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

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The Delft Sand, Clay & Rock Cutting Model. And for the cavitating cutting process: Fci di w g (z 10) hi w (6-74) In which: d 1 sin( ) hb sin( ) sin( ) sin( ) hi sin( ) hb sin( ) sin( ) h sin( ) i (6-75) And: d 2 sin( ) hb sin( ) cos( ) sin( ) hi sin( ) hb cos( ) sin( ) h sin( ) i (6-76) The values of the 4 coefficients are determined by minimizing the cutting work that is at that shear angle where the derivative of the horizontal force to the shear angle is zero. The coefficients c1, c2, d1 and d2 are given in Miedema (1987 September) and in 0 and 0 for the non-cavitating cutting process and 0 and 0 for the cavitating cutting process as functions of , , and the ratio hb/hi. 6.11.1. Approximations. Assuming δ=2/3·φ the coefficients can be approximated by: α=30° and hb/hi=1: 0.0509 0.0341 1 2 c 0.0427 e and c 0.0343 e 0.0516 1 2 d 0.3027 e and d 0.3732 0.0219 (6-77) α=30° and hb/hi=2: 0.0511 0.0356 1 2 c 0.0455 e and c 0.0304 e 0.0490 1 2 d 0.4795e and d 0.5380 0.0159 (6-78) α=30° and hb/hi=3: 0.0512 0.0348 1 2 c 0.0457 e and c 0.0312 e 0.0478 1 2 d 0.6418e and d 0.7332 0.0094 (6-79) α=45° and hb/hi=1: 0.0577 0.0255 1 2 c 0.0485 e and c 0.0341 e 0.0603 1 2 d 0.2618e and d 0.0287 0.0081 (6-80) Page 150 of 454 TOC Copyright © Dr.ir. S.A. Miedema
Saturated Sand Cutting. α=45° and hb/hi=2: 0.0580 0.0238 1 2 c 0.0545 e and c 0.0281 e 0.0577 1 2 d 0.3764e and d 0.0192 0.0017 (6-81) α=45° and hb/hi=3: 0.0589 0.0199 1 2 c 0.0551 e and c 0.0286 e 0.0563 1 2 d 0.4814e and d 0.0295 0.0116 (6-82) α=60° and hb/hi=1: 0.0688 2 1 2 c 0.0474 e and c 0.2902 0.0203 0.000334 0.0722 1 2 d 0.2342e and d 1.0548 0.0343 (6-83) α=60° and hb/hi=2: 0.0686 2 1 2 c 0.0562 e and c 0.3550 0.0235 0.000403 0.0695 1 2 d 0.3148e and d 1.2737 0.0516 (6-84) α=60° and hb/hi=3: 0.0692 2 1 2 c 0.0593 e and c 0.3785 0.0250 0.000445 0.0680 1 2 d 0.3889e and d 1.4708 0.0685 (6-85) The shear angle β can be approximated by, for the non-cavitating case: hb 0.0037 (6-86) 3 h i The shear angle β can be approximated by, for the cavitating case: 1 2 hb 1 0.057 (6-87) 6 7 h i Copyright © Dr.ir. S.A. Miedema TOC Page 151 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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Which Cutting Mechanism for Which K
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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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A Wedge in Hyperbaric Rock Cutting.
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15.4. Nomenclature. A Wedge in Hype
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Exercises. Chapter 16: Exercises. 1
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Exercises. 16.2.8. Calc.: Bulldozer
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Exercises. 16.3. Chapter 3: The Gen
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Exercises. 16.4.5. MC: Hyperbaric R
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Exercises. 16.6. Chapter 6: Water S
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Exercises. 2 2 1 w c i c g v h
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Exercises. F: Determine the pore pr
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Exercises. E sp Fh vc Fh Fh 10
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Exercises. 1,000 Pore Pressures on
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Exercises. A tensile strength of -2
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Exercises. Shear Stress vs. Normal
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Exercises. 70 60 50 40 Shear Stress
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Exercises. 16.8.4. Calc.: Cutting F
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Exercises. 16.8.5. Calc.: Cutting F
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Exercises. 16.9. Chapter 9: Hyperba
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Bibliography. Chapter 17: Bibliogra
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Bibliography. Miedema, S. (1989, De
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Figures & Tables. Chapter 18: Figur
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Figures & Tables. Figure 5-20: The
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Figures & Tables. Figure 8-5: Const
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Figures & Tables. Figure 12-11: The
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18.2. List of Figures in Appendices
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Figures & Tables. Figure U-2: Speci
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Figures & Tables. Figure Y-27: A la
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Figures & Tables. 18.3. List of Tab
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18.4. List of Tables in Appendices.
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Appendices. Chapter 19: Appendices.
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Active & Passive Soil Failure Coeff
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Dry Sand Cutting Coefficients. Appe
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Dry Sand Cutting Coefficients. B.1.
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Dry Sand Cutting Coefficients. B.2
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Dry Sand Cutting Coefficients. B.3
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Dry Sand Cutting Coefficients. Perc
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Dimensionless Pore Pressures p1m &
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The Shear Angle β Non-Cavitating.
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The Shear Angle β Non-Cavitating.
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Appendix E: The Coefficient c1. The
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The Coefficient c1. Table E-3: c1 f
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Appendix F: The Coefficient c2. The
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The Coefficient c2. Table F-3: c2 f
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Appendix G: The Coefficient a1. The
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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 &
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Y.6 Clamshell Dredges. Applications
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Y.7 Bucket Wheel Dredges. Applicati
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Y.8 Braun Kohle Bergbau. Applicatio
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Y.9 Deep Sea Mining. Applications &
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Y.10 Cable Trenching. Applications
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Y.11 Offshore Pipeline Trenching. A
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Y.12 Dry Trenching. Applications &
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Applications & Equipment. Y.13 PDC
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Applications & Equipment. Y.14 Bull
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Applications & Equipment. Y.15 Dry
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Y.16 Tunnel Boring Machines. Applic
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Publications. Appendix Z: Publicati
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Publications. 52. Miedema, S.A.,
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