Location of Active Earth Pressure Force

Equation: a resultant force acts through the centroid of its pressure diagram. For a triangle, the centroid is one third of its height up from the wide end. Values: with level backfill and no surcharge, the active pressure is σh = Ka·γ·z. It grows linearly from zero at the top (z = 0) to its maximum at the base (z = H), so the diagram is a triangle with its wide end at the base. Step 1: the triangle's centroid is H/3 above its wide end. Step 2: the wide end is at the base, so the resultant acts H/3 above the base (for a 5 m wall, 1.67 m). H/2 is correct only for a uniform (rectangular) pressure, such as the part caused by a surcharge.