Problem $1.$ Two samples were collected from the embankment of a levee to assess the soils' susceptibility to internal erosion. The results of the mechanical sieve analysis and hydrometer test are shown below for both soils. On a single five$-$cycle semi$-$logarithmic graph, plot the grain size distribution curves for each soil. Determine the effective size $(D_{50})$ as well as the coefficient of uniformity $(C_u)$ and the coefficient of curvature $(C_c).$ Also determine the percentage of gravel, sand, and silt$/$clay according to the USCS standards.

Hint, see file on how to create a semi$-$logarithmic graph

$\backslash$table$[[\backslash$table$[[$US Standard$],[$Sieve Size$]],$Opening Size,Percent Passing By Weight$],[,,$Soil $1,$Soil $2],[,75mm,100,],[,38mm,-,-],[,19mm,90,-],[$#$4,9\mathrm{.}5mm,85,100],[$#$10,4\mathrm{.}75mm,79,88],[$#$20,2\mathrm{.}0mm,68,80],[$#$40,0\mathrm{.}85mm,-,74],[$#$60,0\mathrm{.}425mm,35,72],[$#$100,0\mathrm{.}250mm,-,-],[$#$140,0\mathrm{.}150mm,-,63],[$#$200,0\mathrm{.}106mm,25,51],[,0\mathrm{.}075mm,22,31],[,40m,20,22],[,20m,17,16],[,10m,13,12],[,5m,7,-],[,2m,4,2]]$