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

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7.8. Experiments in Clay. The Delft Sand, Clay & Rock Cutting Model. 7.8.1. Experiments of Hatamura & Chijiiwa (1977B). Hatamura & Chijiiwa (1977B) carried out experiments in sand, clay and loam. The experiments were carried out with blade angles α of 30°, 45°, 60°, 75° and 90°, layer thicknesses hi of 0.05, 0.10 and 0.15 m and cutting velocities vc of 0.05, 0.10 and 0.14 m/sec. The blade had a fixed length L4 of 0.2 m and a fixed width w of 0.33 m. The clay/loam had a dynamic cohesion c of 27.9 kPa and a dynamic adhesion a of 13.95 kPa. Hatamura & Chijiiwa (1977B) only give the dynamic cohesion and adhesion, not the static ones. Based on equation (7-53) an average strengthening factor of about 1.5 can be determined. This factor may however vary with the blade angle and layer thickness. Hatamura & Chijiiwa (1977B) measured the shear angle β, the total cutting force and the direction of the total cutting force. The also determined the location of the acting points of the different forces. In the model they derived they used the horizontal and vertical force equilibrium equations and the equilibrium of moments equation combined with their measured acting points. By solving the 3 equilibrium equations, they solved the horizontal cutting force, the vertical cutting force and the shear angle, based on 3 equations with 3 unknowns. The theory as derived here assumes a shear angle where there is a minimum horizontal force, based on the minimum cutting energy principle. So the two approaches are different. Hatamura & Chijiiwa (1977B) found that cutting tests with cutting angles of 30° and 45° were according to the Tear Type, while the larger cutting angles followed the Flow Type of cutting mechanism. This tells something about the tensile strength of the material. Based on the above an ac ratio r of 0.5-0.7 can be derived. Figure 7-27 shows that a tensile strength to cohesion σT/c ratio of about 0.2 may explain this. So it is assumed that the tensile strength is 20% of the cohesion. Figure 7-44, Figure 7-45 and Figure 7-46 show the results of the experiments and the calcultations. The calculations are carried out for both the Flow Type and the Tear Type. The shear angles predicted are 5°-10° larger than the ones measured, however the tendency is the same. The measured total cutting forces match the predicted cutting forces very well for the Tear Type for blade angles of 30° and 45° and for the Flow Type for blade angles of 60°, 75° and 90°. The theory does predict the Tear Type and the Flow Type for the corresponding blade angles. The directions measured of the total cutting force also match the theory very well if the correct cutting mechanism is considered. So apparently the total cutting forces and the direction of these forces can be predicted well, but the shear angle gives differences. We should consider that the shear angle as used in the theory here is a straight line, a simplification. In reality the shear plane may be curved, leading to different values of the shear angle measured. For the Tear Type it is not clear what definition Hatamura & Chijiiwa (1977B) used to determine the shear angle. Is it the point where the secondary tensile crack reaches the surface? This explains some of the differences between the measured and calculated shear angles. Overall, the theory as developed here predicts the cutting forces and the direction of these forces very well. The force for a 60° blade and 0.05 m layer thickness is smaller than expected based on the Flow Type of cutting process. This is caused by the Curling Type as shown below. Figure 7-45 shows that the experiment with a layer thickness of 0.05 m with a blade angle of 60° gives a smaller cutting force than estimated. Analyzing the 60° experiments as a function of the layer thickness gives Figure 7-47. This figure shows that up to a layer thickness of about 0.08 m there will be a Curling Type of cutting process. Above 0.08 m there will be a Flow Type of cutting process, while above about 0.20 m there will be a Tear Type of cutting process. Once the Tear Type is present, the force will drop to the lower Tear Type curve as is visible in the 30° and 45° experiments. Since all 3 cutting mechanisms were present in the experiments of Hatamura & Chijiiwa (1977B), it is not possible to find just one equation for the cutting forces. Each of the 3 cutting mechanisms has its own model or equation. Figure 7-48 shows the 30° experiment. It is clear from the figure that at 0.10 m layer thickness the cutting mechanism of of the Tear Type. Page 234 of 454 TOC Copyright © Dr.ir. S.A. Miedema
Clay Cutting. Shear Angle β vs. Blade Angle α 60 55 hi=0.05 m Flow Type 50 hi=0.10 m Flow Type Shear Angle β (Degrees) 45 40 35 30 25 20 15 hi=0.15 m Flow Type Experiments hi=0.05 m Experiments hi=0.10 m Experiments hi=0.15 m hi=0.05 m Tear Type 10 hi=0.10 m Tear Type 5 hi=0.15 m Tear Type 0 30 45 60 75 90 Blade Angle α (Degrees) © S.A.M. Figure 7-44: The shear angles measured and calculated. Total Cutting Force F t vs. Blade Angle α 3000 Total Cutting Force F t (N) 2800 2600 2400 2200 2000 1800 1600 1400 1200 1000 800 600 400 200 hi=0.05 m Flow Type hi=0.10 m Flow Type hi=0.15 m Flow Type Experiments hi=0.05 m Experiments hi=0.10 m Experiments hi=0.15 m hi=0.05 m Tear Type hi=0.10 m Tear Type hi=0.15 m Tear Type 0 30 45 60 75 90 Blade Angle α (Degrees) © S.A.M. Figure 7-45: The total cutting force measured and calculated. Copyright © Dr.ir. S.A. Miedema TOC Page 235 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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Rock Cutting: Atmospheric Condition
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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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