b$)$ A foundation $3m4m,$ transferring a pressure of $200k\frac{N}{m^2},$ is located at a depth of $1\mathrm{.}5m$ in a layer of sand $6m$ thick for which the modulus of elasticity, $E_s$ is $30000k\frac{N}{m^2}$ and Poisson's ratio, ${}_s=0\mathrm{.}3.$ A water table is located $2\mathrm{.}0m$ below the base of the foundation. The dry unit weight of sand above the water table, $=17k\frac{N}{m^3}$ and the saturated unit weight of sand just below the water table, ${}_{\text{s}\text{a}\text{t}}=18k\frac{N}{m^3}.$ The sand layer is underlain by a normally consolidated clay layer, $4m$ thick, for which the value of $E_s$ is $15000k\frac{N}{m^2}$ and Poisson's ratio, $=0\mathrm{.}35.$ The clay layer has a specific gravity of $2\mathrm{.}65$ and a compression index of $0\mathrm{.}3.$ The saturated unit weight of clay, ${}_{\text{s}\text{a}\text{t}}=19k\frac{N}{m^3}.$ A hard stratum lies below the clay layer. Assume rigid foundation. Estimate the total settlement due to elastic settlement, $S_e$ and consolidation settlement, $S_c.$

$(10$ Marks$)$

Use $=\frac{{}_w(G_s+e{S}_r)}{1+e}$