In this chapter
you will find the modeling of the forces on the fluke and the shank. The
influences of the angles will be given.
Cutting theory of
Miedema is still valid for the fluke part of the anchor forces. For determining
the forces on the shank, the strip footing theory will be used.
Phase 3
For phase 3, two shear zones are taken into
account. This will lead to a geometry as discussed below.
Forces on the soil layer
As discussed
before; the cohesion, adhesion, inertial forces and water tension can be
neglected. For the above figure a force balance can be calculated.
The shear force
and the normal force are related according:
and
Where:
Internal friction angle of the sand
External friction angle fluke/sand
The grain forces
will be:
and
The weight of the soil can be determined by using the geometry below:
Dimensions
of the soil layer
with:
Where:
Angle of the fluke
in the sand
Angle of the shear
zone
Angle between fluke and shank
Total fluke length
Length of the shank
in the sand
Density of the in
situ sand
For the
determination of the forces on the fluke and the shank, two different theories
will be used. For the fluke the cutting theory of Miedema is valid, therefore
forces on the soil layer and on the fluke are the same as discussed in
situation 2.
For the forces on
the shank the strip footing theory can be used. This theory is based on the
fundamentals of Brinch Hansen and is a generalization of the Prantl theory.
Forces on the anchor
To determine the
friction Brinch Hansen force P on the shank we can make use of:
Where c is
cohesion and q is the external load on the soil
Because c and q
are zero in this case (no cohesion and no external force on the soil), P will
only be a function of the soil weight part of the function, so:
Hereby is a correction
factor for inclination factors of the load. The factor
is a shape factor for
the shape of the load.
In this case only
a load perpendicular to the soil will be considered, so will be removed from
the formula.
Inserting :
where:
y = the length of the shank in the sand
(at a moment in time).
B= the width of the shank
Now the friction
part of the shank has to be determined.
For the friction
of the shank, the next formula is valid:
Ffriction
= σn tan(δ) y h
Where:
σn =
δ =
External friction angle
y = the
length of the shank in the sand
h = the
height of the shank
It is possible now
to plot the results for P and Ffriction (see example) then it is
possible to find out if the downward force of the fluke is big enough to pull
the shank through the seabed and further.
It is also possible
now to make a total force and moment balance, to predict the trajectory of
the anchor.
Forces on the
anchor