Please show calculations for part d and e$.$ A $6$ meter thick clay layer has the following properties: ${}_p^{\text{'}}=80$kPa,$C_c=0\mathrm{.}08,C_r=0\mathrm{.}02,$

$e_{\text{@}}=0\mathrm{.}8,{}_{\text{s}\text{a}\text{t}}=19\mathrm{.}8k\frac{N}{m^3},{}_w=9\mathrm{.}8k\frac{N}{m^3},c_v=0\mathrm{.}12\frac{m^2}{m}$onth. This clay layer overlies a

sand layer. Groundwater level is at the ground surface. A building will be constructed on this

soil. A thin layer of crushed stone $($uniform gravel with angular particles$)$ is laid on the

surface so that the foundation slab is not in direct contact with the clay. The building is large

enough to assume one$-$dimensional consolidation. The construction will take exactly $6$

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

When completed, the building will apply $100$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 $1$ year after the end of

construction.

c$)$ Calculate the consolidation settlement at $1$ year after the end of construction, relative to the

beginning of construction. Divide the clay into two equal sublayers.

d$)$ Calculate effective stress at depths of $0,1\mathrm{.}5,3,4\mathrm{.}5$ and $6$ meters at $1$ year after the end of

construction. Plot the effective stress distribution with depth, at this time, on the same graph

with the effective stress distributions before loading, and the distribution a long time later.

e$)$ Recalculate the total consolidation settlement of the lower sublayer, if the foundation were

placed at the depth of $3m,$ carrying the same super$-$structure.