Discussion
The saturated density for a fully saturated soil is:
(Symbols have their usual meanings)
Answer: D
The saturated density is \(\frac{G+e}{1+e}\rho w\).
Take a soil element with unit volume of solids. Its total volume is \(1 + e\). The solids have mass \(G\rho_w\), and when saturated the voids hold water of mass \(e\rho_w\):
\[ \begin{aligned} \rho_{sat} &= \frac{G\rho_w + e\rho_w}{1 + e} \\ &= \frac{G + e}{1 + e}\rho_w \end{aligned} \]
This is the general form \(\frac{G + Se}{1 + e}\rho_w\) with the degree of saturation S = 1. The option with \(G + eS\) over \(1 + w\) uses the wrong denominator, \(G + S\) drops the void ratio from the water term, and \(G + w\) adds a water content to a specific gravity.
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