Question $3$: A cylindrical sample of soil $50mm$ in diameter $100mm$ long was subjected to axial and radial effective stresses. When the vertical displacement was $2mm,$ the soil failed. The stresses at critical state are $({}_1^{\text{'}}{)}_{cs}=280$kPa and $({}_3^{\text{'}}{)}_{cs}=100$kPa. The change in soil volume at failure was $800m{m}^3.$

Which failure criterion is appropriate to interpret the test data?

Determine a$)$ the axial strain at failure, b$)$ the volumetric strain at failure, c$)$ the critical state friction angle, and d$)$ the inclination of the slip plane to the horizontal plane.