Given, single drainage for both sample and for field layer,
t₁=20 min
d₁=24 mm= 2.4 cm
d₂ =4 m = 400cm
Since, for same degree of consolidation of 50%, T_v is same,
\(t?\frac{d^2}{C_r}\)
Therefore, \(\frac{t_2}{t_1} =(\frac{d_2}{d_1} )^2\)
So, \(t_2=t_1 (\frac{d_2}{d_1})^2=20(\frac{400}{2.4})^2=386 \,days.\)

In soil mechanics, isochrones represent water levels in piezometric tubes at same time. The slope of isochrones at any point at a given time indicates rate of change of pore pressure with depth.

The coefficient of consolidation is calculated from equation of,
\(c_v=\frac{(T_v)_{90} d^2}{t_{90}}, \)
where, c_v=coefficient of consolidation
(T_v)₉₀=time factor corresponding to 90% consolidation
t₉₀=elapsed time for 90% consolidation
d=average drainage path for pressure increment.

The coefficient of consolidation is given by,
\(C_v=\frac{k}{m_v ?_w}\)
where, k=coefficient of permeability
m_v=coefficient of volume change
?_w=unit weight of water.

From calculations consideration of a consolidation test data, change in thickness can be both positive and negative. The negative sign denotes decrease height due to loading and positive sign denotes increase in height due to unloading of specimen.

In three dimensional consolidation of sand drain, for case of radial symmetry,
C_vx=C_vy =C_vr
? governing consolidation equation is,
\(\frac{?\overline{u}}{?t}=C_{vr} (\frac{\overline{u}}{?r^2}+\frac{1}{r}\frac{?\overline{u}}{?r})+C_{vz}\frac{?^2 \overline{u}}{?z^2}.\)

The consolidation test data are used to find:

• voids ratio and coefficient of volume change
• coefficient of consolidation
• coefficient of permeability.

The consolidation settlement ??_f of element of thickness dz is calculated under average effective pressure increment ???. Therefore, final settlement is integration of ??_f.
? \(?_f=?_0^Hm_v ??? dz.\)

Prior to Barron?s work, Rendulic in 1935 solved differential equation of consolidation by radial flow to a well. Skempton is known for his pore pressure parameters A and B.

The compression resulting from a long term static load and consequent escape of pore water is consolidation, as according to Terzaghi, every process involving a decrease in water content of a saturated soil without replacement of water by air is process of consolidation.