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Foundation Engineering

Infinite Slopes -Dry Cohesionless Soil

The infinite ...

Question

The infinite sand slope shown in the figure is one the verge of sliding failure. The ground water table coincides with the ground surface. Unit weight of water $γ_{w} = 9.81 k N / m^{3}$ .

The value of the effective angle of internal friction (in degrees upto one decimal place) of the sand is
34.33

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Solution

The correct option is A 34.33
$F . O . S = \frac{S h e a r s t r e n g t h (τ_{f})}{S h e a r s t r e s s (τ)}$

$F . O . S = \frac{γ_{s u b} H c o s^{2} β t a n ϕ}{γ_{s a t} H c o s β s i n β}$

$1 = \frac{γ_{s u b} t a n ϕ}{γ_{s a t} t a n β}$

$1 = \frac{(21 - 9.81) t a n ϕ}{21 t a n 20^{\circ}}$

$t a n ϕ = \frac{21 \times t a n 20^{\circ}}{11.19}$

$ϕ = {34.33}^{\circ}$

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