Question

The relationship between γd, G and e is given by ______

(a) γd = \(\frac{Gγ_w}{1-e}\)

(b) γd = \(\frac{G+γ_w}{1+e}\)

(c) γd = \(\frac{Gγ_w}{1+e}\)

(d) γd = \(\frac{Gγ_w}{e}\)

I have been asked this question in semester exam.

This key question is from Functional Relationships topic in chapter Preliminary Definitions and Relationships of Geotechnical Engineering I

Answer 1

Right answer is (c) γd = \(\frac{Gγ_w}{1+e}\)

The explanation is: The dry unit weight is given by,

γd = \(\frac{W_d}{V} = \frac{γ_s*V_s}{V}\)

when Vs = 1, we have V = (1+e)

γd = γs*1/(1+e)

But  γs = Gγw

∴ γd = \(\frac{Gγ_w}{1+e}\).