Active Force on a Retaining Wall

Equation: Rankine active force, Pa = ½·Ka·γ·H². It is the area of the triangular pressure diagram, whose pressure grows from 0 at the top to Ka·γ·H at the base. Values: Ka = 1/3 is the active pressure coefficient given. γ = 18 kN/m³ is the backfill unit weight. H = 5 m is the wall height retained. Step 1: pressure at the base, Ka·γ·H = (1/3)(18)(5) = 30 kPa. Step 2: area of the triangle, Pa = ½ × 30 × 5 = 75 kN/m. Leaving out the ½ gives 150 kN/m, which treats the pressure as uniform; ½γH² without Ka gives 225 kN/m.