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AimThe 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 diagramFor the situation as described, a free body diagram can be made. The following forces have to be taken into account:
Determination of the forcesBefore 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:
The constant of gravitation is set to be 9.81 m/s2.
Cutting force GLet 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.
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 systemFor 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:
OutputThe 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
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