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

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The Delft Sand, Clay & Rock Cutting Model. Figure M-25: α=45°, h i=141 mm, h b=141 mm. ................................................................................................. M-74 Figure M-26: α=60°, h i=58 mm, h b=173 mm. ................................................................................................... M-75 Figure M-27: α=60°, h i=87 mm, h b=173 mm. ................................................................................................... M-76 Figure M-28: α=60°, h i=173 mm, h b=173 mm. ................................................................................................. M-77 Figure N-1: Blade angle 30 degrees – Deviation angle 00 degrees ................................................................... N-79 Figure N-2: Blade angle 30 degrees – Deviation angle 15 degrees ................................................................... N-80 Figure N-3: Blade angle 30 degrees – Deviation angle 30 degrees ................................................................... N-81 Figure N-4: Blade angle 45 degrees – Deviation angle 00 degrees ................................................................... N-82 Figure N-5: Blade angle 45 degrees – Deviation angle 15 degrees ................................................................... N-83 Figure N-6: Blade angle 45 degrees – Deviation angle 30 degrees ................................................................... N-84 Figure N-7: Blade angle 45 degrees – Deviation angle 45 degrees ................................................................... N-85 Figure N-8: Blade angle 60 degrees – Deviation angle 00 degrees ................................................................... N-86 Figure N-9: Blade angle 60 degrees – Deviation angle 15 degrees ................................................................... N-87 Figure N-10: Blade angle 60 degrees – Deviation angle 30 degrees ................................................................. N-88 Figure N-11: Blade angle 60 degrees – Deviation angle 45 degrees ................................................................. N-89 Figure O-1: Specific energy and production in sand for a 30 degree blade. ..................................................... O-91 Figure O-2: Specific energy and production in sand for a 45 degree blade. ..................................................... O-92 Figure O-3: Specific energy and production in sand for a 60 degree blade. ..................................................... O-93 Figure P-1: No cavitation, the angles θ, β, δ m and λ as a function of the blade angle α for φ=30º and δ=20º. .. P-95 Figure P-2: No cavitation, the cutting forces as a function of the blade angle α for φ=30º and δ=20º. ............ P-95 Figure P-3: No cavitation, the angles θ, β, δ m and λ as a function of the blade angle α for φ=35º and δ=23º. .. P-96 Figure P-4: No cavitation, the cutting forces as a function of the blade angle α for φ=35º and δ=23º. ............ P-96 Figure P-5: No cavitation, the angles θ, β, δ m and λ as a function of the blade angle α for φ=40º and δ=27º. .. P-97 Figure P-6: No cavitation, the cutting forces as a function of the blade angle α for φ=40º and δ=27º. ............ P-97 Figure P-7: No cavitation, the angles θ, β, δ m and λ as a function of the blade angle α for φ=45º and δ=30º. .. P-98 Figure P-8: No cavitation, the cutting forces as a function of the blade angle α for φ=45º and δ=30º. ............ P-98 Figure Q-1: Cavitating, the angles θ, β, δ m and λ as a function of the blade angle α for φ=30º and δ=20º. ..... Q-99 Figure Q-2: Cavitating, the cutting forces as a function of the blade angle α for φ=30º and δ=20º. ................ Q-99 Figure Q-3: Cavitating, the angles θ, β, δ m and λ as a function of the blade angle α for φ=35º and δ=23º. ... Q-100 Figure Q-4: Cavitating, the cutting forces as a function of the blade angle α for φ=35º and δ=23º. .............. Q-100 Figure Q-5: Cavitating, the angles θ, β, δ m and λ as a function of the blade angle α for φ=40º and δ=27º. ... Q-101 Figure Q-6: Cavitating, the cutting forces as a function of the blade angle α for φ=40º and δ=27º. .............. Q-101 Figure Q-7: Cavitating, the angles θ, β, δ m and λ as a function of the blade angle α for φ=45º and δ=30º. ... Q-102 Figure Q-8: Cavitating, the cutting forces as a function of the blade angle α for φ=45º and δ=30º. .............. Q-102 Figure S-1: The boundaries of the FEM model. ............................................................................................... S-109 Figure S-2: The boundaries of the 60/59 degree calculations. ......................................................................... S-109 Figure S-3: The equipotential lines. ................................................................................................................. S-110 Figure S-4: The equipotential lines in color. .................................................................................................... S-110 Figure S-5: The flow lines or stream function. ................................................................................................ S-111 Figure S-6: The stream function in colors. ....................................................................................................... S-111 Figure S-7: The pore pressures in the shear zone A-B, at the bottom of the wedge A-D, on the front of the wedge C-A and on the blade C-D ......................................................................................................... S-112 Figure S-8: The coarse mesh. ........................................................................................................................... S-113 Figure S-9: The fine mesh. ............................................................................................................................... S-113 Figure S-10: The equipotential lines. ............................................................................................................... S-114 Figure S-11: The equipotential lines in color. .................................................................................................. S-114 Figure S-12: 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. ....................................................................................................... S-115 Figure S-13: Equipotential lines of pore pressures........................................................................................... S-116 Figure S-14: Equipotential distribution in color. .............................................................................................. S-116 Figure S-15: The flow lines or stream function. .............................................................................................. S-117 Figure S-16: The stream function in colors. ..................................................................................................... S-117 Figure S-17: 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. ....................................................................................................... S-118 Figure T-1: The forces on the wedge for a 60º blade. ...................................................................................... T-119 Figure T-2: The forces on the wedge for a 75º blade. ...................................................................................... T-120 Figure T-3: The forces on the wedge for a 90º blade. ...................................................................................... T-121 Figure T-4: The forces on the wedge for a 105º blade. .................................................................................... T-122 Figure T-5: The forces on the wedge for a 120º blade. .................................................................................... T-123 Figure U-1: Specific energy and production in clay for a 30 degree blade. .................................................... U-125 Page 444 of 454 TOC Copyright © Dr.ir. S.A. Miedema
Figures & Tables. Figure U-2: Specific energy and production in clay for a 45 degree blade. .................................................... U-126 Figure U-3: Specific energy and production in clay for a 60 degree blade. .................................................... U-127 Figure V-1: The shear angle β as a function of the blade angle α and the ac ratio r. ...................................... V-129 Figure V-2: The sum of the blade angle and the shear angle. ......................................................................... V-129 Figure V-3: The horizontal cutting force coefficient λ HF as a function of the blade angle α and the ac ratio r. ... V- 130 Figure V-4: The horizontal cutting force as a function of the blade angle α and the ac ratio r (c=400 kPa). . V-130 Figure V-5: The vertical cutting force coefficient λ VF as a function of the blade angle α and the ac ratio r. . V-131 Figure V-6: The vertical cutting force as a function of the blade angle α and the ac ratio r (c=400 kPa). ..... V-131 Figure V-7: The transition Flow Type vs. Tear Type. .................................................................................... V-132 Figure V-8: The shear angle β vs. the blade angle α for the Tear Type. ......................................................... V-133 Figure V-9: The horizontal cutting force coefficient λ HT/r T. ........................................................................... V-133 Figure V-10: The vertical cutting force coefficient λ VT/r T. ............................................................................. V-134 Figure V-11: The vertical cutting force coefficient λ VT/r T zoomed. ................................................................ V-134 Figure V-12: The ratio h b/h i at the transition Flow Type/Curling Type. ......................................................... V-135 Figure V-13: The shear angle for the Curling Type ........................................................................................ V-135 Figure V-14: The horizontal cutting force coefficient λ HC. ............................................................................. V-136 Figure V-15: The vertical cutting force coefficient λ VC. ................................................................................. V-136 Figure W-1: The shear angle β as a function of the blade angle α and the internal friction angle φ for shear failure. ................................................................................................................................................. W-137 Figure W-2: The brittle (shear failure) horizontal force coefficient λ HF. ........................................................ W-137 Figure W-3: The brittle (shear failure) vertical force coefficient λ VF. ........................................................... W-138 Figure W-4: The specific energy to UCS ratio. .............................................................................................. W-138 Figure W-5: The tensile/shear failure criterion based on BTS/Cohesion. ...................................................... W-139 Figure W-6: The tensile/shear failure criterion based on UCS/BTS. ............................................................. W-139 Figure W-7: The tensile/shear failure criterion based on BTS/Cohesion. ...................................................... W-140 Figure W-8: The tensile/shear failure criterion based on UCS/BTS. ............................................................. W-140 Figure W-9: The tensile/shear failure range based on BTS/Cohesion for φ=20º. .......................................... W-141 Figure W-10: The tensile/shear failure range based on UCS/BTS for φ=20º. ............................................... W-141 Figure W-11: The tensile/shear failure range based on BTS/Cohesion for φ=0º. .......................................... W-142 Figure W-12: The tensile/shear failure range based on UCS/BTS for φ=0º. ................................................. W-142 Figure W-13: The tensile/shear failure range based on BTS/Cohesion for φ=5º. .......................................... W-143 Figure W-14: The tensile/shear failure range based on UCS/BTS for φ=5º. ................................................. W-143 Figure W-15: The tensile/shear failure range based on BTS/Cohesion for φ=10º. ........................................ W-144 Figure W-16: The tensile/shear failure range based on UCS/BTS for φ=10º. ............................................... W-144 Figure W-17: The tensile/shear failure range based on BTS/Cohesion for φ=15º. ........................................ W-145 Figure W-18: The tensile/shear failure range based on UCS/BTS for φ=15º. ............................................... W-145 Figure W-19: The tensile/shear failure range based on BTS/Cohesion for φ=20º. ........................................ W-146 Figure W-20: The tensile/shear failure range based on UCS/BTS for φ=20º. ............................................... W-146 Figure W-21: The tensile/shear failure range based on BTS/Cohesion for φ=25º. ........................................ W-147 Figure W-22: The tensile/shear failure range based on UCS/BTS for φ=25º. ............................................... W-147 Figure W-23: The tensile/shear failure range based on BTS/Cohesion for φ=30º. ........................................ W-148 Figure W-24: The tensile/shear failure range based on UCS/BTS for φ=30º. ............................................... W-148 Figure W-25: The tensile/shear failure range based on BTS/Cohesion for φ=35º. ........................................ W-149 Figure W-26: The tensile/shear failure range based on UCS/BTS for φ=35º. ............................................... W-149 Figure W-27: The tensile/shear failure range based on BTS/Cohesion for φ=40º. ........................................ W-150 Figure W-28: The tensile/shear failure range based on UCS/BTS for φ=40º. ............................................... W-150 Figure W-29: The tensile/shear failure range based on BTS/Cohesion for φ=45º. ........................................ W-151 Figure W-30: The tensile/shear failure range based on UCS/BTS for φ=45º. ............................................... W-151 Figure W-31: The brittle (tensile failure) horizontal force coefficient λ HT. ................................................... W-153 Figure W-32: The brittle (tensile failure) vertical force coefficient λ VT. ........................................................ W-153 Figure W-33: The brittle (tensile failure) horizontal force coefficient λ HT (DSCRCM, logarithmic). .......... W-154 Figure W-34: The brittle (tensile failure) horizontal force coefficient λ HT (Evans, logarithmic). ................. W-154 Figure W-35: The shear angle β as a function of the blade angle α and the internal friction angle φ for shear failure, corrected. ................................................................................................................................. W-155 Figure W-36: The brittle (tensile failure) horizontal force coefficient λ HT, corrected. ................................... W-155 Figure W-37: The brittle (tensile failure) vertical force coefficient λ VT , corrected. ...................................... W-156 Figure X-1: The ratio h b,m/h i for a 30 degree blade. ........................................................................................ X-157 Figure X-2: The shear angle β for a 30 degree blade. ..................................................................................... X-157 Figure X-3: The horizontal cutting force coefficient λ HC for a 30 degree blade. ............................................. X-158 Copyright © Dr.ir. S.A. Miedema TOC Page 445 of 454
Page 1:
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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14.4. Nomenclature. A Wedge in Atmo
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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
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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
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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 461 and 462: Figures & Tables. Chapter 18: Figur
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Page 469: 18.2. List of Figures in Appendices
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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.
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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
Page 517 and 518: The Shear Angle β Cavitating. Appe
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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
Page 603 and 604:
Force Triangles. Figure T-5: The fo
Page 605 and 606:
Specific Energy in Clay. Appendix U
Page 607 and 608:
Specific Energy in Clay. 6000 Speci
Page 609 and 610:
Clay Cutting Charts. Appendix V: Cl
Page 611 and 612:
Clay Cutting Charts. The Vertical C
Page 613 and 614:
Clay Cutting Charts. Shear Angle β
Page 615 and 616:
Clay Cutting Charts. V.3 The Curlin
Page 617 and 618:
Rock Cutting Charts. Appendix W: Ro
Page 619 and 620:
Rock Cutting Charts. W.2 The Transi
Page 621 and 622:
Rock Cutting Charts. A & B: Tensile
Page 623 and 624:
Page 625 and 626:
Page 627 and 628:
Page 629 and 630:
Page 631 and 632:
Page 633 and 634:
Rock Cutting Charts. W.5 Brittle Te
Page 635 and 636:
Rock Cutting Charts. W.6 Brittle Te
Page 637 and 638:
Hyperbaric Rock Cutting Charts. App
Page 639 and 640:
Hyperbaric Rock Cutting Charts. 100
Page 641 and 642:
Hyperbaric Rock Cutting Charts. X.2
Page 643 and 644:
Page 645 and 646:
Page 647 and 648:
Page 649 and 650:
Page 651 and 652:
Page 653 and 654:
Page 655 and 656:
Page 657 and 658:
Page 659 and 660:
Page 661 and 662:
Page 663 and 664:
Page 665 and 666:
Applications & Equipment. Appendix
Page 667 and 668:
Y.2 Bucket Ladder Dredges. Applicat
Page 669 and 670:
Y.3 Cutter Suction Dredges. Applica
Page 671 and 672:
Applications & Equipment. Figure Y-
Page 673 and 674:
Applications & Equipment. Y.4 Trail
Page 675 and 676:
Page 677 and 678:
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:
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The Delft Sand, Clay & Rock Cutting Model, 2019a

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