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Determine the shear strength of soil (in kN/m2 units) in terms of effective stress on a plane within a saturated soil mass at a point where the total stress is 220 N/m2 and the pore water pressure is 120 kN/m2. The effective stress shear strength parameters for the soil are: cohesion = 16 kN/m2 and angle of internal friction = 30 . (take sin 30 = 0.5, tan 30 = 0.6; cos 30 = 0.9)

Determine the shear strength of soil (in kN/m2 units) in terms of effective stress on a plane within a saturated soil mass at a point where the total stress is 220 N/m2 and the pore water pressure is 120 kN/m2. The effective stress shear strength parameters for the soil are: cohesion = 16 kN/m2 and angle of internal friction = 30 . (take sin 30 = 0.5, tan 30 = 0.6; cos 30 = 0.9) Correct Answer 76

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

Calculation:

Given,

Total stress (σ) = 220 kN/m2, pore water pressure (u) = 120 kN/m2

C' = 16 kN/m2, ϕ = 30° , tan30° = 0.6

∵ S = C' + σ̅ tanϕ 

S = 16 + (220 - 120) × tan30° 

S = 16 + 100 × 0.6 = 76 kN/m2

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