a$)$ Provide a technical explanation for how vertical drains accelerate the

consolidation process in fine soils. Can their use lead to a reduction in the final

consolidation settlement? $[3]$

$($b$)$ What is the physical significance of the coefficients of consolidation cv and ch$?[2]$

$($c$)$ A soft clay layer with mv $=0\mathrm{.}225$ m$2$

$/$MN$,$ cv $=2\mathrm{.}5$ m$2$

$/$year and ch $=1\mathrm{.}5$cv is $8$ m

thick and overlies an impermeable limestone$.$ A railway embankment is to be

constructed over a $6-$month period and will subject the centre of the clay layer to

an increase in vertical total stress of $125$ kPa. It is anticipated that the railway will

be laid on top of the embankment $15$ months after the start of construction, after

which only $25$ mm settlement is permissible. Assuming, for convenience, that

consolidation settlement commences at the half$-$way point of embankment

construction, calculate an appropriate spacing for $93$ mm $\backslash$times $4$ mm prefabricated

vertical drains installed on a triangular grid.