$(40$ points total$)$ A very long $($into the page$)$ embankment is constructed over a layered system of sand and clay, as shown in the schematic below. The properties shown for the clay were obtained by conducting a laboratory consolidation test on a specimen prepared from an undisturbed sample collected at the mid$-$depth of the clay layer.

$($a$)(10$ pts$)$ The embankment soil was excavated from a local borrow area. The in$-$situ phase properties of the soil in the borrow area were $w=10\mathrm{.}0\%$ and $S=45\%.$ Given $G_s=2\mathrm{.}70,$ how many cubic yards of borrow soil, $($total volume$)$ had to be excavated to construct a $100-$ft$-$long $($into the page$)$ portion of the embankment?

$($b$)(15$ pts$)$ Determine the effective stress $($psf$)$ at the center of the clay layer, directly under the center of the embankment, assuming that the the embankment has been in place for a very long time.

$($c$)(15$ pts$)$ How much ultimate settlement $($inches$)$ you would expect at the center of the embankment crest due to primary consolidation of the clay caused by the embankment load?