emphProblem $1$: Three standard drained triaxial tests were performed on a cohesionless soil at

the same confining pressure of $300$ kPa for three different void ratios; e $=0\mathrm{.}69$ e $=0\mathrm{.}74$;$,$ and

e $=0\mathrm{.}79.$ The results of the tests are reported in Figure $1.$ For these tests:

a$)$ Pair each curve with its initial void ratio.

b$)$ Find the peak $($failure$)$ friction angle and the axial strain at failure for each test.

c$)$ Are the friction angles the same? Explain.

d$)$ Estimate the critical state $($large strain condition$)$ friction angle.

e$)$ Compute the shear and normal stress on the failure plane at failure for the denser soil.

f$)$ Compute the dilatancy rate $($d$$vol$/$d$$a$)$ at the peak friction angle.