A $5$ meter thick clay layer has the following properties: ${}_p^{\text{'}}=80$kPa,$CR=0\mathrm{.}04,RR=0\mathrm{.}01,$

${}_{\text{s}\text{a}\text{t}}=18k\frac{N}{m^3},c_v=0\mathrm{.}026\frac{m^2}{m}$onth. This clay layer overlies a sand layer. Groundwater

level is at the ground surface. A building will be construcled on this soil. The building is large

enough to assume one$-$dimensional consolidation. The construction will take exactly $1$ year,

during which the load can be assumed to increase linearly with time, starting from $0.$ When

completed, the building will apply $180$kPa additional stress to the soil.

a$)$ Plot the variation of over$-$consolidation ratio with depth, before construction.

b$)$ Calculate the average degree of consolidation for this layer at $1\mathrm{.}5$ years after the end of

construction.

c$)$ Calculate the consolidation settlement at $1\mathrm{.}5$ years after the end of construction, relative to

the beginning of construction. Do not divide the clay into sublayers.

d$)$ Calculate effective stress at depths of $0,1,2\mathrm{.}5,4$ and $5$ meters at $1\mathrm{.}5$ years after the end of

construction. Plot the effective stress distribution with depth, at $t.$

e$)$ Calculate the hydraulic gradient due to consolidation at the depth of $1$ meter at $1\mathrm{.}5$ years

after the end of construction. What is the direction of flow?