$A g i v e n c o h e s i o n l e s s s o i l h a s e_{m a x} = 0.85, e_{m i n} = 0.5. I n t h e f i e l d, t h e s o i l i s c o m p a c t e d t o a m a s s d e n s i t y o f 1800 k g / m^{3} a t w / c 8 % a n d d e n s i t y o f w a t e r 1000 k g / m^{3} a n d G_{s} = 2.7. T h e r e l a t i v e d e n s i t y i s$ ( in % )

56.43

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60.25

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62.87

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65.71

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Solution

The correct option is D 65.71
$e_{m a x} = 0.85$

$e_{m i n} = 0.5$

$ρ_{f i e l d} = 1800 k g / m^{3} a t w / c = 8 %$

$ρ_{w} = 1000 k g / m^{3}$

$G_{s} = 2.7$

$R e l a t i v e d e n s i t y = D_{r} = ?$

$ρ_{t} = \frac{G ρ_{w} (1 + w)}{1 + e} = \frac{2.7 \times 1000 (1.08)}{1 + e}$

$\Rightarrow 1 + e = \frac{2.7 \times 1000 \times 1.08}{1800}$

$\Rightarrow e = 0.62$

$\Rightarrow D_{r} =$ Relative density

= $\frac{e_{m a x} - e}{e_{m a x} - e_{m i n}} \times 100$

$= \frac{0.85 - 0.62}{0.85 - 0.5} \times 100 = 65.714 %$

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