If the water content of a fully saturated soil mass is 100%, then the voids ratio of the sample is:

G = ys/yw = (Ws/Vs)/(Ww/Vw) -------------------------- (1)

e = Vv/Vs

substituting Vs value in (1)

we get 

Ww/Vw x G = eWs/Vv

or Ww/Ws x G = eS

or 

eS/G =1

S =1

therefore e = G