Question

The relationship between γsat, γd, γ and S is ______

(a) γ = γd*S[γsat-γd]

(b) γ = \(\frac{γ_d}{S[γ_{sat}-γ_d]}\)

(c) γ = γd+S[γsat-γd]

(d) γ = γd-S[γsat-γd]

I got this question during an online exam.

The doubt is from Functional Relationships in section Preliminary Definitions and Relationships of Geotechnical Engineering I

Answer 1

Correct option is (c) γ = γd+S[γsat-γd]

For explanation: The bulk unit weight is given by,

\(γ = \frac{(G+eS) γ_w}{(1+e)}  \,or\, γ = G\frac{γ_w}{(1+e)} + S\frac{eγ_w}{(1+e)}\)

\(γ = γ_d+S[\frac{(G+e) γ_w}{(1+e)} – \frac{G γ_w}{(1+e)}]\)

γ = γd+S[γsat-γd].