Active Thrust on a Retaining Wall
Worked example: Ka 0.30, γ 18 kN/m³, H 5 m → Pa = 67 500 N/m — press Try an example to run it live, then adjust anything.
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Active Thrust on a Retaining Wall explained
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 . Its area — the total thrust per metre of wall — is , and because the diagram is triangular the resultant acts at H/3 above the base, not at mid-height. A 5 m wall with = 0.30 and γ = 18 kN/m³ takes = 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 formula
- = Active thrust per metre of wall (N/m)
- = Active earth pressure coefficient
- = Unit weight of backfill (kN/m³)
- = Height of wall (m)
Missing one of these? Work it out first, then come back
- Active thrust per metre of wall — Hooke's Law, Elastic Potential Energy
- Active earth pressure coefficient — Rankine Active Earth Pressure Coefficient, Rankine Passive Earth Pressure Coefficient
- Unit weight of backfill — Total Vertical Stress (σ = γz), Terzaghi Ultimate Bearing Capacity (Strip Footing)
- Height of wall — Gravitational Potential Energy (U = mgh), Area of a Triangle