GATE 2017 CE (CE1) – Question 21

Geotechnical Engineering · Stress distribution in soils, Boussinesq theory, pressure bulbs · 1 mark · Multiple choice

A uniformly distributed line load of 500 kN/m acts on the ground surface. Using Boussinesq theory, find the ratio of vertical stress at depth 2 m to that at depth 4 m directly below the load line.

0.25
0.5
2.0
4.0

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Correct answer: (C) 2.0

Explanation

Directly below an infinite line load of intensity $q$, the vertical stress is $\sigma_z=2q/(\pi z)$. It is inversely proportional to depth, rather than to depth squared as for a point load. Therefore $\sigma_z(2)/\sigma_z(4)=4/2=2.0$, option C; the load intensity cancels.

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