Clay layer A with single drainage and coefficient of consolidation Cv takes 6 months to achieve 50% consolidation. The time taken by clay layer B of the same thickness with double drainage and coefficient of consolidation $$\frac{{{\text{Cv}}}}{2}$$ to achieve the same degree of consolidation is

Cv= 6 months
Cv/2=6/2=3 months

For Clay Layer A : Cv = 6 months ( single drainage )
Clay Layer B : Cv / 2 ( double drainage )
Here,
Cv = 6 months
Cv / 2 = 6 / 2 = 3
Hence,
Cv = 3 months

Cv=(tv/t)×d^2
1st - Cv=(tv/6)×H^2
2nd - Cv/2=(tv/t)×(H/2)^2

(tv/6)×H^2 = 2(tv/t)×(H^2/4)
1/6= 1/2t
2t=6
t=3 months

(Cv×6)/H^2 = (Cv/2)×t/ (2H)^2

Tv=Cv.t/d²
In case of clay layer A
Tv=Cv.6/d² ( Take d=h for single drainage)
Tv=Cv.6/h2
In case of clay layer B
Tv=Cv.t/d² (Take d=h/2 for double drainage)
From equations
t=3 months

(Cv×6)/H^2 = (Cv/2)×t/ (2H)^2

How?