Geotechnical Engineering
Geotechnical Engineering tests effective stress, seepage, consolidation settlement, shear strength, bearing capacity, slope stability, and earth-retaining structures. Most exam errors come from using total stress where drained effective stress governs, or from misplacing the water table in a profile.
Effective stress and strength
Effective vertical stress is σ′ = σ − u. Above the water table, use bulk or dry unit weight; below it, use saturated unit weight and full hydrostatic pressure. Drained shear strength is τ = c′ + σ′ tan φ′. For a normally consolidated clay, consolidation settlement is Sc = [Cc H / (1 + e0)] log[(σ′0 + Δσ) / σ′0].
Bearing and stability
Terzaghi bearing capacity combines cohesion, surcharge, and self-weight terms with φ-dependent factors. Slope stability compares resisting shear strength to equilibrium shear stress; the factor of safety must exceed the required value. Retaining-wall design must consider active and passive earth pressures, water pressure, surcharge, and drainage.
Worked example
A deposit has 10 ft of sand with γ = 120 pcf above the water table and 10 ft of saturated sand with γsat = 125 pcf below it. At 20 ft depth: σv = 10(120) + 10(125) = 2,450 psf. Pore pressure u = 10(62.4) = 624 psf. Effective stress σ′v = 2,450 − 624 = 1,826 psf. If an analyst incorrectly uses γsat above the water table, the result is too high and unconservative for settlement and strength checks.
Traps
Use effective stress in drained strength and consolidation, not total stress. Do not apply hydrostatic pressure above the water table unless capillary effects are explicitly modeled. Watch unit conversions between pcf, psf, and ksf. In bearing-capacity problems, confirm whether the water table is above, at, or below the footing base.
Key points
- Effective stress equals total stress minus pore pressure.
- Use saturated unit weight only below the water table.
- Drained strength depends on effective normal stress.
- Consolidation settlement uses the compression index and initial void ratio.
- Water pressure and drainage control retaining-wall design.