$7\mathrm{.}51$ Figure P$7\mathrm{.}51$ shows a $20m$ thick layer of normally consolidated clay $)=(18\mathrm{.}6k\frac{N}{m^3}$ that is one$-$dimensionally loaded by ${}_v=60$kPa. The clay layer is below a $3m$ thick layer of granular fill $)=(19\mathrm{.}6k\frac{N}{m^3},$ and a dense, compacted glacial till underlies the clay. The water table is located at the top of the clay layer. A $1-$D consolidation test is performed on a $2\mathrm{.}20cm$ thick, doubly drained specimen from the middle of the clay layer. When the stress conditions from the field $($including the ${}_v=60$kPa $)$ are applied to this specimen, it takes $4$min for $90\%$ average consolidation to occur.

Figure P$7\mathrm{.}51$

Figure P$7\mathrm{.}51$ Full Alternative Text ${?}^{}$

a$.$ From the lab test data, determine $c_v$ for the soil.

b$.$ Compute the pore pressure at depth $18m$ before and immediately after the $60$kPa stress is applied.

c$.$ Compute the total vertical stress $({}_v)$ at depth $18m$ after the $60$kPa stress is applied in the field.

d$.$ At depth $18m,$ compute the effective vertical stress $({}_{*}^{\text{'}})5$ years after the $60$kPa is applied.