Rankine Passive Earth Pressure

What is this formula?

The Rankine Passive Earth Pressure equation calculates the passive earth pressure coefficient for a cohesionless soil.

Passive earth pressure develops when a retaining structure moves toward the soil mass, mobilizing the soil's resistance to compression.

The passive coefficient is significantly larger than the active coefficient and is commonly used when evaluating lateral resistance.

When to use it

Use this formula when analyzing:

- Sheet pile walls

- Retaining walls

- Buried structures

- Pile foundations

- Abutments

- Lateral resistance systems

The equation assumes:

- Homogeneous soil

- Horizontal ground surface

- No wall friction

- Cohesionless soil

Example

A sandy soil has:

φ = 30°

Formula:

Kp = (1+sinφ)/(1-sinφ)

Substitution:

Kp = (1+sin30°)/(1-sin30°)

Kp = (1+0.5)/(1-0.5)

Kp = 3.0

Result:

Kp = 3.0

Applications

- Passive soil resistance

- Sheet pile design

- Foundation lateral stability

- Excavation support

- Retaining structures

Note

This formula is based on Rankine's passive earth pressure theory and assumes ideal conditions. Actual passive resistance can be affected by wall friction, construction methods, groundwater, layered soils, and displacement limitations. Many design codes apply reduction factors to passive resistance for safety.