Consolidation settlement

clay settlementtime factorprimary consolidationhow long will it settle

How far a normally consolidated clay settles under new load, and the time factor that governs how many years it takes.

Consolidation Settlement of Normally Consolidated Clay

S_c = \frac{C_c\,H}{1 + e_0}\log_{10}\!\frac{\sigma'_f}{\sigma'_0}

Primary consolidation settlement of a normally consolidated clay layer from its compression index, thickness and the stress increase applied.

Time Factor for Consolidation

T_v = \frac{c_v\,t}{H_{dr}^{2}}

Dimensionless time factor of Terzaghi consolidation theory, with the coefficient of consolidation entered in m²/s and the longest drainage path.

Time Factor from Degree of Consolidation (U ≤ 60%)

T_v = \frac{\pi}{4}\left(\frac{U}{100}\right)^{2}

Terzaghi's parabolic approximation relating the time factor to the average degree of consolidation, valid for U of 60 percent or less.

How they fit together

Load a saturated clay and it does not settle at once. The water has to leave, and clay is close to impermeable, so settlement a sand finishes in hours can take a clay decades. The magnitude comes from the compression index and the change in effective stress; the timing comes from the coefficient of consolidation and, crucially, the square of the drainage path.

That square is where estimates go wrong. Double the layer thickness and settlement takes four times as long — and the drainage path is the full thickness if water can only escape upward, but half of it if there is a permeable layer beneath. Get that boundary wrong and the answer is out by a factor of four before any soil property is even questioned.