$1.$ A soil profile is shown in the figure.

a$.$ Calculate the unit weights of the sand and clay. Determine the total stress, pore water pressure and effective stresses at points A$,$ B and C$.$ Plot stress versus depth for all three stresses.

b$.$ Calculate the saturated unit weight of the sand. If the water table rises to the top of the ground surface, what is the change in the effective stress at the bottom of the clay layer. $($Hint: you should use the saturated unit weight of sand if it is submerged$).$

c$.$ How many meters must the groundwater table be raised to decrease the effective stress by $15\backslash (\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}^\{2\}\backslash )$ at the bottom of the clay layer? $($Hint: you should use the saturated unit weight of sand for portions of it that are below the groundwater table$).$ Show your calculations