The Slow Squeeze
When a building or embankment loads saturated clay, the soil doesn't compress instantly. Water trapped in microscopic pores initially carries the entire load as excess pore pressure. Over time — weeks, months, or decades — this water slowly squeezes out through the clay's tortuous pore network. As pore pressure dissipates, the effective stress on the soil skeleton increases and the clay compresses. This process, consolidation, is why buildings on clay can continue settling long after construction ends.
Terzaghi's One-Dimensional Theory
Terzaghi's 1925 consolidation theory models pore pressure dissipation as a diffusion process, governed by the coefficient of consolidation c_v. The dimensionless time factor T_v = c_v·t/H_dr² unifies all consolidation problems: regardless of layer thickness or soil type, the degree of consolidation U depends only on T_v. The simulation plots the isochrones — curves showing pore pressure distribution at different times — as water progressively drains from the clay layer.
Settlement Magnitude
Total primary settlement depends on the compression index C_c, initial void ratio e₀, layer thickness H, and the stress increment Δσ. The logarithmic relationship S = C_cH·log₁₀((σ₀'+Δσ)/σ₀')/(1+e₀) means that doubling the load doesn't double settlement — the response is fundamentally nonlinear. Normally consolidated clays (never previously loaded beyond current stress) settle much more than overconsolidated clays, which have a stiffer initial response governed by the recompression index C_r.
Drainage & Time
Consolidation time scales with the square of the drainage path length H_dr. For double drainage (permeable layers above and below), H_dr = H/2; for single drainage, H_dr = H. This quadratic dependence is why a 1 m laboratory specimen consolidates in minutes while a 10 m field layer takes years. Vertical drains exploit this relationship by reducing the drainage path from the layer thickness to half the drain spacing, potentially accelerating consolidation by orders of magnitude.