Soil Mechanics
Soil is a mix of solid grains, water and air. Learn phase relationships (void ratio, porosity, water content, saturation, unit weights), effective stress, permeability and Darcy's law, compaction, and Mohr–Coulomb shear strength.
Unlike steel or concrete, soil wasn't manufactured to a specification — it's a natural, variable material made of particles with water and air in between. Its strength and stiffness depend on how tightly packed it is and on the water pressure in its pores.
Terzaghi's principle of effective stress — soil behaviour is governed by the stress carried by the grains, not by total stress — is the foundation of all geotechnical engineering.
An analogy
A soil is like a sponge full of marbles: squeeze it and the water must flow out before the marbles can pack closer. The grains carry the load; the water pushes back.
Three phases
Solids, water and air. Relationships between their volumes and weights (e, n, w, S, γ) describe how dense and wet a soil is. Dry soil has S = 0; saturated soil below the water table has S = 100 %.
Effective stress
Total vertical stress at depth is the weight of everything above. Pore water pressure u = γ_w × depth below the water table pushes grains apart. Effective stress σ′ = σ − u controls strength and compressibility — raising the water table lowers σ′ and weakens soil; pumping it down increases σ′ and causes settlement.
Permeability and seepage
Water flows through soil according to Darcy's law. k ranges from 10⁻² m/s (gravel) to 10⁻¹⁰ m/s (clay). Flow nets estimate seepage under dams and into excavations; upward seepage can cause boiling/piping when effective stress drops to zero.
Shear strength, drainage and compaction
Strength follows Mohr–Coulomb with c′ and φ′ (effective, drained) or undrained strength c_u for rapid loading of clays. Triaxial and direct shear tests measure them. Compaction (Proctor test) increases density to the maximum dry density at optimum moisture content — specified for embankments and fills.
Formulas
- Phase relations:
S·e = w·G_s, n = e/(1 + e) - Bulk unit weight:
γ = (G_s + S e) γ_w / (1 + e) - Effective stress:
σ′ = σ − u - Darcy's law:
q = k · i · A, i = Δh/L - Mohr–Coulomb:
τ_f = c′ + σ′ tan φ′
Worked example: Phase relationships
Given: G_s = 2.7, e = 0.7, w = 20 %
Find: S, γ, γ_d.
- S = wG_s/e = 0.54/0.7 = 77 %
- γ = (2.7 + 0.54) × 9.81/1.7 = 18.7 kN/m³
- γ_d = 2.7 × 9.81/1.7 = 15.6 kN/m³
Answer: S = 77 %, γ = 18.7, γ_d = 15.6 kN/m³
Worked example: Effective stress
Given: γ = 18 kN/m³ above WT at 2 m; γ_sat = 20 below; Depth 5 m
Find: σ, u, σ′.
- σ = 18 × 2 + 20 × 3 = 96 kPa
- u = 9.81 × 3 = 29.4 kPa
- σ′ = 66.6 kPa
Answer: σ′ ≈ 66.6 kPa
Common mistakes
- Wrong: Using total stress for strength of drained soils. — Right: Use effective stress σ′ = σ − u with c′, φ′.
- Wrong: Using bulk unit weight below the water table for effective stress. — Right: Use submerged unit weight γ′ = γ_sat − γ_w.
Applications
- Foundations & earthworks: Every bearing, settlement and embankment calculation uses these properties.
- Dewatering & excavations: Seepage and effective stress govern base heave and stability.
- Dams & levees: Seepage control, filters and piping prevention.
Key takeaways
- Soil = solids + water + air; use phase relations.
- σ′ = σ − u controls behaviour.
- Darcy: q = kiA.
- τ_f = c′ + σ′ tan φ′.
Going further
- Critical state soil mechanics: Unifies strength and volume change: soils deform to a critical void ratio under continued shear.
- Unsaturated soils: Matric suction adds apparent cohesion — lost when soils wet up (collapse, landslides).
- In-situ testing: SPT, CPT and vane tests estimate strength and stiffness without sampling.