Question #$1$: A sample of clay was tested in an unconfined compressive test and yielded the results shown in the graph below. The sample failed by creating a failure plane at an angle of $62$ degrees counterclockwise from the horizontal $($major principal plane$).$

a$)$ Determine the maximum compressive strength and undrained shear stress $($kPa$)(2)$

b$)$ Determine the normal and shear stresses on the failure plane. $(2)$

c$)$ Determine the sensitivity of the clay if it was remolded and retest but failed at a maximum compressive stress of $)(1)$

d$)$ Determine the maximum shear stress, $c_u,$ and the deviator stress, ${}_d,$ if an undisturbed sample of the same clay was tested in a U$-$U triaxial compression test with an all$-$around confining pressure of $300$kPa. $(1)$

e$)$ Determine the ultimate limit states bearing capacity for a square footing resting on this clay. Assume short$-$term shear strength parameters govern. $(1)$