Question

The relationship between γ’, G and e is ______

(a) \(γ’=\frac{(G+1) γ_w}{(1+e)}\)

(b) \(γ’=\frac{(G-1) γ_w}{(1+e)}\)

(c) \(γ’=\frac{(G-1) γ_w}{(1-e)}\)

(d) \(γ’=\frac{G γ_w}{(1+e)}\)

This question was addressed to me at a job interview.

My doubt is from Functional Relationships topic in chapter Preliminary Definitions and Relationships of Geotechnical Engineering I

Answer 1

The correct answer is (b) \(γ’=\frac{(G-1) γ_w}{(1+e)}\)

For explanation I would say: The submerged unit weight is given by,

γ’ = γsat – γw

γ’ = \(\frac{(G+e) γ_w}{(1+e)} – γ_w\)

∴ \(γ’=\frac{(G-1) γ_w}{(1+e)}\).