# 12.5: The Non-Cavitating Wedge

- Page ID
- 29363

To illustrate the results of the calculation method, a non-cavitating case will be discussed. 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 60^{o} 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 λ 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

**e**

_{2}

**=0.35**,

**e**

_{3}

**=0.55**and

**e**

_{4}

**=0.32**, based on the finite element calculations carried out by Ma (2001).

Figure 12-22 and Figure 12-23 show the results of the calculations. Figure 12-22 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 12-23 shows the horizontal and vertical cutting forces, with and without a wedge.

The wedge angles found are smaller than

**90**, which would match the theory of Hettiaratchi and Reece (1975). The shear angle

^{o}-φ**β**is around 20

^{o}, but it is obvious that a larger internal friction angle gives a smaller shear angle

**β**. The mobilized external friction angle varies from plus the maximum mobilized external friction angle to minus the maximum mobilized external friction angle as is also shown in the force diagrams in Figure 12-21.

Figure 12-23 shows clearly how the cutting forces become infinite when the sum of the 4 angles involved is 180^{o} and become negative when this sum is larger than 180^{o}. So the transition from the small cutting angle theory to the wedge theory occurs around a cutting angle of 70^{o}, depending on the soil mechanical parameters and the geometry of the cutting process.