For a soil sample of unit weight γ, void ratio e, porosity n, degree of saturation S and water content w, which of the following relation is correct?
- An = γ/(1 + e)
- Bγ = (G + Se)γw/(1 + e)Correct
- Ce = w γ/S
- De = n/(1 − e)
Solution
Concept
Unit weight relation
Formula
γ = (G + Se) γw/(1 + e)
Step-by-step solution
1. Total weight = (G + Se) γw per unit solid volume; total volume = 1 + e. 2. γ = (G + Se)γw/(1 + e). 3. Also e = n/(1 − n), not n/(1 − e); e = wG/S, not wγ/S.
Explanation
Option B is the standard relation.
Why the other options are wrong
A, C and D are wrongly written.
Shortcut
γ = (G + Se)γw/(1 + e).
Correct answer: B) γ = (G + Se)γw/(1 + e)