Q. Deformation Equation for settlement?

When a load is applied on an elastic body, it results in strain. The summation of strain over a length is deformation or settlement. In the soil media, the strain (deformation/unit length) is produced primarily by a combination of particle rolling, slippage and sliding displacements. The deformation AH, is the statistical summation of the strain in that direction. Hence, along the direction of stressed depth

D_i = Depth over which the foundation is resting.

= Strain (depends on Hooke's law), and

Most of the strain occurs directly beneath the footing, upto a depth of 0.3 to 0.5 B.