Q$2.$ The initial stresses on a soil sample at a depth of $2$ m in the field are $1=$ $$vo and $3=$ $$ho $=$ ko $.$ $$vo$,$ where ko is the lateral earth pressure coefficient at rest. The bulk unit weight and critical state friction angle of soil are $17\mathrm{.}5$ kN$/$m$3$ and $34$ degrees, respectively. The soil is then brought to shear failure $($critical state$)$ by reducing $3$ while keeping $1$ constant. Sketch Mohr$-$Coulomb failure criteria for the soil. Show the Mohr circles at initial state and critical state with corresponding stress values on them. Determine the following at critical state: major and minor principal stresses, maximum shear stress, and normal effective stress and shear stress on failure plane.