$12\mathrm{.}6$ Refer to Figure $12\mathrm{.}42.$ Given: $H_1=2\mathrm{.}5m,H_2=2\mathrm{.}5m,$

$H_3=3m,$ and $=100k\frac{N}{m^2}.$ Also,

Sand: $e=0\mathrm{.}64,G_s=2\mathrm{.}65$

Clay: $e=0\mathrm{.}9,G_s=2\mathrm{.}75,LL=55$

Estimate the primary consolidation settlement of the clay layer assuming that it is

normally consolidated.Problem $12\mathrm{.}6$

Note that the unit weights needed for your calculations are provided below

Calculate the initial effective stress at the middle of the clay layer, sigma$\_0\text{'}=$

$k\frac{N}{m^2}$

$($Express your answer with two decimal places$)$

Estimate the compression index using Skempton's equation for undisturbed clays, $Cc=$

$($Express your answer with three decimal places$)$

Unit weights:

$12\mathrm{.}6,{}_{d(sand)}=\frac{(2\mathrm{.}65)(9\mathrm{.}81)}{1+0\mathrm{.}64}=15\mathrm{.}85k\frac{N}{m^3}$

${}_{\text{s}\text{a}\text{n}\text{d}}^{\text{'}}=\frac{(2\mathrm{.}65-1)(9\mathrm{.}81)}{1+0\mathrm{.}64}=9\mathrm{.}87k\frac{N}{m^3}$

${}_{\text{c}\text{l}\text{a}\text{y}}^{\text{'}}=\frac{(2\mathrm{.}75-1)(9\mathrm{.}81)}{1+0\mathrm{.}9}=9\mathrm{.}04k\frac{N}{m^3}$

Question $6$

Problem $12\mathrm{.}6$

The primary consolidation in clay $Sc=,m$

$($Express your answer with three decimal places; note that the unit for Sc is m$)$