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

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The Delft Sand, Clay & Rock Cutting Model. Figure 9-6: The Crushed Type cutting mechanism. .............................................................................................300 Figure 9-7: The forces on the layer cut in rock (hyperbaric). ...............................................................................301 Figure 9-8: The forces on the blade in rock (hyperbaric). ....................................................................................301 Figure 9-9: The horizontal cutting force coefficient λ HF for a 60 degree blade, h b/h i=1. .....................................303 Figure 9-10: The vertical cutting force coefficient λ VF for a 60 degree blade, h b/h i=1. ........................................303 Figure 9-11:The shear angle β, for a 60 degree blade, h b/h i=1. ............................................................................304 Figure 9-12: The E sp/UCS ratio, for a 60 degree blade, h b/h i=1. ..........................................................................304 Figure 9-13: The Tear Type cutting mechanism in rock under hyperbaric conditions. .......................................305 Figure 9-14: The Chip Type cutting mechanism in rock under hyperbaric conditions. .......................................305 Figure 9-15: The Curling Type or balling. ...........................................................................................................306 Figure 9-16: The equilibrium of moments on the layer cut in hyperbaric rock. ...................................................306 Figure 9-17: The ratio h b,m/h i for a 60 degree blade. ............................................................................................309 Figure 9-18:The shear angle β for a 60 degree blade ...........................................................................................309 Figure 9-19: The horizontal cutting force coefficient λ HC for a 60 degree blade. ................................................310 Figure 9-20: The vertical cutting force coefficient λVC for a 60 degree blade. Positive downwards. ...................310 Figure 9-21: The E sp/UCS ratio, for a 60 degree blade. .......................................................................................311 Figure 9-22: The theory of hyperbaric cutting versus the Zijsling (1987) experiments. .....................................313 Figure 9-23: The specific energy E sp and the drilling strength S, theory versus the Zijsling (1987) experiments. .......................................................................................................................................................314 Figure 9-24: The ratio h b,m/h i for a 110 degree blade. ..........................................................................................315 Figure 9-25:The shear angle β for a 110 degree blade. ........................................................................................315 Figure 9-26: The horizontal cutting force coefficient λ HC for a 110 degree blade. ..............................................316 Figure 9-27: The vertical cutting force coefficient λVC for a 110 degree blade. Positive upwards. ......................316 Figure 9-28: The E sp/UCS ratio, for a 110 degree blade. .....................................................................................317 Figure 9-29: The specific energy E sp in rock versus the compressive strength (UCS) for a 110º blade...............319 Figure 9-30: The specific energy E sp in rock versus the compressive strength (UCS) for a 45º blade. ...............320 Figure 9-31: The specific energy E sp in rock versus the compressive strength (UCS) for a 60º blade. ...............321 Figure 10-1: The occurrence of a wedge. .............................................................................................................325 Figure 10-2: The forces on the layer cut when a wedge is present.......................................................................329 Figure 10-3: The forces on the wedge. .................................................................................................................329 Figure 10-4: The forces on the blade when a wedge is present. ...........................................................................330 Figure 10-5: The moments on the wedge. ............................................................................................................330 Figure 11-1: Definitions. ......................................................................................................................................333 Figure 11-2: Alternative geometry of the layer cut. ............................................................................................333 Figure 11-3: The cutting mechanism. ..................................................................................................................333 Figure 11-4: The forces on the layer cut when a wedge is present.......................................................................336 Figure 11-5: The forces on the wedge. .................................................................................................................337 Figure 11-6: The forces on the blade when a wedge is present. ...........................................................................337 Figure 11-7: The moments on the wedge. ............................................................................................................338 Figure 11-8: The shear angle, wedge angle and mobilized external friction angle calculated with wedge. .........339 Figure 11-9: The total cutting force. ....................................................................................................................340 Figure 11-10: The direction of the total cutting force. .........................................................................................340 Figure 11-11: The shear angle of Hatamura & Chijiiwa (1977B) versus the calculated shear angles, with and without wedge. ..............................................................................................................................341 Figure 11-12: The shear angle, wedge angle and mobilized external friction angle calculated with wedge. .......341 Figure 11-13: The total force of Hatamura & Chijiiwa (1977B) versus the calculated total force, with and without wedge. ...........................................................................................................................................342 Figure 11-14: The direction of the cutting force of Hatamura & Chijiiwa (1977B) versus the calculated force direction, with and without wedge. ...............................................................................................342 Figure 12-1: Failure pattern with rake angle of 120º. ...........................................................................................345 Figure 12-2: Sand cutting with a wedge, definitions. ...........................................................................................346 Figure 12-3: The cutting mechanism. ..................................................................................................................346 Figure 12-4: The forces on the layer cut in saturated sand with a wedge. ...........................................................348 Figure 12-5: The forces on the wedge in saturated sand. .....................................................................................348 Figure 12-6: The forces on the blade in saturated sand with a wedge. .................................................................348 Figure 12-7: The volume balance over the shear zone. ........................................................................................351 Figure 12-8: Possible flow lines. ..........................................................................................................................351 Figure 12-9: The boundaries of the FEM model. .................................................................................................352 Figure 12-10: Pore pressure distribution on the shear plane A-B, the bottom of the wedge A-D, the blade D-C and the front of the wedge A-C. ...........................................................................................................352 Page 440 of 454 TOC Copyright © Dr.ir. S.A. Miedema
Figures & Tables. Figure 12-11: The parallel resistor method. .........................................................................................................353 Figure 12-12: The coarse mesh. ...........................................................................................................................354 Figure 12-13: The fine mesh. ...............................................................................................................................354 Figure 12-14: Equipotential lines of pore pressures. ............................................................................................355 Figure 12-15: Equipotential distribution in color. ................................................................................................355 Figure 12-16: The flow lines or stream function. .................................................................................................356 Figure 12-17: The stream function in colors. .......................................................................................................356 Figure 12-18: The equilibrium of moments on the wedge in water saturated sand. .............................................357 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 ; h i=1; h b=3; k i/k max=0.25 .....................................................................................................358 Figure 12-20: The moment versus the shear angle for 4 different wedge angles for: α=90 0 ; δ=28 0 ; φ=42 0 ; h i=1; h b=3; k i/k max=0.25 ..........................................................................................................................359 Figure 12-21: The forces on the wedges at 60, 75, 90, 105 and 120 cutting angles. ...................................360 Figure 12-22: No cavitation, the angles θ, β, δ m and λ as a function of the blade angle α for φ=30º and δ=20º. 361 Figure 12-23: No cavitation, the cutting forces as a function of the blade angle α for φ=30º and δ=20º. ............361 Figure 12-24: Cavitating, the angles θ, β, δ m and λ as a function of the blade angle α for φ=30º and δ=20º. ......363 Figure 12-25: Cavitating, the cutting forces as a function of the blade angle α for φ=30º and δ=20º. .................363 Figure 12-26: The lower and upper limit where a static wedge can exist for the non-cavitating cutting process. .......................................................................................................................................................364 Figure 12-27: The lower and upper limit where a static wedge can exist for the cavitating cutting process. ......364 Figure 12-28: The lower limit where the wedge starts to occur. ..........................................................................365 Figure 12-29: Cross section of the cutting tank. ..................................................................................................367 Figure 12-30: Front view of the test facility. ........................................................................................................368 Figure 12-31: The blade mounted under the carriage .........................................................................................369 Figure 12-32: The camera in front of the window. .............................................................................................369 Figure 12-33: Cover with camera behind the blade. ............................................................................................369 Figure 12-34: The Perspex window in the blade. .................................................................................................370 Figure 12-35: View of the cutting process through the Perspex window. ............................................................370 Figure 12-36: Cutting forces for cutting depths (h i) from 3 to 7 cm; blade angle 60°. .......................................371 Figure 12-37: Cutting forces for cutting depths (h i) from 3 to 7 cm; blade angle 75°. .......................................372 Figure 12-38: Cutting forces for cutting depths (h i) from 3 to 7 cm; blade angle 90°. .......................................373 Figure 12-39: The dynamic wedge. ......................................................................................................................374 Figure 13-1: The occurrence of a wedge in clay cutting. .....................................................................................377 Figure 13-2: The forces on the layer cut in clay cutting with a wedge. ...............................................................380 Figure 13-3: The forces on the wedge in clay cutting. .........................................................................................380 Figure 13-4: The forces on the blade when cutting clay with a wedge. ...............................................................381 Figure 13-5: The equilibrium of moments on the wedge when cutting clay. .......................................................381 Figure 14-1: Definitions. ......................................................................................................................................385 Figure 14-2: The forces on the layer cut when a wedge is present.......................................................................388 Figure 14-3: The forces on the wedge. .................................................................................................................388 Figure 14-4: The forces on the blade when a wedge is present. ...........................................................................389 Figure 14-5: The moments on the wedge. ............................................................................................................389 Figure 15-1: Definitions. ......................................................................................................................................393 Figure 15-2: The forces on the layer cut when a wedge is present.......................................................................396 Figure 15-3: The forces on the wedge. .................................................................................................................397 Figure 15-4: The forces on the blade when a wedge is present. ...........................................................................397 Figure 15-5: The moments on the wedge. ............................................................................................................398 Figure 16-1: The horizontal cutting forces. ..........................................................................................................412 Figure 16-2: The specific energy. ........................................................................................................................412 Figure 16-3: The pore pressures on blade and shear plane...................................................................................413 Figure 16-4: The horizontal cutting forces. ..........................................................................................................416 Figure 16-5: The specific energy. ........................................................................................................................416 Figure 16-6: The pore pressures on blade and shear plane...................................................................................417 Figure 16-7: The Mohr circles. ............................................................................................................................419 Figure 16-8: The Mohr circles for a tensile strength of -2 MPa. Tensile Failure. ................................................421 Figure 16-9: The Mohr circles for a tensile strength of -10 MPa. Shear Failure. .................................................421 Figure 16-10: The Mohr circles with tensile strength of -10 MPa (UCS=100 MPa, φ=20º). Shear Failure. ......423 Figure 16-11: The Mohr circles with tensile strength of -5 MPa (UCS=100 MPa, φ=20º). Tensile Failure. .....424 Figure 16-12: The Mohr circles with tensile strength of -10 MPa (UCS=60 MPa, φ=20º). Shear Failure. ........426 Figure 16-13: The Mohr circles with tensile strength of -3 MPa (UCS=60 MPa, φ=20º). Tensile Failure. .......428 Copyright © Dr.ir. S.A. Miedema TOC Page 441 of 454
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The Delft Sand, Clay & Rock Cutting
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Chapter 1: Introduction. 1.1. Appro
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Introduction. In dry sand cutting t
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Chapter 2: Basic Soil Mechanics. 2.
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Basic Soil Mechanics. 2.2.2. Soil C
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Basic Soil Mechanics. soil characte
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Basic Soil Mechanics. 2.3. Soils. 2
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Basic Soil Mechanics. 2.3.2. Clay.
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Basic Soil Mechanics. 2.3.3. Rock.
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Basic Soil Mechanics. Figure 2-12:
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Basic Soil Mechanics. Figure 2-15 B
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2.4. Soil Mechanical Parameters. Ba
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Basic Soil Mechanics. 2.4.2.4. Impo
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Basic Soil Mechanics. Table 2-3: Em
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Basic Soil Mechanics. 2.4.3.4. Poro
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Basic Soil Mechanics. 3 3 2 l e 3 g
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Basic Soil Mechanics. 46 Friction a
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Basic Soil Mechanics. c tan (2-
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2.4.9. Unconfined Tensile Strength.
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Basic Soil Mechanics. 2.5. Criteria
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Basic Soil Mechanics. increase, to
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Basic Soil Mechanics. Table 2-14: T
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2.6. Soil Mechanical Tests. 2.6.1.
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Basic Soil Mechanics. be regarded a
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2.6.5.1. Consolidated Drained (CD).
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Basic Soil Mechanics. 2.8. The Mohr
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Basic Soil Mechanics. Squaring equa
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Basic Soil Mechanics. 2.9. Active S
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Basic Soil Mechanics.
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Basic Soil Mechanics. 2.10. Passive
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cos sin cos sin 1 1 sin
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Basic Soil Mechanics. 2.11. Summary
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2.12. Shear Strength versus Frictio
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Basic Soil Mechanics. 2.13. Nomencl
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The General Cutting Process. Chapte
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The General Cutting Process. 10. β
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The General Cutting Process. The fo
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The General Cutting Process. W2 si
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The General Cutting Process.
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The General Cutting Process.
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3.6. The Snow Plough Effect. The Ge
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The General Cutting Process. The ve
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3.6.5. The Resulting Cutting Forces
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The General Cutting Process. Q c Pc
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Which Cutting Mechanism for Which K
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4.6. Summary. Which Cutting Mechani
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Chapter 5: Dry Sand Cutting. 5.1. I
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Dry Sand Cutting. The force K1 on t
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Dry Sand Cutting. Horizontal Cuttin
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Dry Sand Cutting. 2 v s i VD F
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Dry Sand Cutting. Horizontal Cuttin
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Dry Sand Cutting. Shear Angle β vs
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Dry Sand Cutting. 5.6. Specific Ene
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5.8. Experiments in Dry Sand. 5.8.1
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Dry Sand Cutting. 5.8.2. Wismer & L
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Chapter 6: Saturated Sand Cutting.
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Saturated Sand Cutting. 2 ci c i F
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Saturated Sand Cutting. the Waterlo
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Saturated Sand Cutting. The normal
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Saturated Sand Cutting. Figure 6-8:
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Saturated Sand Cutting. Figure 6-10
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6.7. The Blade Tip Problem. Saturat
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Saturated Sand Cutting. s2 0.8 L
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Saturated Sand Cutting. However Fig
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Saturated Sand Cutting. S1=L1*(1-I/
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Saturated Sand Cutting. 6.9. Determ
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' h Saturated Sand Cutting.
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Saturated Sand Cutting. α=45° and
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Saturated Sand Cutting. 6.12.1. Spe
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Saturated Sand Cutting. 100.0 SPT v
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Saturated Sand Cutting. 6.12.2. The
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Saturated Sand Cutting. 6.13. Exper
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Saturated Sand Cutting. The tests a
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Saturated Sand Cutting. old laborat
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Saturated Sand Cutting. 6.13.2. Tes
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Saturated Sand Cutting. side effect
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Saturated Sand Cutting. 6.13.7. Com
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Saturated Sand Cutting. which the t
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Saturated Sand Cutting. The dimensi
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Saturated Sand Cutting. 10 Partial
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Saturated Sand Cutting. The equatio
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Saturated Sand Cutting. 0.30 No Cav
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Saturated Sand Cutting. P4 (bar) P3
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Saturated Sand Cutting. 10.0 8.0 Fh
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Saturated Sand Cutting. Preal Real
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Clay Cutting. Chapter 7: Clay Cutti
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Clay Cutting. 7.3. The Influence of
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Clay Cutting. From this equation, s
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Clay Cutting. a material on which a
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Clay Cutting. 7.3.4. The Proposed T
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Clay Cutting. 100 90 Shear Strength
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Clay Cutting. 7.3.6. Abelev & Valen
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Clay Cutting. 2500 The Strain Rate
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Clay Cutting. 7.4. The Flow Type. 7
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Clay Cutting. F s ch i w s ah b
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Clay Cutting. Figure 7-22 shows the
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Clay Cutting. The Horizontal Cuttin
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Clay Cutting. 7.5. The Tear Type. 7
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7.5.3. The Mobilized Shear Strength
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7.5.4. The Resulting Cutting Forces
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Clay Cutting. Vertical Cutting Forc
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Clay Cutting. This gives for the no
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Clay Cutting. Substituting equation
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Clay Cutting. Figure 7-34: The equi
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Clay Cutting. Vertical Cutting Forc
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Clay Cutting. 0.30 Vertical Cutting
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Clay Cutting. 1000 Clay Cutting Esp
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Clay Cutting. Shear Angle β vs. Bl
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Clay Cutting. Horizontal Cutting Fo
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Clay Cutting. 7.9. Nomenclature. a
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Rock Cutting: Atmospheric Condition
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8.2.3. Based on UTS and UCS. Rock C
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8.2.5. Hoek & Brown (1988). Rock Cu
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8.3. Cutting Models. Rock Cutting:
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8.3.5. The Nishimatsu Model. Rock C
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sin Rock Cutting: Atmospheric Cond
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Rock Cutting: Hyperbaric Conditions
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9.8. Specific Energy Graphs. Rock C
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The Occurrence of a Wedge. Chapter
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The Occurrence of a Wedge. 19. A fo
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The Occurrence of a Wedge. h 4 4
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10.3. The Equilibrium of Moments. T
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A Wedge in Dry Sand Cutting. Chapte
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A Wedge in Dry Sand Cutting. The no
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A Wedge in Dry Sand Cutting. Figure
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11.4. Results of some Calculations.
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A Wedge in Dry Sand Cutting. 11.5.
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A Wedge in Dry Sand Cutting. 11.6.
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A Wedge in Saturated Sand Cutting.
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12.4. The Equilibrium of Moments. A
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12.8. Experiments. A Wedge in Satur
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12.10. Nomenclature. A Wedge in Sat
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A Wedge in Clay Cutting. Chapter 13
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A Wedge in Clay Cutting. on the equ
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A Wedge in Clay Cutting. Figure 13-
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A Wedge in Clay Cutting. L3 L7
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A Wedge in Atmospheric Rock Cutting
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A Wedge in Atmospheric Rock Cutting
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Page 417 and 418: 14.4. Nomenclature. A Wedge in Atmo
Page 419 and 420: A Wedge in Hyperbaric Rock Cutting.
Page 425 and 426: 15.4. Nomenclature. A Wedge in Hype
Page 427 and 428: Exercises. Chapter 16: Exercises. 1
Page 429 and 430: Exercises. 16.2.8. Calc.: Bulldozer
Page 431 and 432: Exercises. 16.3. Chapter 3: The Gen
Page 433 and 434: Exercises. 16.4.5. MC: Hyperbaric R
Page 435 and 436: Exercises. 16.6. Chapter 6: Water S
Page 437 and 438: Exercises. 2 2 1 w c i c g v h
Page 439 and 440: Exercises. F: Determine the pore pr
Page 441 and 442: Exercises. E sp Fh vc Fh Fh 10
Page 443 and 444: Exercises. 1,000 Pore Pressures on
Page 445 and 446: Exercises. A tensile strength of -2
Page 447 and 448: Exercises. Shear Stress vs. Normal
Page 449 and 450: Exercises. 70 60 50 40 Shear Stress
Page 451 and 452: Exercises. 16.8.4. Calc.: Cutting F
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Page 455 and 456: Exercises. 16.9. Chapter 9: Hyperba
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Page 461 and 462: Figures & Tables. Chapter 18: Figur
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Page 475 and 476: Figures & Tables. 18.3. List of Tab
Page 477 and 478: 18.4. List of Tables in Appendices.
Page 479 and 480: Appendices. Chapter 19: Appendices.
Page 481 and 482: Active & Passive Soil Failure Coeff
Page 483 and 484: Dry Sand Cutting Coefficients. Appe
Page 485 and 486: Dry Sand Cutting Coefficients. B.1.
Page 489 and 490: Dry Sand Cutting Coefficients. B.2
Page 495 and 496: Dry Sand Cutting Coefficients. B.3
Page 497 and 498: Dry Sand Cutting Coefficients. Perc
Page 499 and 500: Dimensionless Pore Pressures p1m &
Page 501 and 502: The Shear Angle β Non-Cavitating.
Page 503 and 504: The Shear Angle β Non-Cavitating.
Page 505 and 506: Appendix E: The Coefficient c1. The
Page 507 and 508: The Coefficient c1. Table E-3: c1 f
Page 509 and 510: Appendix F: The Coefficient c2. The
Page 511 and 512: The Coefficient c2. Table F-3: c2 f
Page 513 and 514: Appendix G: The Coefficient a1. The
Page 515 and 516: The Coefficient a1. Table G-3: a1 f
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The Shear Angle β Cavitating. Appe
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The Shear Angle β Cavitating. Tabl
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Appendix I: The Coefficient d1. The
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The Coefficient d1. Table I-3: d1 f
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Appendix J: The Coefficient d2. The
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The Coefficient d2. Table J-3: d2 f
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The Properties of the 200 μm Sand.
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Experiments in Water Saturated Sand
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The Snow Plough Effect. Appendix N:
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The Snow Plough Effect. 10.0 8.0 Fh
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The Snow Plough Effect. 20.0 16.0 F
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Specific Energy in Sand. Appendix O
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Specific Energy in Sand. 2500 Speci
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Occurrence of a Wedge, Non-Cavitati
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Occurrence of a Wedge, Non-Cavitati
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Occurrence of a Wedge, Cavitating.
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Occurrence of a Wedge, Cavitating.
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Pore Pressures with Wedge. Appendix
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Pore Pressures with Wedge. Table R-
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Pore Pressures with Wedge. Table R-
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FEM Calculations with Wedge. Append
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FEM Calculations with Wedge. Figure
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S.3 The 75 Degree Blade. FEM Calcul
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Appendix T: Force Triangles. Force
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Force Triangles. Figure T-3: The fo
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Force Triangles. Figure T-5: The fo
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Specific Energy in Clay. Appendix U
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Specific Energy in Clay. 6000 Speci
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Clay Cutting Charts. Appendix V: Cl
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Clay Cutting Charts. The Vertical C
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Clay Cutting Charts. Shear Angle β
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Clay Cutting Charts. V.3 The Curlin
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Rock Cutting Charts. Appendix W: Ro
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Rock Cutting Charts. W.2 The Transi
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Rock Cutting Charts. A & B: Tensile
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Rock Cutting Charts. W.5 Brittle Te
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Rock Cutting Charts. W.6 Brittle Te
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Hyperbaric Rock Cutting Charts. App
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Hyperbaric Rock Cutting Charts. 100
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Hyperbaric Rock Cutting Charts. X.2
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Applications & Equipment. Appendix
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Y.2 Bucket Ladder Dredges. Applicat
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Y.3 Cutter Suction Dredges. Applica
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Applications & Equipment. Figure Y-
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Applications & Equipment. Y.4 Trail
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Y.5 Backhoe Dredges. Applications &
Page 679 and 680:
Y.6 Clamshell Dredges. Applications
Page 681 and 682:
Page 683 and 684:
Y.7 Bucket Wheel Dredges. Applicati
Page 685 and 686:
Y.8 Braun Kohle Bergbau. Applicatio
Page 687 and 688:
Y.9 Deep Sea Mining. Applications &
Page 689 and 690:
Page 691 and 692:
Y.10 Cable Trenching. Applications
Page 693 and 694:
Y.11 Offshore Pipeline Trenching. A
Page 695 and 696:
Y.12 Dry Trenching. Applications &
Page 697 and 698:
Applications & Equipment. Y.13 PDC
Page 699 and 700:
Applications & Equipment. Y.14 Bull
Page 701 and 702:
Applications & Equipment. Y.15 Dry
Page 703 and 704:
Y.16 Tunnel Boring Machines. Applic
Page 705 and 706:
Publications. Appendix Z: Publicati
Page 707 and 708:
Publications. 52. Miedema, S.A.,
Page 710:
show all

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

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