Question $(50\%)$: For a landfill $($i$.$e$.$ solid waste containment area$)$ planned to be constructed in a suburban area, a side slope including sand $-$ geomembrane interface is to be designed. In a purpose to properly evaluate the stability issues of this side slope containing composite layered systems, in the laboratory, the direct shear tests were conducted on sand $-$ geomembrane interfaces and the following results were obtained:

$\backslash$table$[[$Normal Stress $($kPa$),$Shear Strength $($kPa$)],[25,14],[100,52],[200,100],[400,190]]$

$($a$)[25\%],$ Plot the Mohr$-$Coulomb failure envelope and obtain sand geomembrane interface characteristics such as the angle of interface shear resistance $()$ and the adhesion $($c$).$

$($b$)[25\%]$ Using the interface shear characteristics for the sand $-$ geomembrane interface you obtained in part a$,$ find the Factor of Safety for a $4($H$)$ to $1($V$)$ slope constructed by covering geomembrane with a sand layer for protection. Please, perform your calculations based on Side Slope Cover Soil Stability $-$ Finite Slope with Uniform Thickness. Given that the slope is $25$ m long with a uniformly thick cover soil of $250$ mm at a unit weight of $19k\frac{N}{m^3}.$ The soil has an internal friction angle of $32.$ Assume that $C=0,C_a=0$ and $c_a=0$ for conservative design purposes. Please, provide a further comment on the suitability of the sand material selected to construct a composite layered system along with geomembrane considering the factor of safety you have just calculated.