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1.4 Rankines active Earth Pressure Theory

Rankines Theory: As originally proposed, Rankines theory of lateral earth pressure is applied to uniform cohisionless soil only. Later it was extended to cohesive soils by Resal and Bell. The theory has also been extended to stratified, partially immersed and submerged soil.

This theory is valid when:

The back of the wall is vertical and smoothThe level of the soil behind the wall is horizontalSoil mass is semi-infinite, homogeneous, dry and cohesionless The length of the wall is long in comparison to the height sothat it can be treated two dimensional situations.Rankines Theory assumes that failure will occur when the maximum principal stress at any point reaches a value equal to thetensile stressin a simple tension specimen at failure. This theory does not take into account the effect of the other two principal stresses. Rankines theory is satisfactory for brittle materials, and not applicable to ductile materials.

This theory is also called theMaximum Stress Theory.

The Rankine theory assumes a frictionless soil-wall interface and a vertical wall (no wall slope).1.5 Coulombs theory: He highlighted that if the wall is not friction less unlike assumed in Rankines case the lateral earth pressure applied by the soil is not normal to the wall but at an angle or in other word has both horizontal and a vertical components.

Solutions from the coulomb theory can be obtained from the situations when the back of the wall is not vertical but is inclined at an angle to the horizontal and the soil behind the wall is not horizontal but inclined at an angle to the horizontalAssumptions:

The backfill is dry and cohesionless, homogeneous, istropic and elastically undeformable but breakable.The slip surface is the plane which passes through the heel of the wall.The sliding wedge itself acts as a rigid body and the value of earth pressure is obtained by considering the limiting equilibrium of the sliding wedge as a whole.