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17.23: Appendix W- Rock Cutting Charts

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    W.1 Brittle Shear

    Screen Shot 2020-09-04 at 1.08.18 AM.png
    Figure W-1: The shear angle β as a function of the blade angle α and the internal friction angle φ for shear failure.
    Screen Shot 2020-09-04 at 1.09.33 AM.png
    Figure W-2: The brittle (shear failure) horizontal force coefficient λHF.
    Screen Shot 2020-09-04 at 1.10.20 AM.png
    Figure W-3: The brittle (shear failure) vertical force coefficient λVF.
    Screen Shot 2020-09-04 at 1.13.38 AM.png
    Figure W-4: The specific energy to UCS ratio.

    In all figures an example is given for a 60o blade and an internal friction angle of 20o.

    W.2 The Transition Brittle Shear/Brittle Tensile A

    Screen Shot 2020-09-04 at 1.21.30 AM.png
    Figure W-5: The tensile/shear failure criterion based on BTS/Cohesion.

    Below the lines the cutting process is subject to shear failure, above the lines to tensile failure. The curves are based on the shear angle resulting from shear failure.

    Screen Shot 2020-09-04 at 1.22.24 AM.png
    Figure W-6: The tensile/shear failure criterion based on UCS/BTS.

    In all figures an example is given for a 60o blade and an internal friction angle of 20o.

    W.3 The Transition Brittle Shear/Brittle Tensile B

    Screen Shot 2020-09-04 at 1.23.41 AM.png
    Figure W-7: The tensile/shear failure criterion based on BTS/Cohesion.

    Below the lines the cutting process is subject to shear failure, above the lines to tensile failure. The curves are based on the shear angle resulting from tensile failure.

    Screen Shot 2020-09-04 at 1.26.27 AM.png
    Figure W-8: The tensile/shear failure criterion based on UCS/BTS.

    In all figures an example is given for a 60o blade and an internal friction angle of 20o.

    Screen Shot 2020-09-04 at 1.28.52 AM.png
    Figure W-9: The tensile/shear failure range based on BTS/Cohesion for φ=20o.
    Screen Shot 2020-09-04 at 1.29.47 AM.png
    Figure W-10: The tensile/shear failure range based on UCS/BTS for φ=20o.

    In all figures an example is given for a 60o blade and an internal friction angle of 20o.

    W.4 Transition Ranges Brittle Shear/Brittle Tensile

    Screen Shot 2020-09-04 at 1.31.03 AM.png
    Figure W-11: The tensile/shear failure range based on BTS/Cohesion for φ=0o.
    Screen Shot 2020-09-04 at 1.31.48 AM.png
    Figure W-12: The tensile/shear failure range based on UCS/BTS for φ=0o.
    Screen Shot 2020-09-04 at 1.32.58 AM.png
    Figure W-13: The tensile/shear failure range based on BTS/Cohesion for φ=5o.
    Screen Shot 2020-09-04 at 1.33.49 AM.png
    Figure W-14: The tensile/shear failure range based on UCS/BTS for φ=5o.
    Screen Shot 2020-09-04 at 1.34.27 AM.png
    Figure W-15: The tensile/shear failure range based on BTS/Cohesion for φ=10o.
    Screen Shot 2020-09-04 at 1.35.30 AM.png
    Figure W-16: The tensile/shear failure range based on UCS/BTS for φ=10o.
    Screen Shot 2020-09-04 at 1.36.11 AM.png
    Figure W-17: The tensile/shear failure range based on BTS/Cohesion for φ=15o.
    Screen Shot 2020-09-04 at 1.36.54 AM.png
    Figure W-18: The tensile/shear failure range based on UCS/BTS for φ=15o.
    Screen Shot 2020-09-04 at 1.41.27 AM.png
    Figure W-19: The tensile/shear failure range based on BTS/Cohesion for φ=20o.
    Screen Shot 2020-09-04 at 1.42.14 AM.png
    Figure W-20: The tensile/shear failure range based on UCS/BTS for φ=20o.
    Screen Shot 2020-09-04 at 1.42.55 AM.png
    Figure W-21: The tensile/shear failure range based on BTS/Cohesion for φ=25o.
    Screen Shot 2020-09-04 at 1.45.53 AM.png
    Figure W-22: The tensile/shear failure range based on UCS/BTS for φ=25o.
    Screen Shot 2020-09-04 at 1.46.44 AM.png
    Figure W-23: The tensile/shear failure range based on BTS/Cohesion for φ=30o.
    Screen Shot 2020-09-04 at 1.47.49 AM.png
    Figure W-24: The tensile/shear failure range based on UCS/BTS for φ=30o.
    Screen Shot 2020-09-04 at 1.51.28 AM.png
    Figure W-25: The tensile/shear failure range based on BTS/Cohesion for φ=35o.
    Screen Shot 2020-09-04 at 1.53.08 AM.png
    Figure W-26: The tensile/shear failure range based on UCS/BTS for φ=35o.
    Screen Shot 2020-09-04 at 1.55.47 AM.png
    Figure W-27: The tensile/shear failure range based on BTS/Cohesion for φ=40o.
    Screen Shot 2020-09-04 at 1.57.20 AM.png
    Figure W-28: The tensile/shear failure range based on UCS/BTS for φ=40o.
    Screen Shot 2020-09-04 at 1.59.04 AM.png
    Figure W-29: The tensile/shear failure range based on BTS/Cohesion for φ=45o.
    Screen Shot 2020-09-04 at 1.59.52 AM.png
    Figure W-30: The tensile/shear failure range based on UCS/BTS for φ=45o.

    W.5 Brittle Tensile Failure based on Brittle Shear Shear Angle

    Screen Shot 2020-09-04 at 2.02.25 AM.png
    Figure W-31: The brittle (tensile failure) horizontal force coefficient λHT.
    Screen Shot 2020-09-04 at 10.05.44 AM.png
    Figure W-32: The brittle (tensile failure) vertical force coefficient λVT.
    Screen Shot 2020-09-04 at 10.06.38 AM.png
    Figure W-33: The brittle (tensile failure) horizontal force coefficient λHT (DSCRCM, logarithmic).
    Screen Shot 2020-09-04 at 10.08.06 AM.png
    Figure W-34: The brittle (tensile failure) horizontal force coefficient λHT (Evans, logarithmic).

    The Evans approach gives much higher values, since it is based on reaching the tensile strength in the whole failure plane. The DSCRCM model assumes reaching the tensile strength only at the start of the tensile crack.

    W.6 Brittle Tensile Failure based on Brittle Tensile Shear Angle

    Screen Shot 2020-09-04 at 10.23.32 AM.png
    Figure W-35: The shear angle β as a function of the blade angle α and the internal friction angle φ for shear failure, corrected.
    Screen Shot 2020-09-04 at 10.27.14 AM.png
    Figure W-36: The brittle (tensile failure) horizontal force coefficient λHT, corrected.
    Screen Shot 2020-09-04 at 10.28.05 AM.png
    Figure W-37: The brittle (tensile failure) vertical force coefficient λVT , corrected.

    17.23: Appendix W- Rock Cutting Charts is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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