Foundation, Concrete and Earthquake Engineering

### Consequence of Making Assumptions in Pressure Distribution below Footing

Contact pressure is the upward pressure produced by soil reaction on the underside of the footing.  These soil reaction is assumed uniform in deriving different relationship for soil-structure interaction problem. But actually a footing are not flexible as well as contact pressure is not uniform, necessitating more investigation for actual contact pressure distribution.
Factor Influencing Contact Pressure

The actual distribution of contact pressure depends upon a number of factors such as

1) Elastic properties of footing

2) Elastic properties of soil

3) Thickness of footing

Different characteristics of contact pressure distribution under flexible and rigid footings are described below:

Contact Pressure On Saturated Clay

Flexible Footing

When a footing is flexible, it deforms into shape of bowel, with the maximum deflection at the center. The contact pressure distribution is uniform.

Rigid Footing

When a footing is rigid, the settlement is uniform. The contact pressure distribution is minimum at the center and the maximum at the edges. The stresses at the edges in real soils can not be infinite as theoretically determined for an elastic mass. In real soils, beyond a certain limiting value of stress, the plastic flow occurs and the pressure becomes finite.

 Fig: Qualitative contact pressure distribution under flexible and rigid footing resting on    saturated clay and subjected to a uniformly distributed load q.

Contact pressure on sand

Flexible footing
In this case, the edges of flexible footing undergo a large settlement than at the centre. The soil at the centre is confined and, therefore, has a high modulus of elasticity and deflects less for the same contact pressure. The contact pressure is uniform.

Rigid footing
If the footing is rigid, the settlement is uniform. The contact pressure increases from zero at the edges to a maximum at the centre. The soil, being unconfined at edges, has low modulus of elasticity. However, if the footing is embedded, there would be finite contact pressure at edges.
 Fig: Qualitative contact pressure distribution under flexible and rigid footing resting on sandy soil and subjected to a uniformly distributed load q.

Thus it is observed that the contact pressure distribution for flexible footing is uniform for both clay and sand. The contact pressure for rigid footing is maximum at the edges for footing on clay, but for rigid footings on sand, it is minimum at the edges.

Consequence of assuming uniformity in pressure

For convenience, the contact pressure is assumed to be uniform for all types of footings and all types of soils if load is symmetric.
The above assumption of uniform pressure distribution will result in a slightly unsafe design for rigid footing on clays, as the maximum bending moment at centre is underestimated. It will give a conservative design for rigid footings on sandy (cohessionless) soils, as the maximum bending moment is overestimated. However, at the ultimate stage just before failure, the soil behaves as an elasto-plastic material ( and not an elastic material) and the contact pressure is uniform and the assumption is justified at the ultimate stage.