PROBLEM $4$: $[25$ POINTS$]$

Three direct shear tests were performed on a clayey sand soil $(30\%$ clay; $70\%$ sand$).$ The area of each of the samples was $4$ in $4$ in$.$ The results of the shear stress vs$.$ shear strain are shown below.

a$)$ Determine the maximum shear stresses defined at $3\%$ shear strain $($Show your work on the graph$).$

b$)$ Fill in the table below with the proper units! $psf=\frac{lb}{ft2}$

c$)$ Using your calculator, determine the regression parameters and conclude what is the Mohr Coulomb failure equation after properly identifying each parameter.

d$)$ Draw the shear stress vs normal stress graph and properly label all three points on the graphs along with the trendline. $[$Draw it on the graph paper$]$

e$)$ Determine if point $M(250,150)$ is a failure point or not.

$\backslash$table$[[$Normal Stress $[$psf$],$Shear Stress $[$psf$]],[,],[,],[,]]$