Active Thrust on a Retaining Wall

Pa=12KaγH2P_a = \tfrac{1}{2}\,K_a\,\gamma\,H^{2}

Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!

Learning zone

Active pressure grows linearly with depth, so the pressure diagram on a wall retaining dry granular fill is a triangle of height H and base K_a γ H. Its area — the total thrust per metre of wall — is ½ K_a γ H², and because the diagram is triangular the resultant acts at H/3 above the base, not at mid-height. A 5 m wall with K_a = 0.30 and γ = 18 kN/m³ takes P_a = 0.5 × 0.30 × 18 × 25 = 67.5 kN per metre of wall, applied 1.67 m up.

The trap is the square. Thrust goes as H², and the overturning moment as H³, so a wall that is 20% taller than planned carries 44% more force and 73% more moment. The second and far more dangerous trap is water. Saturate the backfill and you replace γ with γ′ ≈ 9.7 kN/m³ but add a full hydrostatic triangle at 9.81 kN/m³ with a coefficient of 1.0, roughly tripling the total thrust. Almost every retaining wall that has ever fallen over did so after rain, with a blocked weep hole. Drain the backfill, and drain it with free-draining stone and a filter, not with hope.

Active Thrust on a Retaining Wall
Pa=12KaγH2P_a = \tfrac{1}{2}\,K_a\,\gamma\,H^{2}
Where
  • PaP_a= Active thrust per metre of wall
  • KaK_a= Active earth pressure coefficient
  • γ\gamma= Unit weight of backfill
  • HH= Height of wall
Missing one of these? Work it out first, then come back