Square root of time method for cv

Taylor's square root of time method finds $c_v$ from a consolidation test for a load increment, using the observed dial reading against $\sqrt t$.

 dial                  
 reading |*.
         |  *.          straight line
    d0   |-----*.______  (extended to √t axis → d0 corrected)
         |       \ *  .
         |  line OB  \   *  *  *
         |  at 1.15x  C
         +-----------|--------------> √t
                    √t90

Procedure

1. Plot the dial gauge reading (settlement) $d$ on the y-axis against the square root of time $\sqrt t$ on the x-axis.
2. The initial part of the curve is a straight line (theoretical curve up to $U = 60\%$). Extend it back to cut the y-axis at the corrected zero reading $d_0$ (this corrects for initial compression).
3. Draw a second line from $d_0$ with abscissa 1.15 times the first (the slope of the line is 1/1.15 of that of the first line).
4. The intersection of this second line with the experimental curve gives $\sqrt{t_{90}}$, for 90% consolidation.
5. Compute the coefficient of consolidation, using $T_v = 0.848$ at $U = 90\%$:

$$c_v = \frac{0.848\,H_{dr}^2}{t_{90}}$$

where $H_{dr}$ is the average drainage path during the load increment (half the average specimen thickness for double drainage).