Soil mechanics definition: The angle of internal friction φ of a soil mass is the angle whose…

Introduction / Context:
In shear strength theory for soils, the angle of internal friction φ characterizes frictional resistance between particles. It appears in the Mohr-Coulomb criterion, relating shear stress to normal stress on a potential failure plane.

Given Data / Assumptions:

• Soil is considered under drained, frictional conditions (c ≈ 0 for clean sands).
• Maximum resistance refers to limiting shear at failure.

Concept / Approach:
At failure, for cohesionless soils, τ = σ * tan φ on the critical plane, where τ is shear stress and σ is the normal effective stress. Hence tan φ is the ratio of limiting shear resistance to normal pressure on that plane.

Step-by-Step Explanation:
Identify the failure condition: shear/normal ratio reaches its maximum.Write τ / σ = tan φ → tan φ represents the ratio of maximum resistance to normal pressure.

Verification / Alternative check:
For granular soils, direct shear and triaxial tests yield approximately linear envelopes in τ–σ space, with slope equal to tan φ.

Why Other Options Are Wrong:
Using sine or cosine would not match the Mohr-Coulomb frictional definition.Cotangent statement is not the conventional definition and inverts the intended ratio.

Common Pitfalls:

• Confusing φ with the angle of repose; they are related but not always identical under all conditions.

Final Answer:
tangent is equal to the ratio of maximum resistance to sliding on an internal plane to the normal pressure on that plane