GATE 2018 CE (CE2) – Question 54
At X in saturated sand, total horizontal and vertical stresses are 170 and 300 kPa, with zero shear on those planes. Static pore pressure is 30 kPa and excess pore pressure at failure is 94.50 kPa. Effective cohesion is zero and friction angle is 36°. Shear strength on the failure plane, to two decimals, is ______ kPa.
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Correct answer: 51.50 to 53.50
Explanation
Total pore pressure is $30+94.50=124.50$ kPa. Effective principal stresses are 175.5 and 45.5 kPa, so Mohr-circle centre C = 110.5 kPa. For zero cohesion, failure-plane shear strength is $C\sin\phi\cos\phi=110.5\sin36^\circ\cos36^\circ=52.55$ kPa. The rounded data’s small inconsistency lies within the accepted interval.