Consider that a force P is acting on the surface of a half-space (Boussinesq’s problem). The expression for the vertical stress ( σ z ) at any point (r, z), within the half-space is given as, $\rm \sigma_z=\frac{3P}{2\pi} \frac{z^3}{_{(r^2+z^2)}\frac{5}{2}}$ where, r is the radial distance, and z is the depth with downward direction taken as positive. At any given r, there is a variation of σ z along z, and at a specific z, the value of σ z will be maximum. What is the locus of the maximum σ z ?

GATE 2023 Civil Engineering PYQ — Geotechnical Engineering

GATE 2023Set 1PYQMCQanswer keyexplanationmedium

Geotechnical Engineering · Foundations

Concept intelligence

Drill mode: soil mechanics · 28/77

Studying seriously for GATE CSE?

Keep browsing free. Pro unlocks the paid study loop: explanations, topic mastery, mistake notebook, and custom PYQ drills.

Recurring concept

Foundations has appeared in GATE Civil Engineering 16 times across 4 years (2022, 2023, 2024, 2025).