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Examoogle • User • info@examoogle.com • EE-2024-8821
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A dry soil sample weighing 100 g has volume of 60 ml and specific gravity 2.5. Its void ratio is
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5
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5
Given: Mass of dry soil M = 100 g, Total volume V = 60 ml (or cm³), Specific gravity G = 2.5. Density of water is taken as 1 g/cm³.
Mass of dry soil M = 100 g, Total volume V = 60 ml (or cm³), Specific gravity G = 2.5. Density of water is taken as 1 g/cm³.
e=ddG⋅γw−1=MG⋅V−1
Calculate Dry Density
Dry density (ρd) is the ratio of the mass of dry soil to the total volume.
ρd=VM=60100=35≈1.667 g/cm3
Use Void Ratio Formula
The relationship between dry density (ρd), specific gravity (G), and void ratio (e) is given by ρd=1+eG⋅ρw.
1+e=ρdG⋅ρw
Solve for Void Ratio
Substituting ρw=1 g/cm3, G=2.5, and ρd=1.667.
1+e=1.6672.5×1=1.5⟹e=1.5−1=0.5
B is correct because the calculated void ratio using the phase relationship ρd=1+eG⋅ρw results in exactly 0.5.
Understanding soil phase diagrams is fundamental to solving problems in Geotechnical Engineering, often used alongside Darcy's Law and Consolidation theory.