Problem $3$: Two CU triaxial tests are performed on a sample of saturated, overconsolidated, highplasticity clay. At failure, the results are as follows:

Test $1$: ${}_3=30$kPa,$Q=0\mathrm{.}45kN,A=0\mathrm{.}01m^2,u=10$kPa

Test $2$: ${}_3=60$kPa,$Q=0\mathrm{.}70kN,A=0\mathrm{.}01m^2,u=20$kPa

where ${}_3$ is the total confinement stress, $Q$ is the vertical load on the sample, $A$ is the sample cross section, and $u$ is the water stress $($pore pressure$).$

a$.$ Calculate ${}_3,{}_1,{}_3^{\text{'}},$ and ${}_1^{\text{'}}$ at failure.

b$.$ Draw the Mohr circle at failure in the $$ vs$.{}^{\text{'}}$ set of axes.

c$.$ Draw the failure envelope and find the effective stress strength parameters $c^{\text{'}}$ and ${}^{\text{'}}.$

$1$