Question $1$:

Based on the soil and loading conditions listed or illustrated below, provide answers to the following

questions $($note: the $125$kPa surcharge is the load that initiates consolidation$).$

$($a$)$ Calculate the ultimate consolidation settlement. Consider the

clay layer as one uniform layer with OCR$=1$ and that the $125$

kPa surcharge stress acts equally at all depths.

$($b$)$ How long will it take for $0\mathrm{.}05,0\mathrm{.}25,$ and $0\mathrm{.}5m$ of settlement to

occur.

$($c$)$ How do the times calculated in part $($b$)$ change if the underlying

dense sand is replaced with an impermeable bedrock.

$($d$)$ How long would it take for the ultimate settlement $($practically

defined as $95\%$ settlement$)$ computed in Part $($a$)$ to occur?

Sand properties:

${}_{\text{d}\text{r}\text{y}}($ above water table $)=1\mathrm{.}8M\frac{g}{m^3}$

${}_{\text{s}\text{a}\text{t}}($ below water table $)=2\mathrm{.}2M\frac{g}{m^3}$

Soft clay properties $({}_s$ is the mass density of solids$)$

$C_V=8{10}^{-4}c\frac{m^2}{s},C_c=0\mathrm{.}25,$ and $C_r=0\mathrm{.}031$

Soft

clay

${}_s=2660k\frac{g}{m^3}$