Isochrones, one and two way drainage

An isochrone is a curve showing the variation of excess pore water pressure $u$ with depth at a given time $t$. For a clay layer of thickness $H$ under a uniform loading $\Delta\sigma$:

• At $t=0$: $u = \Delta\sigma$ at all depths (the entire load is taken by the water).
• At $0<t<\infty$: $u$ falls near the drainage faces and stays highest in the interior.
• At $t=\infty$: $u = 0$ everywhere (consolidation complete).

One-way drainage (drainage at the top only)

  top drain ----|------------> u
  z=0           |  \  t=t
                |   \   ___
                |    \ /   t=0 (rectangular, Δσ)
        z=H     |___impervious___
   u = 0 at top for all t>0; u = Δσ for t=0; u = 0 for t = ∞

The isochrone at time $t$ starts at $u=0$ at the top drain, increases with depth, and reaches its maximum at the impervious base, which it meets with zero slope ($\partial u/\partial z = 0$). The drainage path is $H_{dr} = H$.

Two-way drainage (top and bottom)

  top drain ---|     u = 0
               |  .--.
  mid-depth    | (    )  t=t  symmetrical
               |  '--'
  bottom drain |     u = 0

The isochrones are symmetrical about the mid-depth; $u = 0$ at both faces for $t>0$ and the maximum is at the centre. The drainage path is $H_{dr} = H/2$, so consolidation is four times as fast.

The area between an isochrone and the initial rectangular line gives the consolidation that has taken place.