Height $of$ Sample $=H_{\text{i}\text{n}\text{i}\text{t}\text{i}\text{a}\text{l}}-$ Dial Reading

During a soils investigation, a clay layer was first encountered at a depth of $2$ feet and found to have a thickness of $20$ feet. The SM $-$ Silty SAND soils above this clay have an average unit weight of $115$ pcf$.$ Ground water table is $3$ feet below surface. An undisturbed sample was taken at a depth of $25$ to $27$ feet and a consolidation test was performed on it$.$ Below the clay is a SW $-$ Well graded SAND starting at $35$ feet depth. Initial measurements and test results are presented below:

Consolidation Test Sample:

Initial Sample Height $-0\mathrm{.}5000$ in

Sample Diameter $-2\mathrm{.}50$ in

Sample Weight $-72\mathrm{.}8g($initial weight of solids and water$)$

Gs $=$ Specific Gravity $-2\mathrm{.}70$

Wc $\%=$ Initial Water Content $-37\mathrm{.}2\%$

Sample was double$-$drained.

Using this data,

Determine the initial total, dry, and submerged unit weights of the clay.

Determine the saturation $)=(V\frac{w}{V}v$ of the sample.

Determine the vertical effective stress at the sample depth $(6ft).$

Using the square root of time $($Taylor$)$ method, find $H_{90}($Height at $90\%$ consolidation$)$ and t$90($time for $90\%$ consolidation$)$ for the $0\mathrm{.}5ksf$ load. Clearly show your procedure on a proper sqrt $($time$)$ v Height graph.

Find the coefficient of consolidation $(c_v)$ for the $0\mathrm{.}5ksf$ loading.