$(20,$ Mitchell Book Problem $3\mathrm{.}1)$ An embankment of $15$ m height is to be constructed on the soil profile shown in Figure within a period of $18$ months. Assume $\frac{?}{PI}=30,C_v=1{10}^{-7}{m}^2{s}^{-1}$ in the crustal zone and $1{10}^{-6}{m}^2{s}^{-1}$ in the underlying clay, $k_h=2k_v,St=8$ for the foundation soil and $=18kN{m}^{-3}$ for the embankment $($top width $15$ m and $cot=2.($Note: $St=$ undisturbed vane strength divided by remolded vane strength$)$

a$.$ Consider the possibilities of constructing this embankment by stage construction with sand drains and with berms.

b$.$ If compacted fill for berms cost $$2\mathrm{.}80$ per $m^3$ plus a cost of $$200\mathrm{.}00$ per meter of embankment strike length for additional right of way, and sand drains cost $$4\mathrm{.}25$ per meter of sand drain, recommend the most economical method of construction.