Question

If z-axis is considered to be directed downward from ground surface, then the stress component in y-axis at a point at a depth z due to self weight of soil above it is ___________

(a) \(σ_y=\frac{1}{1-μ}γz\)

(b) σy=μγz

(c) \(σ_y=\frac{μ}{1-μ}\)

(d) \(σ_y=\frac{μ}{1-μ}γz \)

This question was addressed to me in an interview for job.

This question is from Stresses due to Self Weight topic in division Stress Distribution of Geotechnical Engineering I

Answer 1

Correct answer is (d) \(σ_y=\frac{μ}{1-μ}γz \)

The explanation is: On simplifying the compatibility equation in terms of stresses with respect to Poisson’s ratio is given by

\(σx=σy=\frac{μ}{1-μ}γz \)

Where σx,σy are the normal stresses in x and y direction respectively

μ= Poisson’s ratio

\(K_o=\frac{μ}{1-μ}\)   is the coefficient of lateral pressure at rest.