DHARMCOMPRESSIBILITY AND CONSOLIDATION OF SOILS 223and the pore water by the water in the cylinder. The more compressible the soil, the longer the
time required for consolidation; the more permeable the soil, the shorter the time required.
There is one important aspect in which this analogy fails to simulate consolidation of a
soil. It is that the pressure conditions are the same throughout the height of the cylinder,
whereas the consolidation of a soil begins near the drainage surfaces and gradually progresses
inward. In may be noted that soil consolidates only when effective stress increases; that is to
say, the volume change behaviour of a soil is a function of the effective stress and not the total
stress.
Similar arguments may be applied to the expansion characteristics under the decrease
of load.
An alternative mechanical analogy to the consolidation process is shown in Fig. 7.20.
A cylinder is fitted with a number of pistons connected by springs to one another. Each
of the compartments thus formed is connected to the atmosphere with the aid of standpipes.
The cylinder is full of water and is considered to be airtight. The pistons are provided with
perforations through which water can move from one compartment to another. The topmost
piston is fitted with valves which may open or close to the atmosphere. It is assumed that any
pressure applied to the top piston gets transmitted undiminished to the water and springs.
Initially, the cylinder is full of water and weights of the pistons are balanced by the
springs; the water is at atmospheric pressure and the valves may be open. The water level
stands at the elevation PP in the standpipes as shown. The valves are now closed, the water
level continuing to remain at PP. An increment of pressure ∆σ is applied on the top piston. It
will be observed that the water level rises instantaneously in all the stand pipes to an elevation
QQ, above PP by a height h = ∆σ/γw. Let all the valves be opened simultaneously with the
application of the pressure increment, the time being reckoned from that instant. The height
of the springs remains unchanged at that instant and the applied increment of pressure is
fully taken up by water as the hydrostatic excess pressure over and above the atmospheric. An
equal rise of water in all the standpipes indicates that the hydrostatic excess pressure is the
same in all compartments immediately after application of pressure. As time elapses, the water
level in the pipes starts falling, the pistons move downwards gradually and water comes out
through the open valves. At any time t = t 1 , the water pressure in the first compartment is
least and that in the last or the bottommost is highest, as indicated by the water levels in the
standpipes. The variation of hydrostatic excess pressure at various points in the depth of the
cylinder, as shown by the dotted lines, varies with time. Ultimately, the hydrostatic excess
pressure reduces to zero in all compartments, the water levels in the standpipes reaching
elevation PP; this theoretically speaking, is supposed to happen after the lapse of infinite
time. As the hydrostatic excess pressure decreases in each compartment, the springs in each
compartment experience a corresponding pressure and get compressed. For example, at time
t = t 1 , the hydrostatic excess pressure in the first compartment is given by the head PJ; the
pressure taken by the springs is indicated by the head JQ, the sum of the two at all times
being equivalent to the applied pressure increment; that is to say, it is analogous to the effective
stress principle: σ = σ+u, the pressure transferred to the springs being analogous to
intergranular or effective stress in a saturated soil, and the hydrostatic excess pressure to the
neutral pressure or excess pore water pressure.