Boussinesq Point Load Stress Distribution

Reference

The Boussinesq solution spreads a surface load through an elastic ground mass, and it underlies almost every settlement and stress influence chart.

The equation

Δσ = 3 Q z³ / (2π R⁵), R² = r² + z²
  • Q is the point load in kilonewtons
  • z is depth below the surface, r the horizontal offset
  • R is the straight line distance from load to the point considered

Worked example

Directly beneath a 500 kilonewton column load, at 2 meters depth, the added vertical stress is 3 × 500 × 8 / (2π × 32) = 59.7 kilopascals. Move sideways just 2 meters at the same depth and it falls by roughly a factor of six.

When to use it

Superpose point solutions to build pads, strips, and rafts, or use the two to one rule for a quick check. Elasticity is a fiction soils tolerate at working loads, which is why the method survives.

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