GATE 2022 CE (CE1) – Question 32
A concentrated vertical load of 3000 kN is applied on a horizontal ground surface. Points P and Q are at depths 1 m and 2 m below the ground, respectively, along the line of application of the load. Considering the ground to be a linearly elastic, isotropic, semi-infinite medium, the ratio of the increase in vertical stress at P to the increase in vertical stress at Q is ________. (in integer)
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Correct answer: 4
Explanation
On the vertical axis below a surface point load, Boussinesq stress is $\Delta\sigma_z=3P/(2\pi z^2)$.
The common load and constants cancel in the ratio: $\Delta\sigma_P/\Delta\sigma_Q=(2/1)^2=\mathbf4$.