About Lateral Earth Pressure Calculator
The lateral earth pressure calculator evaluates the Rankine active and passive earth-pressure coefficients, Ka = tan^2(45 - phi/2) and Kp = tan^2(45 + phi/2), and the resulting horizontal thrust on a smooth, vertical wall retaining a level, cohesionless backfill. For a dry backfill with no surcharge the active thrust reduces to the textbook result Pa = 0.5*Ka*gamma*H^2, acting at one third of the wall height above the base.
Enter the friction angle phi, the soil unit weight gamma, the wall height H, and, optionally, a uniform surcharge and a water table depth with a saturated unit weight. The tool superposes the triangular soil pressure, the rectangular surcharge pressure, and the hydrostatic water pressure, then reports the total thrust, the line of action, and the pressure at the base of the wall.
How It Works
- Choose the active or passive case (active for a wall free to move away from the backfill, passive for a wall pushed into the soil).
- Enter the friction angle phi (degrees), unit weight gamma (kN/m3), and wall height H (m).
- Optionally add a uniform surcharge q (kPa) and a water table depth with a saturated unit weight to include hydrostatic pressure.
- The calculator computes Ka and Kp, builds the lateral pressure diagram by superposition, and integrates it to find the total thrust and its line of action.
Worked Example
A 5 m high wall retains a dry sand with phi = 30 deg and gamma = 18 kN/m3, with no surcharge. The active coefficient is Ka = tan^2(45 - 15) = 1/3. The active thrust is Pa = 0.5*Ka*gamma*H^2 = 0.5 * (1/3) * 18 * 5^2 = 75 kN per metre run, acting at H/3 = 1.67 m above the base. The lateral pressure increases linearly from zero at the top to Ka*gamma*H = (1/3)*18*5 = 30 kPa at the base.
Formulas
- Rankine active coefficient
Ka = tan^2(45 - phi/2) = (1 - sin phi) / (1 + sin phi)- Rankine passive coefficient
Kp = tan^2(45 + phi/2) = (1 + sin phi) / (1 - sin phi)- Active thrust (dry backfill, no surcharge)
Pa = 0.5 * Ka * gamma * H^2 at H/3 above the base- Surcharge thrust
Pq = K * q * H acting at H/2 above the base- Hydrostatic water thrust
Pw = 0.5 * gamma_w * Hw^2 with gamma_w = 9.81 kN/m3
Standards & References
- Rankine (1857) earth-pressure theory
- Eurocode 7 (EN 1997) limit states
- Craig, Soil Mechanics
Frequently Asked Questions
What is the difference between active and passive earth pressure?
Active pressure develops when a wall moves away from the soil and the backfill expands to its minimum strength, giving the smaller coefficient Ka. Passive pressure develops when a wall is pushed into the soil, mobilising its maximum resistance, giving the larger coefficient Kp. For phi = 30 degrees, Kp is nine times Ka.
Where does the resultant thrust act?
For a triangular soil-pressure diagram the resultant acts at one third of the wall height above the base. A uniform surcharge adds a rectangular block acting at the mid-height, and water adds a triangular block acting at one third of the submerged height, so the combined line of action is the area-weighted average.
How is a water table handled?
Below the water table the calculator uses the buoyant (submerged) unit weight to compute the effective horizontal soil pressure and adds a separate hydrostatic water thrust of 0.5*gamma_w*Hw^2. This effective-stress approach correctly captures the large increase in total thrust caused by groundwater behind a wall.
Does Rankine theory account for wall friction or a sloping backfill?
No. The basic Rankine method used here assumes a smooth vertical wall and a horizontal, cohesionless backfill. For wall friction use Coulomb theory, and apply the inclined-backfill form of the Rankine coefficients when the ground surface slopes.