Q$\mathrm{.}4.$ A$)$ Two soil samples from the same soil type have the same dry density of $14\mathrm{.}14k\frac{N}{m}3.$ The first one has $wc=9\mathrm{.}5\%$ and the second was saturated, then double oedometer tests for both samples are performed. If $Gs=2\mathrm{.}7,$ e $($@$1$kPa$)=1\mathrm{.}2,C_1=0\mathrm{.}09($for both saturated and unsaturated condition$),C_c=0\mathrm{.}30($for saturation condition$),$ saturated Preconsolidation pressure $=25$kPa, unsaturated Preconsolidation pressure $=190$kPa,$S_r=0\mathrm{.}90,R=0\mathrm{.}30,$ Find the collapse potential for the flowing net stresses: $10$kPa,$25$ kPa,$50$kPa,$100$kPa,$190$kPa,$400$kPa,$800$kPa,$2600$kPa and draw the results. Note: $CP\%==(A\frac{C}{l}+e_e{)}^{**}100($before & after wetting$).$

$(15$ Marks$)$

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$)$

Equations: $=-\frac{RT}{v_{vo}{w}_v}ln(\frac{\frac{?}{\text{b}\text{a}\text{r}}(u{)}_v}{\frac{?}{\text{b}\text{a}\text{r}}(u{)}_{v_0}})$

$e_{\text{u}\text{n}\text{s}-\text{I}\text{I}\text{I}}=\frac{e_{NCL}{S}_{rc}}{(S_r{)}^R}$