure 3-5: The Crushed Type. ..............................................................................................................................77
Figure 3-6: The forces on the layer cut. .................................................................................................................78
Figure 3-7: The forces on the blade. ......................................................................................................................78
Figure 3-8: The Curling Type of cutting mechanism. ............................................................................................81
Figure 3-9: The general equilibrium of moments. .................................................................................................81
Figure 3-10: The Tear Type cutting mechanism in clay. ......................................................................................82
Figure 3-11: The Chip Type cutting mechanism in rock. .....................................................................................82
Figure 3-12: The Mohr circle for UCS and cohesion. ............................................................................................83
Figure 3-13: The Mohr circles of the Tear Type. ...................................................................................................85
Figure 3-14: The forces on the layer cut. ...............................................................................................................86
Figure 3-15: Urban winter service vehicle with snowplow (commons.wikimedia.org). ........................................88
Figure 3-16: The 3D cutting process. .....................................................................................................................88
Figure 3-17: Velocity conditions............................................................................................................................89
Figure 3-18: Force directions. ................................................................................................................................89
Figure 3-19: A piece of a program showing the iteration scheme. .........................................................................92
Figure 4-1: The Shear Type in dry sand cutting. ....................................................................................................95
Figure 4-2: The Shear Type in saturated sand cutting. ...........................................................................................96
Figure 4-3: The Curling Type in clay and loam cutting. ........................................................................................98
Figure 4-4: The Flow Type in clay and loam cutting. ............................................................................................98
Figure 4-5: The Tear Type in clay and loam cutting. .............................................................................................98
Figure 4-6: The Crushed Type in atmospheric rock cutting. ................................................................................100
Figure 4-7: The Chip Type in atmospheric rock cutting. .....................................................................................100
Figure 4-8: The Crushed Type in hyperbaric rock cutting. ..................................................................................101
Figure 5-1: The cutting mechanism in dry sand, the Shear Type. ........................................................................105
Figure 5-2: Dry sand modeled according to the Flow Type. ...............................................................................105
Figure 5-3: The cutting process, definitions. ........................................................................................................105
Figure 5-4: The forces on the layer cut in dry sand. .............................................................................................106
Figure 5-5: The forces on the blade in dry sand. ..................................................................................................106
Figure 5-6: The shear angle β as a function of the blade angle α for h b/h i=2. ......................................................108
Figure 5-7: The horizontal cutting force coefficient λ HD as a function of the blade angle α for h b/h i=2. ............109
Figure 5-8: The vertical cutting force coefficient λ VD as a function of the blade angle α for h b/h i=2. ................109
Figure 5-9: The alternative shape of the layer cut. ...............................................................................................110
Figure 5-10: The shear angle β as a function of the blade angle α for h b/h i=2. ....................................................111
Figure 5-11: The horizontal cutting force coefficient λ HD as a function of the blade angle α for h b/h i=2. ..........113
Figure 5-12: The vertical cutting force coefficient λ VD as a function of the blade angle α for h b/h i=2. ..............113
Figure 5-13: The percentage inertial force for a layer thickness h i=1.0 m, blade height h b=1.0 m and a cutting
velocity v c=0.5 m/sec. ...................................................................................................................114
Figure 5-14: The percentage inertial force for a layer thickness h i=1.0 m, blade height h b=1.0 m and a cutting
velocity v c=15.7 m/sec. .................................................................................................................114
Figure 5-15: The shear angle β, including the effect of inertial forces.................................................................115
Figure 5-16: The horizontal cutting force coefficient λ HI. ....................................................................................115
Figure 5-17: The vertical cutting force coefficient λ VI. ........................................................................................116
Figure 5-18: A dredging wheel used in the German braunkohl mines (www.wikiwand.com). ...........................118
Figure 5-19: The shear angle versus the blade angle. ..........................................................................................119
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