Question

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

(a) \(e=\frac{wG}{S}\)

(b) e = wGS

(c) \(e=\frac{wS}{G}\)

(d) \(e=\frac{GS}{w}\)

The question was posed to me by my school teacher while I was bunking the class.

My question is taken from Functional Relationships in portion Preliminary Definitions and Relationships of Geotechnical Engineering I

Answer 1

Correct answer is (a) \(e=\frac{wG}{S}\)

To elaborate: The degree of saturation is given by

S=\(\frac{V_w}{V_V}=\frac{e_w}{e}\)      where ew = water void ratio=eS   ——-(1)

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

w = \(\frac{e_wγ_w}{γ_s*1}\)

But γs = Gγw

∴ w = \(\frac{e_wγ_w}{Gγ_w}= \frac{e_w}{G}\)

ew = wG ———–(2)

from equation (1) and (2)

\(e=\frac{wG}{S}\).