Question

The principal stress relationship on a failure plane is given by _______

(a) σ1=σ3 tan^2 α

(b) σ1=2c tan⁡α-σ3 tan^2 α

(c) σ1=2c tan⁡α+σ3

(d) σ1=2c tan⁡α+σ3 tan^2 α

I had been asked this question by my college director while I was bunking the class.

This intriguing question originated from Active Earth Pressure of Cohesive Soils topic in division Failure Envelopes & Earth Pressure of Geotechnical Engineering II

Answer 1

Correct answer is (d) σ1=2c tan⁡α+σ3 tan^2 α

Best explanation: The principal stress relationship on a failure plane is given by,

σ1=2c tan⁡α+σ3 tan^2 α,

Where, σ1=major principal stress

σ3=minor principal stress

\(α=(45°+\frac{φ}{2}), \)

φ=angle of internal friction

c=cohesion.