Rankine Active Earth Pressure Theory

Rankine's active earth pressure theory is a fundamental approach in geotechnical engineering for calculating the lateral earth pressure exerted by soil on retaining walls under active earth pressure conditions. It assumes the soil behind the wall is homogeneous and isotropic with a horizontal backfill surface, and that there is no friction between the soil and the wall. The theory considers a planar failure surface inclined at $\displaystyle 45^\circ + \frac{\phi}{2}$ where $\phi$ is the soil's internal friction angle. The active earth pressure coefficient for cohesionless soil is given by . For cohesive soils, the lateral active earth pressure combines the effects of soil weight and cohesion via , where is the soil unit weight, is the wall height, and is soil cohesion. This theory reflects the minimum lateral pressure when the retaining wall moves away and the soil mass expands. It is widely used for design and optimization of earth retaining structures, helping ensure safety from sliding and overturning failures. Engineers must recognize the assumptions and limitations of Rankine's formula to apply it appropriately or choose more advanced methods when necessary. The clear formulas enable straightforward calculation of soil pressures needed to size retaining walls effectively and economically.