Rankine Passive Earth Pressure Coefficient
Also known as Kp · passive earth pressure
Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!
Learning zone
Passive pressure is the mirror image of active: instead of letting the soil spread, you shove the wall into it and ask how hard it pushes back. The soil has to lift and ride up a failure wedge, so the resistance is large — at φ = 30°, K_p = tan²(60°) = 3.0, exactly nine times the active coefficient. That factor of K_p/K_a = 9 at 30° (and 13.6 at 35°) is the whole reason a sheet pile wall can be held by an embedded toe.
The trap is deformation. Full passive resistance needs wall movement of 2–4% of the wall height in dense sand and up to 10% in loose — one to two orders of magnitude more than active pressure needs. A retaining structure that is only allowed to move 5 mm has mobilised perhaps a quarter of K_p, which is why most codes ask you to divide passive resistance by a factor of 1.5 to 2 before relying on it, or to ignore the top metre entirely because it may be dug up for services. The second trap is wall friction: for passive pressure it helps a great deal, and Rankine's smooth-wall assumption is conservative here in a way it is not on the active side.
- = Passive earth pressure coefficient
- = Angle of internal friction
- Passive earth pressure coefficient — Rankine Active Earth Pressure Coefficient, At-Rest Earth Pressure Coefficient (Jaky)
- Angle of internal friction — Rankine Active Earth Pressure Coefficient, At-Rest Earth Pressure Coefficient (Jaky)