Expert-level geotechnical engineering covering soil classification, shear strength, consolidation, foundation design, slope stability, and retaining structures.
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USCS: unified soil classification system, grain size and plasticity-based. Grain size: gravel, sand, silt, clay based on particle size distribution. Atterberg limits: liquid limit, plastic limit, plasticity index for fine soils. Relative density: measure of sand compactness, Dr = e_max minus e over e_max minus e_min. Compaction: Proctor test determines optimal moisture content for maximum dry density.
Mohr-Coulomb: tau_f = c plus sigma prime tan phi, cohesion plus friction. Drained vs undrained: sand drains fast, clay drains slow under load. Effective stress: sigma prime = sigma minus u, pore pressure reduces effective stress. Triaxial test: measure shear strength at different confining pressures. SPT and CPT: in-situ tests correlate to strength and stiffness parameters.
Primary consolidation: volume change from pore pressure dissipation in clay. Terzaghi theory: cv dU over dz2 = dU over dt, diffusion of excess pore pressure. Settlement calculation: delta = Cc times H over 1 plus e0 times log sigma_f over sigma_0. Time rate: T_v = cv times t over H2, use time factor chart. Secondary compression: creep settlement after primary consolidation complete.
Bearing capacity: Terzaghi and Meyerhof equations for shallow foundations. Net bearing pressure: gross minus overburden pressure. Pile capacity: end bearing plus skin friction, static and dynamic methods. Group effects: pile group efficiency, settlement of pile groups. Mat foundation: uniform pressure distribution, used on weak or variable soils.
| Pitfall | Fix |
|---|---|
| Ignoring differential settlement | Check settlement variation across structure footprint |
| Wrong drainage condition for clay | Use undrained strength for short term, drained for long term |
| Underestimating secondary compression | Account for creep in organic soils and soft clays |
| Missing groundwater in slope stability | Pore pressure dramatically reduces factor of safety |
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Expert-level abstract algebra knowledge. Use when working with groups, rings, fields, modules, Galois theory, representation theory, or algebraic structures. Also use when the user mentions 'group', 'ring', 'field', 'homomorphism', 'isomorphism', 'normal subgroup', 'quotient group', 'Sylow theorem', 'Galois theory', 'polynomial ring', 'ideal', 'module', 'vector space', or 'representation theory'.
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Expert-level acoustics knowledge. Use when working with sound waves, acoustic propagation, resonance, standing waves, Doppler effect, room acoustics, ultrasound, noise control, musical acoustics, or architectural acoustics. Also use when the user mentions 'sound wave', 'decibel', 'frequency', 'resonance', 'standing wave', 'Doppler effect', 'acoustic impedance', 'reverberation', 'ultrasound', 'noise control', 'harmonics', or 'sound intensity'.
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Expert-level aerodynamics covering subsonic and supersonic flow, lift and drag, airfoil theory, boundary layers, compressible flow, and CFD methods.
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Expert-level air quality engineering covering pollutant sources, atmospheric dispersion, air quality standards, emission controls, and air quality modeling.
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Expert-level aircraft structures covering structural design philosophy, wing and fuselage analysis, fatigue and damage tolerance, composite structures, and certification.
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Expert-level algorithms and complexity theory covering sorting, searching, graph algorithms, dynamic programming, greedy algorithms, NP-completeness, and algorithm design paradigms.
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