Rankine's theory (maximum-normal stress theory), developed in 1857 by William John Macquorn Rankine,[1] is a stress field solution that predicts active and passive earth pressure.
It assumes that the soil is cohesionless, the wall is frictionless, the soil-wall interface is vertical, the failure surface on which the soil moves is planar, and the resultant force is angled parallel to the backfill surface.
The equations for active and passive lateral earth pressure coefficients are given below.
For the case where β is 0, the above equations simplify to Rankine's Theory says that failure will occur when the maximum principal stress at any point reaches a value equal to the tensile stress in a simple tension specimen at failure.
The resistance offered by the soil to an object pushing against it is referred to as "passive pressure".