Question $4$

a$)$ You wish to use shallow foundations to support a $2$ storey masonry building constructed without

a basement. Exterior walls will apply $200kN$ per metre to strip footings constructed at a depth $1\mathrm{.}5$

$m$ below ground. Assume the footings are $2\mathrm{.}0m$ wide and $20m$ long in each direction.

The soil is a relatively thin layer of normally consolidated clay overlying stiff bedrock at a depth

of $6m.$ The till has $c^{\text{'}}=0,{}^{\text{'}}=23,{}^{\text{'}}=19\mathrm{.}6k\frac{N}{m^3},$ Poisson's ratio, $v=0\mathrm{.}33.$ Consolidation testing

has measured an average $m_v=1\mathrm{.}35{10}^{-4}kP{a}^{-1}$ corresponding to a constrained modulus of $7408$

kPa$(M=\frac{1}{m_v}).$ The depth to water table $=3\mathrm{.}5m.$

Using the method for $C_s,$ how much immediate settlement would you expect?

Hint: Remember that the constrained modulus is different from the deformation $($Young$\text{'}$s$)$

modulus. State all of your assumptions clearly. You may neglect the mass of the concrete.

b$)$ How would the settlement change if the modulus increased with depth at a rate of $2000kP\frac{a}{m}.$ For this

case, assume the modulus of the footing is $23,500$MPa and the footing thickness, $t$ is $300mm.$