Problem $2-$ Use of sublayers

Predict the total settlement $(S)$ of the footing shown below. Include contributions from both settlement of the natural sand layer $($use the maximum settlement value$)$ and consolidation settlements. Use superposition of the settlements to determine the total ultimate settlement. Immediate settlement $(S_i)$ is not an issue because the footing is resting on the sand layer.

Use two sublayers of equal $10$ ft thickness in the CL layer with the undisturbed samples located at the mid height of the layers. Use the appropriate stress chart to determine ${}_v$ in the CL layer and please show your stress diagrams with profiles of ${}_{vo}^{\text{'}},{}_v$ and ${}_f^{\text{'}}$ over the entire depth $($i$.$e$.$ both sand and CL soil$).$ The change in soil from sand to clay does not influence the determination of ${}_v.$ Use superposition of the sublayer settlements to determine the total ultimate settlement.

How many days does it take for $U_{\text{a}\text{v}\text{e}}$ to reach $90\%?$ We ignore sublayers when evaluating time rate, just use one $20$ ft layer.

$q=3,000$ psf $=1\mathrm{.}5$ tsf

Square footing: $B=L=7ft7ft$

SP layer: ${}_m=105pcf$

Sample $1$:

Sample depth $=5ft$ below top of CL soil

${}_p^{\text{'}}=900psf$

$e_0=1\mathrm{.}0$

$C_c=0\mathrm{.}4$;$C_r=0\mathrm{.}04$

${}_{\text{s}\text{a}\text{t}}=114\mathrm{.}5pcf$

Sample $2$:

Sample depth $=15ft$ below top of CL soil

${}_p^{\text{'}}=1,100psf$

$e_0=1\mathrm{.}2$

$C_c=0\mathrm{.}4$;$C_r=0\mathrm{.}04$

${}_{\text{s}\text{a}\text{t}}=110pcf$

$C_v=20f\frac{t^2}{y}r$

when comparea to the CL soll adove$)$