12.6: The Cavitating Wedge

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Also for the cavitating process, a case will be discussed. The calculations are carried out for blade angles α of 65^o, 70^o, 75^o, 80^o, 85^o, 90^o, 95^o, 100^o, 105^o, 110^o, 115^o and 120^o, while the smallest angle is around 60o depending on the possible solutions. Also the cutting forces are determined with and without a wedge, so it’s possible to carry out step 6.

The case concerns a sand with an internal friction angle φ of 30^o, a soil interface friction angle δ of 20^o fully mobilized, a friction angle δ between the soil cut and the wedge equal to the internal friction angle, an initial permeability k_i of 6.2*10^-5 m/s and a residual permeability k_max of 17*10^-5 m/s. The blade dimensions are a width of 0.25 m and a height of 0.2 m, while a layer of sand of 0.05 m is cut with a cutting velocity of 0.3 m/s at a water depth of 0.6 m, matching the laboratory conditions. The values for the acting points of the forces, are e₂=0.35, e₃=0.55 and e₄=0.32, based on the finite element calculations carried out by Ma (2001).

Figure 12-24 and Figure 12-25 show the results of the calculations. Figure 12-24 shows the wedge angle θ, the shear angle β, the mobilized internal friction angle λ and the mobilized external friction angle δ_e as a function of the blade angle α. Figure 12-25 shows the horizontal and vertical cutting forces, with and without a wedge.
With the cavitating cutting process, the wedge angle θ always results in an angle of 90^o-φ, which matches the theory of Hettiaratchi and Reece (1975).The reason of this is that in the full cavitation situation, the pore pressures are equal on each side of the wedge and form equilibrium in itself. So the pore pressures do not influence the ratio between the grain stresses on the different sides of the wedge. From Figure 12-25 it can be concluded that the transition point between the conventional cutting process and the wedge process occurs at a blade angle of about 77 degrees.

In the non-cavitating cases this angle is about 70 degrees. A smaller angle of internal friction results in a higher transition angle, but in the cavitating case this influence is bigger. In the cavitating case, the horizontal force is a constant as long as the external friction angle is changing from a positive maximum to the negative minimum. Once this minimum is reached, the horizontal force increases a bit. At the transition angle where the horizontal forces with and without the wedge are equal, the vertical forces are not equal, resulting in a jump of the vertical force, when the wedge starts to occur.