Anchor settling
Up Anchor geometry Penetration initiation Failure wedge Anchor settling

Aim

The aim of this submodel is to calculate which forces and accelerations are applied to the anchor when the blade is penetrating the soil in the settling phase.

Free body diagram

For the situation as described, a free body diagram can be made. The following forces have to be taken into account:

  1. Weight of the anchor

  2. Weight of the soil projected on the blade

  3. Cohesion

  4. Adhesion

  5. Pulling forces on the anchor line

  6. Friction forces on the anchor line

  7. Cutting force

  8. Friction forces shaft

Determination of the forces

Before all the forces can be calculated, some data have to be known. You can think about the length of the part of the anchor line and shaft that is in the soil and geometrical data, like:

  • Effective areas
  • Position where all the forces are applied
  • Penetration angle β
  • Failure wedge properties

The constant of gravitation is set to be 9.81 m/s2

Forces (kN)

Input variables

Required calculation / Output submodel

A

Weight anchor M (t)

M×g

B

Position anchor blade
X (m), Y (m)
Penetration angle β (rad)
Density
soil ρ soil (t/m3)

Submodel failure wedge

C

Cohesion soil c (kN/m2)
Area boundary layer wedge
A wig (m2)

c × A wedge / Submodel failure wedge

D

Adhesion soil a (kN/m2)
Blade area A blade  (m2)

a × A blade / Submodel geometry

E

T anchor (t) (kN)

 Input parameter

F

Angle anchor line and shaft ζ (rad)
Adhesion soil a (kN/m2
)
Diameter anchor line d

L(x,y)=Z(x,y)/cos(ζ)
L×d×a  / Submodel geometry

Remark: in real situation a cutting force line perpendicular on the line will occur, this is not taken in account in this model

G

Soil stresses σy
Cohesion force C
Cutting angle α

See 'Cutting force G' beneath
 

H

L shaft (m)
Position shaft Xs (m), Ys (m)
Angle anchor line and shaft ζ (rad)
Diameter shaft dshaft (m)
Adhesion soil a (kN/m2)
Shaft coefficients Cshaft

L shafteff(x,y)=Z(x,y)/cos(ζ)
L shafteff < L schaft
L
shafteff×dshaft× a× Cshaft

/ Submodel geometry

Cutting force G

Let us consider two particles of soil, where a wedge is driven in between. We want to know the size of the force (in x-direction) acting on the wedge.

 The particles (with the wedge on top, not in between) are pushed together by 3 forces, the cohesion of the material, the stress in the soil in y-direction and the local decreased pressure caused by dilatance.

The cutting force of the wedge has to overrule these forces. The forces, which push the particles together, act perpendicular on the surface of the wedge. So the forces acting on both sides of the wedge are:

The wedge will be pushed downwards so we want to know the force on the wedge in x-direction. This is:

                              

So the cutting force should be larger than:

This is correct if we assume that the point of the wedge is small compare to the size of the particles. But if we consider sand or clay this is not true. We cannot sharpen the points of an anchor that much.

We should bring an extra force in to account, a force resulting of an area multiplied with the maximal stress which can occur in the soil in the x-direction. This stress is related to the stresses in the soil in y-direction, because the shear force, which the soil can stand, is limited.

By pushing the wedge in the soil, the stresses in y-direction are increased, which will also increase the maximum stress in x-direction.

 

This brings the total cutting force to the following formula:

Evaluation of the system

For the calculation of the forces and accelerations, Newtons laws have to be considered.

The x-axes is defined to be parallel to the anchor blade, the y-axed is pointed perpendicilar upward.

Fx = m× ax

Fy =  m × ay

M=Iβ''

The resulting force Fy have to be 0, because otherwise the anchor will break out.

It is assumed that the force C only works in y-direction and has no contribution in x-direction.

Equilibrium in x-direction yields:

 Equilibrium in y-direction yields:

As derived earlier, C = c × A wedge. Because the effective area is given by the submodel 'failure wedge', the minimum required cohesion can be calculated now.

Equilibrium in moments around the front of the anchor yields:

Output

The sub model can deliver the new penetration acceleration for the calculated time step and a warning when the given cohesion is smaller than the required cohesion.

 

Copyright © 2005 Project group 1
Last modified: 10/27/05