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GATE 2021 AG – Question 28

Soil and Water Conservation Engineering · Soil Mechanics · 1 mark · Numerical answer

A naturally deposited cohesionless infinite soil slope is 25°. Internal-friction angle30°. Find factor of safety, to two decimals.

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Correct answer: 1.22 to 1.25

Explanation

For a dry cohesionless infinite slope, the ratio of resisting to driving shear is $FS=\tan\phi/\tan\beta$. Thus $FS=\tan30^\circ/\tan25^\circ=1.23813$,or **1.24**. Unit weight and depth cancel because cohesion is zero.

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