E$7\mathrm{.}3.$ A sample of saturated clay is normally compressed in a triaxial cell by increasing the cell pressure and holding the axial length constant. The axial effective stress is $K_1$ times the radial effective stress, and the specific volume $v$ is given by

$v=v_{}-ln{p}^{\text{'}}$

where $v_{}$ and $$ are soil constants, and $p^{\text{'}}$ is the mean normal stress. The samples are then subjected to undrained compression tests. with the cell pressure held constant. Derive an expression for the normalised pore pressure at failure $(($:$\frac{u_f}{q_f}$