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4.3: Cutting Clay

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    29438
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    In clay the cutting processes are dominated by cohesion and adhesion (internal and external shear strength). Because of the φ=0 concept, the internal and external friction angles are set to 0. Gravity, inertial forces and pore pressures are also neglected. This simplifies the cutting equations. Clay however is subject to strengthening, meaning that the internal and external shear strength increase with an increasing strain rate.

    The reverse of strengthening is creep, meaning that under a constant load the material will continue deforming with a certain strain rate. Under normal circumstances clay will be cut with the Flow Type mechanism, but under certain circumstances the Curling Type or the Tear Type may occur. The Curling Type will occur when the blade height is large with respect to the layer thickness, hb/hi, the adhesion is high compared to the cohesion a/cand the blade angle α is relatively big. The Tear Type will occur when the blade height is small with respect to the layer thickness, hb/hi, the adhesion is small compared to the cohesion a/c and the blade angle α is relatively small.

    Clay cutting is dominated by cohesive (internal shear strength) and adhesive (external shear strength) forces. The basic cutting mechanism is the Flow Type. Cutting a thin layer, combined with a high adhesive force may result in the Curling Type mechanism. Cutting a thick layer combined with a small adhesive force and a low tensile strength may result in the Tear Type mechanism. This is covered in Chapter 7: Clay Cutting.

    Screen Shot 2020-08-17 at 11.25.21 AM.png
    Figure 4-3: The Curling Type in clay and loam cutting.
    Screen Shot 2020-08-17 at 11.26.08 AM.png
    Figure 4-4: The Flow Type in clay and loam cutting.
    Screen Shot 2020-08-17 at 11.26.45 AM.png
    Figure 4-5: The Tear Type in clay and loam cutting.

    The forces K1 and K2 on the blade, chisel or pick point are now:

    \[\ \begin{array}{left} \mathrm{K}_{1}=& \frac{\mathrm{W}_{2} \cdot \sin (\delta)+\mathrm{W}_{1} \cdot \sin (\alpha+\beta+\delta)+\mathrm{G} \cdot \sin (\alpha+\delta)}{\sin (\alpha+\beta+\delta+\varphi)} \\ &+\frac{-\mathrm{I} \cdot \cos (\alpha+\beta+\delta)-\mathrm{C} \cdot \cos (\alpha+\beta+\delta)+\mathrm{A} \cdot \cos (\delta)}{\sin (\alpha+\beta+\delta+\varphi)} \end{array}\tag{4-13}\]

    \[\ \begin{aligned} \mathrm{K}_{2}=& \frac{\mathrm{W}_{2} \cdot \sin (\alpha+\beta+\varphi)+\mathrm{W}_{1} \cdot \sin (\varphi)+\mathrm{G} \cdot \sin (\beta+\varphi)}{\sin (\alpha+\beta+\delta+\varphi)} \\ &+\frac{+\mathrm{I} \cdot \cos (\varphi)+\mathrm{C} \cdot \cos (\varphi)-\mathrm{A} \cdot \cos (\alpha+\beta+\varphi)}{\sin (\alpha+\beta+\delta+\varphi)} \end{aligned}\tag{4-14}\]

    The normal forces N1 on the shear plane and N2 on the blade are:

    \[\ \mathrm{N}_{1}=\mathrm{K}_{1} \cdot \cos (\varphi) \quad\text{ and }\quad \mathrm{N}_{2}=\mathrm{K}_{2} \cdot \cos (\delta)\tag{4-15}\]

    The horizontal and vertical forces on the blade, chisel or pick point are:

    \[\ \mathrm{F}_{\mathrm{h}}=-\mathrm{W}_{2} \cdot \sin (\alpha)+\mathrm{K}_{2} \cdot \sin (\alpha+\delta)+\mathrm{A} \cdot \cos (\alpha)\tag{4-16}\]

    \[\ \mathrm{F}_{\mathrm{v}}=-\mathrm{W}_{2} \cdot \cos (\alpha)+\mathrm{K}_{2} \cdot \cos (\alpha+\delta)-\mathrm{A} \cdot \sin (\alpha)\tag{4-17}\]

    The equilibrium of moments around the blade tip is:

    \[\ \left(\mathrm{N}_{1}-\mathrm{W}_{1}\right) \cdot \mathrm{R}_{1}-\mathrm{G} \cdot \mathrm{R}_{3}=\left(\mathrm{N}_{2}-\mathrm{W}_{2}\right) \cdot \mathrm{R}_{2}\tag{4-18}\]

    Analyzing these equations results in the following conclusions:

    • At normal cutting angles in dredging, the argument of the cosine in the cohesive term of Kis greater than 90 degrees, resulting in a small positive term as a whole. Together with the adhesive term, this gives a positive normal stress on the shear plane. The minimum normal stress however equals the normal stress on the shear plane, minus the radius of the Mohr circle, which is the cohesion. The result may be a negative minimum normal stress. If this negative minimum normal stress is smaller than the negative tensile strength, the Tear Type will occur. This occurrence depends on the ratio between the adhesive force to the cohesive force. A large ratio will suppress the Tear Type.

    • The adhesive force on the blade is proportional to the (mobilized) length of the blade, so the Curling Type may occur. The cohesive force on the shear plane is proportional to the (mobilized) cohesion, so the Tear Type may occur. The occurrence of the Curling Type or Tear Type depends on the ratio of the adhesive force to the cohesive force. A large ratio results in the Curling Type, a small ratio in the Tear Type.

    • When the argument of the sine in the denominator gets close to 180 degrees, the forces become very large. If the argument is greater than 180 degrees, the forces would become negative. Since both conditions will not happen in nature, nature will find another cutting mechanism, the wedge mechanism. In clay this is not likely to occur, since there are only two angles in the argument of the sine in the denominator. It would require very large blade angles to occur.


    This page titled 4.3: Cutting Clay is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Sape A. Miedema (TU Delft Open Textbooks) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.