An $9$ ft thick soil layer has the following properties:

Initial effective stress at the midpoint $=2000$ psf

Initial void ratio, $e_0=1\mathrm{.}5$

Compression index, $C_c=0\mathrm{.}2$

Recompression index, $C_r=0\mathrm{.}028$

Preconsolidation stress $=2500$ psf

A foundation will be built above this layer and will cause a change in vertical stress of $1000$ psf at the midpoint of the layer.

What is the amount of settlement $(\frac{?}{{?}_{\frac{?}{?}}H})$ in inches expected due to the consolidation of this soil layer caused by the foundation? Round your answer to the nearest $0\mathrm{.}1$ inch.