Question

The relationship between γd, γ and w is given by _______

(a) γd = γ(1+w)

(b) γd = γ *(1+w)

(c) γd = \(\frac{γ}{(1+w)}\)

(d) γd = γ+1+w

The question was asked in homework.

I want to ask this question from Functional Relationships topic in portion Preliminary Definitions and Relationships of Geotechnical Engineering I

Answer 1

The correct answer is (c) γd = \(\frac{γ}{(1+w)}\)

The best explanation: The water content is given by,

\(w=\frac{W_w}{W_d}\)

hence \(1+w=\frac{(W_w + W_d)}{W_d} = \frac{W}{W_d}\)

\(W_d=\frac{W}{(1+w)}\)

\(γ_d=\frac{W_d}{V} = \frac{W}{(1+w)V}\)

∴ γd = \(\frac{γ}{(1+w)}\).