Question

The relationship between γ, S, G and e is ______

(a) γ=\(\frac{(GS+e) γ_w}{(1+e)}\)

(b) γ=\(\frac{(G+eS) γ_w}{(1+e)}\)

(c) γ=\(\frac{(G+e)S γ_w}{(1+e)}\)

(d) γ=\(\frac{(G+e) γ_w}{(1+e)S}\)

This question was posed to me in examination.

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

Answer 1

Right answer is (b) γ=\(\frac{(G+eS) γ_w}{(1+e)}\)

Explanation: The bulk unit weight is given by,

\(γ=\frac{W}{V} = \frac{(γ_s*V_s+ γ_w *V_w)}{V}\)

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

γ = \(\frac{(γ_s*1 + γ_w * e_w)}{(1+e)}\)

since ew = e*S and γs = Gγw

γ = \(\frac{(Gγ_w*1 + γ_w * e*S)}{(1+e)}\)

γ=\(\frac{(G+eS) γ_w}{(1+e)}\).