An infinitely long slope is made up of a $c - ϕ$ soil having the properties : cohesion (c) = 20 kPa and dry unit wt $(γ_{d}) = 16 k N / m^{3}$ . The angle of inclination and critical height of the slope are $40^{\circ}$ and 5 m respectively. To maintain the limiting equilibrium, the angle of internal friction of the soil (in degree)
22.44

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Solution

The correct option is A 22.44
$H = \frac{C}{γ_{d} (t a n β - t a n ϕ) c o s^{2} β}$
$C = 20 k p a$
$γ_{d} = 16 k N / m^{3}$
$β = 40^{\circ}$
$H = 5 m$
$ϕ = ?$
$5 = \frac{20}{16 (t a n 40^{\circ} - t a n ϕ) c o s^{2} 40^{\circ}}$

$t a n 40 - t a n ϕ = 0.426$

$\Rightarrow t a n ϕ = 0.413$

$ϕ = {22.44}^{\circ}$

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The correct option is A 22.44H=Cγd(tanβ−tanϕ)cos2β C=20kpa γd=16kN/m3 β=40∘ H=5m ϕ=? 5=2016(tan40∘−tanϕ)cos240∘ tan40−tanϕ=0.426 ⇒tanϕ=0.413 ϕ=22.44∘