Time Factor Tv and Drainage Path

T_{v} = \frac{C _{v} t}{H _{d r}^{2}} U \approx \frac{π T _{v}}{4} (U < 0.6)

Cv is the coefficient of vertical consolidation. Hdr is the longest drainage path: H/2 if double-drained, H if single-drained. Tv ≈ 0.197 for U=50% (Handbook). Time to a given U scales with Hdr².

$T_{v}$: Time factor
$C_{v}$ (m²/yr): Coefficient of consolidation
$H_{d r}$ (m): Drainage path

Step-by-step solved example

Cv=0.020 m²/yr, clay H=4.0 m double-drained, t=3.0 yr. Tv and approximate U?

Drainage path Hdr: single- or double-drained clay layer.

1. Hdr
Double-drained: Hdr=2.0 m.
2. Tv
Tv=0.020×3 / 4 = 0.015. U≈√(π×0.015/4)=√0.0118=0.11 (11%).
$T_{v} = 0.015$

Answer: Tv=0.015, U≈11%

10 practice questions

0/10 correct

1.Double drainage Hdr=

2.To quadruple time for the same U you would

3.Tv for U=50% is about

4.The √(π Tv/4) approx is for

5.Single-drained clay twice as thick takes

6.U is

7.Sand drains / wicks shorten Hdr by

8.Cv has units

9.A laboratory U vs log t plot is used to find

10.If Tv=0.197 and Hdr=1 m, t=