Question

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

Answer 1

Correct Answer - Option 3 : 25 kN/m²

Concept:

We know,

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

σ₁ = σ₃tan² (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 = q_u

⇒ c = \(\frac{q_u}{2}\)        ...(2)

Here,

c - Cohesion (kN/m²)

q_u - Unconfined compressive strength (kN/m²)

σ₃ - Confining stress (kN/m²)

σ₁ - Major principal stress (kN/m²)

Calculation:

Given,

q_u = 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