In a triaxial test carried, out on a cohesion less soil

In a triaxial test carried, out on a cohesion less soil sample with a cell pressure of 20 kPa, the observed value of applied stress at the point of failure was 40 kPa. The angle of internal friction of the soil is

C = 0
σ₁ = σ₃ tan² α + 2 c tan α
σ₃ = 20 kN/m²
σ_d = 40 kN/m²
σ₁ = σ₃ + σ_d = 20 + 40
= 60 kN/m²
⇒ 60 = 20 tan² α + 0
∴ tan² α = 3
∴ α = 60°

α = 45 +	Φ
	2

⇒ 60 = 45 +	Φ
	2

∴ Φ = 30°