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# Effective lengths

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# Effective lengths

The strip lengths Le that appear in figure below will be determined so that the reinforcements will develop a frictional force that satisfies the equality  Fr = Ti

On the base of these lengths and of the Rankine's wedge dimensions, the global length Lo of the strips to use can be determined. Generally, the strips used have the same length for all the height of the wall.

The anchorage length depends on the friction coefficient  f = tan(δ)  between soil and reinforcement, being d an opportune fraction of the internal friction angle of the soil f.

If the strip is rough enough δ=φ, while for smooth metals d is about 20° to 25°.

Schematic representation of reinforcement length

For strips of b·Lesize or for unitary width and Le, length geotextile sheets, both faces develop friction; for circular bars, the frictional resistance is developed along the perimeter. In either case, the friction is given by the product of f and the normal pressure at the reinforcement calculated as  p0 = γ·zi  where zi  is the average distance from the soil surface to the reinforcement.

 For bars For strips For sheets

If in the previous formulas the sign ≥ was replaced with the equal sign, the safety factor Fs is equal to 1. If is assumed Fs > 1, the Le value is necessarily bigger than the one given by these formulas.