GATE CE 2023 Set 1 — Question 41
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Geotechnical Engineering → Stress Distribution in Soils → Boussinesq's Theory
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Question
Consider that a force is acting on the surface of a half-space (Boussinesq’s problem). The expression for the vertical stress () at any point (), within the half-space is given as,where, is the radial distance, and is the depth with downward direction taken as positive. At any given , there is a variation of along , and at a specific , the value of will be maximum. What is the locus of the maximum ?
Correct answer
(A) z² = (3)/(2) r²
Solution
To find the maximum for a given , we differentiate with respect to and set it to zero.Dividing by :
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