A $1\mathrm{.}0mm$ thick LLDPE geomembrane with a mobilized allowable stress of $7,000$kPa is installed on a $3($horizontal$)$ to $1($vertical$)$ slope as shown in Figure $1.$ The $300mm(=d_{CS})$ thick cover soil is of unit weight of $16\mathrm{.}5k\frac{N}{m^3}.$ The friction angle between the geomembrane and the soil is $30.$

$($a$)$ Determine the side slope angle $.$

$(2)$

$2$ of $5$

$($b$)$ Determine the allowable force per $m$ width of the geomembrane.

$(2)$

$($c$)$ Derive the equation for the determination of the runout length $(L_{RO}).$ State your assumptions used in your derivation.

$($d$)$ Determine the runout length and state your assumptions clearly.

$($e$)$ If there is not enough space for the runout, what would you propose to solve the problem

$(1)$