Problem $2$

A $\backslash (2\backslash$mathrm$\{$~m$\}\backslash$times $2\backslash$mathrm$\{$~m$\}\backslash )$ footing has to carry a column load of $1000$ kN as shown. The ground water table is at a depth of $2$ m $,$ and the saturated unit weight of the stiff clay layer is $\backslash (21\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ).$ Consolidation test was conducted on the undisturbed clay sample, and one increment of loading data with time is presented in the following table. At $"0"$ time, the sample height was $2\mathrm{.}314$ cm $,$ and the void ratio was $0\mathrm{.}7.$ Perform the following tasks:

TASK $1$: What is the sample height and void ratio after $24$ hours?

TASK $2$: What is the Compression Index $\backslash (\backslash$mathrm$\{$C$\}\_\{\backslash$mathrm$\{$c$\}\}\backslash )$ during this load increment?

TASK $3$: What is the Coefficient of Consolidation, $\backslash (\backslash$mathrm$\{$C$\}\_\{\backslash$mathrm$\{$v$\}\}\backslash )?$

TASK $4$: If the modulus of elasticity of the top sand layer is $\backslash (35,000\backslash$mathrm$\{$kPa$\}\backslash ),$ then what is the strain in that layer after the construction of the footing?

TASK $5$: What is the consolidation settlement of the clay layer due to $1000$ kN load? Assume that the soil is normally consolidated.

TASK $6$: What is the total settlement under the footing?

TASK $7$: How long will it take for the consolidation settlement to occur?

TASK $8$: How long will it take for the clay layer to settle $\backslash (60\backslash \%\backslash )$ of the consolidation settlement?

TASK $9$: What is the excess pore water pressure in the clay layer right after the application of the load?

TASK $10$: What is the remaining excess pore water pressure at $4$ m into the clay layer after the time calculated in Task $8?$

$\backslash (\backslash$left$($q$\_\{\backslash$mathrm$\{$u$\}\}=\backslash$right$.\backslash )$ unconfined compressive strength; $\backslash ($ w$\_\{\backslash$mathrm$\{$L$\}\}=\backslash )$ liquid limit; $\backslash ($ w$\_\{\backslash$mathrm$\{$p$\}\}=\backslash )$ plastic limit; $\backslash ($ w$\_\{\backslash$mathrm$\{$N$\}\}=\backslash )$ water content $\backslash ()\backslash )$