$(25$ points$)$

A $7m$ thick granular fill is to be placed over a $20m$ thick soil deposit of silty clay.

Computations show that considerable time would be required for primary consolidation if

drainage is in vertical direction only. For this reason, it is decided to speed up consolidation

by using vertical drains with a spacing of $3m($triangular pattem$)$ and fully penetrating the

clay layer, Figure $4.$

A theory of consolidation similar to the Terzaghi theory can be developed for vertical

compression, bowever, with radial as well as vertical drainage. According to such a theory,

the relationship between average degree of consolidation and the time factors is

$U=T-$exp$(-\frac{8}{3}{T}_h-4T_v)$

where

$T_{,}=\frac{{}_{3}t}{d^2}$;$T_{,}=\frac{c,t}{H^2}$

en is coefficient of consolidation corresponding to vertical compression and horizontal

drainage.

cr is the coefficient of consolidation corresponding to vertical compression and vertical

drainage.

$d$ is the spacing of the vertical drains.

$H$ is the maximum drainage distance in the vertical direction within the silty clay.

Compute the following:

a$.$ Settlement resulting from primary consolidation of silty clay.

b$.$ Time for $95\%$ primary consolidation with the vertical drains installed as shown in Figure

c$.$ Settlement resulting from consolidation of the silty clay after a design life of $50$ years if

vertical drains are installed to speed up primary consolidation.

d$.$ Time for $95\%$ primary consolidation if the vertical drain spacing is increased to $6m.$