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8.9: Resulting Forces and Mohr Circles

  • Page ID
    34845
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    Screen Shot 2020-08-23 at 1.49.24 PM.png
    Figure 8-49: Horizontal cutting force: α=60o, UCS=100 MPa, φ=20o, hi=0.1 m & w=0.1 m.
    Screen Shot 2020-08-23 at 1.50.24 PM.png
    Figure 8-50: Vertical cutting force: α=60o, UCS=100 MPa, φ=20o, hi=0.1 m & w=0.1 m.

    Figure 8-49 and Figure 8-50 show the horizontal and vertical cutting forces. The transition tensile failure/shear failure occurs at a tensile strength of about -8.5 MPa, so 8.5% of the UCS value. From a tensile strength of -8.5 MPa (8.5% UCS) to -20 MPa (20% UCS), both tensile failure and shear failure are possible. Below a tensile strength of -20 MPa (20% UCS) only shear failure is possible. Figure 8-51 and Figure 8-52 show the Mohr circles for tensile strengths of -8.5 MPa (8.5% UCS) and -20 MPa (20% UCS). One can see that with a tensile strength of -8.5 MPa both tensile failure and shear failure are possible, with a tensile strength of -20 MPa also both tensile failure and shear failure are possible. It should be mentioned here that the forces shown are peak forces, so average forces may reduce to 50%-60%. So the two limiting cases are shown.

    Screen Shot 2020-08-23 at 1.51.48 PM.png
    Figure 8-51: Mohr circles tensile strength -8.5 MPA.
    Screen Shot 2020-08-23 at 1.53.00 PM.png
    Figure 8-52: Mohr circles tensile strength -20 MPa.
    Screen Shot 2020-08-23 at 1.53.47 PM.png
    Figure 8-53: The tensile vs. shear failure range based on the BTS to cohesion ratio.
    Screen Shot 2020-08-23 at 1.54.31 PM.png
    Figure 8-54 The tensile vs. shear failure range based on the UCS to BTS ratio.

    8.9: Resulting Forces and Mohr Circles is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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