Previous Year Questions: Soil Mechanics | Soil Mechanics - Civil Engineering (CE) PDF Download

Soil Properties

Q1:  For Sand Of Uniform Spherical Particles, The Void Ratios In The Loosest And The Densest States Are _____ And _____ Respectively.       [GATE 1991: 2 Marks]
Ans: 0.91, 0.35
Sol:
In loosest state, the soil particles are arranged in a cubical array in which each soil particle is surrounded by 6 soil particles.

Volume of Spherical soil particle = (d/2)³ x 4π / 3

Assume the cube side as   1 x 1 x 1 unit.
Total volume = 1 cubic unit.
The number of spherical particles in 1 cubic unit is   1/d x 1/d x 1/d =1 / d3

Thus, Volume of soil solids = Volume of single soil particle x number of particles

Thus void ratio in loosest state,

Similarly, in densest state, the soil particles are arranged in a rhombohedral array in which each soil particle is surrounded by 12 soil particles.
The volume of soil solids remains constant.
Thus, Volume of soil solids,

V_soil = π/6 = 0.523
Total volume, V = (1 - cos α)√(1 + 2 cos α)
Here, α = 360° / 12
= 60°
⇒ V = 0.707 m³
Now, Volume of voids, V_voids = V - V_soil
⇒ V_voids = 0.707 - 0.523
⇒ V_voids = 0.184 m3

Thus void ratio in densest state,
e_min = V_voids / V_soil
⇒ e_min = 0.184 / 0.523

⇒ e_min = 0.35

Soil Compaction