$4\mathrm{.}0(20$ marks$)$

Consider the soil profile shown in Figure $3\mathrm{.}0$ subjected to the uniformly distributed load, $,$ on the ground surface. Given: $=45k\frac{N}{m^2},H_1=1\mathrm{.}4m,H_2=2\mathrm{.}8m,$ and $H_3=4\mathrm{.}9m.$ Soil characteristics are

Sand: ${}_d=17\mathrm{.}6k\frac{N}{m^3}$;${}_{\text{s}\text{a}\text{t}}=19\mathrm{.}3k\frac{N}{m^3},$ Note: $C_c=0\mathrm{.}009(LL-10)$

Clay: ${}_{\text{s}\text{a}\text{t}}=18\mathrm{.}7k\frac{N}{m^3}$;$LL=46$;$e=0\mathrm{.}71$;$C_s=(\frac{1}{5})C_c$

Estimate the primary consolidation settlement of the clay if

a$.$ The clay is normally consolidated

b$.$ The preconsolidation pressure, ${}_c^{\text{'}}=100k\frac{N}{m^2}$

Figure $3\mathrm{.}0$