B$)$ A Standard proctor $($SP$)$ compaction curve has the data shown in the table below. If Gs$=2\mathrm{.}7,$ the void ratios at normal consolidate line equal to $0\mathrm{.}645$ and $0\mathrm{.}517$ for stresses $596$kPa and $2696$kPa, respectively., $S_r=0\mathrm{.}85,R=0\mathrm{.}40).$ Find the Modified Proctor $($MP$)$ curve $($dry density and the water content for degree of saturations $($Sr$)$: $50\%,70\%,85\%,$ and $90\%)$ and Optimum moisture content $($OMC$)$ and maximum dry density $()$ of MP$.$

$\backslash$table$[[\backslash$table$[[$Standard proctor $($SP$)],[$compaction curve$]],$w$.$c$.(\%),14\mathrm{.}9,17\mathrm{.}8,18\mathrm{.}4,20\mathrm{.}2],[$Dry Unit Weight $(k\frac{N}{m^3}),16\mathrm{.}1,16\mathrm{.}9,17\mathrm{.}0,16\mathrm{.}8]]$

$(10$ Marks$)$