Calculate active soil pressure, total lateral force, and line of action from Ka or friction angle, soil unit weight, and wall height.
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Active Soil Pressure Formula
The active soil pressure calculation uses the active earth pressure coefficient, soil unit weight, and wall height or depth. If you enter the friction angle instead of Ka, the calculator first estimates Ka using the Rankine formula for level backfill and a vertical wall with no wall friction.
K_a = (1 - sin(phi))/(1 + sin(phi))
p_a = K_a*gamma*H
P_a = 0.5*K_a*gamma*H^2
y = H/3
- Ka = active earth pressure coefficient
- phi = soil internal friction angle, in degrees
- gamma = soil unit weight, in kN/m³ or lb/ft³
- H = depth or retaining wall height, in m or ft
- pa = active lateral pressure at depth H, in kPa or psf
- Pa = total active force per unit length of wall, in kN/m or lb/ft
- y = line of action of the resultant force above the base
If you choose the Ka input mode, the entered coefficient is used directly. If you choose the friction angle φ input mode, Ka is calculated first, then used in the pressure and force equations. The pressure result is the lateral pressure at the bottom of the entered depth. The total force result is the area of the triangular pressure diagram over the wall height. For this triangular distribution, the resultant force acts at H/3 above the base.
Typical Soil Unit Weights and Active Pressure Coefficients
Use these values only for rough checking. Actual design values should come from soil data for the site.
| Soil type | Typical unit weight, γ | Typical friction angle, φ | Approx. Ka |
|---|---|---|---|
| Loose sand | 15 to 17 kN/m³, 95 to 110 lb/ft³ | 28° to 30° | 0.33 to 0.36 |
| Medium dense sand | 17 to 19 kN/m³, 105 to 120 lb/ft³ | 32° to 35° | 0.27 to 0.31 |
| Dense sand or gravel | 19 to 22 kN/m³, 120 to 140 lb/ft³ | 36° to 40° | 0.22 to 0.26 |
| Silty sand | 17 to 20 kN/m³, 105 to 125 lb/ft³ | 28° to 34° | 0.28 to 0.36 |
Result Interpretation
| Result | Meaning | Common use |
|---|---|---|
| Ka | Multiplier that converts vertical overburden pressure into active lateral pressure | Checking assumed soil pressure conditions |
| Active pressure at depth H | Maximum lateral pressure at the bottom of the wall or entered depth | Pressure diagram and local wall checks |
| Total active force over H | Resultant lateral force per unit length of wall | Sliding, overturning, and bearing checks |
| Line of action | Location of the resultant force for a triangular pressure distribution | Moment calculations about the wall base |
Example Problems
Example 1: Metric calculation using Ka
Suppose Ka = 0.3333, γ = 18 kN/m³, and H = 3 m.
Active pressure at depth H:
p_a = 0.3333*18*3 = 18.00 kPa
Total active force:
P_a = 0.5*0.3333*18*3^2 = 27.00 kN/m
Line of action:
y = 3/3 = 1.00 m above base
Example 2: Imperial calculation using friction angle
Suppose φ = 30°, γ = 120 lb/ft³, and H = 10 ft.
First calculate Ka:
K_a = (1 - sin(30))/(1 + sin(30)) = 0.3333
Active pressure at depth H:
p_a = 0.3333*120*10 = 400 psf
Total active force:
P_a = 0.5*0.3333*120*10^2 = 2000 lb/ft
Line of action:
y = 10/3 = 3.33 ft above base
FAQ
What assumptions are used for Ka from the friction angle?
When you enter φ, the calculator uses the Rankine active earth pressure equation. This assumes a simple active pressure case, usually treated as a vertical wall with level backfill, cohesionless soil, and no wall friction. Sloping backfill, wall friction, surcharge loads, groundwater, compaction loads, or cohesive soil behavior can change the pressure.
Why is the total active force one-half of KaγH²?
For dry cohesionless soil with no surcharge, lateral pressure increases linearly with depth. It is zero at the surface and reaches KaγH at the base. The pressure diagram is triangular, so the resultant force equals the area of that triangle: one-half times the base pressure times the wall height.
Where does the active force act on the wall?
For the triangular pressure distribution used here, the resultant active force acts at H/3 above the base of the wall. This location is used when calculating overturning moment. If the pressure diagram is not triangular, such as when surcharge or water pressure is included, the line of action may be different.