Limitations of Boussinesq and Westergaard

Both theories assume an ideal elastic soil; real soil only approximates this.

Boussinesq's theory (point load on a half-space)

• The soil is a semi-infinite, homogeneous, isotropic, linearly elastic mass (stress is proportional to strain).
• The soil is weightless and continuous; the stress-strain relation does not depend on the stress level.
• The load acts at the surface of a horizontal half-space as a point load (loaded areas are handled by integration).
• It is valid only while the stresses are well below failure and the soil is fairly uniform. It gives results close to observed values for homogeneous deposits, and somewhat high stresses for stratified soils.

Limitations: real soils are neither perfectly elastic nor homogeneous; layered soils, a stiff layer below, or a very soft layer limit its use. It also ignores the effect of foundation depth (the load is taken at the surface).

Westergaard's theory

• The soil is an elastic medium reinforced by thin, perfectly rigid horizontal sheets (e.g. sand or silt layers within clay) which allow no lateral strain.
• Poisson's ratio is taken as zero ($\nu = 0$).
• It suits stratified, anisotropic deposits (alternating sand and clay) and soft clay with thin sand seams. It gives a lower stress than Boussinesq (about 2/3 on the load axis).

Limitations: the assumptions of perfectly rigid layers and $\nu = 0$ are idealised, and the actual stress usually lies between the two theories.