Question

The relationship between γsat, G and e is _______

(a) \(γ_{sat}=\frac{(G*e) γ_w}{(1+e)}\)

(b) \(γ_{sat}=\frac{(G-e) γ_w}{(1+e)}\)

(c) \(γ_{sat}=\frac{(G+e) γ_w}{(1+e)}\)

(d) \(γ_{sat}=\frac{(G+e)}{(1+e)}\)

The question was posed to me in final exam.

I would like to ask this question from Functional Relationships in division Preliminary Definitions and Relationships of Geotechnical Engineering I

Answer 1

Correct answer is (c) \(γ_{sat}=\frac{(G+e) γ_w}{(1+e)}\)

To elaborate: The saturated unit weight is given by,

\(γ_{sat}=\frac{W_{sat}}{V} = \frac{W_d+W_w}{V}\)

∴ \(γ_{sat}=\frac{(γ_s*V_s + γ_w *V_w)}{V}\)

When Vs = 1, Vw = e and V = 1+e

\(γ_{sat}=\frac{(γ_s*1 + γ_w *e)}{(1+e)} = \frac{(Gγ_w+ γ_w e)}{(1+e)}\)

\(γ_{sat}=\frac{(G+e) γ_w}{(1+e)}\).