Overview
This lecture reviews core concepts and problem-solving techniques in geotechnical engineering relevant for the FE Civil exam, focusing on soil classification, phase relations, lab/field tests, effective stress, bearing capacity, and slope stability.
Soil Classification & Index Properties
- Soil classification uses systems like USCS and AASHTO, based on grain size and plasticity.
- Sieve size #4 separates gravel/sand; #200 separates sands/silts/clays (fines).
- Well-graded soils have a wide range of particle sizes; poorly/uniformly graded soils mostly one size.
- Uniformity coefficient (Cu = D60/D10) and coefficient of curvature (Cc = D30²/(D10×D60)) help classify grading.
- Plasticity Index (PI = Liquid Limit - Plastic Limit) indicates soil's plasticity.
- For fine-grained soils, location above/below the "A-line" in the plasticity chart helps distinguish between clays and silts.
Phase Relations & Soil Properties
- Soils consist of three phases: solids, water, and air.
- Water content = (weight of water / weight of solids) × 100%.
- Specific gravity (Gs) = (mass of solids / volume of solids) / (density of water).
- Degree of saturation (S) = (volume of water / volume of voids) × 100% or S = w × Gs / e.
- Use phase diagrams to organize and solve for unknowns in soil problems.
Lab & Field Testing
- Proctor test (standard or modified) determines maximum dry density of soil.
- Nuclear density gauge and sand cone are used in the field to measure in-place density.
- Sieve analysis provides particle size distribution for classification.
Compaction & Relative Density
- Relative compaction = (field dry unit weight / lab maximum dry unit weight) × 100%.
- Relative density (Dr) formula: Dr = [(γ_field - γ_min) / (γ_max - γ_min)] × (γ_max / γ_field).
- Specifications typically require certain levels of relative compaction for construction acceptance.
Effective Stress & Shear Strength
- Effective vertical stress: σ' = (total stress) – (pore water pressure).
- For soils below the water table, subtract water’s unit weight from total stress for effective stress.
- Shear strength in sands (non-cohesive): τ = σ_n × tan(ϕ); in clays (cohesive): τ = c + σ_n × tan(ϕ).
- Triaxial test uses principal stresses to determine friction angle (ϕ): sinϕ = radius / average normal stress in Mohr’s circle.
Retaining Walls & Bearing Capacity
- Lateral earth pressure: P_a = ½ k_a γ H² (ka is the active earth pressure coefficient).
- Surcharge adds a uniform horizontal pressure to the wall.
- Passive earth pressure (kp) provides resistance; kp >> ka for typical soils.
- Bearing pressure under footings: check with both vertical load and overturning moment (eccentricity).
- Use q_toe and q_heel to confirm entire footing stays in compression; compare to allowable bearing capacity.
Settlement & Consolidation
- Compression index (Cc) and recompression index (Cr) estimate expected settlement from loading.
- Cc ≈ 0.009 × (LL–10); Cr ≈ Cc/6.
- Settlement calculation may require partitioning between recompression and virgin compression depending on preconsolidation pressure.
Slope Stability
- Factor of safety = (resisting forces) / (driving forces).
- Mobilizing force is W × sin(α); resisting force includes normal force × tan(ϕ) plus cohesion × length.
- A factor of safety above 1 indicates stability.
Soil Stabilization & General Concepts
- Soil stabilization methods include mechanical compaction, chemical admixtures, and geotextiles.
- Clearing and grubbing increase erosion risk and are not stabilization methods.
Key Terms & Definitions
- USCS — Unified Soil Classification System used for soil identification.
- Uniformity Coefficient (Cu) — D60/D10, indicates grading range.
- Plasticity Index (PI) — Difference between liquid and plastic limit.
- Proctor Test — Lab test to determine soil’s maximum dry density.
- Effective Stress (σ') — Stress carried by soil skeleton: total stress minus pore water pressure.
- Bearing Capacity — Maximum stress soil can support under a foundation without failure.
Action Items / Next Steps
- Review index property definitions and soil classification charts (especially USCS/AASHTO).
- Practice drawing and using phase diagrams for phase relation problems.
- Memorize key formulas: Cu, Cc, PI, effective stress, compaction, and factor of safety.
- Solve additional practice problems, especially in settlement/consolidation and slope stability.
- Update notes with any corrections or new examples as you review.