Rankine Passive Earth Pressure Coefficient
Rankine Passive Earth Pressure Coefficient
The passive coefficient sets the large resistance soil offers when a wall pushes into it — the reverse of the active case.
Rankine’s passive coefficient is K_p = (1 + sin φ)/(1 − sin φ). where φ is the angle of internal friction.
Inputs
phi := 0.5236=0.52
Apply Rankine’s passive-pressure formula.
K_p := (1 + sin(phi))/(1 - sin(phi))=3
Results
Passive pressure is much larger than active (here K_p = 3 versus K_a = 1/3). It provides the resistance that anchors sheet piles and retaining structures.
Assumptions & limitations
- Cohesionless soil.
- Smooth vertical wall, horizontal backfill.
- Full passive mobilisation (large movement).