Active Earth Pressure (Rankine) Calculator

How to use this calculator

1. Enter the soil's angle of internal friction phi in degrees, its unit weight gamma in kN/m3, and the retained height H in metres.
2. Optionally add a uniform surcharge q in kPa (e.g. traffic or stockpile load) — it adds Ka*q of pressure over the full height.
3. Optionally set the sheet-pile depth factor (1.2 to 1.4) to see a preliminary embedment estimate. Read Ka, Kp, the base pressure, and the total active thrust per metre run.

How it works

Rankine's theory for a smooth vertical wall with level, cohesionless backfill gives the active coefficient Ka = tan^2(45 - phi/2) and the passive coefficient Kp = tan^2(45 + phi/2). The active pressure grows linearly with depth: p = Ka*gamma*z, reaching Ka*gamma*H at the base, so the total soil thrust per metre of wall is Pa = 0.5*Ka*gamma*H^2, acting at H/3 above the base. A uniform surcharge q adds a constant Ka*q over the whole height, contributing Ka*q*H to the thrust.

The passive thrust (soil resisting the wall) is Pp = 0.5*Kp*gamma*H^2. For a cantilever sheet pile in granular soil, a rough required embedment is d0 = H*sqrt(Ka/(Kp - Ka)), and designers typically drive to 1.2-1.4 x d0 to build in a factor of safety. That embedment figure here is a first-pass estimate only — it ignores water pressure, cohesion, wall friction, sloping backfill and load factors. Every result should be checked against the governing standard and a competent geotechnical engineer.

Worked example

4 m wall, medium-dense sand. For phi = 30 degrees, gamma = 18 kN/m3, H = 4 m and no surcharge: Ka = tan^2(45 - 15) = 0.3333 and Kp = 3. Active pressure at the base = 0.3333 x 18 x 4 = 24 kPa. Total active thrust Pa = 0.5 x 0.3333 x 18 x 4^2 = 48 kN per metre run, acting 4/3 = 1.333 m above the base. Passive thrust Pp = 0.5 x 3 x 18 x 4^2 = 432 kN/m. A sheet-pile theoretical depth d0 = 4 x sqrt(0.3333/(3 - 0.3333)) = 1.414 m, factored (x1.3) to about 1.838 m as a first-pass estimate only.

Common mistakes

• Entering phi in radians. The formula uses degrees — phi = 30 means 30 degrees; the tool converts to radians internally.
• Confusing pressure (kPa, the value at a depth) with thrust (kN per metre run, the integrated force). The design force on the wall stem is the thrust Pa, not the base pressure.
• Treating the sheet-pile embedment as a design depth. It is a granular-soil, no-water, first-pass estimate only — it is not a substitute for a full geotechnical design with water table, factors and moment checks.

Frequently asked questions

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