$($a$)$ Design a mechanically stabilized earth $($MSE$)$ wall $8$ m high using metal strips to hold a coarse$-$grained backfill soil and to be able to carry a surcharge of $20$ kPa $.$ The galvanized steel ties have a yield sterngth of $2\mathrm{.}5{10}^{5}k\frac{N}{m^2}$ and a rate of corrosion of $0\mathrm{.}025m\frac{m}{?}$ year. The backfill and base soil properties are given in the diagram below. $(25\%)$

Assumptions:

Design life $=50$ years, $FS=3,S_v=0\mathrm{.}50m,S_H=1\mathrm{.}0m,w=75mm.$

$($b$)$ Estimate the seismic increment of active earth pressure $({}_E^{\text{'}})$ on the MSE wall given. $(10\%)$

$q_s=20$kPa

Natural soil:

$=20k\frac{N}{m^3}$

${}^{\text{'}}=35$

$c=35$kPa