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

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8.10. Example. The Delft Sand, Clay & Rock Cutting Model. In this chapter and in Appendix W many graphs are given with a red or green rectangle giving the value of the different parameters for an α=60º blade and an internal friction angle φ=20º. The external friction angle is assumed to be δ=2/3·φ. Most graphs are dimensionless, but Figure 8-49, Figure 8-50, Figure 8-51 and Figure 8-52 are based on a compressive strength UCS=100 MPa, a blade width w=0.1 m and a layer thickness hi=0.1 m. 8.10.1. Step 1: Brittle Shear. The the shear angle β=43.3º, horizontal force coefficient λHF=1.912, the verticle force coefficient λVF=0.572 and the Esp/UCS ratio=0.669. This gives a horizontal force Fh=0.669 MN, a vertical force Fv=0.200 MN and a specific energy of Esp=66.9 MPa. These values are peak values, but for comparison reasons these values will be used. 8.10.2. Step 2: The Transition Brittle Shear/Brittle Tensile. The transitions brittle shear/brittle tensile occur for UCS/BTS=4.985 and UCS/BTS=11.75. This can also be written as BTS=0.085·UCS and BTS=0.2·UCS, so BTS=8.5 MPa and BTS=20 MPa. BTS or UTS are considered positive numbers, while tensile strength is considered to be negative in this book. This means that below the Lower Limit BTS=8.5 MPa brittle shear failure cannot exist, so there is always brittle tensile failure. Above the Upper Limit BTS=20 MPa brittle tensile failure cannot exist, so there is always brittle shear failure. In between, both can exist , even at the same time, according to Figure 8-19 the Chip Type. Figure 8-49 and Figure 8-50 show the horizontal and vertical cutting forces as a function of the tensile strength for the case considered. Interpolation curves are shown, simulating the simultaneous occurrence of brittle shear and brittle tensile failure according to the Chip Type. For this interpolation the following method is used: First define a factor f according to: BTS LowerLimit BTS f 1 BTS UpperLimit BTS f 0 BTS LowerLimit BTS BTS UpperLimit BTS UpperLimit BTS BTS f UpperLimit BTS LowerLimit BTS p (8-140) Now the resulting cutting forces can be determined with: F F f F 1 f h h,TearType h,ShearType F F f F 1 f v v,TearType v,ShearType (8-141) The power p used in Figure 8-49 and Figure 8-50 is p=1, a linear transition from tensile failure to shear failure, the Chip Type. Page 294 of 454 TOC Copyright © Dr.ir. S.A. Miedema
Rock Cutting: Atmospheric Conditions. 8.10.3. Step 3: Applying Tensile Strengths of -5 MPa, -10 MPa and -25 MPa. From Figure 8-49 and Figure 8-50 the horizontal and vertical peak forces can be determined. They are given in the following table. Between brackets estimated average values, based on a 60% ratio between average and peak values. Table 8-3: Resulting forces and specific energy. Tensile Strength Fh (N) Fv (MN) Esp (MPa) Esp/UCS (%) -5 MPa 0.207 (0.124) 0.062 (0.037) 20.7 (12.4) 20.7 (12.4) -10 MPa 0.446 (0.268) 0.134 (0.080) 44.6 (26.8) 44.6 (26.8) -25 MPa 0.669 (0.401) 0.200 (0.120) 66.9 (40.1) 66.9 (40.1) The UCS/BTS ratio of 10 matches the findings of Roxborough (1987) giving a specific energy of about 25% of the UCS value. Esp 0.25 U.C.S. 0.11 (8-142) 8.11. Nomenclature. a, a Adhesive shear strength kPa A Adhesive force on the blade kN BTS Brazilian Tensile Strength kPa c, c Cohesive shear strength kPa cm Mobilized cohesive shear strength kPa C Cohesive force on shear plane kN Esp Specific energy kPa F Force kN Fc Cutting force on chisel Evans model kN Fn Normal force on chisel Evans model kN Fch Horizontal force component Evans model kN Fcv Vertical force component Evans model kN Fh Horizontal cutting force kN Fv Vertical cutting force kN g Gravitational constant (9.81) m/s² G Gravitational force kN hi Initial thickness of layer cut m hb Height of the blade m K1 Grain force on the shear plane kN K2 Grain force on the blade kN I Inertial force on the shear plane kN n Power in Nishimatsu model - N1 Normal grain force on shear plane kN N2 Normal grain force on blade kN p Stress in shear plane Nishimatsu model kPa p0 Stress at tip of chisel Nishimatsu model kPa Pc Cutting power kW Q Production m 3 r Radius in Evans model m r Adhesion/cohesion ratio - r1 Pore pressure on shear plane/cohesion ratio - r2 Pore pressure on blade/cohesion ratio - R Radius of Mohr circle kPa R Force on chisel Evans model kN Copyright © Dr.ir. S.A. Miedema TOC Page 295 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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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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