Question $2($from Wood $1990$ E$2\mathrm{.}2)$:

A conventional isotropically consolidated undrained triaxial compression test, with the cell pressure ${}_r$ held constant, is carried out on a sample of stiff overconsolidated clay. The stress:strain relationship is found to be linear up to failure, so it is deduced that the clay behaves as an isotropic perfectly elastic material.

Part A: After an axial strain ${}_a=0\mathrm{.}9$ per cent, the deviator stress is measured to be $90$kPa. For this stage of the test, calculate the values of ${}_a,p,p^{\text{'}},u,{}_a^{\text{'}},{}_r^{\text{'}},{}_r$ and $E_u.$

Part B: At this time, the axial stress and cell pressure are kept constant, and the sample is allowed to drain so that the pore pressures dissipate and the sample undergoes a volumetric strain ${}_p=0\mathrm{.}3$ per cent.

i$)$ What are the values of ${}_a^{\text{'}},{}_r^{\text{'}},u,p^{\text{'}},q,$ for this stage of the test. Note that these values should be found as the difference between Part A and Part B$.$

ii$)$ What are the values of the elastic constants $K^{\text{'}},G^{\text{'}},E^{\text{'}},$ and $v^{\text{'}}?$

iii$)$ What are the values of ${}_r$ and ${}_a$ for the drained stage of the test? Note that in the drained stage of this test, the stress change is isotropic and therefore the strain change is also isotropic.

iv$)$ What are the values of ${}_r$ and ${}_a$ from the initial consolidation stage $($cumulative strain from the beginning of the test$)?$