Soil Phase Relations and Classification

Soil is a mix of solid grains, water and air. Almost every geotechnical calculation starts with the phase relations between them.

Phase relations

The key link: S e = w G.

Unit weights:

• Bulk: γ = (G + Se)γ_w/(1 + e)
• Dry: γ_d = Gγ_w/(1 + e) = γ/(1 + w)
• Saturated: γ_sat = (G + e)γ_w/(1 + e)
• Submerged: γ' = γ_sat − γ_w = (G − 1)γ_w/(1 + e)

Relative density of sands: D_r = (e_max − e)/(e_max − e_min).

Consistency limits (Atterberg)

As a fine soil dries it passes from liquid to plastic to semi-solid to solid states:

• Liquid limit (LL): Casagrande cup, 25 blows; or cone penetrometer.
• Plastic limit (PL): rolls into 3 mm threads that just crumble.
• Shrinkage limit (SL): below it, losing water does not reduce volume.
• Plasticity index I_p = LL − PL; liquidity index I_L = (w − PL)/I_p; consistency index I_c = (LL − w)/I_p.
• Activity = I_p / (% clay finer than 2 µm). High activity: montmorillonite.

Grain size

• Sieve analysis for coarse soils; hydrometer (Stokes' law) for fines.
• Coefficient of uniformity C_u = D₆₀/D₁₀; coefficient of curvature C_c = D₃₀²/(D₁₀ D₆₀).
• Well graded: C_u > 4 (gravel) or > 6 (sand), and 1 ≤ C_c ≤ 3.

IS classification

• Coarse soils (more than 50% retained on the 75 µm sieve): gravel (G) or sand (S), with W, P, M or C.
• Fine soils: silt (M), clay (C), organic (O), with L (LL < 35), I (35–50) or H (LL > 50) compressibility, using the plasticity chart A-line: I_p = 0.73(LL − 20).

Worked example

A soil has w = 20%, G = 2.7 and e = 0.6 (γ_w = 9.81 kN/m³).

• S = wG/e = 0.54/0.6 = 0.9.
• γ_d = 2.7 × 9.81/1.6 = 16.55 kN/m³; γ = γ_d (1 + w) = 19.87 kN/m³.

Practice