Surcharge Force on a Retaining Wall

Equation: a uniform surcharge adds the same lateral pressure at every depth, σh = Ka·q. That pressure acts over the full wall height, so the force is the area of a rectangle: Pq = Ka·q·H, acting at H/2. Values: Ka = 1/3 is given. q = 20 kPa is the surcharge on the backfill. H = 5 m is the wall height, which is the height the pressure acts over. Step 1: lateral pressure from the surcharge, σh = Ka·q = (1/3)(20) = 6.67 kPa. It is constant from top to bottom because the surcharge adds the same vertical stress at every depth. Step 2: force, Pq = σh·H = 6.67 × 5 = 33.3 kN/m, acting 2.5 m above the base. Using ½·Ka·q·H = 16.7 kN/m treats the surcharge pressure as a triangle like the soil's own pressure. 100 kN/m is q·H and 50 kN/m is ½·q·H, both of which forget Ka.