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

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The Delft Sand, Clay & Rock Cutting Model. Teta2 = Alpha + Beta Teta3 = Pi - Beta Teta4 = Pi + Beta Lmax = Hi / Sin(Beta) L1 = Hb / Sin(Alpha) L4 = 0.9 * Hi *(Hi/Hb)^0.5*(1.85*Alpha)^2*(Ki/Kmax)^0.4 N = 100 StepL = Lmax / N P = 0 DPMax = RhoW * G * (Z + 10) For I = 0 To N L = I * StepL + 0.0000000001 ‘Determine the 4 lengths S1 = (Lmax - L) * (Pi/2+Teta1) + L1 S2 = 0.8*L * Teta2 S3 = 0.8*L * Teta3 S4 = (Lmax - L) * Teta4 + L4 ‘Determine the 4 resistances R1 = S1 / Kmax R2 = S2 / Kmax R3 = S3 / Ki R4 = S4 / Ki ‘Determine the total resistance Rt = 1 / (1 / R1 + 1 / R2 + 1 / R3 + 1 / R4) ‘Determine the pore vacuum pressure in point I DP = RhoW * G * Vc * E * Sin(Beta) * Rt ‘Integrate the pore vacuum pressure P = P + DP ‘Store the pore vacuum pressure in point I P1(I)=DP Next I ‘Store the pore vacuum pressure at the tip of the blade Ptip=DP ‘Determine the average pore vacuum pressure with correction for integration P1m = (P - Ptip / 2) / N ‘Determine the pore vacuum pressure on the blade ‘Determine the 2 lengths S1=L1 S2=0.8*Lmax*Teta2 ‘Determine the 2 resistances R1=S1/Kmax R2=S2/Kmax ‘Compensate R2 for the number of intervals and the geometry R2=R2*N*1.75*(Hi*Sin(Alpha)/(Hb*Sin(Beta)) ‘Determine the effective resistance Rt=1/(1/R1+1/R2) ‘Determine the total flow over the blade at the tip of the blade Q=Ptip/(RhoW*G*Rt) ‘Determine the two flows, Q1 over the blade and Q2 from entrainment Q1=Ptip/(Rhow*G*R1) Q2=Ptip/(Rhow*G*R2) ‘Determine the pressure effect near the tip of the blade TipEffect=Int(0.05*N*Alpha) ‘Now determine the pore vacuum pressure distribution on the blade P=0 For I = 1 To N ‘Determine the length of the top of the blade to point I Page 142 of 454 TOC Copyright © Dr.ir. S.A. Miedema
Saturated Sand Cutting. S1=L1*(1-I/N) ‘Determine the resistance of the top of the blade to point I R1=S1/Kmax ‘Determine the effective resistance in point I Rt=1/(1/R1+1/R2) ‘Determine the flow at the tip of the blade IF I>TipEffect THEN Q=Q-Q2 ELSE Q=Q+Q2 END IF ‘Determine the 2 flows Q1=Q*Rt/R1 Q2=Q*Rt/R2 ‘Determine the pore vacuum pressure in point I DP=Rhow*G*Q*Rt ‘Integrate the pore vacuum pressure P = P + DP ‘Store the pore vacuum pressure in point I P2(I)=DP Next I ‘Determine the average pore vacuum pressure with correction for integration P2m = (P - Ptip / 2) / N Figure 6-21: A small program to determine the pore pressures. 0.500 Pore Pressures on the Blade (α=30º) & the Shear Plane (β=30º) - kmax/ki=4 & hb/hi=3 Dimensionless Pore Pressure p 1 & p 2 (-) 0.475 0.450 0.425 0.400 0.375 0.350 0.325 0.300 0.275 0.250 0.225 0.200 0.175 0.150 0.125 0.100 0.075 0.050 0.025 p1 p2 0.000 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Percentage of Blade & Shear Plane (%) B-C A © S.A.M. Figure 6-22: The dimensionless pressures on the blade and the shear plane, α=30°, β=30°, ki/kmax=0.25, hi/hb=1/3. Figure 6-21 shows a program listing to determine the pore pressures with the analytical/numerical method. Figure 6-22, Figure 6-23 and Figure 6-24 show the resulting pore vacuum pressure curves on the shear plane and on the blade for 30, 45 and 60 degree blades with a hi/hb ratio of 1/3 and a ki/kmax ratio of 1/4. The curves match both the FEM calculations and the experiments very well. Copyright © Dr.ir. S.A. Miedema TOC Page 143 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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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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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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