The Delft Sand, Clay & Rock Cutting Model, 2019a

A Wedge in Saturated Sand Cutting.
Figure 12-2 shows the definitions of the cutting process with a static wedge. A-B is the shear plane where dilatation
occurs. A-C is the front of the static wedge and forms a pseudo cutting blade. A-C-D is the static wedge, where C-
D is the blade, A-D the bottom of the wedge and A-C the pseudo blade or the front of the wedge.
The sand wedge theory is based on publications of Hettiaratchi and Reece (1975), Miedema (1987 September),
He et al. (1998), Yi (2000), Miedema et al. (2001), Yi et al. (2001), Ma (2001), Miedema et al. (2002A), Miedema
et al. (2002B), Yi et al. (2002), Miedema (2003), Miedema et al. (2003), Miedema (2004), Miedema et al. (2004),
He et al. (2005), Ma et al. (2006A), Ma et al. (2006B), Miedema (2005), Miedema (2006A), Miedema (2006B).
12.2. The Equilibrium of Forces.
Figure 12-4, Figure 12-5 and Figure 12-6 show the forces occurring at the layer cut, the wedge and the blade, while
Figure 12-18 shows the moments occurring on the wedge. The forces are:
The forces acting on the layer A-B are:
1. A normal force acting on the shear surface N1, resulting from the effective grain stresses.
2. A shear force S1 as a result of internal friction N1·tan(φ.
3. A force W1 as a result of water under pressure in the shear zone.
4. A force normal to the pseudo blade N2, resulting from the effective grain stresses.
5. A shear force S2 as a result of the soil/soil friction N2·tan(λ between the layer cut and the wedge pseudo
blade. The friction angle λ does not have to be equal to the internal friction angle φ in the shear plane, since
the soil has already been deformed.
6. A force W2 as a result of water under pressure on the wedge.
The forces acting on the wedge front or pseudo blade A-C when cutting soil, can be distinguished as:
7. A force normal to the blade N2, resulting from the effective grain stresses.
8. A shear force S2 as a result of the soil/soil friction N2·tan(λ between the layer cut and the wedge pseudo
blade. The friction angle λ does not have to be equal to the internal friction angle φ in the shear plane, since
the soil has already been deformed.
9. A force W2 as a result of water under pressure on the pseudo blade A-C.
The forces acting on the wedge bottom A-D when cutting soil, can be distinguished as:
10. A force N3, resulting from the effective grain stresses, between the wedge bottom and the undisturbed soil.
11. A shear force S3 as a result of the soil/soil friction N3·tan(φ between the wedge bottom and the undisturbed
soil.
12. A force W3 as a result of water under pressure on the wedge bottom A-D.
The forces acting on a straight blade C-D when cutting soil, can be distinguished as:
13. A force normal to the blade N4, resulting from the effective grain stresses.
14. A shear force S4 as a result of the soil/steel friction N4·tan( between the wedge and the blade.
15. A force W4 as a result of water under pressure on the blade.
To determine the cutting forces on the blade, first the cutting forces on the pseudo blade have to be determined by
taking the horizontal and vertical equilibrium of forces on the layer cut B-A-C. The shear angle β is determined
by minimizing the cutting energy.
The horizontal equilibrium of forces:
F h K 1 sin( ) W 1 sin( ) W 2 sin( ) K 2 sin( ) 0
(12-1)
The vertical equilibrium of forces:
F v K 1 cos( ) W 1 cos( ) W 2 cos( ) K 2 cos( ) 0
(12-2)
The force K1 on the shear plane is now:
K
1
W2 sin( ) W1 sin( )
sin( )
(12-3)
Copyright © Dr.ir. S.A. Miedema TOC Page 347 of 454