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

A Wedge in Saturated Sand Cutting.
Figure 12-7: The volume balance over the shear zone.
Figure 12-8: Possible flow lines.
To be independent of the ratio between the initial permeability ki and the maximum permeability kmax , kmax has
to be replaced with the weighted average permeability km before making the measured water under pressures
dimensionless.
The water vacuum pressures in the sand package on and around the blade are numerically determined using the
finite element method. A standard FEM software package is used (Segal (2001)). Within this package and the use
of the available "subroutines" a program is written, with which water vacuum pressures can be calculated and be
output graphically and numerically. As shown in Figure 12-9, the SEPRAN model is made up of three parts, the
original sand layer, the cut sand layer, and the wedge. The solution of such a calculation is however not only
dependent on the physical model of the problem, but also on the next points:
1. The size of the area in which the calculation takes place.
2. The size and distribution of the elements
3. The boundary conditions
The choices for these three points have to be evaluated with the problem that has to be solved in mind. These
calculations are about the values and distribution of the water under-pressures in the shear zone and on the blade,
on the interface between wedge and cut sand, between wedge and the original sand layer. A variation of the values
for point 1 and 2 may therefore not influence this part of the solution. This is achieved by on one hand increasing
the area in which the calculations take place in steps and on the other hand by decreasing the element size until the
variation in the solution was less than 1%. The distribution of the elements is chosen such that a finer mesh is
present around the blade tip, the shear zone and on the blade, also because of the blade tip problem. A number of
boundary conditions follow from the physical model of the cutting process, these are:
For the hydrostatic pressure it is valid to take a zero pressure as the boundary condition.
The boundary conditions along the boundaries of the area where the calculation takes place that are located
in the sand package are not determined by the physical process.
For this boundary condition there is a choice among:
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