Question
Download Solution PDFThe void ratio at the densest, loosest and the natural state of a sand deposit are 0.3, 0.7 and 0.5, respectively. The relative density of the deposit is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
\({{\rm{I}}_{\rm{d}}} = \frac{{{{\rm{e}}_{{\rm{max}}}} - {\rm{e}}}}{{{{\rm{e}}_{{\rm{max}}}} - {{\rm{e}}_{{\rm{min}}}}}}{{\rm{I}}_{\rm{d}}} = \frac{{\frac{1}{{\left( {{{\rm{\gamma }}_{\rm{d}}}} \right){\rm{min}}}} - \frac{1}{{{{\rm{\gamma }}_{\rm{d}}}}}}}{{\frac{1}{{\left( {{{\rm{\gamma }}_{\rm{d}}}} \right)}}}}\)
Where,
Id = Relative Denisty of soil, emax = maximum void ratio, emin = minimum void ratio, e = natural void ratio, γd,min= dry density of soil at its loosest state, and γd,max= dry density of soil at its densest state
Calculation:
emax = 0.7, emin = 0.3, and natural void ratio (e) = 0.5
\({{\rm{I}}_{\rm{d}}} = \frac{{0.7 - 0.5}}{{0.7 - 0.3}} = \frac{{0.2}}{{0.4}} = 0.5\)
Expressing it in percentage = 0.5 × 100 = 50%Last updated on Jul 8, 2025
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