Problem $4.$ A footing is to be located $2$m below ground level, as shown below. The dimension of the footing is $1\mathrm{.}5$m x $2$m and carrying a load of $2000$ kN$.$ The results of the consolidation test is shown in the figure

a$)$ Estimate the expected primary consolidation settlement for the normally consolidated clay layer, if e$0=0\mathrm{.}65$

b$)$ A laboratory consolidation test on a specimen taken from the clay layer shown was tested. The

specimen was $25\mathrm{.}4$ mm in thickness and drained on one side. The time required for the specimen to reach $35\%$ consolidation was $12$ min $.$ Compute the required time$($ in months$)$ for the clay layer to settle $0\mathrm{.}10$ meter.

c$)$ Estimate the expected consolidation settlement if the preconsolidation pressure is $\backslash$sigma $$ c $=130$kN$/$m$2.$

d$))$ estimate the excess pore water pressure remaining in the clay and the corresponding vertical effective stress after $10$ months at the middle of the clay layer

e$)$ if the settlement analysis for a proposed structure indicates $10$ cm$.$of settlement in $1$ year and an ultimate settlement of $30$ cm$.$ this analysis is based on the assumption that the under lying clay layer is drained at both its top and bottom surfaces. However, there are some indications that there may be no bottom drainage. For this case, determine the ultimate settlement and time required for $10$cm of settlement.