Time Factor for Consolidation

Terzaghi's one-dimensional consolidation equation is a diffusion equation, and like every diffusion problem it collapses onto a single dimensionless group: time multiplied by a diffusivity and divided by the square of the distance the water has to travel. Two clay layers with the same $T_v$ are at the same stage of consolidation regardless of their absolute size, which is exactly what lets a 20 mm oedometer specimen predict a 6 m layer. A clay with $c_v$ = 3×10⁻⁷ m²/s draining 3 m reaches $T_v$ = 3×10⁻⁷ × 8.64×10⁶ s ÷ 9 = 0.288 after 100 days.

The trap is $H_{dr}$, and it is a factor-of-four trap because it is squared. $H_{dr}$ is the longest path a water molecule must travel to escape, so a clay layer sandwiched between two sand layers drains both ways and $H_{dr}$ is half the layer thickness; a clay on bedrock drains one way and $H_{dr}$ is the full thickness. Get it wrong and your predicted time is out by four. This is also the whole logic of wick drains and sand drains: you cannot change $c_v$, but installing vertical drains at 1.5 m centres turns a 10 m vertical path into a 0.75 m horizontal one and cuts the consolidation time by a factor of nearly two hundred.