Problem $2$

A triaxial test was performed on a dry cohesionless soil under a confining pressure $($i$.$e$.,$ lateral pressure$)$ of $144\mathrm{.}0k\frac{N}{m^2}.$ Assume that the sample failed when the deviator stress reached $395\mathrm{.}8k\frac{N}{m^2}.$ Complete the parts below. In your solution include the Mohr's circle for the soil sample.

$($a$)$ Find the soil's cohesion and angle of internal friction

$($b$)$ For the sample, determine the orientation $($angle $)$ of the failure plane.

$($c$)$ For the sample, use your Mohr's circle to determine the shear stress and normal stress on the failure plane.