Rankine Earth Pressure Coefficients

Reference

Rankine theory gives the limiting horizontal pressures a soil mass can exert on or accept from a wall, bracketing every retaining design.

The equation

Ka = tan²(45 – φ/2), Kp = tan²(45 + φ/2)
  • Ka is the active coefficient, the minimum push on a yielding wall
  • Kp is the passive coefficient, the maximum resistance available
  • Both apply to smooth vertical walls with level backfill

Worked example

Sand with friction angle 32 degrees gives Ka of 0.307. Behind a wall at 5 meters depth with unit weight 18, active pressure is 0.307 × 90 = 27.7 kilopascals, and the total active thrust on the wall grows with the square of its height.

When to use it

Active pressure needs a little wall movement to mobilize and passive needs a lot, so factor passive resistance heavily. Water behind a wall adds full hydrostatic pressure on top of the soil terms, and it usually dominates.

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