$(25\%)$ Problem $3.$ Water was pumped from an aquifer, shown in Figure P$3,$ for domestic use. The original groundwater level was at the top of the soft $($NC: normally consolidated$)$ clay layer. After drawing water, the groundwater table drops $10m.$ Thus, the ground subsides. All necessary information about soil layers is given in the figure.

a$)$ What are the values of pore$-$water pressure, total stress, and effective vertical stress at a point in the midpoint of the clay layer before and after drawing water?

b$)$ Assuming the subsidence is due to the settlement of only the soft clay, estimate the ultimate consolidation settlement of the ground surface.

Hint: notice the difference between the initial and final effective stress, causing consolidation.

c$)$ A decision was made to recharge the aquifer by pumping the water back from a canal nearby. If the groundwater table returned to its original level, would the ground surface return to its original elevation or not, and why? Show your calculation to support your answer, i$.$e$.,$ what is the swelling$/$rebound of the clay layer if any?

Lightly cemented sand$/$gravel:

${}_d=15\mathrm{.}6k\frac{N}{m^3}$

${}_{\text{s}\text{a}\text{t}}=19\mathrm{.}5k\frac{N}{m^3}$

Clay:

${}_d=16\mathrm{.}2k\frac{N}{m^3}$

${}_{\text{s}\text{a}\text{t}}=20\mathrm{.}1k\frac{N}{m^3}$

$e_0=0\mathrm{.}9$

$C_c=0\mathrm{.}6$

$C_s=C_r=0\mathrm{.}05$

$c_v=0\mathrm{.}04\frac{m^2}{y}r.$

Aquifer sand and gravel:

${}_d=17\mathrm{.}2k\frac{N}{m^3}$

${}_{\text{s}\text{a}\text{t}}=20\mathrm{.}5k\frac{N}{m^3}$

Figure P$3$