Question

During the state of shear failure, which of the following principal stress relationship exist?

(a) σ1 = σ tan α + 2c tan α

(b) σ1 = σ3 tan2 α + 2c tan α

(c) σ1 = 2c tan α

(d) σ1 = σ3 tan α

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I'd like to ask this question from Minimum Depth of Foundation: Rankine’s Analysis topic in portion Bearing Capacity of Geotechnical Engineering II

Answer 1

Correct choice is (b) σ1 = σ3 tan2 α + 2c tan α

Best explanation: During the state of shear failure (plastic equilibrium), the following principal stress relationship exists σ1 = σ3 tan2 α + 2c tan α

for cohesion-less soil,σ1 = σ3 tan2 α.