Answer: d) ac = 1 – S
The ratio of the volume of air voids to the volume of voids in the air content.
ac = Va / Vv …(i)
The volume of water volume to the volume of voids in a given soil mass is called a degree of saturation.
S = Vw / Vv…(ii)
As we know that the volume of air & volume of water is combined, called a volume of void.
i.e. Vv = Vw + Va
∴ Va = Vv – Vw…(iii)
After substituting equation (iii) in equation (i), then we will get,
ac = Vv – Vw / Vv
ac = (Vv / Vv) – (Vw / Vv)
ac = 1 – (Vw / Vv)
ac = 1 – S…(from equation (ii))
∴ac = 1 – S is the correct relationship between the degree of saturation & air content in soil sample.