# Coulomb Theory of Earth Pressure Coulomb’s theory states that the total lateral earth pressure is equal to the reaction exerted by the retaining wall when the wedge of soil tends to slide and acts at an angle 8 with the normal to the back of the wall.

1. The backfill is dry, cohesionless, isotropic, Backfill can be inclined.
2. There would be friction between the wall and the soil.
3. Failure plane is assumed to be a plane surface (but actually curved), Sliding wedge is assumed to be a rigid
body.
• Active earth pressure decreases while considering wall friction and passive earth pressure increases by considering wall friction.
• The position and line of action of earth pressure will be known in advance. The line of action of earth pressure will act at 1/3 depth from the bottom and will be inclined at an angle of from the normal to the wall.
• δ is approximately taken as
• The earth’s pressure is assumed to be the reaction given by the wall.
• For coulomb theory, the static equilibrium not satisfied in nature, i.e instead the force triangle (Fig.17), all the forces must pass through one point.
• Trial edge is selected at some angle „θ „.
• Trial edge will be having forces W, R, P as shown in Fig. the direction and magnitude of all the forces is known.
• By assuming various trial wedges at a different angle the value of „P‟ will be calculated.
• For Active Earth Pressure, P is the highest value obtained for various trial wedges.
• For Passive Earth Pressure, P is the minimum value.
• Rankine Earth Pressure theory overestimates the active earth pressure and underestimates the passive earth pressure.
• On compacting the soil, active earth pressure decreases while passive earth pressure increases.
• If the wall is smooth,
• When =0 than Column and Rankine result matches i.e wall must be vertical, the soil is cohesionless and backfill angle is 0
• For the masonry gravity wall, the Coulomb wedge theory is preferred while designing cantilever and counterfeit retaining wall, Rankine theory is preferred.
• For Abutment, the soil is taken as rest, for assessing the stability of the soil, while active pressure is considered when assessing the adequacy of a structural element of abutment and passive pressure is considered when integral abutment under thermal effect.
• Weep holes are provided at the back of the retaining wall to reduce the build-up of hydrostatic pressure.

### Coulomb Theory of Earth Pressure

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