Geotechnical engineering Study Guide

📖 Core Concepts Geotechnical engineering – Civil‑engineering discipline that studies the behavior of soils and rocks for design and construction. Effective stress – Stress carried by the soil skeleton: $\sigma' = \sigma - u$ (total stress $\sigma$ minus pore‑water pressure $u$). Shear strength (Mohr‑Coulomb) – $\tau = c + \sigma' \tan \phi$; $c$ = cohesion, $\phi$ = internal friction angle. Darcy’s law – $q = k i A$; $q$ = discharge, $k$ = permeability, $i$ = hydraulic gradient, $A$ = flow area. Earth‑pressure theories – Coulomb (inclined slip plane, frictional resistance) vs. Rankine (vertical/horizontal stress, assumes no wall friction). Bearing capacity – Maximum pressure a foundation can transmit without shear failure; depends on $c$, $\phi$, $\sigma'$, and foundation geometry. Settlement – Vertical movement of a foundation caused by soil compression (elastic, consolidation, or immediate). Ground improvement – Techniques (vibro‑compaction, dynamic compaction, grouting, geosynthetics) that increase density, strength, or stiffness. Geosynthetics functions – Drainage, filtration, reinforcement, separation, containment. Seismic geotechnics – Evaluation of soil response to earthquakes (liquefaction, amplification) using shear‑wave velocity profiles. Observational method – Construction‑stage monitoring that permits design changes based on real‑time performance data. --- 📌 Must Remember Effective stress equation: $\sigma' = \sigma - u$ (always subtract pore pressure). Mohr‑Coulomb shear strength: $\tau = c + \sigma' \tan \phi$. Darcy’s law: $q = k i A$ (linear flow in low‑velocity, fully saturated conditions). Coulomb vs. Rankine earth pressure: Coulomb accounts for wall friction & sloping failure plane; Rankine assumes smooth wall & planar failure. Key design steps: (1) Estimate loads → (2) Obtain soil parameters (investigation) → (3) Check bearing capacity & settlement → (4) Choose foundation type. Ground‑improvement selection: Use densification (vibro‑compaction) for loose sands, grouting for cohesionless or soft clays, geosynthetics for reinforcement/filtration. Liquefaction potential: High when $S{PT}$ (standard penetration) < 15 m, $Vs$ < 150 m/s, and cyclic stress ratio exceeds cyclic strength. --- 🔄 Key Processes Geotechnical Investigation Desk study → Site reconnaissance → Subsurface exploration (drilling, test pits). Retrieve disturbed & undisturbed samples → Laboratory tests (grain‑size, Atterberg limits, permeability, triaxial/shear). Optional geophysical surveys (SEIS, GPR) → Compile soil profile & property database. Foundation Design Workflow Determine load magnitude & eccentricity. Select candidate foundation (shallow spread, deep pile, raft). Compute bearing capacity (e.g., Terzaghi’s equation for strip footings). Estimate settlement (elastic + consolidation). Verify against allowable limits → Iterate with different foundation size or improvement method. Slope‑Stability Analysis (limit‑equilibrium) Define potential failure surface. Compute driving shear stress $\taud$ along surface. Compute resisting shear strength $\taur = c + \sigma' \tan \phi$. Factor of safety $FS = \frac{\sum \taur}{\sum \taud}$; design $FS \ge 1.5$ (typical). Ground Improvement Selection Diagnose deficiency (low density, high permeability, low strength). Match deficiency → technique (e.g., loose sand → vibro‑compaction; soft clay → cement grouting). Design parameters (energy, spacing, depth) → Verify improvement via post‑treatment testing. --- 🔍 Key Comparisons Coulomb vs. Rankine Earth Pressure Coulomb: Includes wall friction $\delta$, assumes planar slip surface at angle $\beta$. Rankine: Assumes smooth wall ($\delta = 0$) and vertical/horizontal stress state; simpler but less accurate for rough walls. Geosynthetic Types Geotextile – Filtration & separation. Geogrid – Tensile reinforcement, improves stiffness. Geocell – 3‑D confinement, raises bearing capacity. Soil Improvement Techniques Densification (vibro‑compaction) – Increases density of granular soils; not suitable for clays. Grouting – Increases strength of both granular and cohesive soils by cementing particles; slower and more costly. --- ⚠️ Common Misunderstandings “Effective stress = total stress” – Forgetting pore pressure leads to over‑estimating strength, especially in saturated conditions. “Higher $c$ always means safe foundation” – Cohesion is only part of shear strength; $\sigma'$ and $\phi$ can dominate in deep or heavily loaded cases. “Geosynthetics replace all structural fill” – They supplement but do not eliminate the need for adequate fill compaction. “Liquefaction only occurs in loose sands” – Even dense sands can liquefy under high cyclic stresses; evaluate cyclic stress ratio, not just density. --- 🧠 Mental Models / Intuition Effective stress as “soil’s own weight” – Imagine the soil skeleton bearing the load after water pressure is “pushed out”. Shear strength as “friction + glue” – $c$ is the glue (cohesion), $\sigma' \tan \phi$ is the friction that grows with normal stress. Earth pressure: “Push vs. Pull” – Coulomb’s model accounts for the wall “pulling” on the soil (friction), Rankine treats the wall as a neutral “push”. Ground improvement = “adding bricks to a weak wall” – Reinforcement or densification adds “bricks” (strength/stiffness) to a vulnerable structure. --- 🚩 Exceptions & Edge Cases Very soft clays – Terzaghi’s bearing capacity may underestimate failure; use Meyerhof or Vesic corrections. Highly permeable soils – Darcy’s law becomes non‑linear at high velocities (Forchheimer effect). Slope stability with seepage – Pore‑water pressures reduce $\sigma'$; need seepage analysis (e.g., using the method of slices with pore pressure corrections). Geosynthetics in aggressive chemical environments – May degrade; select chemically resistant polymers. --- 📍 When to Use Which Choose Coulomb earth‑pressure when wall friction and backfill slope are significant. Use Rankine for quick hand calculations on smooth walls with vertical backfill. Select vibro‑compaction for loose, granular deposits > 2 m depth; avoid in silty or clayey soils. Pick cement grouting for soft clays or when increasing both strength and impermeability is required. Apply geogrids when you need tensile reinforcement in a fill (e.g., road base). Employ geotextiles for drainage or to prevent fine‑soil migration through coarse aggregates. --- 👀 Patterns to Recognize “Low $Vs$ + Loose sand + High water table” → Likely liquefaction zone. “$c$ = 0, high $\phi$” → Cohesionless soil (sand/gravel); rely on friction for stability. “Large $u$ (pore pressure) during rapid loading” → Potential for reduced effective stress → check for temporary stability loss. “Disturbed sample → only grain‑size & Atterberg limits reliable” – Use undisturbed samples for strength/permeability tests. --- 🗂️ Exam Traps Confusing total vs. effective stress – A question may give $\sigma$ and $u$ separately; answer must use $\sigma' = \sigma - u$. Mis‑applying Rankine to a rough wall – Distractor will ignore wall friction; correct answer uses Coulomb. Assuming $c$ is always present – Many soils (clean sands) have $c \approx 0$; plugging a non‑zero $c$ yields a wrong shear strength. Selecting grouting for very deep improvements – Grout penetration limits depth; deep improvement is better with piles or deep mixing. Overlooking settlement limits – A design may satisfy bearing capacity but exceed allowable settlement; both must be checked. ---