GATE Civil Engineering (CE) 2020 Shift 2 Solved Paper

Question : 60 of 65

Marks: +1, -0

10 {m}

high slope of dry clay soil (unit weight

=20 {kN} {/} {m}^{3}

), with a slope angle of

45^{∘}

and the circular slip surface, is shown in the figure (not drawn to the scale). The weight of the slip wedge is denoted by

{W}

. The undrained unit cohesion

( {c}_{u})

60 {kPa}

The factor of safety of the slope against slip failure, is

Solution:

Area of circular Arc soil

=\;{Q}/{360} × {Ar}^{2}-\;{1}/{2}

base

× {ht}

=\;{90}/{360} × π × 10^{2}-\;{1}/{2} × 10 × 10

=28.59 {m}^{2}

Weight

d

wedge

=\volume× y=\Area × 1 × y=28.54 × 1 × 20=570.8 {kN}

FOS

=

\text " Re storing Moment"/\text " Overterning Moment" =\;{60 × 10 × π {/} 4 × 10}/{570.8 × 4.48}

=\;{C ×(r Q) × r}/{w × x}

FOS

=1.84

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