17.13: Appendix M- Experiments in Water Saturated Sand

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M.1 Pore pressures and cutting forces in 105 μm Sand

Screen Shot 2020-08-31 at 6.49.10 PM.png — Figure M-1: Dimensionless pore pressures, theory versus measurements.

Screen Shot 2020-08-31 at 6.50.03 PM.png — Figure M-2: Measured absolute pore pressures.

Screen Shot 2020-08-31 at 6.50.58 PM.png — Figure M-3: The cutting forces F_hand F_v, theory versus measurement.

Screen Shot 2020-08-31 at 6.51.32 PM.png — Figure M-3: The cutting forces F_hand F_v, theory versus measurement.

The cutting forces on the blade. Experiments in 105 μm sand, with α=30°, β=30^o, φ=41^o, δ=27^o, n_i=43.6%, n_max=51.6%, ki=0.000062 m/s, k_max=0.000170 m/s, h_i=100 mm, h_b=100 mm, w=0.2 m, z=0.6 m and a partial cavitating cutting process.

Screen Shot 2020-08-31 at 6.56.30 PM.png — Figure M-4: Dimensionless pore pressures, theory versus measurements.

Screen Shot 2020-08-31 at 6.58.29 PM.png — Figure M-5: Measured absolute pore pressures.

Screen Shot 2020-08-31 at 6.59.27 PM.png — Figure M-6: The cutting forces F_h **and F**_v, theory versus measurement.

The cutting forces on the blade. Experiments in 105 μm sand, with α=45°, β=30^o, φ=38^o, δ=25^o, n_i=45.0%, n_max=51.6%, k_i=0.000075 m/s, kmax=0.000170 m/s, h_i=70 mm, h_b=100 mm, w=0.2 m, z=0.6 m and a partial cavitating cutting process.

Screen Shot 2020-08-31 at 7.14.28 PM.png — Figure M-7: Dimensionless pore pressures, theory versus measurements.

Screen Shot 2020-08-31 at 7.15.18 PM.png — Figure M-8: Measured absolute pore pressures.

Screen Shot 2020-08-31 at 7.22.23 PM.png — Figure M-9: The cutting forces F_h **and F**_v, theory versus measurement.

Screen Shot 2020-08-31 at 7.23.05 PM.png — Figure M-9: The cutting forces F_h **and F**_v, theory versus measurement.

The cutting forces on the blade. Experiments in 105 μm sand, with α=60°, β=30^o, φ=36^o, δ=24^o, n_i=44.3%, n_max=51.6%, k_i=0.000067 m/s, k_max=0.000170 m/s, h_i=58 mm, h_b=100 mm, w=0.2 m, z=0.6 m and a partial cavitating cutting process.

M.2 Pore Pressures in 200 μm Sand

Screen Shot 2020-08-31 at 7.26.47 PM.png — Figure M-10: α**=30^o, h**_i=33 mm, h_b=100 mm.

The dimensionless water pore pressures on the blade. Experiments in 200 μm sand, with α=30°, β=30^o, φ=38^o, δ=30^o, n_i=38.53%, n_max=43.88%, k_i=0.000165 m/s, k_max=0.000320 m/s, h_i=33 mm, h_b=100 mm, w=0.2 m, z=0.6 m and a non-cavitating cutting process.

Screen Shot 2020-08-31 at 7.29.36 PM.png — Figure M-11: α**=30^o, h**_i=50 mm, h_b=100 mm.

The dimensionless water pore pressures on the blade. Experiments in 200 μm sand, with α=30°, β=29°, φ=38°, δ=30°, n_i=38.53%, n_max=43.88%, k_i=0.000165 m/s, k_max=0.000320 m/s, h_i=50 mm, h_b=100 mm, w=0.2 m, z=0.6 m and a non-cavitating cutting process.

Screen Shot 2020-08-31 at 10.22.02 PM.png — Figure M-12: α**=30^o, h_i=100 mm, h**_b=100 mm.

The dimensionless water pore pressures on the blade. Experiments in 200 μm sand, with α=30°, β=29°, φ=38°, δ=30°, n_i=38.53%, n_max=43.88%, k_i=0.000165 m/s, k_max=0.000320 m/s, h_i=100 mm, h_b=100 mm, w=0.2 m, z=0.6 m and a non-cavitating cutting process.

Screen Shot 2020-08-31 at 10.32.42 PM.png — Figure M-13: α**=45^o, h**_i=47 mm, h_b=141 mm.

The dimensionless water pore pressures on the blade. Experiments in 200 μm sand, with α=45°, β=25°, φ=38°, δ=30°, n_i=38.53%, n_max=43.88%, k_i=0.000165 m/s, k_max=0.000320 m/s, h_i=47 mm, h_b=141 mm, w=0.2 m, z=0.6 m and a non-cavitating cutting process.

Screen Shot 2020-08-31 at 10.39.22 PM.png — Figure M-14: α**=45^o, h**_i=70 mm, h_b=141 mm.

The dimensionless water pore pressures on the blade. Experiments in 200 μm sand, with α=45°, β=24^o, φ=38^o, δ=30^o, n_i=38.53%, n_max=43.88%, k_i=0.000165 m/s, k_max=0.000320 m/s, h_i=70 mm, h_b=141 mm, w=0.2 m, z=0.6 m and a non-cavitating cutting process.

Screen Shot 2020-08-31 at 10.40.46 PM.png — Figure M-15: α**=45^o, h**_i=141 mm, h_b=141 mm.

The dimensionless water pore pressures on the blade. Experiments in 200 μm sand, with α=45°, β=25°, φ=38°, δ=30°, n_i=38.53%, n_max=43.88%, k_i=0.000165 m/s, k_max=0.000320 m/s, h_i=141 mm, h_b=141 mm, w=0.2 m, z=0.6 m and a non-cavitating cutting process.

Screen Shot 2020-08-31 at 10.43.43 PM.png — Figure M-16: α**=60^o, h**_i=30 mm, h_b=173 mm.

The dimensionless water pore pressures on the blade. Experiments in 200 μm sand, with α=60°, β=19^o, φ=38^o, δ=30^o, n_i=38.53%, n_max=43.88%, k_i=0.000165 m/s, k_max=0.000320 m/s, h_i=30 mm, h_b=173 mm, w=0.2 m, z=0.6 m and a non-cavitating cutting process.

Screen Shot 2020-08-31 at 10.45.55 PM.png — Figure M-17: α**=60^o, h**_i=58 mm, h_b=173 mm.

The dimensionless water pore pressures on the blade. Experiments in 200 μm sand, with α=60°, β=19^o, φ=38^o, δ=30^o, n_i=38.53%, n_max=43.88%, k_i=0.000165 m/s, k_max=0.000320 m/s, h_i=58 mm, h_b=173 mm, w=0.2 m, z=0.6 m and a non-cavitating cutting process.

Screen Shot 2020-08-31 at 10.51.38 PM.png — Figure M-18: α**=60^o, h**_i=87 mm, h_b=173 mm.

The dimensionless water pore pressures on the blade. Experiments in 200 μm sand, with α=60°, β=19°, φ=38°, δ=30°, n_i=38.53%, n_max=43.88%, k_i=0.000165 m/s, k_max=0.000320 m/s, h_i=87 mm, h_b=173 mm, w=0.2 m, z=0.6 m and a non-cavitating cutting process.

Screen Shot 2020-08-31 at 10.53.01 PM.png — Figure M-19: α**=60^o, h**_i=173 mm, h_b=173 mm.

The dimensionless water pore pressures on the blade. Experiments in 200 μm sand, with α=60°, β=20°, φ=38o, δ=30°, n_i=38.53%, n_max=43.88%, k_i=0.000165 m/s, k_max=0.000320 m/s, h_i=173 mm, h_b=173 mm, w=0.2 m, z=0.6 m and a non-cavitating cutting process.

M.3 Cutting Forces in 200 μm Sand

Screen Shot 2020-08-31 at 11.05.03 PM.png — Figure M-20: α**=30°, h**_i=33 mm, h_b=100 mm.

The cutting forces F_h and F_v on the blade. Experiments in 200 μm sand, with α=30°, β=30°, φ=38°, δ=30°, n_i=38.53%, n_max=43.88%, k_i=0.000165 m/s, k_max=0.000320 m/s, h_i=33 mm, h_b=100 mm, w=0.2 m, z=0.6 m and a non-cavitating cutting process.

Screen Shot 2020-08-31 at 11.08.05 PM.png — Figure M-21: α**=30°, h**_i=50 mm, h_b=100 mm.

The cutting forces F_h and F_von the blade. Experiments in 200 μm sand, with α=30°, β=30°, φ=38°, δ=30°, n_i=38.53%, n_max=43.88%, k_i=0.000165 m/s, k_max=0.000320 m/s, h_i=50 mm, h_b=100 mm, w=0.2 m, z=0.6 m and a non-cavitating cutting process.

Screen Shot 2020-08-31 at 11.23.40 PM.png — Figure M-22: α**=30°, h**_i=100 mm, h_b=100 mm.

The cutting forces F_h and F_v on the blade. Experiments in 200 μm sand, with α=30°, β=30^o, φ=38^o, δ=30^o, n_i=38.53%, n_max=43.88%, k_i=0.000165 m/s, k_max=0.000320 m/s, h_i=100 mm, h_b=100 mm, w=0.2 m, z=0.6 m and a non-cavitating cutting process.

Screen Shot 2020-08-31 at 11.26.19 PM.png — Figure M-23: α**=45°, h**_i=47 mm, h_b=141 mm.

The cutting forces F_h and F_v on the blade. Experiments in 200 μm sand, with α=45°, β=30o, φ=38°, δ=30°, n_i=38.53%, n_max=43.88%, k_i=0.000165 m/s, k_max=0.000320 m/s, h_i=47 mm, h_b=141 mm, w=0.2 m, z=0.6 m and a non-cavitating cutting process.

Screen Shot 2020-08-31 at 11.30.32 PM.png — Figure M-24: α**=45°, h**_i=70 mm, h_b=141 mm.

Screen Shot 2020-08-31 at 11.31.10 PM.png — Figure M-24: α**=45°, h**_i=70 mm, h_b=141 mm.

The cutting forces F_h and F_von the blade. Experiments in 200 μm sand, with α=45°, β=30°, φ=38°, δ=30°, n_i=38.53%, n_max=43.88%, k_i=0.000165 m/s, k_max=0.000320 m/s, h_i=70 mm, h_b=141 mm, w=0.2 m, z=0.6 m and a non-cavitating cutting process.

Screen Shot 2020-08-31 at 11.33.27 PM.png — Figure M-25: α**=45°, h**_i=141 mm, h_b=141 mm.

The cutting forces F_h and F_v on the blade. Experiments in 200 μm sand, with α=45°, β=30°, φ=38°, δ=30°, n_i=38.53%, n_max=43.88%, k_i=0.000165 m/s, k_max=0.000320 m/s, h_i=141 mm, h_b=141 mm, w=0.2 m, z=0.6 m and a non-cavitating cutting process.

Screen Shot 2020-08-31 at 11.36.34 PM.png — Figure M-26: α**=60°, h**_i=58 mm, h_b=173 mm.

Screen Shot 2020-08-31 at 11.37.14 PM.png — Figure M-26: α**=60°, h**_i=58 mm, h_b=173 mm.

The cutting forces F_h and F_von the blade. Experiments in 200 μm sand, with α=45°, β=30^o, φ=38^o, δ=30^o, n_i=38.53%, n_max=43.88%, k_i=0.000165 m/s, k_max=0.000320 m/s, h_i=58 mm, h_b=173 mm, w=0.2 m, z=0.6 m and a non-cavitating cutting process.

Screen Shot 2020-08-31 at 11.43.39 PM.png — Figure M-27: α**=60°, h**_i=87 mm, h_b=173 mm.

Screen Shot 2020-08-31 at 11.44.16 PM.png — Figure M-27: α**=60°, h**_i=87 mm, h_b=173 mm.

The cutting forces F_h and F_v on the blade. Experiments in 200 μm sand, with α=45°, β=30°, φ=38°, δ=30°, n_i=38.53%, n_max=43.88%, k_i=0.000165 m/s, k_max=0.000320 m/s, h_i=87 mm, h_b=173 mm, w=0.2 m, z=0.6 m and a non-cavitating cutting process.

Screen Shot 2020-09-01 at 3.44.25 PM.png — Figure M-28: α**=60°, h**_i=173 mm, h_b=173 mm.

Screen Shot 2020-09-01 at 3.45.05 PM.png — Figure M-28: α**=60°, h**_i=173 mm, h_b=173 mm.

The cutting forces F_h and F_v on the blade. Experiments in 200 μm sand, with α=45°, β=30°, φ=38°, δ=30°, n_i=38.53%, n_max=43.88%, k_i=0.000165 m/s, k_max=0.000320 m/s, h_i=173 mm, h_b=173 mm, w=0.2 m, z=0.6 m and a non-cavitating cutting process.