GATE CE 2022 Set 1 — Question 32
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Geotechnical Engineering → Stress Distribution in Soils → Boussinesq's Theory
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Question
A concentrated vertical load of is applied on a horizontal ground surface. Points P and Q are at depths and 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)
Correct answer
4 to 4
Solution
According to Boussinesq's theory, the increase in vertical stress () at a depth directly below a concentrated point load (where radial distance ) is given by:Let and .The ratio of the increase in vertical stress at P to that at Q is:Thus, the ratio is .
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