Problem $4$

The soil profile at a site is shown below. The water table lies at a depth of $0\mathrm{.}3$ m below the ground level. The bulk and saturated unit weights of the sand are $15k\frac{N}{m^3}$ and $16k\frac{N}{m^3}$ respectively.

a$)$ Calculate the total settlement if the water table drops $1$ m $.$

$Cc=0\mathrm{.}4,Cs=0\mathrm{.}08.$

$e=0\mathrm{.}7$

Preconsolidation pressure $=50k\frac{N}{m^2}$

${}_c^{\text{'}}=50\frac{kN}{m^2}$

${}_0^{\text{'}}=(0\mathrm{.}5m)(15\frac{kN}{m^2})+(1m)(16\frac{kN}{m^2}-9\mathrm{.}81\frac{kN}{m^3})$

$+(2\mathrm{.}5m)(18\frac{kN}{m^3}-9\mathrm{.}81\frac{kN}{m^3})$

${}_0^{\text{'}}=34\mathrm{.}165$

Case $1$:

$[$:$0\mathrm{.}08log(\frac{50}{34\mathrm{.}165})+\frac{0\mathrm{.}4log64\mathrm{.}45}{log50}$