Consolidation - The Mechanics of Soils and Foundations - page 218

15.3 Isochrones
Solutions to Eq. (15.9) can be represented graphically by plotting the variation of u
with depth at given times. The resulting family of curves are called isochrones. A sim-
ple way to visualize isochrones is to imagine a set of standpipes inserted into the
consolidating soil below a rapidly constructed embankment as shown in Fig. 15.3(a).
Before construction water rises in the standpipes to the steady state water table in
the drain at the surface where the initial and long term pore pressures are u 0 = u ∞ .

Undrained construction of the embankment a dd s a total stress σ at the surface,

which gives rise to initial excess pore pressures u i throughout the soil. The ini-

tial excess pore pressures registered by the standpipes are uniform with depth and
water rises to the same height in all the pipes, as shown by the broken (initial) line in
Fig. 15.3(a). The corresponding isochrone for t

= σ

= 0 is shown in Fig. 15.3(b). (Notice

that because γ ≈ 2 γ

w the standpipes must project well above the maximum height of

the embankment.)
At a time shortly after construction excess pore pressure at the top of the soil near the
drain will have reduced to zero and excess pore pressures will have reduced elsewhere,
so the variation of the levels of water in the standpipes is similar to that shown by the
curved broken line. This broken line gives the shape of the isochrone at a particular
time. After a very long time all the excess pore pressures have dissipated and the levels
of water in the standpipes are at the long term steady state groundwater table; the
isochrone for t is the final broken line.

Figure 15.3(b) shows a set of is o chrones for the one-dimensional consolidation illus-
trated in Fig. 15.3(a) plot te d as u against depth z . Each isoch ro ne corresponds to a
particular time: for t

=∞

= 0, u i = σ at all depths and at t =∞ , u ∞ = 0.

15.4 Properties of isochrones
Isochrones must satisfy the one-dimensional consolidation equation together with the
drainage boundary conditions, and these requirements impose conditions on the geom-
etry and properties of isochrones. Consolidation, with dissipation to a drain at the
surface, as shown in Fig. 15.3, starts near the surface and progresses down through

Figure 15.3 Isochrones for one-dimensional consolidation.