$(20$ points$)$ Refer to the Figure below, given that $y=3\mathrm{.}66m,H_0=2\mathrm{.}44m,$ unit weights of

sand and clay layer are $21\mathrm{.}2k\frac{N}{m^3}$ and $17\mathrm{.}27k\frac{N}{m^3},$ respectively. The clay stratum is

normally consolidated with an initial void ratio of $1\mathrm{.}2$ and compression index of $0\mathrm{.}2.$ The

weight of structure causes a stress of $28\mathrm{.}8k\frac{N}{m^2}$ at the mid height of the clay layer.

a$.$ Calculate the primary settlement in the clay layer.

b$.$ If the primary consolidation settlement will require approximately $8$ years, estimate the

total settlement over a $20-$year time span, considering effects of secondary compression

$(C_a=0\mathrm{.}04C_c).$