Answer:
A) For a double drainage system the time taken for total settlement will differ from that of a single drainage system, because in a double drainage case clay water escapes from both sides unlike in a single drainage case. hence water and air will be be expulsed faster for a double drainage making it attain total settlement faster.
B) for only single = 12 years
Explanation:
Given data :
ultimate clay settlement = 32 cm
settlement of clay in 3 years = 7.5 cm
Cv ( coefficient of consolidation ) = 1.5 x 10^-4 cm^2 /s
A) For a double drainage system the time taken for total settlement will differ from that of a single drainage system, because in a double drainage case clay water escapes from both sides unlike in a single drainage case. hence water and air will be be expulsed faster for a double drainage making it attain total settlement faster.
note : Total settlement is the same in both drainage system.
B) Determine how long it will take for 7.5 cm of settlement to occur if there is only single
applying the relation below
Tv = Cv t / H^2
where Tv = time factor , d = thickness of layer , H = drainage path
Given that Tv and Cv are constant in both cases
t ∝ H^2 hence
[tex]\frac{t1}{t2} = \frac{H^21}{H^22}[/tex] ------ ( 1 )
t1 = time for single drainage for d meters , t2 = time for double drainage for d meters
equation 1 can be rewritten as
t1/t2 = d^2 / (d/2)^2
∴ t1 = 4t2
given that t2 = 3 years ( value gotten from question )
t1 = 4 * 3 = 12 years