In a medium$-$fine clean sand with unit weight of $17\mathrm{.}5k\frac{N}{m^3},$ a standard penetration test is carried out. The groundwater table is at a depth of $3\mathrm{.}0m$ below the ground surface. The $N_{60}$ values are given below.

$\backslash$table$[[$Depth $($m$),1\mathrm{.}5,3\mathrm{.}0,4\mathrm{.}5,6\mathrm{.}0,7\mathrm{.}5],[N_{60},15,21,18,27,39]]$

Determine the following parameters at these depths:

$($a$)$ Relative density using Meyerhof $(1957),$ and Cubrinovski & Ishihara $(1999)$ correlations.

$($b$)$ Friction angles at this depth using Peck et al$.(1974),$ Schmertmann $(1975),$ Hatanaka & Uchida $(1996)$ correlations.

$($c$)$ Equivalent modulus of elasticity $(E_s).$ Assume an overconsolidation ratio of $1\mathrm{.}5.$