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$6.$ For the profile shown below, compute the vertical effective stress $({}_v^{\text{'}})$ at Point A at the location shown in the soil profile for scenario $($a$)$ and $($b$).$

$($a$)$ For the soil profile shown above $[5$ Points$]$

${}^{\text{'}}V=17k\frac{N}{m^3}(3m)+17\mathrm{.}5k\frac{N}{m^3}(2M)-9\mathrm{.}79k\frac{N}{m}{m}^3(2m)$

$=51k\frac{N}{m^2}+15\mathrm{.}42tan(28)+10$

$=51.k\frac{N}{m^2}+18\mathrm{.}20$

${}^{\text{'}}V=69\mathrm{.}20k\frac{N}{m^2}$

$($b$)$ If the ground water table rises to a height of $3$ m above the ground surface $[5$ Points$].$

${}^{\text{'}}r=17\mathrm{.}5k\frac{N}{m^3}(5m)-9\mathrm{.}79(5m)=38\mathrm{.}55k\frac{N}{m^2}$

$=38\mathrm{.}55k\frac{N}{m^2}tan(28)+10$

${}^{\text{'}}V=30\mathrm{.}50k\frac{N}{m^2}$