Phase 3


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.

Fluke and shank in the soil

Phase 3

 

Forces on the soil layer

 

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


The Weight of the soil will be:

 

 

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

                       

 

Forces on the fluke and the shank

 

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                  = Normal stress on the area of the shank

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