Geotechnical Engineering
Geotechnical engineering governs how the ground carries load, holds water, and pushes on the structures buried in it. The PE tests it through effective stress, phase (weight-volume) relationships, earth pressure, seepage, consolidation settlement, and bearing capacity. Because soil behavior is unforgiving and site-specific, these fundamentals recur throughout foundations, retaining walls, and slope stability.
Total Stress, Pore Pressure, and Effective Stress
The single most important idea in soil mechanics is Terzaghi's effective-stress principle: σ' = σ - u. Total vertical stress at depth is the sum of each layer's unit weight times its thickness (σ = Σγh). Pore water pressure at depth z_w below the water table is u = γ_w·z_w, with γ_w = 9.81 kN/m^3 (often rounded to 10). Effective stress — the stress actually carried by grain-to-grain contact — controls strength and compression, not total stress. This explains a favorite exam scenario: lowering the water table by dewatering reduces u, which raises σ', which increases strength but also causes settlement. Above the water table, u = 0 (ignoring capillarity) and σ' = σ.
Phase Relationships (Weight-Volume)
Soil is a three-phase mix of solids, water, and air, and a family of ratios connects them. Void ratio e = V_v/V_s; porosity n = V_v/V = e/(1+e); water content w = W_w/W_s; degree of saturation S = V_w/V_v, with S·e = w·G_s as the master identity. Dry unit weight strips out water: γ_d = γ/(1+w). Using specific gravity of solids G_s, γ_d = G_s·γ_w/(1+e) and, for saturated soil, γ_sat = (G_s + e)·γ_w/(1+e). Buoyant (effective) unit weight is γ' = γ_sat - γ_w. These let you march from a lab measurement to any field quantity; the exam typically hands you two of {G_s, e, w, S} and asks for a unit weight.
Lateral Earth Pressure
Retaining structures feel horizontal pressure that depends on wall movement. Rankine's active coefficient (wall moving away from the soil, least pressure) is K_a = tan^2(45 - φ/2); the passive coefficient (wall pushed into the soil, greatest pressure) is K_p = tan^2(45 + φ/2) = 1/K_a. The at-rest state (no movement) uses Jaky's equation K_0 = 1 - sin φ, and heavily overconsolidated clays can have K_0 exceeding 1.0. For a cohesionless backfill of height H, the pressure grows linearly with depth, so the resultant active thrust is P_a = ½·K_a·γ·H^2, acting at H/3 above the base (the centroid of the triangular pressure diagram). Passive resistance is the same form with K_p and is what mobilizes in front of a wall or below a footing.
Seepage, Permeability, and the Quick Condition
Darcy's law governs slow flow through soil: the Darcy (superficial) velocity is v = k·i, where k is hydraulic conductivity and i is the hydraulic gradient (head loss per length). The actual pore or seepage velocity is faster because water squeezes through voids only: v_s = v/n. Coarse soils drain fast — clean gravel has the highest permeability, clay the lowest, differing by many orders of magnitude. A flow net solves two-dimensional seepage: Q = k·H·(N_f/N_d), where N_f is the number of flow channels and N_d the number of equipotential drops. When upward seepage reduces effective stress to zero, sand loses all strength and boils — the quick (piping) condition. It occurs at the critical hydraulic gradient i_c = (G_s - 1)/(1 + e) = γ'/γ_w, typically near 1.0.
Consolidation and Settlement
Saturated clay settles slowly as pore water is squeezed out and load transfers to the soil skeleton — this is primary consolidation. Primary settlement of a normally consolidated clay is S = (C_c·H/(1+e_0))·log(σ'_f/σ'_0), where C_c is the compression index. Whether a clay is normally consolidated (current stress equals its maximum past stress) or overconsolidated (it has felt more before) determines which index and formula apply; overconsolidated clay compresses far less until the load exceeds its preconsolidation pressure. The rate of settlement uses the time factor T_v = c_v·t/H_dr^2, where H_dr is the longest drainage path (half the layer for double drainage). A crucial consequence: doubling the drainage path quadruples the time to reach a given percent consolidation, because time scales with H_dr squared (T_v = 0.197 at 50%). Secondary compression (creep) continues afterward at essentially constant effective stress.
Shear Strength, Bearing Capacity, and Foundations
Soil strength follows Mohr-Coulomb: τ = c + σ'·tan φ. Clean sand (c = 0) has τ = σ'·tan φ; saturated clay under undrained loading is analyzed as φ = 0 with τ = c_u, a constant. Terzaghi's bearing capacity for a strip footing is q_ult = c·N_c + q·N_q + ½·γ·B·N_γ, where the bearing factors N_c, N_q, N_γ grow with φ (for φ = 0, N_c = 5.14). Allowable bearing is q_ult divided by a factor of safety, typically 2.5–3. When shallow footings would be too large or the near-surface soil is weak, engineers switch to deep (pile) foundations, whose capacity is the sum of skin friction and end bearing: Q_ult = Q_s + Q_p. For a pile in clay the skin friction uses the alpha method, Q_s = α·c_u·(surface area). Classification (USCS, Atterberg limits, grain-size Cu and Cc) and the SPT N-value — which correlates with the relative density or consistency of the soil — feed all of these design steps.
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