# A soft saturated clayey soil tested unconfined gave axial stress of 50 kN/m2 at failure. The shear strength of the soil is

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A soft saturated clayey soil tested unconfined gave axial stress of 50 kN/m2 at failure. The shear strength of the soil is
1. 50 kN/m2
2. 100 kN/m2
3. 25 kN/m2
4. None of the above

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Correct Answer - Option 3 : 25 kN/m2

Concept:

We know,

As per triaxial stress, the relationship between principal stress and cohesion -

σ1 = σ3tan(45° + ϕ/2) + 2 × c × tan(45° + ϕ/2)        ...(1)

For clayey soil subjected unconfined triaxial test, ϕ = 0° and σ3 = 0 kN/m2

From (1)

σ1 = 2c = qu

c = $\frac{q_u}{2}$        ...(2)

Here,

c - Cohesion (kN/m2)

qu - Unconfined compressive strength (kN/m2)

σ3 - Confining stress (kN/m2)

σ1 - Major principal stress (kN/m2)

Calculation:

Given,

qu = 50 kN/m2

From (2)

c = $\frac{50}{2}$ = 25 kN/m2

We know,

As per columb's theory, shear stress is given by -

τ = c + $\bar{σ}$ tanϕ

For clayey soil, ϕ = 0°

τ = c = 25 kN/m2