5.2 Geotechnical Engineering

Soil Classification and Index Properties

Geotechnical Engineering ties Structural for the heaviest weighting (about 9 to 14 questions). The first skill is classifying soil with the Unified Soil Classification System (USCS).

Coarse-grained soils (more than 50 percent retained on the No. 200 sieve) use the first letter for the dominant particle and W/P for gradation. Fine-grained soils use the plasticity chart with the Atterberg limits: liquid limit (LL), plastic limit (PL), and plasticity index PI = LL − PL.

Phase Relationships

Soil is a three-phase mixture of solids, water, and air. Memorize:

• Void ratio: e = V_v / V_s
• Porosity: n = V_v / V_total = e / (1 + e)
• Degree of saturation: S = V_w / V_v
• Moisture content: w = W_w / W_s

The master relationship Se = w·G_s (G_s = specific gravity of solids) links saturation, moisture, and void ratio and appears constantly in FE problems.

Effective Stress

Terzaghi's effective-stress principle governs soil behavior:

σ' = σ − u

where σ' is effective stress, σ is total vertical stress (sum of γ·z layer by layer), and u is pore water pressure (= γ_w · h_w below the water table). Effective stress — not total stress — controls strength and settlement.

Consolidation and Settlement

For a normally consolidated clay, primary consolidation settlement is:

S_c = (C_c · H) / (1 + e_0) · log( (σ'_0 + Δσ') / σ'_0 )

where C_c is the compression index, H is the clay layer thickness, e_0 is the initial void ratio, σ'_0 is the initial effective stress, and Δσ' is the stress increase. Overconsolidated clays use the recompression index C_r below the preconsolidation pressure.

Shear Strength

The Mohr-Coulomb failure criterion: τ_f = c + σ'·tan φ, where c is cohesion and φ is the effective friction angle. Clean sands are cohesionless (c ≈ 0); saturated clays in undrained loading use τ_f = s_u (undrained shear strength, φ = 0 analysis).

Bearing Capacity and Lateral Earth Pressure

Terzaghi ultimate bearing capacity of a strip footing:

q_ult = c·N_c + q·N_q + 0.5·γ·B·N_γ

N_c, N_q, N_γ are bearing-capacity factors that depend only on φ (tabulated in the Reference Handbook). Allowable bearing = q_ult / FS, with FS typically 3.

Rankine lateral earth pressure coefficients for level backfill:

• Active: K_a = (1 − sin φ) / (1 + sin φ) = tan²(45° − φ/2)
• Passive: K_p = (1 + sin φ) / (1 − sin φ) = tan²(45° + φ/2)
• At-rest: K_0 = 1 − sin φ

Slope Stability Basics

For an infinite slope or simple circular failure, the factor of safety is the ratio of resisting strength to driving shear. For a dry cohesionless infinite slope, FS = tan φ / tan β, where β is the slope angle — failure is independent of slope height. The ordinary method of slices and Bishop's simplified method extend this to layered slopes; on the FE you only need the FS concept and the cohesionless shortcut.

Reference Handbook Tip

USCS and the plasticity chart are under 'Soil Classification'; phase relations and Se = wG_s under 'Soil Properties'; bearing factors and Rankine coefficients under 'Foundations / Earth Retaining Structures.'