Geotechnical Engineering

DHARM

COMPRESSIBILITY AND CONSOLIDATION OF SOILS 231

7.6 Graphical Presentation of Consolidation Relationships

One-dimensional consolidation, subject to the condition of constant initial hydrostatic excess
pressure, is the type of consolidation that is of major interest. It applies in the laboratory
consolidation tests and is usually assumed, although it generally is not strictly applicable, in
the cases of consolidation in the field. Equations 7.27 and 7.30 give the final results of the
mathematical solution for this case.
A graphical presentation of the results indicated by Eq. 7.27 is given in Fig. 7.22. By
assigning different values of z/H and T, different values of Uz are solved and plotted to obtain
the family of curves shown. The tedious computations involved in this will no longer be re-
quired in view of the utility of the chart.
Figure 7.22 presents an excellent pictorial idea of the process of consolidation in an
especially instructive manner. At the start of the process, t = 0 and T = 0, and Uz is zero for all
depths. The heavy vertical line representing Uz = 0 indicates that the process of dissipation of
excess pore pressure has yet to begin. It is seen that consolidation proceeds most rapidly at the
drainage faces and least rapidly at the middle of the layer for double drainage conditions. (For
single drainage conditions, consolidation proceeds least rapidly at the impermeable surface).
At any finite time factor, the consolidation ratio is 1 at drainage faces and is minimum at the
middle of the layer. For example, for T = 0.20: Uz = 0.23 at z/H = 1; Uz = 0.46 at z/H = 0.5 and
1.5; and Uz = 0.70 at z/H = 0.25 and 1.75. This indicates that at a depth of one-eighth of the
layer, consolidation is 70% complete; at a depth of one-fourth of the layer, consolidation is 46%
complete; while, at the middle of the layer, consolidation is just 23% complete. The distribu-
tion is somewhat parabolic in shape. As time elapses and the time factor increases, the per
cent consolidation at every point increases. Finally, after a lapse of theoretically infinite time,
consolidation is 100% complete at all depths, the hydrostatic excess pressure is zero as all
applied pressure is carried by the soil grains.
0

0.5

1.00

1.50

2.00

z/H

0 0.2 0.4 0.6 0.8 1.0

Consolidation ratio, Uz

T=0

T = 0.05

0.10

0.15

0.20 0.30 0.40

0.500.600.700.800.843

0.90

T=¥

Fig. 7.22 Graphical solution for consolidation equation