Which is the correct equation of shear stress on soil?

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OSSC JE Civil Mains Official Paper: (Held On: 16th July 2023)
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  1. τ = c - σ ⋅ tan φ 
  2. τ = σ + c ⋅ tan φ
  3. τ = c + σ ⋅ tan φ
  4. τ = c tan φ + σ

Answer (Detailed Solution Below)

Option 3 : τ = c + σ ⋅ tan φ
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Concept:

(i) As per Mohr Coulomb's Theory Shear strength of soil is given as,

S = C + σ tanϕ 

Where, C = Cohesion, σ = Normal stress, ϕ = friction angle

(ii) The original form of the coulomb's equation was in terms of total normal stress.

(iii) After Terzaghi establishment of effective stress principle, it was found that the shear strength of soil depends on effective parameter not total parameter

S = C' + σ̅ tanϕ 

Where, C' = Effective cohesion, σ̅ = Effective stress, ϕ = Effective friction angle

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