The term coefficient of consolidation C_v used in equation is adopted to indicate combined effects of permeability and compressibility of soil on rate of volume change.

The expansion index is a fairly straight line on semi log plot. The expansion index is a measure of volume increase due to removal of pressure. The expansion index is also a dimensionless quantity like compression index.

The abscissa at U=90% is roughly equal to 1.15 times abscissa at U=60%. It is represented in diagram.
b/a=1.15.

Since water occupies voids between soil particles and when force is applied, water is squeezed out and re is decrease in volume of soil. Therefore, decrease in volume of soil is equal to volume of water squeeze out.

The average drainage path for pressure increment is calculated from formula of,
\(d=\frac{1}{2} \left[\frac{H_{?}-H_f}{2}\right] \)
where, H₁=initial height of specimen under initial load
and H_f=final height of specimen under final load.

A soil that has never experienced a vertical effective stress that was greater than its present vertical effective stress is called a normally consolidated (NC) soil.

Since we know,
?=tan^-1(y/x) ?????-(1)
? differentiating (1) with respect to x, we get,
\(\frac{??}{?x}=\frac{-sin?}{r}.\)

Since height H_S of solids of specimen is calculated from expression,
\(H_s=\frac{W_d}{GA?_w}\) and dry weight in relation to dry mass is given by,
\(W_d=\frac{M_d}{?_w}.\) Therefore, The height H_s of solids of specimen with respect to weight of dried specimen is,
\(H_s=\frac{W_d}{GA}.\)

The coefficient of consolidation is given by formula,
\(C_v=\frac{k}{m_v?_v}\). Therefore, on rearranging equation,
? k=C_v m_v ?_v.

In three dimensional consolidation of sand drain, having radial symmetry, governing consolidation equation is,
\(\frac{?\overline{u}}{?t}=C_{vr} (\frac{?\overline{u}}{?r^2}+\frac{1}{r}\frac{?\overline{u}}{?r})+C_{vz}\frac{?^2 \overline{u}}{?z^2}\), in this one dimensional flow part of equation is,
\(\frac{?\overline{u}}{?t}=C_{vr} \frac{?\overline{u}}{?r^2}\).