$CO$#$4,6,8$ Related to the Course Project: Groundwater pumping is expected to lower the

water table $7$ feet at a site near New Orleans, as indicated in the Figure below. Compute

the expected settlement of the clay layer as a result of this pumping. For simplification,

assume that the unit weight of the sand does not change with pumping $($use ${}_t={}_{\text{s}\text{a}\text{t}}$ even

after the sand is no longer saturated$)$ and treat the clay as a single layer. The Compression

Index $(C_c),$ the Swelling Index or $C_r),$ and the preconsolidation stress $({}^{\text{'}}c)$ of the clay

are determined in the lab by testing a representative undisturbed Shelby tube sample

located at the center of the clay layer, as indicated in the Figure.

Figure. Site conditions before and after pumping.