Coulomb’s made the following assumptions in the development of his theory.
The assumptions are:
- The soil is isotropic and homogeneous.
- The surface of rupture is a plane.
- The failure wedge is a rigid body.
- There is friction between and the wall.
- Back of wall need not be vertical.
- Failure is two dimensional.
- The soil is cohesionless.
- Coulomb’s equation of shear strength is valid.
Coulomb made his derivation based on limit equilibrium approach.
Figure 3.25 below shows the cross section of a retaining Wall. Equilibrium analysis of failure wedge ABC involves:
- Weight of wedge ABC (magnitude and direction known)
- Pa (direction known, magnitude unknown)
- R (direction known, magnitude unknown)
Hence, from the triangle of forces can be drawn and Pa can be determined.
Weight of wedge ABC
From Triangle ABC,
Area of Triangle ABC =
Triangle of Forces for W, Pa and R
From the sine rule,
Substituting the value of W from the equation into we get,
In order to get the maximum value of Pa,
When, (leveled backfilled), (no wall friction), then . The point of application of Pa is at a distance of H/3 above the base of the wall.