GATE Civil Engineering (CE) 2018 Shift 2 Solved Paper

Question : 52 of 65

Marks: +1, -0

The total horizontal and vertical stresses at a point

X

in a saturated sandy medium are 170

{kPa}

and

300 {kPa}

, respectively. The static pore-water pressure is

30 {kPa}

. At failure, the excess porewater pressure is measured to be

94.50 {kPa}

, and the shear stresses on the vertical and horizontal planes passing through the point

X

are zero. Effective cohesion is 0 kPa and effective angle of internal friction is

36^{∘}

. The shear strength (in

{kPa}

, up to two decimal places) at point

{X}

Solution:

∵ \;\; σ_{n}=\;{300+170}/{2}+\;{300-170}/{2} \cos 2 α

α= \;\; 45^{∘}+\;{36^{∘}}/{2}=63^{∘}

⇒ \;\; σ_{n}=196.79

σ_{n}^{'}=σ_{n}-u=196.79-(30+94.5)

σ_{n}^{'}=72.29 {N}{/} {mm}^{2}

⇒ \;\; τ=C+σ_{n}^{'} \tan φ=72.29 \tan 36

= \;\; 52.52 {N} {/} {mm}^{2}

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