Cohesion & Friction Angle

Cohesion (c) and angle of internal friction (φ) are the two Mohr-Coulomb shear-strength parameters of soil. Together they define the soil's shear strength: τ = c + σ × tan φ, where τ is shear stress on a plane and σ is normal stress on that plane. Cohesion (kPa) is the soil's intrinsic shear strength at zero normal stress — primarily a property of clay minerals and inter-particle bonding. Friction angle (degrees) is the angle of internal friction — primarily a property of granular packing and inter-particle friction. Indian Standard IS 2720 Part 13 (triaxial test), Part 11 (direct shear test) provide standard methods for measuring c and φ.

Classification by parameter dominance: (a) Pure cohesive soil (clay) — φ ≈ 0, c = undrained shear strength cu (IS 2720 Part 11). For undrained loading of saturated clay: shear strength = cu (constant with depth). Typical Indian clays: cu = 25-200 kPa. (b) Pure cohesionless soil (sand, gravel) — c ≈ 0, φ = 28-40°. Loose sand: φ = 28-30°. Medium sand: 32-35°. Dense sand: 36-40°. Gravel: φ = 36-42°. (c) C-φ soil (silty clay, gravel mixed with fines) — both c and φ are non-zero. Common in Indian residual soils, weathered rock zones, laterite, and decomposed-rock fill.

Design use of c and φ: (a) bearing capacity computations per Terzaghi's equation: qu = c × Nc + γ × D × Nq + 0.5 × γ × B × Nγ, where Nc, Nq, Nγ are bearing capacity factors that depend on φ; (b) lateral earth pressure: Ka = (1 − sin φ) / (1 + sin φ) for granular, modified for cohesion; (c) slope stability: shear strength along potential failure surface = c × A + (W cos α) × tan φ, where A is failure-surface area, W is weight above, α is failure-surface angle. For routine Indian projects: SPT correlations + 1-2 triaxial tests on representative samples are standard practice. For important structures (dams, deep excavations), comprehensive lab and in-situ testing are mandatory.