Geotechnical Engineering for the FE Exam
Geotechnical engineering applies soil mechanics principles to the design and analysis of foundations, retaining walls, slopes, and earthwork. It is a significant portion of the FE Civil exam and requires understanding both soil properties and how they affect engineering design.
Soil Properties and Classification
Phase Relationships
Soil is a three-phase material consisting of solids, water, and air. Key relationships include:
- Void ratio (e): Volume of voids divided by volume of solids. e = V_v / V_s
- Porosity (n): Volume of voids divided by total volume. n = V_v / V_total = e / (1 + e)
- Degree of saturation (S): Volume of water divided by volume of voids. S = V_w / V_v. Ranges from 0 (dry) to 1 (saturated).
- Water content (w): Weight of water divided by weight of solids. w = W_w / W_s
- Unit weight: Total weight divided by total volume. gamma = W / V
- Specific gravity of solids (G_s): Ratio of the density of soil solids to the density of water. Typically 2.65 to 2.70 for most minerals.
These quantities are interrelated. The reference handbook contains the formulas connecting them. Practice converting between different phase properties.
Soil Classification Systems
- Unified Soil Classification System (USCS): Classifies soils based on grain size distribution and Atterberg limits. Coarse-grained soils are classified by grain size (gravel vs sand) and gradation. Fine-grained soils are classified by plasticity (CL, CH, ML, MH, OL, OH).
- AASHTO Classification: Used primarily in transportation engineering. Groups soils from A-1 (best for subgrade) through A-7 (worst for subgrade).
Atterberg Limits
Atterberg limits define the boundaries between different consistency states of fine-grained soils:
- Liquid limit (LL): Water content at which soil transitions from plastic to liquid behavior.
- Plastic limit (PL): Water content at which soil transitions from semisolid to plastic behavior.
- Plasticity index (PI): PI = LL - PL. Indicates the range of water content over which the soil behaves plastically.
Effective Stress
The effective stress principle is the most fundamental concept in geotechnical engineering:
sigma' = sigma - u
Where sigma' is effective stress, sigma is total stress, and u is pore water pressure. Effective stress controls soil behavior: strength, compressibility, and shear resistance all depend on effective stress, not total stress.
To calculate effective stress at a point below the ground surface:
- Calculate total vertical stress by summing the weight of all soil layers above
- Calculate pore water pressure (u = gamma_w * h_w, where h_w is the height of water above the point)
- Subtract pore water pressure from total stress
Permeability and Seepage
Permeability measures how easily water flows through soil. Darcy's law governs seepage:
q = k * i * A
Where q is the flow rate, k is the hydraulic conductivity (permeability), i is the hydraulic gradient, and A is the cross-sectional area.
The hydraulic gradient is: i = delta_h / L, where delta_h is the head loss and L is the flow path length.
Consolidation
Consolidation is the time-dependent compression of saturated fine-grained soils due to the expulsion of pore water under load. Key concepts:
- Primary consolidation: Settlement caused by pore water pressure dissipation.
- Compression index (C_c): Slope of the virgin compression curve on an e-log(sigma') plot.
- Preconsolidation pressure: The maximum past effective stress the soil has experienced.
- Normally consolidated (NC): Current effective stress equals the preconsolidation pressure.
- Overconsolidated (OC): Current effective stress is less than the preconsolidation pressure.
- Time rate: The time factor T_v relates time, drainage distance, and coefficient of consolidation.
Shear Strength
The Mohr-Coulomb failure criterion defines soil shear strength:
tau_f = c' + sigma' * tan(phi')
Where c' is the effective cohesion, sigma' is the effective normal stress, and phi' is the effective friction angle.
- Cohesionless soils (sands): c' is approximately 0. Strength depends entirely on friction angle and effective stress.
- Cohesive soils (clays): Both c' and phi' contribute to strength. Undrained shear strength (s_u) is used for rapid loading conditions.
Bearing Capacity
Bearing capacity is the maximum pressure a foundation can exert on soil without causing failure. Terzaghi's bearing capacity equation (for a strip footing) is:
q_u = c * N_c + q * N_q + 0.5 * gamma * B * N_gamma
Where N_c, N_q, and N_gamma are bearing capacity factors that depend on the friction angle. The reference handbook provides these factors.
Lateral Earth Pressure
Lateral earth pressure is the horizontal pressure exerted by soil against a retaining structure:
- At-rest pressure: K_0 = 1 - sin(phi'). For walls that do not move.
- Active pressure: K_a = tan^2(45 - phi'/2). For walls moving away from the soil.
- Passive pressure: K_p = tan^2(45 + phi'/2). For walls being pushed into the soil.
Geotechnical engineering requires comfort with both concepts and calculations. Practice converting between soil phase properties, calculating effective stress profiles, and applying bearing capacity and earth pressure formulas until these become routine.