Granular Mechanics of the Rankine’s Lateral Pressure on Retaining Walls Under General Conditions

Rankine’s theory of lateral pressure in granular backfill is based on the hypothesis that the slip lines are straight. Despite this hypothesis, the achievement of the equations for the case of sloping wall and backfill is relatively difficult. However, when using the principles of granular mechanics, this problem is simplified to an elementary exercise in Statics. The definition of the associated and conjugate bands allows finding the global contact forces in any rhombic element of an infinite slope, under the condition that it obeys the Mohr-Coulomb law of plasticity. Knowing the contact area between a band and the back side of the retaining wall, the lateral pressure of the backfill is obtained, which is found to increase linearly with depth and depends on sines and cosines of the inclination angles of the back face, the slope of the backfill, and the angle of the associated bands. The lateral force is attained by integrating the pressure along the back face of the retaining wall, and can be verified with those resultants obtained previously by using the theory of plasticity. Granular mechanics allows for the complete generalization of the Rankine’s theory by means of very simple calculations.