Punching shear may occur in loose sand with relative density less than _____.

Asked in SSC JE 11/10/2023 (Morning)

Detailed Explanation

Relative density I_D tells us how dense a sand is compared with its loosest and densest possible states. It is a good guide to which failure mode a footing on sand will show.

Why “35%” Is Correct

The usual guide is: general shear for I_D above about 70%, local shear between about 35% and 70%, and punching shear for I_D below about 35%. Some textbooks put the lower limit at 30%; of the options given, 35% is the right one.

The three modes of bearing capacity failure (Vesic). General shear: a continuous slip surface runs from the footing edge to the ground surface, which heaves; the load–settlement curve shows a clear peak. Local shear: slip surfaces form under the footing but do not reach the surface; heave is slight. Punching shear: the footing pushes straight down, shearing the soil vertically along its edges, with no heave. Typical relative density: above about 70%, about 35–70%, and below about 35% (some books quote 30%).

Why the Other Options Are Wrong

A. 55%: 55% is in the medium dense (local shear) range.
C. 45%: 45% is also in the local shear range.
D. 65%: 65% is near the dense end, close to general shear.

Key Point

I_D < ~35% → punching; 35–70% → local; > 70% → general shear.

Key Concepts for Students

Relative density I_D = (e_max − e)/(e_max − e_min).
Footing depth also matters: deep footings tend towards punching.
Loose sand under a footing compresses a lot before failure.

Practice more: this is question 9 in Shallow and Deep Foundation MCQs – Part 1. Try the whole set and check every answer instantly.