Rankine Passive Earth Pressure in Retaining Wall Design

Rankine's passive earth pressure theory addresses the lateral force exerted by soil when it compresses against a retaining wall as the soil mass moves toward the structure. This condition creates a failure plane inclined at $\displaystyle 45^\circ + \frac{\phi}{2}$, where $\phi$ represents the soil's internal friction angle. The theory applies to cohesionless, homogeneous, isotropic soils with a horizontal backfill surface and assumes no friction between the wall and soil. The passive earth pressure coefficient, , is calculated as , which is then used to find the soil pressure at depth using , with as the soil unit weight. The resultant passive thrust acts at one-third the wall height from the base and is crucial for estimating maximum soil forces resisting wall movement. Understanding and applying Rankine's theory ensures accurate design of retaining structures subject to lateral soil resistance during excavation or seismic events, preventing underestimation of forces and enhancing structural safety.