Problem $2$

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 $\backslash ($ q$-$p$^\{\backslash$prime$\}\backslash )$ 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$)\backslash ($ e$=0\mathrm{.}40\backslash )$ and $($ii$)\backslash ($ e$=0\mathrm{.}60\backslash ).$ 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?