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Rankine versus Coulomb theory

Short answer

Rankine assumes a smooth vertical wall, horizontal backfill, plastic equilibrium throughout the mass, and thrust parallel to the surface. Coulomb assumes a planar failure wedge, includes wall friction, allows inclined wall back and sloping backfill, and determines thrust from wedge force equilibrium.

What are the differences between Rankine's and Coulomb's theories of lateral earth pressure (assumptions and four basic differences)?

Assumptions

Rankine's theory:

  • The soil is homogeneous, isotropic, semi-infinite and the wall back is vertical and smooth (no wall friction).
  • The backfill surface is horizontal or a plane slope and the wall moves enough to reach the plastic state.
  • Failure occurs by a state of plastic equilibrium in the whole soil mass; pressure acts parallel to the backfill slope.

Coulomb's theory:

  • Soil is dry, homogeneous, isotropic and cohesionless.
  • The failure surface is a plane through the heel of the wall; the failing wedge slides as a rigid body.
  • Wall friction (δ\delta) acts on the back face; the wall back can be inclined and the backfill can slope.
  • The resultant is found by wedge force equilibrium.

Four basic differences

PointRankineCoulomb
ApproachStress state in soil mass (plastic equilibrium)Force equilibrium of a sliding wedge
Wall frictionNeglected (δ=0\delta = 0)Considered (δ≠0\delta \ne 0)
Wall back / backfillVertical back, plane surfaceAny inclined back and sloping backfill
Direction of thrustParallel to backfill surfaceAt angle δ\delta to the normal to the wall
Failure surfacePlanes through whole massPlane through the heel
CohesionCan include ccOnly cohesionless (basic form)
ResultSimple, slightly conservative for activeMore accurate for active, less accurate for passive when δ>ϕ/3\delta > \phi/3

✓ Answer checked by Claude Sonnet 5.5

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