Q $1$

$($a$)$ Define the terms well$-$graded, uniform and gap$-$graded, as used in describing particle size distributions of soils. Illustrate your answers by sketching typical particle size distributions for a well$-$graded silty sand, a uniform clay and a gap$-$graded sandy silt on the particle size distribution chart in Figure Q$1.$ Hand$-$drawn chart is acceptable provided that the boundaries between different types of soils are delineated and that the percentage of passing is indicated

$[10]$

$($b$)$ Soil A and Soil $B$ have the same void ratio $e=0\mathrm{.}6.$ Their maximum void ratios are determined to be $e_{\text{m}\text{a}\text{x}}=1$ and $e_{\text{m}\text{a}\text{x}}=0\mathrm{.}9$ for Soil A and Soil B $,$ respectively. Their minimum void ratios are $e_{\text{m}\text{i}\text{n}}=0\mathrm{.}56$ and $e_{\text{m}\text{i}\text{n}}=0\mathrm{.}43.$ What can be inferred from the data about the properties of the soils? State your reasoning.

$[7]$

$($c$)$ After the construction of a concrete retaining wall, back$-$fill material from a nearby borrow pit was brought into the excavation behind the wall and compacted to a final void ratio of $0\mathrm{.}6.$ Given that the soil in the borrow pit has a void ratio of $1\mathrm{.}2,$ determine the volume of borrow material needed to construct $1m^3$ of compacted backfill. Given that the borrow pit soil has a water content of $15\%$ and $G_s=2\mathrm{.}75,$ determine the unit weight of the compacted backfill.