For the proposed $30-$ft high geotextile$-$reinforced embankment and the slip trial$-$surface shown in the next page, determine the following:

a$)$ Factor of safety with no geotextile $($GT$)$ reinforcement,

b$)$ Number of GT reinforcement layers and spacing required to raise the FS to $1\mathrm{.}5.$

c$)$ Required GT embedment length behind the slip surface in order to mobilize the allowable tensile strength with transfer efficiency $(E\%)=80\%$ and $FS=1\mathrm{.}5.$

d$)$ Total length of each GT layer.

e$)$ Suggested construction orientation of GT layers.

f$)$ Final design diagram showing all necessary details

Other information:

Embankment soil:

$c=250$ DSE, $=10,$ and $=110$ DC$.$ and Slope angle, $=45.$

Foundation soil:

$c=520psf=16,$ and $=110$ BCE

$GT$ :

Allowable tensile strength, $T_{\text{a}\text{l}\text{l}\text{o}\text{w}}=1700l\frac{b}{f}t($machine direction$)$

Allowable tensile strength, $T_{\text{a}\text{l}\text{l}\text{o}\text{w}}=1300l\frac{b}{f}t($cross$-$machine direction$)$

Slice weight, arc length and inclination: Use the following table:

$\backslash$table$[[$Slice #$,$Weight, kips$/$ft$,L(ft),$Inclination angle, $($degrees$)],[1,16\mathrm{.}6,25\mathrm{.}5,57],[2,30,13\mathrm{.}5,38],[3,31\mathrm{.}5,11\mathrm{.}2,24],[4,23\mathrm{.}2,11\mathrm{.}2,10],[5,12\mathrm{.}3,10\mathrm{.}4,-3],[6,5\mathrm{.}2,17\mathrm{.}5,-15]]$

$R=44ft$

Use the scale given to obtain other dimension$($s$)$ if needed.