Question

The relationship between e, S and na  is ______

(a) \(n_a=e*\frac{1+S}{1+e}\)

(b) \(n_a=e*\frac{1-S}{1-e}\)

(c) \(n_a=\frac{1-S}{1+e}\)

(d) \(n_a=e*\frac{1-S}{1+e}\)

I have been asked this question in class test.

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

Answer 1

The correct option is (d) \(n_a=e*\frac{1-S}{1+e}\)

To elaborate: The percentage air voids is given by,

\(n_a=\frac{V_a}{V}\)

Va = Vv – Vw = e – ew

And V = Vs+Vv = 1+e

∴ na=\(\frac{e-e_w}{1+e}\)

Since ew = eS

\(n_a=e*\frac{1-S}{1+e}\).