Soil Mechanics: Bearing Capacity, Shear Strength
Terzaghi's equation, compaction vs consolidation, and shear strength parameters — the fundamentals of every foundation interview.
Key formulas
qult = c·Nc + γ·Df·Nq + 0.5·γ·B·Nγ
Terzaghi ultimate bearing capacity (strip): Shape factors convert it to square/circular footings; Nc, Nq, Nγ are functions of φ.
qsafe = (qult − γ·Df) / FOS + γ·Df, FOS ≈ 2.5–3
Safe bearing capacity: Net ultimate capacity divided by factor of safety, plus restoring the overburden.
τ = c′ + σ′·tanφ′
Mohr-Coulomb: Always use effective stress for drained/long-term problems; total stress for quick undrained ones.
Cheat sheet
- ▸Terzaghi bearing capacity (strip footing): qult = c·Nc + q·Nq + 0.5·γ·B·Nγ — cohesion, surcharge and width terms; local shear failure reduces N values.
- ▸Failure modes: general shear (dense/ stiff soil), local shear (loose sand, soft clay), punching (very compressible soil under footing).
- ▸Compaction is the expulsion of AIR (immediate, by rollers — OMC from Proctor test); consolidation is the slow expulsion of WATER under sustained load (time-dependent, Terzaghi 1-D theory).
- ▸Shear strength (Mohr-Coulomb): τ = c + σ·tanφ. UU test (quick, total stress, undrained φ ≈ 0 for saturated clay), CU, CD (drained, effective stress parameters c′, φ′).
- ▸Effective stress σ′ = σ − u controls strength and settlement; pore water pressure u changes without changing total stress (e.g. rapid loading or rain).
- ▸Standard Proctor: OMC and maximum dry density define field compaction targets; field density checked by sand-cone/core-cutter methods.
Compaction vs Consolidation
| Aspect | Compaction | Consolidation |
|---|---|---|
| What is expelled | Air | Water |
| Time scale | Immediate (mechanical) | Slow (days–years) |
| Trigger | Rollers, rammers, vibration | Sustained static load |
| Saturation change | Yes (partial) | No (soil stays saturated) |
| Test / theory | Proctor test (OMC, MDD) | Terzaghi 1-D theory, Cv |
| Reversibility | Partially reversible (bulking) | Not reversible in engineering time |
Visual
General shear failure beneath a strip footing:
q (surcharge)
═════╧═════ footing B
______/\________/\________ ground heave
│ shear zones (Wedge I, radial II, Rankine III)
▼ failure surfaces reach the surface for general shearTop 4 campus interview questions
MCQ mastery quiz
1. In Terzaghi's equation, the term 0.5·γ·B·Nγ arises from…
2. Consolidation of a clay layer involves the expulsion of…
3. For a saturated clay under rapid (undrained) loading, shear strength is best taken as…
4. Quicksand condition occurs when…