Vertical displacement under a circular rigid foundation

[Alvarobg]

Hello,

I have found in several publications the expression for the Vertical displacement under a circular rigid foundation under a vertical load, P (in other words if I am not wrong: vertical displacement under an area carrying an uniform load, p):

It is derived from Boussinesq half space theory, but I am not able to deduce it. Can anybody provide me any idea or references proving it?

Thank you.

 

[GeoEnvGuy]

Depending on the underlying soils that equation could be applied to cohesionless soils (sand) but would not be appropriate for cohesive materials (clay). It also doesn't account for the depth of deposit or influence factors.

If you are looking to determine the displacement that would require completing a geotechnical investigation to estimate Young's modulus or coefficient of compressibility. That would provide you with the settlement bearing capacity.

The first stage of site investigation is desktop and it informs the engineer of the anticipated subsurface conditions. By precluding the site investigation the design engineer cannot accept any responsibility for providing a safe and economical design.

 

[Alvarobg]

Hello, thank you for your reply.

I am working in a theoretical way. I would like to understand why the vertical displacement is that metioned in a Boussines half-space under a circular rigid foundation in order to calculate the theoretical expression in a Boussinesq half-space under a RING rigid foundation.