Question

The lateral strain in the horizontal direction is _______

(a) \(∈_h=\frac{1}{E} [σ_h-μ(σ_v)] \)

(b) \(∈_h=\frac{1}{E} [σ_h-μ(σ_h-σ_v)]\)

(c) \(∈_h=\frac{1}{E} [σ_h-μ(σ_h+σ_v)]\)

(d) \(∈_h=\frac{1}{E} [σ_h-(σ_h-σ_v)]\)

I had been asked this question in a national level competition.

I want to ask this question from Earth Pressure at Rest in chapter Failure Envelopes & Earth Pressure of Geotechnical Engineering II

Answer 1

Right choice is (b) \(∈_h=\frac{1}{E} [σ_h-μ(σ_h-σ_v)]\)

For explanation I would say: The lateral strain ∈h in the horizontal direction is given by,

\(∈_h=\frac{1}{E} [σ_h-μ(σ_h-σ_v )],\)

where, σh =horizontal stress

σv =vertical stress

E=elastic modulus

μ= Poisson’s ratio.