$CO$#$4,5,6,8,9$ Consider the layer of fully saturated clay represented in the Figure below.

Before the construction of the rectangular footing $(BxL),$ the Compression Index $(C_c)$ and

the Swelling Index $(C_s)$ of the clay are determined in the lab by testing a representative

undisturbed sample $($initially located at the center of the clay layer$),$ and the values are $0\mathrm{.}3$

and $0\mathrm{.}035,$ respectively.

a$)$ Compute the vertical effective stress $({}_v^{\text{'}})$ in kPa at the center of the clay layer prior to the

construction of the footing and consider that this stress is representative of the clay layer.

b$)$ Assuming the dimensions of the rectangular footing are $B=2\mathrm{.}5m$ and $L=2\mathrm{.}25m,$ and the

external force is $Q=2000kN,$ use the Boussinesq solution to determine the increase in

vertical stress $()$ in kPa at the center of the clay layer below the center of the footing.

c$)$ Assuming that the increase in vertical stress at the center of the clay layer obtained from

the previous section is $=60$kPa, determine the ultimate primary consolidation settlement

in the following two cases: $($a$)$ assuming OCR$=1$ and $($b$)$ assuming OCR$=1\mathrm{.}7.$

NOTE: assume that the stress values at the center of the clay layer are representative for

the whole layer.

d$)$ In Table $1,$ you have the results from the oedometer test $($double drainage conditions$)$

performed on the representative $25mm$ thick undisturbed clay sample. Considering these

data, determine the Coefficient of Consolidation $(c_v)$ in $m\frac{m^2}{m}in$ by using the "log $t$

method".

NOTE: use a semi$-$logarithmic scale. The graph must be included in the solution.

Table $1.$ Time$-$settlement readings for stress increase from $50$ to $100k\frac{N}{m^2}$

e$)$ Predict the time and how much settlement will develop in the clay layer at $50\%$ and $95\%$

of consolidation if OCR$=1?$ Assume that the bottom boundary is impermeable.

NOTE: time units in $[$days$],$ and settlement units in $]$

f$)$ Predict the time and how much settlement will develop in the clay layer at $50\%$ and $95\%$

of consolidation if the lower boundary is fully permeable and OCR $=1?$

NOTE: time units in $[$days$],$ and settlement units in $[$mm$]$