Exercise One:

a$)$ A geotechnical engineer is examining a soil sample to determine its suitability for a specific construction site. The sample, collected from a depth known to retain moderate moisture, has a void ratio of $0\mathrm{.}72$ and a natural water content of $12\%.$ Laboratory tests reveal that the specific gravity Gs of the soil particles is $2\mathrm{.}72.$

The engineer needs to assess the following:

i$)$ Determine the sample's dry density and in$-$situ $($moist$)$ density in $k\frac{N}{m^3}.$

ii$)$ For an ideal compaction scenario, calculate the additional water $(k\frac{N}{m^3})$ that would be required to reach $80\%$ saturation of the sample, assuming no volume change.

iii$)$ The project specifications indicate that the soil may need to reach a water content as high as $30\%$ to enhance certain properties. Is this achievable without altering the current void ratio?

iv$)$ Given site load$-$bearing requirements, assess whether the soil could feasibly be compacted to achieve a dry density of $23\mathrm{.}5k\frac{N}{m^3},$ and if not, suggest a reason why this target may be challenging.

b$)$ An engineer is evaluating the moisture characteristics of a soil sample for a project that requires fully saturated conditions. Laboratory data for the soil sample at varying degrees of saturation are provided below:

$\backslash$table$[[$Soil Density $(K\frac{g}{m^2}),$Degree of Saturation $(\%)],[1690,45],[1808,75]]$

Given this information, determine the weight of water $($in kilograms$)$ that would occupy $7$ cubic meters of this soil once it is fully saturated. Explain any assumptions about the relationship between soil density and saturation that might affect the calculation.