Consider a poorly graded silica sand. Using the plots provided below, answer the following questions:

$($a$)$ Draw the effective stress path of a drained triaxial compression test on the $$ plot below.

The initial effective isotropic confining pressure is $200$ kPa. Find the drained strength and

void ratio at critical state.

$($b$)$ Sketch possible stress$-$axial strain and axial strain$-$volumetric strain curves of the drained

triaxial compression test in $($a$).$ Consider two different initial void ratios: $($i$)=0\mathrm{.}40$ and $($ii$)$

$=0\mathrm{.}60.$ Comment on the results. Sketch your plots with axes aligned to the plots below.

$($c$)$ Find the undrained shear strengths at critical state when the void ratios are $0\mathrm{.}40$ and $0\mathrm{.}60$ at

an effective isotropic confinement of $200$ kPa. Does the initial effective stress matter to the

undrained critical shear strength value? Does the initial effective stress matter to the pore

pressure generated during undrained shearing?