A clay has $=0\mathrm{.}05,N=3\mathrm{.}32,=0\mathrm{.}2,$ and ${}^{\text{'}}=30.$ Suppose the clay is normally consolidated under the $K_0$ condition

$0\mathrm{.}5).$

a$.$ The formula for the $K_{0}NCL$ line be $v=N_{K_0}-ln(p^{\text{'}}).$ Find $N_{K0}($hint: the $N_0-$consolidation $NCL$ line is also on the yield surface$).$

b$.$ Suppose the clay is consolidated with $K_0=0\mathrm{.}5$ to the stress ${}_{v0}^{\text{'}}=200k\frac{N}{m^2}$ and ${}_{h0}^{\text{'}}=100k\frac{N}{m^2}.$ After the consolidation, the clay subjected to undrained shear to failure. Please estimate $s_u,u_f,$ and $v_f.$