$[10$ points$]$ The data recorded during a shear box test on a sand sample, $10cm10cmx3cm,$ at a constant vertical force of $1200N$ are shown in the table below. A negative sign denotes vertical expansion.

$($a$)$ Plot graphs of $(1)$ horizontal forces versus horizontal displacements and $(2)$ vertical displacements versus horizontal displacements;

$($b$)$ Would you characterize the behavior of this sand as that of a dense or loose sand? Explain your answer.

$13$

$($c$)$ Determine $(1)$ the maximum or peak shear stress; $(2)$ the critical state shear stress; and $(3)$ the peak and critical state frictional angles.

Table $4.$ Direct shear test data

$\backslash$table$[[\backslash$table$[[$Horizontal$],[$displacement$],[(mm)$